MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimental and Applied Mechanics

Conference Proceedings of the Society for Experimental Mechanics Series

Series EditorTom ProulxSociety for Experimental Mechanics, Inc.,Bethel, CT, USA

For further volumes:http://www.springer.com/series/8922

Gordon A. Shaw • Bart Prorok • LaVern A. Starman

Editors

MEMS and Nanotechnology, Volume 6

Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics

EditorsGordon A. ShawNIST, GaithersburgMD, USA

Bart ProrokAuburn UniversityAL, USA

LaVern A. StarmanAir Force Institute of TechnologyWright Patterson Air Force BaseOH, USA

ISSN 2191-5644 ISSN 2191-5652 (electronic)ISBN 978-1-4614-4435-0 ISBN 978-1-4614-4436-7 (eBook)DOI 10.1007/978-1-4614-4436-7Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2011923429

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Preface

MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimental and AppliedMechanics represents one of seven volumes of technical papers presented at the Society for Experimental Mechanics’

(SEM) 12th International Congress and Exposition on Experimental and Applied Mechanics, held at Costa Mesa, California,

June 11–14, 2012. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Challenges in

Mechanics of Time-Dependent Materials, and Processes in Conventional and Multifunctional Materials, Imaging Methods

for Novel Materials and Challenging Applications, Experimental and Applied Mechanics, Mechanics of Biological Systems

and Materials, and Composite Materials and Joining Technologies for Composites.

Each collection presents early findings from experimental and computational investigations on an important area

within Experimental Mechanics. The 13th International Symposium on MEMS and Nanotechnology conference track

was organized byGordonA. Shaw, National Institute of Standards and Technology; Barton Prorok, AuburnUniversity; LaVern

A. Starman, Air Force Institute of Technology; and sponsored by the SEM MEMS and Nanotechnology Technical Division.

Microelectromechanical systems (MEMS) and nanotechnology are revolutionary enabling technologies (ETs). These

technologies merge the functions of sensing, actuation, and controls with computation and communication to affect the way

people and machines interact with the physical world. This is done by integrating advances in various multidisciplinary

fields to produce very small devices that use very low power and operate in many different environments. Today,

developments in MEMS and nanotechnology are being made at an unprecedented rate, driven by both technology and

user requirements. These developments depend on micromechanical and nanomechanical analyses, and characterization of

structures comprising nanophase materials.

To provide a forum for an up-to-date account of the advances in the field of MEMS and nanotechnology and to promote

an alliance of governmental, industrial, and academic practitioners of ET, SEM initiated a Symposium Series on MEMS andNanotechnology.

The 2012 Symposium is the 13th in the series and addresses pertinent issues relating to design, analysis, fabrication,

testing, optimization, and applications of MEMS and nanotechnology, especially as these issues relate to experimental

mechanics of microscale and nanoscale structures. Topics included in this volume are:

Devices and Fabrication

Measurement Challenges in Single Molecule/Single Atom Mechanical Testing

Nanoindentation

Size Effects in Metals

Optical Methods

Reliability, Residual Stress and Tribology

It is with deep gratitude that we thank the organizing committee, session chairs, authors and keynote speakers,

participants, and SEM staff for making the 12th-ISMAN a valuable and unforgettable experience.

The opinions expressed herein are those of the individual authors and not necessarily those of the Society for Experi-

mental Mechanics, Inc.

Gaithersburg, MD, USA Gordon A. Shaw

Auburn, AL, USA Bart Prorok

Wright Patterson Air Force Base, OH, USA LaVern A. Starman

v

Contents

1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

R.P. Weisenberger, R.A. Coutu Jr., and LaVern A. Starman

2 Characterizing External Resistive, Inductive and Capacitive Loads for Micro-Switches . . . . . . . . . . . . . . 11

Benjamin Toler and Ronald Coutu Jr.

3 Principles Involved in Interpreting Single-Molecule Force Measurement of Biomolecules . . . . . . . . . . . . 19

Sithara S. Wijeratne, Nolan C. Harris, and Ching-Hwa Kiang

4 Measurement of the Gold-Gold Bond Rupture Force at 4 K in a Single-Atom Chain

Using Photon-Momentum-Based Force Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Douglas T. Smith and J.R. Pratt

5 A Precision Force Microscope for Biophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Gavin M. King, Allison B. Churnside, and Thomas T. Perkins

6 Hydrodynamic Force Compensation for Single-Molecule Mechanical Testing

Using Colloidal Probe Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Gordon A. Shaw

7 New Insight into Pile-Up in Thin Film Indentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Kevin Schwieker, James Frye, and Barton C. Prorok

8 Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Jennifer Hay, Verena Maier, Karsten Durst, and Mathias G€oken

9 Frequency Multiplication and Demultiplication in MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

David B. Blocher, Alan T. Zehnder, and Richard H. Rand

10 Characterizing Metal Insulator Transition (MIT) Materials for Use as Micro-Switch Elements . . . . . . . . 59

Brent L. Danner and Ronald A. Coutu Jr.

11 Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts . . . . . . . . . . . . . . . . . . . . . . . . 67

Ling Wu, Jean-Claude Golinval, and Ludovic Noels

12 Simultaneous Measurement of Force and Conductance Across Single Molecule Junctions . . . . . . . . . . . . 75

Sriharsha V. Aradhya, Michael Frei, Mark S. Hybertsen, and Latha Venkataraman

13 High Speed Magnetic Tweezers at 10,000fps with Reflected Hg-Lamp Illumination . . . . . . . . . . . . . . . . . 85

Bob M. Lansdorp and Omar A. Saleh

14 Etching Silicon Dioxide for CNT Field Emission Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Nathan E. Glauvitz, Ronald A. Coutu Jr., Peter J. Collins, and LaVern A. Starman

15 Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Benjamin Klusemann, Alain Franz Knorr, Horst Vehoff, and Bob Svendsen

vii

16 Evaluation of Mechanical Properties of Nano-structured Al6061 Synthesized Using Machining . . . . . . . . 111

Paresh S. Ghangrekar, H. Murthy, and Balkrishna C. Rao

17 Hardening Behaviour of Thin Wires Under Loading with Strain Gradients . . . . . . . . . . . . . . . . . . . . . . . 119

Ying Chen, Mario Walter, and Oliver Kraft

18 Mapping the Histology of the Human Tympanic Membrane by Spatial Domain Optical

Coherence Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Corey Rutledge, Michael Thyden, Cosme Furlong, John J. Rosowski, and Jeffery Tao Cheng

19 Opto-Mechanical Characterization of a MEMS Sensor for Real-Time Infrared Imaging . . . . . . . . . . . . . 131

Everett Tripp, Frank Pantuso, Lei Zhang, Ellery Harrington, and Cosme Furlong

20 Global Digital Image Correlation for Pressure Deflected Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Jan Neggers, Johan Hoefnagels, Francois Hild, Stephane Roux, and Marc Geers

21 Design and Development of Internal Friction and Energy Loss Measurement

on Nanocrystalline Aluminum Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

T.-C. Hu, F.-C. Hsu, M.-T. Lin, C.-J. Tong, and Y.-T. Wang

22 Detection of Damage of Epoxy Composites Using Carbon Nanotube Network . . . . . . . . . . . . . . . . . . . . . 149

S. Cardoso, C. Mooney, R. Pivonka, V.B. Chalivendra, A. Shukla, and S.Z. Yang

viii Contents

Chapter 1

Silicon Carbide High Temperature MEMS Capacitive Strain Sensor

R.P. Weisenberger, R.A. Coutu Jr., and LaVern A. Starman

Abstract Strain sensing at high temperatures, greater than 700�F, is often difficult. Traditional strain sensing uses the

piezoresistive effect, which is temperature dependent. To reduce the temperature dependence of the strain sensor one could

be built from a robust material such as silicon carbide, SiC. Making measurements using capacitive effects eliminates the

effects of temperature within the sensing element. Using the more traditional MEMS material silicon is only an option at

lower temperatures. Silicon has good reliability as a mechanical structure to around 900�F, and good electrical properties to300�F. Having good properties above 700�F, silicon carbide is a robust material that has the ability to be used in high

temperature MEMS applications. Using the capacitive effect for measuring strain was the original way to perform this task

until the piezoresistive effect was harnessed. MEMS based capacitive strain sensors that have been built previously are

known as resonant strain sensors, or the double ended tuning fork resonator. One step further from the double ended tuning

fork is a novel capacitive strain sensor device. An examination of the novel approach to measure strain is performed.

Modeling and simulation is presented using L-Edit and Coventorware. This asserts the device’s characteristics and gives the

novel design merit to be used as a strain sensor.

Nomenclature

MEMS Microelectromechanical systems

1.1 Introduction

Experimental analysis of materials based properties use Hooke’s Law of the relationship between material stress and

deformation of that material [1]. Deformation of material occurs throughout, including at its surface. Measuring deformation

at the surface is typically done using a strain sensor. In hypersonic vehicle applications, there is a need to measure this

deformation at high temperatures, often exceeding 700�C [2]. Other applications for high temperature strain measurements,

exceeding 700�C, include oil and gas equipment, nuclear and power station equipment [3].

Hypersonic vehicles experience temperatures in excess of 500�C on inlet ramp surfaces at Mach 5 [2]. On that same

surface, temperatures exceed 700�C at Mach 6. Another point on the hypersonic engine is the stagnation wall of leading

edge, which experiences temperatures exceeding 700�C at Mach 5 [2]. Many points on the hypersonic vehicle could use a

high temperate strain sensor to measure the effects of load introduced to them. During the design and verification process,

conditions must be duplicated at which the intended material would be subjected to in actual flight conditions.

R.P. Weisenberger

Air Force Research Laboratory, 2790 D Street, Wright Patterson Air Force Base, OH 45433, USA

e-mail: [email protected]

R.A. Coutu Jr. (*) • LaVern A. Starman

Air Force Institute of Technology, 2950 Hobson Way, Wright Patterson Air Force Base, OH 45433, USA

e-mail: [email protected]; [email protected]

G.A. Shaw et al. (eds.), MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimentaland Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series 42,

DOI 10.1007/978-1-4614-4436-7_1, # The Society for Experimental Mechanics, Inc. 2013

1

mailto:[email protected]



1.2 Problem Statement and Research Objectives

Measuring strain is difficult in high temperature environments, over 700�F. The objective of this research is to design, model

and simulate a novel strain sensor which operates at this high temperature. Within this document stress, strain, stress strain

relationship is given as a background. An alternative design for measuring strain using a double ended tuning fork is

discussed. Modeling and simulation of a new high temperature capacitive strain sensor made with silicon carbide is tested

with a finite element simulator known as Coventorware#.

1.3 Stress and Strain

When a material, such as a metal, is subjected to a load, stress is present. Stress is the measure of forces internal to a body and

strain is the measure of deformation of the displacement between particles [4]. Uniformly distributed stress occurs when a

system of forces acting on an area gets distributed uniformly over the area. Each element of the described area is subjected to

an equal loading value. Stress at each element will be at the same magnitude which is defined as the average stress value [5].

This is determined by dividing the total force by the total area. Uniformly distributed stress is defined by (1.1). The

assumption is that stress is uniformly distributed within a body.

StresssAverage ¼ TotalForce

TotalArea¼ P

A(1.1)

Where stress exists in a material there is some type of deformation of that material. This is known as strain and represented

by e. Like stress, there are two types of strain, linear strain and shear strain. Linear strain can obtain two notable states, in

tension or compression. Linear strain will be in tension, tensile strain, or increasing (positive) strain, if the material lengthens

in a straight line. Linear strain will be in compression, compressive strain, or decreasing (negative) strain, if the material

shortens in a straight line [5]. Assume a bar of some length L is loaded longitudinally, and assume that bar elongates

uniformly, and the cross sectional area keeps its shape as a plane and perpendicular to the loading axis throughout the

elongation process. This bar is represented in Fig. 1.1. Unit strain of elongated bar is given by (1.2), which represents

average strain. L is the original length of the bar, and d is the total elongation of the bar [5]. Equation 1.2 cannot be used if thebar’s cross sectional area is not constant or of the load is not uniformly distributed. Then strain per unit, or unit strain, is

determined by differential elongation at a point on the bar or dd of a cross sectional length dL, as expressed in (1.3) [5].

Strain ¼ e ¼ dL

(1.2)

e ¼ dddL

(1.3)

Stress and strain are depended upon each other, and related through material properties. Robert Hooke stated this

relationship is accomplished by a constant of proportionality known as the modulus of elasticity, E (need reference). For

the bar subjected to elongation is shown as (1.4). sL is known as the longitudinal stress, elongation direction. eL is the

longitudinal strain.

sL ¼ EeL (1.4)

Strain is measured using a strain sensor [5], a device which is mounted or manufactured on the straining surface that

translates strain into an electrical signal. Conventional strain transducer, known as a strain gauge, uses an insulating flexible

backing that supports a metallic foil element. The flexible backing is adhered to the straining surface, such as a metallic beam

put under stress. The object becomes deformed when the backing flexes and the foil becomes deformed, and changes its

electrical resistance. The foil can be modeled as a strained conductor. Let’s assume a conductor is unrestrained laterally and

is strained in its axial direction, its length will change and its cross section will also change, this effect is known as the

Poisson Effect (reference needed), this is shown in Fig. 1.2. If the strain increases the length of the conductor its cross

sectional area will decrease, and vice versa if strain decreases the length its cross sectional area will increase. Also resistivity

2 R.P. Weisenberger et al.

of the conductor material will change because of the arrangement of the atoms inside, but the volume does not change.

Strain can be found using the ratio of the change in resistance over its original resistance over the gauge factor, defined in

(1.5). The gauge factor related to how the gauge is manufactured and what material the foil element is made from.

DR ¼ Change in resistance due to strain, RG ¼ undeformed resistance, GF ¼ gauge factor defined by the manufacturer,

and e is strain. Which strain is simply defined, in (1.6), as a change in bar length (Dl) over the original length (L).

GF ¼DRRG

� �e

(1.5)

e ¼ DlL

(1.6)

Most commercially available strain transducers can withstand relatively benign temperature environments, or less than

700�F [6]. The insulating flexible backing typically cannot withstand the extreme environments and the metallic foil’s

resistivity changes as a function of temperature. Thus, strain gauges that utilize piezoresistive elements are not desirable at

high temperature [1].

1.4 Silicon Carbide as a Mechanical Material

To make a high temperature strain sensor it needs to be made of material which could withstand that high temperature

environment. One such material is silicon carbide, or SiC. SiC is a one-dimensional polymorphism called polytypism and

exists in more than 250 structural polytypes [7]. There are only three crystalline structures; cubic, hexagonal, and

rhombohedral. All of the polytypes have identical planar arrangement of silicon and carbon atoms. The differences in the

polytypes are in the way the planar arrangements are stacked. The order of stacking determines the types of close packed

structures and their properties. When the layers are stacked a certain way they are depicted with the conventional

nomenclature with a number of SiC double layers with the appending letter, C for cubic, H for hexagonal, R, for

rhombohedral. For example 3C-SiC has cubic lattice with three layers. Each polytype exhibits different properties,

for example 3C-SiC, three cubic layers of SiC, has a bandgap of 2.2 eV and 4H-SiC, four hexagonal layers, has a bandgap

of 3.4 eV [7]. A summary of selected polytypes is given in Table 1.1.

Silicon carbide as a crystalline material for making MEMS devices allows high temperature devices with excellent

mechanical and electrical properties. A more conventional MEMS material with well known properties and manufacturing

abilities is silicon, although silicon based devices are not suited for high temperatures. Silicon material properties degrade

at temperatures greater than 500�C [8]. Electrical properties of silicon cannot operate extendedly above 150�C [9].

Fig. 1.1 Bar subjected

to load and elongation

Fig. 1.2 Conductor

subject to strain

1 Silicon Carbide High Temperature MEMS Capacitive Strain Sensor 3

Using silicon Carbide to produce a MEMS based strain device is a possible option. Silicon carbide allows for many

advantages to include: increased temperature operation, high radiation exposure, corrosive media, and large impact

survivability [8].

1.5 Double Ended Tuning Fork

To make a strain sensor that alleviates high temperature effects on strain measurements one could made from the double

ended tuning fork device. Double ended tuning fork resonant sensors are already in use for high precision strain

measurements [10]. The double ended tuning fork is modeled as a spring mass damping resonator system. The concept is

drawn in Fig. 1.3. A shuttle mass is suspended over a substrate, and is attached at each end to anchors. The anchors are

attached to the substrate. Attached to the shuttle mass are interdigitated fingers. Built next to the interdigitated fingers

are other interlaced interdigitated fingers which are attached to the substrate via anchors [10]. The shuttle mass is allowed to

move toward, and subsequently away from, the interlaced interdigitated fingers [10]. The anchors are mechanically attached

to the substrate. The entire body of the movable double ended tuning fork, shuttle mass, spring supports, interdigitated

fingers, and anchor are all a part of the shuttle assembly. The anchor and interdigitated fingers on each side of the shuttle

mass are to separate fixed components. The shuttle mass assembly can move axially, to and away from the interdigitated

anchor fingers. This structure is fabricated on top of a flexible backing of a minimum thickness, so strain is transmitted

through to the sensor. The flexible backing is allowed to strain as the straining substrate. This is the same technique

conventional strain sensors use in operation.

The double ended tuning fork strain sensor works when stress occurs from within the substrate, directly below the double

ended tuning fork MEMS structure. When the substrate is strained, the distance between the interdigitated fingers and the

spring support anchor gets larger, as shown in Fig. 1.4, this gives you increasing strain. The reverse happens the distance

between the interdigitated fingers gets closer to the anchor, as shown in Fig. 1.5, which gives you decreasing strain.

The interdigitated finger set can be modeled as a parallel plate capacitor modeled as (1.7). The area is dependent on the

shape of the interdigitated fingers and d is the distance between the interdigitated fingers and the anchor. Because strain is

the change in length, DL, over the original length, L, (1.6), the change in distance between the anchor and the interdigitatedfingers, change in d, as reference to the original distance, original d, the change in gap depicts strain. This allows for a strain

sensing effect.

C ¼ eAd

(1.7)

To operate the sensor, the sensor is driven by a frequency modulated voltage that puts the spring mass damper shuttle

mass system into oscillation. That frequency is dependent on capacitance, and is found by varying the frequency until

oscillation. When strain is applied to the substrate, the interdigitated fingers separate and the oscillation frequency changes

[10]. The frequency is adjusted again until oscillation is again achieved. Capacitance is backed out and strain can be

determined.

Table 1.1 Selected properties

of silicon carbideProperty (unit) Unit 3C-SiC 6H-SiC

Yield strength (109 Nm�2)

Knoop hardness kgmm�2 3,300 2,917

Young’s modulus Gpa 448 448

Density gcm�3 3.21 3.21

Lattice constant A 4.359 a0: 3.08

c0: 15.12

Thermal expansion coefficient 10�6 K�1 2.9 4.2

Thermal conductivity Wcm�1 K�1 4.9 4.9

Sublimes at �C T > 3,100 T > 3,100

Energy gap eV 2.2 2.99

Dielectric constant 9.7 10

Electron mobility cm2V�1 s�1 1,000 400

Hole mobility cm2V�1 s�1 40 50


Fig. 1.3 Double ended

tuning fork

Fig. 1.4 Increasing strain

Fig. 1.5 Decreasing strain


1.6 Capicitive Strains Sensor Design

Double ended tuning fork strain sensors have the ability to measure strain greater than 0.11 mm [8], but lack the ability to

measure larger surface areas, allowing them to be used on large scale testing apparatuses and making it not usable for

hypersonic vehicle testing which require large surface area strain measurements. A new sensor design which can allow an

increase in surface area and subsequentlymeasured capacitance across the device is designed. This device can also be scalable

to allow larger measuring areas depending on stresses expected in the measured material. The design takes the good things

about the double ended tuning forkmodifies to eliminate the need to frequency tune. The design eliminates the moving shuttle

and increases the number of interdigitated fingers. The device’s requirement to tune to the proper frequency would be

eliminated, allowing for a passive measuring of capacitance. Figure 1.6 shows the modified version of the strain sensor.

This new sensor allows for growth by increasing the quantity of interdigitated fingers. This can be done by increasing the

number of interdigitated finger sets, shown in Fig. 1.6, or by increasing the number of axial finger sets. Each axial finger set

is connected to subsequent axial finger sets. Each interdigitated finger sets is fixed to the surface of the substrate, which could

still be a flexible backing material or a stiff substrate of the measured material. There are no “floating” pieces. Everything is

anchored. The interdigitated fingers are however cantilever beams, i.e. only anchored at the root of the beam.

A simple capacitance equation is developed based on the concept that the interdigitated fingers are treated as a parallel

plate capacitor, shown in (1.8). This simple model does not include effects from the surface of the substrate. Cross finger

effects, or effects from fingers located two or more positions away only the interdigitated finger sets. It also does not include

fringe effects. Figure 1.7 depicts variables used to create the equation. NIDFS and NAFS are dependent on the interdigitated

finger sets and the number of axial finger sets respectively, which are dependent on the size of strain sensor required and are

not determined at this time. LO is original distance between the axial finger sets, depicted as LS in Fig. 1.7 which equals the

original length LO minus the change in length DL.

Csensor ¼ NAFS� NIDF

� e½LT � ðLO � DLÞ��ðTÞLG

þ eðWTÞ�ðTÞðLO � DLÞ

� �þ eðWTÞ�ðTÞðLO � DLÞ

� �(1.8)

As shown, the capacitance is dependent on DL, or change in length, which comes from strain, e. Using (1.6) strain can bedetermined; L is the overall sensing length, or length between each anchor, which does not including anchors and non

sensing features, original strain sensor length can be found by adding the number of axial finger sets over the length of the

sensor, as shown in (1.8).

Fig. 1.6 New sensor design


A simple axial finger set design is modeled and simulated in Coventorware#. Coventorware# is a custom built MEMS

software written by Coventor# for multiphysics finite element modeling and simulation. Figure 1.8 depicts the simple axial

finger set. One end of the substrate is fixed, the load reaction end, and the other end a load is introduced into it, introduced

load end. An electric potential, creating electric flux, is applied between the positive and negative fingers. To determine if

capacitance increases as strain is applied three forces are simulated 0, 531, and 1,062 mN/mm2. As stated before when the

interdigitated finger set model is subjected to load, stress and strain exist within the material causing the fingers to separate,

giving an increase or decrease of capacitance.

1.6.1 Sensor Fabrication

The overall process of making the sensor begins with a handle silicon wafer. An oxide is grown, with a poly-SiC “flexible

backing” layer grown on top. This makes a SiCOI or silicon carbide on insulator wafer. A nitride passivation layer is added

for signal isolation. N-type doped poly-SiC traces are formed, for signal egress. A second sacrificial oxide layer is grown

within the poly-SiC, and it is patterned to form the anchors. The poly-SiC mechanical layer is added and patterned to form

the interdigitated finger pattern. After the device is created, the mechanical layer is released along with the sacrificial oxide

between the carrier wafer and the “flexible backing” poly-SiC, and is complete. The completed process is depicted in profile

in Fig. 1.9, and subsequent released device is depicted in profile in Fig. 1.10.

Fig. 1.7 Variables used in the new strain sensor

Fig. 1.8 Interdigitated finger set in Coventorware#


1.7 Results

The results of change of capacitance from Coventorware# are shown in Figs. 1.11 and 1.12. Figure 1.11 shows

displacement in meters and force in micronewtons per square meter. It also shows that as force increases strain increases.

Figure 1.12 shows capacitance in farads and force in micronewtons per square meter. It also shows that as force increases

capacitance also increases.

The results show that the interdigitated finger set is a good parallel plate capacitor design for measuring strain using the

capacitive effect, even though the magnitudes are fairly small, on the order of 5.62e–16F, If the quantity of interdigitated

finger sets in increased, thus increasing the amount of capacitance that is produced. It also increases the area that is available

to measure strain on the surface.

Mechanical LayerSacrificial Oxide 2

Sacrificial Oxide 1

Si Carrier Wafer

Signal LayerNitride Passivation Layer

Device Substrate

Fig. 1.9 Unreleased strain

sensor process

Mechanical LayerSignal LayerNitride Passivation Layer

Device Substrate

Fig. 1.10 Released strain

sensor process

Force vs. displacement7

x 10-7

6

5

4

3

2

1

00 500 1000 1500 2000 2500

disp

lace

men

t

Fig. 1.11 Force versus

displacement


1.8 Conclusions

The objective of this research; to design, model and simulate a novel high temperature strain sensor, was met. First stress,

strain, and the stress strain relationship were discussed. The double ended tuning fork resonant strain sensor was discussed.

Silicon carbide as MEMS materials was discusses. The high temperature strain sensor was discussed, designed, modeled and

simulated to determine if the interdigitated finger set was able to be used as a capacitive strain sensor. This design can be

increased on the mass scale to satisfy the design requirements. This design is a viable solution testing of strain measurements

on high temperature hypersonic components, for which the Air Force Research Lab’s Air Vehicles Directorate has research

programs.

References

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3. Hezarjaribi Y, Hamidon MN, Keshmiri SH, Bahadorimehr AR (2008) Capacitive pressure sensors based on MEMS, operating in harsh

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2008, pp 184–187

4. Murray WM, Miller WR (1992) Fundamental concepts for strain gages, ch. 1. In: The bonded electrical resistance strain gage. Oxford

University Press, New York, pp 3–41

5. MurrayWM,Miller WR (1992) Stress–strain analysis and stress–strain relations, ch. 2. In: The bonded electrical resistance strain gage. Oxford

University Press, New York, pp 42–89

6. Hezarjaribi Y (2009) Capacitive pressure sensors based on MEMS, operating in harsh environments. In: ICSE, Johor Bahru, Johor, Malaysia,

pp 184–187

7. Cheung R (2006) Introduction to silicon carbide (SiC) microelectromechanical systems (MEMS). In: Silicon carbide microelectromechanical

systems for harsh environments. Imperial College Press, London, pp 3–4, and p 181

8. Azevedo RG (2007) A SiC MEMS resonant strain sensor for harsh environment applications. IEEE Sens J 7(4):568–576

9. Azevedo RG, Jones DG, Jog AV, Jamshidi B, Myers DR, Chen Li, Fu Xiao-an, Mehregany M, Wijesundara MBJ, Pisano AP (2007) A SiC

MEMS resonant strain sensor for harsh environment applications. IEEE Sens J 7(4):568–576

10. Wojciechowski KE, Boser BE, Pisano AP (2004) A MEMS resonant strain sensor operated in air. In: 17th IEEE international conference on

micro electro mechanical systems 2004 (MEMS), Netherland, pp 841–845

Farads vs. Load

Far

ads

x 10-16

5.62

5.61

5.6

5.59

5.58

5.57

5.56

5.55

0 500 1000 1500 2000 25005.54

Fig. 1.12 Force versus load


Chapter 2

Characterizing External Resistive, Inductive and Capacitive Loads

for Micro-Switches

Benjamin Toler and Ronald Coutu Jr.

Abstract Microelectromechanical systems (MEMS) switches offer much lower power consumption, much better isolation,

and lower insertion loss compared to conventional field-effect transistors and PIN diodes however, the MEMS switch

reliability is a major obstacle for large-volume commercial applications [1]. To enhance reliability, circuit designers

need simple and accurate behavioral models of embedded switches in CAD tools to enable system-level simulations [2].

Where Macro-switch researchers assess electric contact performance based on the type of load that is being switched, in

MEMS literature, micro-switch performance and reliability is characterized by testing the devices under “hot-switched” or

“cold-switched” load conditions; simple models are developed from the “hot” and “cold” characterizations. By applying

macro-switch performance characterization techniques, i.e. examining reliability based on the type of load that is being

switched, clear characterizations of “hot” switching and “cold” switching external resistive, capacitive, and inductive loads

are produced. External resistive loads were found to act as current limiters and should be suitable under certain criteria for

reducing current density through the contact area and thus limiting device failure to mechanical failure modes. Alternatively,

external capacitive loads increased current density under “hot” switching conditions at the moment the micro-switch closes;

which increases the risk for material transfer and device failure. Under DC conditions, the inductive loads had little effect in

either “hot” or “cold” switching environments.

Keywords Micro-switch reliability • Capacitive loads • Resistive loads • Inductive loads • Contact resistance

2.1 Introduction

This paper presents a study of external resistive, inductive, and capacitive loads under “hot” and “cold” switching conditions

and characterizes the effects on micro-switch reliability. Micro-switches consume no DC power and can be manufactured on

low-cost silicon or glass substrates [3]. An example of a micro-switch is shown in Fig. 2.1. Micro-switches with metallic

contacts have low insertion loss and wide operation frequency band from DC to tens of GHz [3]. The combination of

broadband frequency operation and low-cost manufacturability makes them appealing for use in modern telecommunica-

tion, automotive, and defense applications [3]. Despite the advantages of micro-switches, reliability is still a major concern

for many micro-switch applications.

In the literature, there is little detail describing the effects of “hot” switching and “cold” switching external loads on

micro-switch reliability. Because of size and geometry, micro-switches are more sensitive to variations in temperature and

current density than their macro-switch counterparts. Both current density and temperature at the contact area are influenced

by “hot” switching or “cold” switching external loads. Different configurations of external resistive, capacitive, and

inductive loads were examined for their impact to micro-switch reliability in both series and parallel configurations.

Previous work by Yang et al. studied contact degradation in “hot” and “cold” operations of direct contact gold micro-

switches [4]. Their results showed that for both high and low-electric field “hot” switching, material transfer took place due to

transient heat [4]. Also, their study revealed that mechanical wear became the primary effect to contact resistance under “cold”

switching conditions [4]. Characterizations of the external load models were consistent with the results of their experiment.

B. Toler • R. Coutu Jr. (*)

Air Force Institute of Technology, 2950 Hobson Way, WPAFB, OH 45433, USA




11



2.2 Micro-Switch Resistance Modeling

Under plastic deformation, permanent surface change occurs by the displacement of atoms in asperity peaks whereas

neighboring atoms are retained under elastic deformation [5]. For DC micro-switches, asperity peaks, or “a-spots”, are

conducting contact areas [6] which are “small cold welds providing the only conducting paths for the transfer of electrical

current” [7]. To account for the asperity contact area and force under plastic deformation, the well known model from Abbot

and Firestone that assumes sufficiently large contact pressure and no material creep is used [8]. Single asperity contact area

and force are defined using (2.1) and (2.2) [9]:

A ¼ 2pRa (2.1)

FcP ¼ HA (2.2)

where H is the Meyer hardness of the softer material [9], A is contact area, R is asperity peak radius of curvature, and a is

asperity vertical deformation [9]. This study considers contact resistance based on plastic deformation and diffusive electron

transport and is represented using (2.2) as:

RcDP ¼ r2

ffiffiffiffiffiffiffiHpFcP

r(2.3)

The MEMS literature indicates that varying the type of load during testing reveals the physical limitation for

micro-switches [10]. Rebeiz states that a good assumption for failure of the micro-switch is assumed to be when the contact

resistance becomes greater than 5O, which results in an insertion loss of�0.5 dB [3]. According to Rebeiz, the primary cause

of micro-switch failure is due to plastic deformation in the contact interface such as “damage, pitting, and hardening of the

metal contact area [which] is a result of the impact forces between the top and bottom metal contacts” [3]. The description

relates closely to “cold” switching mechanical failure. In “hot” switching, contributors to early micro-switch failure include

“arcing, material transfer, high current density in the contact region, and localized high-temperature spots” [3].

2.3 Cold Switching

“Cold” switching is generally known to be actuating the switch repeatedly without applying RF or DC power during

actuations, limiting the switch lifetime to mechanical failures such as structural fatigue, memory effect, stiction of the

actuators, etc. [10]. Simply put, “cold” switching is powering the circuit off, then actuating the switch off then on, then

Fig. 2.1 Micro-switch

example

12 B. Toler and R. Coutu Jr.

powering the circuit back on. To model “cold” switching, the circuit elements would not contain stored energy at the time the

switch closes and all energy would dissipate between actuations. This limits the types of failures of micro-switches to purely

mechanical failure modes and extends the reliability of the micro-switch. Zavracky et al. reported over 2 � 109 cycles as thelifetime for Au sputtered contacts that were packaged in nitrogen [11]; a considerable difference compared to the 5 � 108cycles Zavracky reported for “hot-switched” contacts. Majumder et al. reports greater than 107 “hot-switched” cycles and

approximately 1011 “cold-switched” cycles for micro-switches with a “platinum group” contact metal [12].

Fretting is a form of structural fatigue which is defined as accelerated surface damage occurring at the interface of

contacting materials subjected to small oscillatory movements [7]. Braunovic states that the lack of published information of

failures due to fretting is because fretting is a “time-related process causing an appreciable effect only after a long period of

time as a result of the accumulation of wear debris and oxides in the contact zone” [7]. However, contact force has significant

influence on the contact resistance in fretting conditions [7]. As the force applied on the contact is increased, the contact

resistance declines until there is a significant amount of wear debris and oxide to form an insulating layer [7]. As the

insulating layer develops, the resistance increases despite larger applications of force. Fretting is a rate dependent

phenomenon and the frequency of oscillations will affect the contact resistance [7].

Another “cold” switch mechanical failure cause is pitting. Pitting and hardening occur when two metals make contact

repeatedly at the same location [3]. The repeated actuations create cavities at the surface and are confined to a point or small

area [7]. The areas are described as being irregularly shaped and are filled with corrosion products over time [7]. The build-

up of corrosion products in conjunction with pitting reduces the area available for current flow and will induce high

temperatures at those areas while the switch is closed. The result will be a localized high temperature failure mode as seen in

“hot” switching conditions.

2.4 Hot Switching

According to Kim, the lifetime of a switch is more restricted by “hot”-switching than by “cold”-switching because most of

the signals that are transmitted through the switch have high power loads in real cases [10]. Electrical failure mechanisms,

like temperature, current density, and material transfer are all factors in reliability under “hot” switching [3]. A major

consideration in “hot” switching is a large temperature rise which occurs in the contact region due to the small contact area

on the a-spots [3]. With a small contact region comes a large contact resistance, which in the case of “hot”-switching will

result in large heat dissipation in that area at the time the switch closes. Increased temperature at these localized points may

soften the contact metal and lead to bridge transfer. A problem with bridge transfer is that the internal stresses cause the

contact metal to shrink and crack [7]. Oxidation then leads to a reduced number of electrical conducting paths thereby

leading to overheating and ultimately mechanical failure [7].

An increase in current density raises the temperature for the contact areas on the cathode and anode. Concerning the

topology of the contact surface, which has asperities, a higher current density will cause high temperature spots at asperities.

The relationship between the temperature in the contact and voltage drop across the contact is described by Pitney as:

V2c ¼ 4LðT2

c � T2oÞ (2.4)

where Vc is the voltage drop across the contact, L is the Lorenz constant, Tc is the temperature in the contact, and To is thebulk temperature [5]. Examining (2.4), an increase in current would result in an increase in temperature due to “I2 R” heating[5]. The resistance is expected to increase because of the metal’s positive temperature coefficient of resistance, a [5].

The equation for resistance Rct, at the new temperature Tc is then:

Rct ¼ Rco 1þ 2

3a Tc � Toð Þ

� �(2.5)

but (2.5) only holds true until a temperature is reached that softening of the metal begins to occur [5]. When the contact

metals are softening, the asperities collapse, increasing their areas to facilitate cooling [5]. The collapsing of asperities

increases the effective contact area and results in a decrease of the contact resistance. This is seen by rearranging (2.2) and

(2.3), which gives contact resistance as a function of area:

Rc ¼ r2

ffiffiffiffiffiffiffiffi1

2Ra

r(2.6)

2 Characterizing External Resistive, Inductive and Capacitive Loads for Micro-Switches 13

and R is asperity peak radius of curvature and a is asperity vertical deformation [9]. As area increases, Rc decreases. High

temperature for the small volumes ofmaterial changes the softness of the contact material and promotes bridge transfer [5]. Likearcing, bridge transfer is a form of material transfer which reduces the effective area of the asperities and increases the contact

resistance [5]. Also, increased temperature decreases the mobility of electrons in a metal, resulting in increased resistivity.

Another “hot” switching characteristic is the potential for arcing between the cathode and anode. As stated by Rebeiz,

when the contact metals first separate, they are very close to each other and very sharp (due to asperities), which result in a

direct field emission [3]. The cause of the arc is explained further, “these electrons flow from cathode to anode, where they

form a tiny spot of great temperature due to the energy dissipation and the high electric field generated form a space charge

of ions . . . the metal vapor arc material transfer always occur[s] from anode to cathode” [3]. Due to arcing, the material

transfer causes the switch to wear out faster when using DC current in a uniform direction.

Considering DC, electro-migration is another form of material transfer which causes micro-switch failure [7]. Electro-

migration is defined as “the forced motion of metal ions under the influence of an electric field” [7]. Atomic flux (J) is given by:

J ¼ D

kTJreZ� (2.7)

D ¼ Doe�Q

kT (2.8)

where D is the diffusion coefficient, J is the current density, r is the electrical resistivity and eZ* is the effective charge, k isthe Boltzmann constant, T is the absolute temperature, Do and Q are the diffusivity constant and activation energy for

diffusion, respectively [7]. As shown by (2.7), atomic flux is directly proportional to current density. Voids form as a result

of electro-migration and ultimately cause device failure [7]. Braunovic states that an increase in current density in the a-spots

can be substantial and create the right conditions for electro-migration to occur [7].

2.5 Circuit Analysis

There are three states to examine in circuit analysis, initial, steady state, and transient. The initial state is for considering that

there is energy stored in the circuit elements; which could be very descriptive for switchingwithout turning off the circuit signal

(“hot-switch”). The transient state is when the switch is first closed and the elements in the circuit are ‘powering’ up.When the

switch has been closed for a relatively long time and the transients have settled, the circuit is now in steady state. Recall that

inductors become a short circuit to DC and a capacitor becomes an open circuit to DC under steady state conditions. Under AC

conditions, the capacitor becomes a short and the inductor becomes open. Based on a given configuration of circuit elements,

themeasured contact resistance can change based on the driven load. Figure 2.2 shows a representation of themeasured contact

resistance versus applied actuation voltage for a switch with a drive electrode 150 mm-wide [13].

As can be seen in Fig. 2.2, the greater actuation voltage produces a lower contact resistance by enhancing the effective

contact area [13]. Scaling down to micro-switches, contact forces are on the order of mN, which is much smaller than their

macro counterparts [4]. With such low contact force, surface contamination and the topology of the contact area become

important considerations for determining resistance [4]. Loading affects the surface conditions by determining the amount of

current flowing through the contact as well as the potential for arcing and material transfer. Both series and parallel

configurations for resistive, capacitive, and inductive loads and combinations of resistive, capacitive, and inductive loads

were examined however, only a model from each resistive, capacitive, and inductive load configuration is shown here.

2.6 Analysis of Resistive Loads

For a resistive load in series, the relationship of current and voltage is linear and will scale for various values of purely

resistive loads until a change in the contact interface occurs. As shown by Fig. 2.3, a resistive load is placed in series with the

contact resistance.

I ¼ V

RL þ Rcð Þ (2.9)


Shown by Fig. 2.4 and (2.9), the current scales as 1

RLþRcfor the configuration in Fig. 2.3; where Rc is the resistance of the

contact under plastic deformation and diffusive electron transport and RL is the resistive load.

Under “cold” switching conditions, the resistance of the contact will change due to material transfer and a change in the

effective contact area [6]. Also, over time, when the device is affected by the failure mechanisms of pitting or fretting,

the contact resistance will dominate the expression and reduce the current until device failure, at which time there is no

current flow. Under “hot” switch conditions the material transfer to be worse due to arcing [3]. Material transfer would be

caused by repetitive actuation with DC currents in a uniform direction [4]. With material transfer comes a lesser effective

area, which increases the contact resistance. While the failure modes may differ between “cold” switching and “hot”

switching, the current limiting effects of resistive loads are the same for both “hot” and “cold” switching conditions.

The effect of a resistive load is different when placed in series or parallel. For series external loads, the addition of a

resistive load causes a current limiting effect. A potential method to increase the reliability of a micro-switch is to

purposefully match the external resistive load with the contact resistance. For equal values of RL and Rc, the current is

effectively halved. Similarly, as the contact resistance decreases, the resistive load limits the amount of current able to flow

through the contact. Limiting current also affects the I2 R losses and therefore restricts temperature; effectively reducing the

probability of failure due to temperature. Also, since the effect of a resistive load equivalent to contact resistance in series

halves the current, using a lower-performance-higher-resistance contact metal could extend the life of the micro-switch

further than using a low resistance high performance contact metal; assuming the higher resistance is due a material property

which affects durability such as hardness.

A resistor in parallel configuration will decrease the current through the contact with a decrease in resistive load. Increasing

the resistive load would increase the current up to the maximum supplied and therefore would increase current density

through the contact; which ultimately would lead to early device failure.With higher than the contact resistance value external

resistive loads, both a “cold” and “hot” switched parallel external resistive load would induce temperature increases leading to

reduced reliability. Lower than the contact resistance values, external resistive loads would enhance reliability by reducing

the current flow through the contact but may defeat any purpose of having a switch since it would act effectively as a short.

Fritting of contaminant films -Quasi-metallic contact

Increased metal-to-metal contact

Maximum contact force(minimum resistance)

Actuation Voltage (V)C

lose

dSw

itch

Res

ista

nce

(Ω)

Vpi Vepi

5.00

4.50

4.00

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0.00

15 20 25 30 35 40 45 50 55 60 65

Fig. 2.2 Representative plot

of measured switch versus

applied actuation voltage [13]

Rc

DC

RL

I

Fig. 2.3 Resistive load in

series with contact resistance


2.7 Analysis of Capacitive Loads

Capacitive loads in series under DC conditions become open circuits in steady state. In Fig. 2.5, an external capacitive load is

in parallel with a micro-switch. In this configuration, the capacitor charges when the switch is open. When the switch

is closed, the capacitor discharges through the switch and effectively increases current density as shown in Fig. 2.6.

Equation 2.10 represents the current through the contact over time as the capacitor discharges upon switch closure.

An increase in current density promotes contact interface deformation via temperature effects, material transfer, and

electro-migration and reduces reliability.

I tð Þ ¼ V

ðRL þ RcÞ 1þ e

�t

CRL�Rc

RLþRc

� �� ! ð2:10Þ

Under “cold” switch conditions, the capacitor would discharge during the time when the signal is stopped until the switch

opens. While the switch is closed and signal is transmitted, the capacitor would charge and then become open. For

configurations where capacitors ‘open’ the circuit, there is no current flow which implies infinite resistance. “Cold”

switching conditions may induce “hot” switching type failure modes such as electro-migration and material transfer since

there is still current flow at the moment the switch closes before the signal is transmitted and before the switch opens after the

signal transmitted is turned off. Likewise, “hot” switching conditions increase the opportunity for material transfer and

interface deformation by increased current density when the capacitor is discharging between actuations. Overall, the

addition of an external capacitive load in parallel is deleterious to reliability.

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Cur

rent

(m

A)

Resistance (Ohms)

Fig. 2.4 Relationship

of current and resistance

Rc

DC

CL

I2

I1Fig. 2.5 Capacitive load

in parallel with contact

resistance


In macro-switches, for contacts with sufficient voltage and current, an arc ignites in the gap created by the actuation [6].

The concept is explained by Holm that during a decreasing load, the contact area diminishes and the contact resistance

increases; the resulting power dissipation occurs at high temperature for a small volume of metal causing it to evaporate

explosively [6]. A plasma develops and an arc is formed immediately on opening the contact [6]. In the case of micro-

switches, field emission produces arc-like effects of material transfer [3].

2.8 Analysis of Inductive Loads

Concerning inductive loads under DC conditions, the inductors become short circuits over time making the effective

resistance limited to the contact resistance. The inductors ‘shorting’ will provide current flow equal to the max possible

current through the contact with the applied voltage; increasing the opportunity for “hot” switching failure modes like

material transfer and electro-migration. When “cold” switched, the natural response for the inductive loads is high resistance

until steady state, when the inductor is ‘energized’. For a micro-switch with an external inductive load in series, the inductor

would initially act as a current buffer until energized by limiting the effective current upon closing the switch. This behavior

reduces the intensity of failure mechanisms at moments when the connection is being made. Compared to “cold” switch

conditions, the inductors would still have some of their energy between actuations during “hot” switching and would have

minimal impact to the resistance of the contact.

Consider the inductive load configuration of Fig. 2.7 in the case of “hot” switching, the inductor would be energized and

discharge current between actuations. In the “cold” switching condition, the inductor affects the time it takes to reach steady

state since it resists change in current during the transient phase. The inductor would act as a current limiter until steady state;

it would gradually increase the amount of current flow based on its value of inductance. For the switch, having an inductor in

series will limit the initial flow of current through the contact area on initial contact. With reduced current at the moment of

initial contact, the switch will be more susceptible to failure caused by plastic deformation over repeated actuations than by

arcing and other electrical failure modes.

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10

Cur

rent

(m

A)

Time

Fig. 2.6 Current through the

contact for a charging external

parallel capacitive load at the

time the switch closes

Rc

DC

LL

I1

Fig. 2.7 Inductive load in

series with contact resistance


2.9 Conclusions

The purpose of this work was to characterize external resistive, capacitive, and inductive loads and their effects on micro-

switch reliability under “hot” and “cold” switch conditions to better define “hot” and “cold” switch condition effects on

reliability. “Cold” switching failure mechanisms included fretting and pitting through repeated actuations. The reliability of

the micro-switch under “cold” switching conditions is limited to the material properties of the contact metals. “Hot”

switching failure mechanisms included material transfer, increased current density, electro-migration, and temperature.

Certain configurations were determined to enhance micro-switch reliability. Specifically, that an external resistive load in

series acts as a current limiter for both “hot” and “cold” switching conditions and reduces the probability of an electrical

failure mode thereby enhancing the reliability of the micro-switch. In addition, there is a possibility of increasing the

reliability of the switch by using a higher resistance contact metals with a matching external resistive load; the current

limiting effect restrict temperature in conjunction with the increased hardness of the higher resistance contact metal would

most likely extend the reliability of the micro-switch further than a low resistance contact metal. Alternatively, it was found

that certain configurations of resistive, inductive, and capacitive loads promote early failure via increased arcing, material

transfer, and current density. An external capacitive load in parallel was determined to be detrimental to micro-switch

reliability under “hot” switching conditions since it compounded the current during discharge and raised the probability for

increased current density, temperature, and material transfer. For “cold” switching conditions, the discharge of the capacitor

essentially continues to provide current through the contact after the signal has stopped transmitting and before the switch

opens; effectively turning a “cold” switching condition into a “hot” switching condition and reducing reliability with the

increased probability of electrical failure. Lastly, the external inductive load for DC conditions reduced susceptibility of

failure via increased current density and temperature by limiting the current at the moment of initial contact in “hot”

switching conditions. “Cold” switching conditions for external inductive loads have negligible effect to contact resistance

and micro-switch reliability.

Acknowledgements The authors would like to thank Lt Col LaVern A. Starman for his support and assistance with theory and analysis. The

authors would also like to extend gratitude to AFIT technicians, Mr. Rich Johnston and Mr. Tom Stephenson for their work.

Disclaimer The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air

Force, Department of Defense, or the U. S. Government.

References

1. Yang Z, Lichtenwalner D, Morris A, Krim J, Kingon A (2009) Comparison of Au and Au-Ni alloys as contact materials for MEMS switches.

IEEE J Microelectromech Syst 18(2):287–295

2. Kaynak M, Ehwald K, Sholz R, Korndorfer F, Wipf C, Sun Y, Tillack B, Zihir S, Gurbuz Y (2010) Characterization of an embedded RF-

MEMS switch. In: 2010 topical meeting on silicon monolithic integrated circuits in RF systems (SiRF), New Orleans, LA

3. Rebeiz G (2004) RF MEMS, theory, design, and technology. Wiley, Hoboken

4. Yang Z, Lichtenwalner D, Morris A, Krim J, Kingon A (2010) Contact degradation in hot/cold operation of direct contact micro-switches.

J Micromech Microeng 20:1–8

5. Pitney K (1973) Ney contact manual. The J. M. Ney Company, Bloomfield

6. Holm R (1967) Electric contacts: theory and applications, 4th edn. Springer, Berlin

7. Braunovic M, Konchits V, Myshkin N (2007) Electrical contacts – fundamentals, applications, and technology. CRC Press, New York

8. Firestone F, Abbot E (1933) Specifying surface quantity – a method based on the accurate measurement and comparison. ASME Mech Eng

55:569

9. Coutu R, Reid J, Cortez R, Strawser R, Kladitis P (2006) Microswitches with sputtered Au, AuPd, Au-on-AuPt, and AuPtCu alloy electrical

contacts. IEEE Trans Components Packag Technol 29(2):341–349

10. Kim J, Lee S, Baek C, Kwon Y, Kim Y (2008) Cold and hot switching lifetime characterizations of ohmic contact RF MEMS switches. IEICE

Electron Expr 5(11):418–423

11. Zavracky P, Majumber S, McGruer N (1997) Micromechanical switches fabricated using nickel surface micromachining. J Microelectromech

Syst 6(1):3–9

12. Majumder S, Lampen J, Morrison R, Maciel J (2003) MEMS switches. IEEE Instrum Meas Mag 6(1):12–15

13. Coutu R, Kladitis P, Starman L, Reid J (2004) A comparison of micro-switch analytic, finite element, and experimental results. Sens Acuat A

Phys 115(2–3):22–258


Chapter 3

Principles Involved in Interpreting Single-Molecule Force

Measurement of Biomolecules

Sithara S. Wijeratne, Nolan C. Harris, and Ching-Hwa Kiang

Abstract Single-molecule manipulation techniques provide a unique tool for a close-up investigation of the complex

biological properties and interactions. During the force measurement, a single molecule is pulled while its force response is

monitored. However, quantifying these non-equilibrium data and using them to understand the structure-function relation-

ship of biological systems have been challenging. We describe the mechanics of nanoscale biomolecules and the use of these

force measurements for the free energy reconstruction using the recently derived non-equilibrium work theorem, i.e.,

Jarzynski’s equality. We also compare the results with those from other phenomenological approaches. Finally, mechanical

characterization of systems such as overstretching transitions of DNA are presented, and the implications and challenges of

these single-molecule force studies are discussed.

3.1 Introduction

Nanoscale manipulation of individual biomolecules, using techniques such as the atomic force microscope (AFM) and laser

optical tweezers (LOT), has increased the scope and depth in studying important biological interactions, e.g., protein folding,

receptor-ligand binding, and double-stranded DNA melting. In recent years, single-molecule manipulation via AFM has

been used to characterize the mechanical properties of various nucleic acids and proteins [1–5]. However, since single-

molecule manipulation experiments are typically performed under non-equilibrium conditions, extracting thermodynamic

properties from these measurements has been difficult. The recently derived Jarzynski’s equality, which relates non-

equilibrium work fluctuations to equilibrium free energy differences, provides the possibility for extracting equilibrium

information from these non-equilibrium single-molecule manipulation data. Here, we describe two examples for analyzing

single-molecule force data. Thermodynamic property of unfolding a muscle protein is analyzed using Jarzynski’s equality,

which is used to reconstruct the free energy landscape associated with this process. The mechanical properties of melting and

overstretching transitions of DNA are revealed using one-dimensional polymer physics models.

3.2 Single-Molecule Manipulation Experiments

In the mid 1990s, researchers developed new techniques to study the intra- and intermolecular forces characterizing specific

interactions between individual molecules. Examples of such interactions include receptor-ligand binding, antibody-antigen

binding, and binding between complementary strands of DNA. Techniques such as AFM [6–8], LOT [9, 10], and magnetic

tweezers [11], biomembrane force probe (BFP) [12], and surface force apparatus experiments [13] had the sensitivity to

measure forces in picoNewton (pN) and distance in subnanometer (nm) resolutions, thus making them suitable for

measuring molecular interaction forces.

In single-molecule manipulation, the coordinate measured is the change in vertical distance between the AFM tip and

sample surface. The biological sample is typically absorbed onto a substrate surface mounted on the AFM piezoelectric

S.S. Wijeratne • N.C. Harris • C.-H. Kiang (*)

Department of Physics and Astronomy, Rice University Houston, Houston, TX 77005, USA




19


actuator, which is controlled by an ultrafast feedback loop, moves the stage vertically to change the tip-sample distance.

Once the probe contacts the sample surface, molecules may adsorb to the AFM tip via either a specific interaction, as is the

case with functionalized AFM probes, or nonspecific interaction, as is the case with DNA and large protein molecules. The

probe is then retracted, extending the attached molecule. The molecule, attached at one end to the substrate and at the other

to the probe, is pulled by the cantilever, causing the cantilever to bend (see Fig. 3.1). The bending of the cantilever is

monitored using an optical lever system and converted to molecular force based on the spring constant of the cantilever and

Hooke’s Law,

F ¼ ksDz; (3.1)

where F is the force (pN), ks is the spring constant of the cantilever (pN/nm), Dz is the cantilever displacement (nm). Dz isdetermined by Dz ¼ VD, where V is the voltage (V) and D is the deflection sensitivity (nm/V). The ability to precisely and

accurately control the tip-sample distance, to move the piezo actuator at a desired speed or maintain a constant force, is

required for single-molecule manipulation experiments. For this reason, modern single-molecule AFMs are equipped with

an independent capacitive sensor that monitors actual stage displacement within an ultrafast feedback loop. Piezo position,

l, is related to molecular end-to-end extension, z, by

z ¼ l� Dz: (3.2)

Therefore, the data are usually presented as force-extension curves.

3.3 Elasticity Models of Biomolecules

In single-molecule manipulation, an external force is applied to an individual molecule attached between a substrate surface

and a flexible AFM cantilever. The mechanics of the molecular response can be described using one-dimensional polymer

elasticity models, of which the two most commonly used are the freely jointed chain (FJC) and the wormlike chain (WLC)

models. The FJC model assumes a polymer chain consisting of n inextensible Kuhn segments of characteristic length lkconnected via freely rotating joints (see Fig. 3.2a). The Kuhn segments are assumed to be orientationally independent, with

no interaction between segments, resulting in an elastic response to the applied force [14],

zðFÞ ¼ lc cothFlkkBT

� �� kBT

Flk

� �; (3.3)

where lc ¼ nlk is the contour length of the polymer, kB is the Boltzmann constant, and T is the absolute temperature. The FJC

model only takes into account the entropic contribution of the polymer chain up to the contour length lc. However, at highforces, it was observed that the enthalpic contribution of individual Kuhn segments resulted in a deviation from the

z

λ

Δz

Cantilever

Stage

Fig. 3.1 AFM single-

molecule manipulation

experiment. One end of the

molecule is attached to the

cantilever tip and the other

end to a gold substrate. The

cantilever spring obeys

Hooke’s law, whereas the

DNA molecule follows the

wormlike chain (WLC)

model (see text)

20 S.S. Wijeratne et al.

non-extensible model [15]. The extensible FJC model (eFJC) [15, 16] accounts for the finite stretch modulus of Kuhn

segments by modeling each segment as a spring with elasticity kseg (see Fig. 3.2b),

zðFÞ ¼ lc cothFlkkBT

� �� kBT

Flk

� �1þ F

kseglk

� �: (3.4)

The WLC model treats a polymer molecule as a homogenous elastic rod, or a wormlike chain, characterized by its

contour length, lc, and persistence length, lp (see Fig. 3.2c). The persistence length, lp, characterizes the bending stiffness ofthe WLC, which assumes for lengths longer than lp, the correlation between tangents to the polymer is lost. The WLC model

is used to fit the force-extension data (Fig. 3.3) to determine the parameters that represent the bending characteristics of the

molecule [17, 18, 19, 20],

FðzÞ ¼ kBT

lp

1

4ð1� zlcÞ2 �

1

4þ z

lc

" #: (3.5)

lk

kseg

lk

lp

a b c d

FJC eFJC WLC eWLC

lp

Fig. 3.2 Polymer elasticity models commonly used to interpret in single-molecule manipulation data. (a) The FJC consists of orientationally

independent, inextensible Kuhn segments of length lk connected via freely rotating joints. (b) The eFJC model accounts for the enthalpic stretching

of Kuhn segments by modeling each segment as a spring with elasticity kseg. (c) The WLC models a polymer molecule as a flexible rod with

stiffness characterized by the persistence length, lp. (d) The extensible WLC (eWLC) model considers the flexible rod in WLC stretchable

0 100 200 300

Separation (nm)

0

200

400

600

For

ce (

pN)

Fig. 3.3 Force-extension curve of titin (I27)8 with WLC model (dashed lines) fit to each individual domain stretching event

3 Principles Involved in Interpreting Single-Molecule Force Measurement of Biomolecules 21

The mechanical extensibility of double-stranded DNA (dsDNA) (Fig. 3.4) is best described by the extensible WLC

model (eWLC),

zðFÞ ¼ lp 1� 1ffiffiffiffiffiffiffiffiffiffiffiffi4blpF

p þ F

K

!; (3.6)

where b ¼ ð1=kBTÞ and K is the elastic stretch modulus for dsDNA.

3.4 Thermodynamic Property from Analysis of Single-Molecule Manipulation Data

3.4.1 Bell’s Model

One commonly used method to obtain thermodynamic data from single-molecule manipulation experiments using an

extension of Bell’s model, was originally used to quantify the effect of applied force in the context of cell-cell adhesion.

According to Bell’s model [21], the lifetime, t, of a bond being stretched by external force is given by,

t ¼ t0 exp½bðE0 � gFÞ�; (3.7)

where 1/t0 is the natural frequency of the atoms in the solid, E0 is the bond energy and g is a parameter dependent on the

structure of the solid. While Bell’s model has been shown to fit data from single-molecule experiments in some cases, it

sometimes fails over broader ranges of pulling velocity and when trying to fit full unfolding force probability distributions.

Other approaches, which assume a particular nonlinear free energy potential with Kramers theory, have been argued to be

able to more accurately reproduce unfolding force distributions from single-molecule experiments [22, 23]. These are

phenomenological approaches, and the results depend largely on parameter fitting.

3.5 Nonequilibrium Work Theorem

In 1997, Christopher Jarzynski derived the nonequilibrium work theorem [24], relating the work performed during

a nonequilibrium process to the corresponding equilibrium free energy difference. Jarzynski’s equality is suitable

for analyzing single-molecule manipulation data, where the measured work value is on the order of thermal fluctuations.

To elucidate how Jarzynski’s equality can be used here, let’s consider the equality using the treatment laid

0 500 1000 1500

Extension (nm)

0

100

200

300

400

For

ce (

pN)

Experimental Data

eFJC

FJC

WLC

eWLC

Fig. 3.4 Experimental

force-extension data for the

stretching of l-dsDNAfitted with different

one-dimensional

polymer models

22 S.S. Wijeratne et al.

out in Ref. [25], for the context of a single-molecule manipulation pulling experiment (Fig. 3.1). For this process,

Jarzynski’s equality states [24, 25],

he�bWi ¼ðdWrðWÞe�bW ¼ e�bDG: (3.8)

The brackets represent an average over infinite realizations of the process. This method allows us to obtain the entire free

energy curve; however, the results are dependent on high quality data and therefore, time consuming.

3.6 Conclusions

Single-molecule manipulation is an emerging technique with the capability to unravel a wealth of information that was

previously outside the realm of real experiments. The possibilities of the biological phenomenon that can be studied are

seemingly endless. We can use single-molecule manipulation to quantify the mechanics and energetics that underly protein

folding and DNA melting. Equilibrium thermodynamics of protein folding can be obtained. We are now moving forward to

apply these techniques to complex biomolecular systems and molecular-cellular, where information about the interactions

and mechanics are of interest. The analysis techniques are easily ported to apply to any force-extension data, and promise to

yield an abundance of information in the years to come.

Acknowledgments We thank NSF DMR-0907676 and Welch Foundation No. C-1632 for support.

References

1. Rief M, Gautel M, Oesterhelt F, Fernandez JM, Gaub HE (1997) Reversible unfolding of individual titin immunoglobulin domains by AFM.

Science 276:1109–1112

2. Harris NC, Song Y, Kiang C-H (2007) Experimental free energy surface reconstruction from single-molecule force spectroscopy using

Jarzynski’s equality. Phys Rev Lett 99:068101

3. Botello E, Harris NC, Sargent J, Chen W-H, Lin K-J, Kiang C-H (2009) Temperature and chemical denaturant dependence of forced unfolding

of titin I27. J Phys Chem B 113:10845–10848

4. Calderon CP, Harris NC, Kiang C-H, Cox DD (2009) Analyzing single-molecule manipulation experiments. J Mol Recognit 22:356

5. Chen W-S, Chen W-H, Chen Z, Gooding AA, Lin K-J, Kiang C-H (2010) Direct observation of multiple pathways of single-stranded DNA

stretching. Phys Rev Lett 105:218104

6. Florin E-L, Moy VT, Gaub HE (1994) Adhesion forces between individual ligand-receptor pairs. Science 264:415–417

7. Lee GU, Kidwell DA, Colton RJ (1994) Sensing discrete streptavidin-biotin interactions with atomic force microscopy. Langmuir 10:354–357

8. Lee GU, Chrisey LA, Colton RJ (1994) Direct measurement of the forces between complementary strands of DNA. Science 266:771–773

9. Ashkin A, Dziedzic JM, Yamane T (1997) Optical trapping and manipulation of single cells using infared laser beams. Nature 330:769–771

10. Kuo SC, Sheetz MP (1993) Force of single kinesin molecules measured with optical tweezers. Science 260:232–234

11. Wang N, Butler JP, Ingber DE (1993) Mechanotransduction across the cell surface and through the cytoskeleton. Science 260:1124–1127

12. Evans E (1991) Entropy-driven tension in vesicle membranes and unbinding of adherent vesicles. Langmuir 7:1900–1908

13. Helm CA, Knoll W, Israelachvili JN (1991) Measurement of ligand-receptor interactions. Proc Natl Acad Sci USA 88:8169–8173

14. Flory PJ (1969) Statistical mechanics of chain molecules. Interscience Publishers, New York

15. Smith SB, Cui YJ, Bustamante C (1996) Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA

molecules. Science 271:795–799

16. Smith SB, Finzi L, Bustamante C (1992) Direct mechanical measurements of the elasticity of the single DNA molecules by using magnetic

beads. Science 258:1122–1125

17. Bustamante C, Marko JF, Siggia ED, Smith S (1994) Entropic elasticity of lambda-phage DNA. Science 265:1599–1600

18. Marko JF, Siggia ED (1995) Stretching DNA. Macromolecules 28:8759–8770

19. Calderon CP, Chen W-H, Lin K-J, Harris NC, Kiang C-H (2009) Quantifying DNA melting transitions using single-molecule force

spectroscopy. J Phys Condens Matter 21:034114

20. Calderon CP, Harris NC, Kiang C-H, Cox DD (2009) Quantifying multiscale noise sources in single-molecule time series. J Phys Chem B

113:138–148

21. Bell GI (1978) Models for the specific adhesion of cells to cells. Science 200:618–627

22. Dudko OK, Hummer G, Szabo A (2006) Intrinsic rates and activation free energies from single-molecule pulling experiments. Phys Rev Lett

96:108101

23. Dudko OK, Mathe J, Szabo A, Meller A, Hummer G (2007) Extracting kinetics from single-molecule force spectroscopy: Nanopore unzipping

of DNA hairpins. Biophys J 92:4188–4195

24. Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78:2690–2693

25. Jarzynski C (2006) Work fluctuation theorems and single-molecule biophysics. Prog Theor Phys Suppl 165:1–17

3 Principles Involved in Interpreting Single-Molecule Force Measurement of Biomolecules 23

Chapter 4

Measurement of the Gold-Gold Bond Rupture Force at 4 K

in a Single-Atom Chain Using Photon-Momentum-Based

Force Calibration

Douglas T. Smith and J.R. Pratt

Abstract We present instrumentation and methodology for simultaneously measuring force and displacement at the atomic

scale at 4 K. The technique, which uses a macroscopic cantilever as a force sensor and high-resolution, high-stability fiber-

optic interferometers for displacement measurement, is particularly well-suited to making accurate, traceable measurements

of force and displacement in nanometer- and atomic-scale mechanical deformation experiments. The technique emphasizes

accurate co-location of force and displacement measurement and measures cantilever stiffness at the contact point in situ at

4 K using photon momentum. We present preliminary results of measurements made of the force required to rupture a single

atomic bond in a gold single-atom chain formed between a gold flat and a gold tip. Finally, we discuss the possible use of the

gold-gold bond rupture force as an intrinsic force calibration value for forces near 1 nN.

4.1 Introduction

The study of nanoscale contacts and nanowires is of great interest in many areas of nanotechnology, because these structures

often exhibit electronic and mechanical properties that vary dramatically from macroscopic structures made from the same

materials. Most notable perhaps is the quantization of electric current through quasi-one-dimensional structures, a phenom-

enon first discussed by Landauer [1, 2] and the topic of many experimental, theoretical, and computational studies performed

since then. Often electrical conductivity, G, is observed to be quantized in units of G0 ¼ 2e2/h, where e is the charge on theelectron and h is Planck’s constant. For a comprehensive review of these studies, and the experimental techniques used to

perform them, see Agraıt et al. [3]. More recently, there have been both experimental and computation studies of stable non-

integer conduction states in nanowires and single-atom chains (an extended string of atoms that is only one atom in diameter)

[4]. In addition, nanowires and single-atom chains can display unusual and sometimes highly reproducible mechanical

behavior, and have been proposed as possible force calibration reference systems for forces at the nanonewton level and

below [5]. In this work, we report new experimental measurements of the force required to break the bond between two Au

atoms in a single-atom chain at 4 K, using the conductance of the chain as an indicator of the chain’s physical configuration.

4.2 Experimental Method

We performed electrical and mechanical studies of Au single-atom chains under vacuum at 4 K using an experimental

platform we refer to as a feedback-stabilized break junction (FSBJ) [6]. The instrument is shown schematically in Fig. 4.1.

The heart of the system is the point of contact between the tip of a Au wire and a Au flat, a detail of which is shown in the

upper right corner of the figure. The Au wire is mounted on a nanopositioning stage (“z-axis”) that allows the wire tip to

make and break contact with the Au flat, and the Au flat is positioned on a lateral positioning stage (“x-axis”) that allows the

D.T. Smith (*)

Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA


J.R. Pratt

Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA



25


Au tip to contact different locations on the Au flat. Parallel to the Au wire is a glass optical fiber the end of which has been

cleaved to form a smooth surface perpendicular to the fiber axis. This cleaved surface is aligned to be parallel to the Au flat,

and is positioned such that when the Au wire tip contacts the flat, the end of the fiber is approximately 100–200 mm away

from the flat. The fiber and the Au wire are mounted securely in a glass double-bore ferrule so that they move together. The

parallel glass and Au surfaces form a Fabry-Perot cavity that is part of a fiber interferometer system located outside of the

cryo-vacuum chamber.

Details of the design and performance of the interferometer are described elsewhere [7], but a key feature is that it

is optimized for long-term stability and is able to detect changes in the length of the Fabry-Perot cavity smaller than 5 pm.

The output of the interferometer system is used to create closed-loop control of the z-axis positioner, and hence the position

of the Au tip relative to the Au flat, with the same long-term stability and precision. Figure 4.2 shows the level of control over

Fig. 4.1 A schematic representation of the feedback-stabilized break junction apparatus. The inset in the upper right corner shows an enlargement

of the break junction region, with the Fabry-Perot cavity and Au probe tip. The break junction experiments are performed in vacuum at 4 K

Fig. 4.2 Observed changes in the length of a Fabry-Perot cavity, as measured by a fiber-optic interferometer system, as the setpoint of a feedback

control loop is varied step-wise by increments corresponding to 500, 100, 50, 10 and 5 pm. The inset is an enlargement of the data for time>200 s.

5 pm changes in cavity length can be clearly resolved

26 D.T. Smith and J.R. Pratt

the cavity length that we achieve; the setpoint of the control loop was changed by increments corresponding to step-wise

movements of the z-axis positioner of 500, 100, 50, 10 and 5 pm, and the data show the observed change in cavity length.

A change in position of 5 pm is clearly visible. This level of long-term stability allows us to draw out gold single-atom chains

and study their electronic and mechanical properties in detail. Individual chains are typically held for 1 or 2 min, but could

often be maintained for 10 min or more. Figure 4.3 presents typical conductance data for a gold nanocontact as the Au tip

position is varied, with movements both toward the Au flat and away from it; a constant 5 mV bias voltage is applied across

the contact, and current is measure with a conventional current preamplifier. (For 5 mV bias, the conductivity G0

corresponds to a current of approximately 390 nA). Stable conduction states are observed for both integer and non-

integer multiples of G0. Conductance drops to zero when the Au single-atom chain (present when G � 1 G0) breaks; a

measureable conductance returns when the Au tip advances and reforms a contact.

4.3 Break Junction Force Measurement

In order to measure the mechanical properties of gold nanowires and single-atom chains, and in particular the tensile force at

which a gold-gold bond in a single-atom chain ruptures and the chain breaks, the experimental arrangement in Fig. 4.1 was

modified to include a cantilever force sensor; the basic design is shown in Fig. 4.4. Here, the Au flat has been replaced by a

glass cantilever that has been gold-coated on both sides; it is shown in side view in the figure. The cantilever is

approximately 2 mm wide, 8 mm long and 100 mm thick, and is clamped at its base in an electrically insulating mount.

An electrical connection at its base allows for the application of a bias voltage across the junction and measurement of

current through the junction. On the front (left) side of the cantilever, the arrangement is identical to the previous instrument,

with an interferometer cavity beside the Au wire to measure and control the position of the Au tip relative to the front surface

of the cantilever. On the back side of the cantilever, a second optical fiber, which is securely mounted in a glass ferrule

attached to the same block as the cantilever base, forms a Fabry-Perot cavity for a second, independent interferometer

system that measures the deflection of the cantilever and hence the force between the Au tip and the flat Au surface on the

front of the cantilever once the stiffness of the cantilever at that location has been determined.

Accurate determination of the cantilever stiffness at the location where the Au tip contacts the Au-coated cantilever

surface is critical to making accurate measurements of the interaction force at the contact. Many mechanical aspects of the

break junction assembly can change when it is cooled from room temperature to 4 K, such as the dimensions of the cantilever,

the mechanical properties of the materials that comprise the cantilever, the clamping conditions at the base of the cantilever

and the positions of the probe tip and optical fibers relative to the base of the cantilever. As a result, making a measurement

of cantilever stiffness at room temperature and assuming that that value was correct at 4 K was not considered to be

sufficiently reliable. Instead, a method was devised to measure the cantilever stiffness at the point of contact in situ at 4 K.

0 500 1000 1500Time (s)

0

1

2

3

4

5

Con

duct

ance

Qua

nta

(2e2

/h)

Fig. 4.3 The conductivity of

an Au break junction, in units

of the conductance quantum

G0 ¼ 2e2/h (where e is thecharge on the electron and

h is Planck’s constant), as the

Au probe contacts the Au flat

and withdraws several times.

Stable conduction states are

observed for both integer

and non-integer values of G0

4 Measurement of the Gold-Gold Bond Rupture Force at 4 K in a Single-Atom. . . 27

With this method, the light source for the optical fiber at the back of the cantilever was temporarily changed outside

the cryo-vacuum chamber during an experiment from the very low-level (� 200 mW) precision infrared laser used in the

interferometer system to a much higher-power incoherent superluminescent diode (SLD) light source with center wave-

length 1,550 nm whose intensity was modulated sinusoidally between 2 and 12 mW at a frequency well below the resonant

frequency of the cantilever. This produced a sinusoidally varying photon momentum force on the cantilever, and the

mechanical response of the cantilever was monitored using the fiber interferometer on the opposite side of the cantilever.

Analysis of this response allowed a determination of the cantilever stiffness at the contact point of 43 N/m. Through careful

consideration of alignment issues and potential sources of error inherent in measuring the photon flux striking the cantilever

[8] and the reflectivity of the Au surface on the cantilever, we estimate the accuracy of the stiffness measurement to be

approximately�3 N/m. With knowledge of the cantilever stiffness, it is then possible to study various mechanical properties

of gold nanocontacts and single-atom chains, such as their stiffness and tensile strength. By measuring the abrupt change in

the cantilever position when a single-atom chain breaks, we have been able to make direct measurements of the Au-Au bond

breaking force, and find it to be consistent with values obtained by density functional theory (DFT) calculations [9] to within

experimental error.

Acknowledgments The authors gratefully acknowledge the many DFT calculations performed by Francesca Tavazza, Lyle Levine, and Anne

Chaka; those calculations were invaluable in the interpretation of the experimental results. This work was funded in part by the Innovations in

Measurement Science program at the National Institute of Standards and Technology.

References

1. Landauer R (1957) Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J Res Dev 1:223

2. B€uttiker M, Imry I, Landauer R, Pinhas S (1985) Generalized many-channel conductance formula with application to small rings. Phys Rev B

31:6207

3. Agraıt N, Yeyati AL, van Ruitenbeek JM (2003) Quantum properties of atomic-sized conductors. Phys Rep 377:81

4. Tavazza F, Smith DT, Levine LE, Pratt JR, Chaka AM (2011) Electron transport in gold nanowires: stable 1-, 2- and 3-dimensional atomic

structures and noninteger conduction states. Phys Rev Lett 107:126802

5. Pratt JR, Shaw GA, Smith DT (2010) Nanomechanical standards based on the intrinsic mechanics of molecules and atoms. In: Proceedings of

the SEM annual conference, Indianapolis, IN, USA, 7–10 June 2010

Fig. 4.4 A schematic representation of the feedback-stabilized break junction instrument after modification to incorporate a cantilever force

sensor (shown here in side view). The cantilever is 2 mm wide by 100 mm thick, and its free length is 8 mm. The optical fibers and Au probe are

located approximately 1 mm down from the free end of the cantilever, and positioned near its center axis; care was taken to assure that the Au

probe and both optical fibers were located the same distance from the base of the cantilever

28 D.T. Smith and J.R. Pratt

6. Smith DT, Pratt JR, Tavazza T, Levine LE, Chaka AM (2010) An ultra-stable platform for the study of single-atom chains. J Appl Phys

107:084307

7. Smith DT, Pratt JR, Howard LP (2009) A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement

measurement. Rev Sci Instrum 80:035105

8. Pratt JR, Wilkinson P, Shaw G (2011). In: Proceedings of the ASME 2011 international design engineering technical conferences (DETC2011-

47455), Washington, DC, USA, 29–31 Aug 2011

9. Tavazza F, Levine LE, Chaka AM (2009) Elongation and breaking mechanisms of gold nanowires under a wide range of tensile conditions.

J Appl Phys 106:043522

4 Measurement of the Gold-Gold Bond Rupture Force at 4 K in a Single-Atom. . . 29

Chapter 5

A Precision Force Microscope for Biophysics

Gavin M. King, Allison B. Churnside, and Thomas T. Perkins

Abstract Mechanical drift between an atomic force microscope (AFM) tip and sample is a longstanding problem that limits

tip-sample stability, registration, and the signal-to-noise ratio during imaging. We demonstrate a robust solution to drift that

enables novel precision measurements, especially of biological macromolecules in physiologically relevant conditions. Our

strategy – inspired by precision optical trapping microscopy – is to actively stabilize both the tip and the sample using locally

generated optical signals. In particular, we scatter a laser off the apex of commercial AFM tips and use the scattered light to

locally measure and thereby actively control the tip’s three-dimensional position above a sample surface with atomic

precision in ambient conditions. With this enhanced stability, we overcome the traditional need to scan rapidly while

imaging and achieve a fivefold increase in the image signal-to-noise ratio. Finally, we demonstrate atomic-scale (�100 pm)

tip-sample stability and registration over tens of minutes with a series of AFM images. The stabilization technique requires

low laser power (<1 mW), imparts a minimal perturbation upon the cantilever, and is independent of the tip-sample

interaction. This work extends atomic-scale tip-sample control, previously restricted to cryogenic temperatures and

ultrahigh vacuum, to a wide range of perturbative operating environments.

5.1 Introduction

Scanning probe microscopes (SPMs) are major enabling tools underlying scientific discovery and technological innovation

at nanometer length scales and are applied across diverse fields. This large family of instruments has captured the

imagination of scientists and the public alike in their ability to image and manipulate individual atoms and molecules.

Since their invention nearly three decades ago, SPMs have proven to be highly versatile tools because they are capable of

operating in a wide variety of conditions and on numerous types of samples. Along these lines, the SPM’s potential to study

the structure, structural energetics, and structural dynamics of individual biological macromolecules in biologically relevant

conditions (i.e., in fluid at room temperature) have made it an exciting addition to the biophysicist’s tool chest.

Despite its successes in biology, the pinnacle of precision and performance in scanning probe microscopy has only been

achieved in highly isolated non-biological environments. While such high precision SPM instruments have led to outstand-

ing research and iconic images in nanoscience [1] they are operated at cryogenic temperatures and are surrounded by nested

layers of vibration isolation in unoccupied, temperature regulated rooms. These heroic levels of largely passive isolation are

G.M. King (*)

Department of Physics and Joint with Biochemistry, University of Missouri, Columbia, MO 65211, USA


A.B. Churnside

JILA, National Institute of Standard and Technology and University of Colorado, Boulder, CO 80309, USA

Department of Physics, University of Colorado, Boulder, CO 80309, USA

T.T. Perkins

JILA, National Institute of Standard and Technology and University of Colorado, Boulder, CO 80309, USA

Department of Molecular, Cellular and Developmental Biology, University of Colorado, Boulder, CO 80309, USA



31


necessary to minimize a major noise source in SPM – unwanted mechanical drift between the scanning probe tip and the

sample. Drift occurs in all scanning probe instruments due to environmental perturbations. When operating such instruments

at liquid helium temperatures, the gold-standard conditions for high precision SPM work, tip-sample drift rates are reduced

to ~0.01 A/min. This extreme instrumental stability facilitates detailed dynamic studies and enables atomic-scale patterning

of matter. In recent work [2], we have shown that it is possible to approach similar levels of tip-sample stability in ambient

“real-world” operating conditions, where instrumental drift rates are typically 1,000-fold higher.

Mechanical drift between an SPM tip and sample limits many aspects of SPM instrument performance and deleteriously

affects diverse applications such as nanopore measurements [3], tip-based nanolithography [4], and high resolution studies

of protein structure [5]. In particular, an atomic force microscope (AFM), the most prominent member of the SPM family,

would benefit from the ability to (1) enhance image resolution by scanning slowly and averaging cantilever response; to (2)

return the tip to a precise feature in an image (e.g., a region of a protein); to (3) hover the tip over a feature for long time

periods to study local dynamics (e.g., conformational fluctuations); and to (4) precisely control the 3D position of the tip

when disengaged from the surface (e.g., force spectroscopy). Unfortunately, none of these important tasks can be achieved

with current AFMs in real-world conditions due to drift. Long-term atomic-scale stability between the tip and sample is

needed to fully exploit the advantages of AFM across a broad array of disciplines.

5.2 Instrumentation

The issue of tip-sample stability has been addressed sporadically in the SPM community, with most researchers focusing on

other means to improve microscope performance such as enhancing tip sharpness or improving the sensitivity of force

detection. In the literature there exists only a handful of drift-compensation methods. Tracking techniques [6–8] can provide

atomic precision in ultrahigh vacuum, but they forfeit scanning or assume unvarying drift rates. Imaging-based techniques

[9] can reduce drift rates to ~500 pm/min in ambient conditions [10], but require predictions of future drift or compensate for

drift only once per image. External optical techniques, applied in one [11, 12] or more dimensions [13–15], have not

achieved atomic-scale tip-sample stability or image registration (<10 nm overlay precision) [15] in ambient conditions.

To surmount the limitations imposed by drift, we developed a unique, ultra-stable AFM measurement platform. Our

approach, which was inspired by precision optical trapping techniques [16–18], establishes a local optical differential

reference frame to control the tip-sample displacement (Fig. 5.1). Briefly, focused lasers of different wavelength (red and

green) locally report tip and sample position by scattering off the apex of the tip itself and a fiducial mark (nanoscale silicon

disk) affixed to the sample plane. Backscattered light is separated by wavelength and collected to yield the 3D position of

each object with atomic precision. This data is used as feedback to piezo stages to actively stabilize the tip position with

Fig. 5.1 Schematic of the ultra-stable AFM technique. (a) Detailed view of the tip and sample shows focused lasers (red and green) scattering offan AFM tip and a nano-scale fiducial mark (silicon disk) engineered into the sample plane. Back-scattered signals were collected and used to

deduce the position of the tip and the sample relative to each laser beam. (b) Two stabilized diode lasers (SDL) at different wavelengths

[l ¼ 810 nm (green), l ¼ 845 nm (red)] were sent into the microscope and focused by a high numerical-aperture (NA ¼ 1.4) objective (Obj).Back-scattered light was efficiently separated from the incoming light by an optical isolator formed by a polarizing beam splitter (PBS) and a

quarter-wave plate (l/4). The signals, at different wavelengths, were separated by dichroic mirrors and detected by independent quadrant

photodiodes (QPD). A third laser [l ¼ 785 nm (blue)] was reflected off the backside of the cantilever for force control. Tip and sample control

were achieved via feedback loops to two piezoelectric (PZT) stages. Blue-shaded components are in optically conjugate planes (Figure reproduced

from Ref. [2] with permission)

32 G.M. King et al.

respect to the sample. The precision of the technique hinges on maintaining extreme 3D differential pointing stability

between the two laser focal volumes. The method requires low laser power (1 mW), is independent of the tip-sample

interaction, and imparts a negligible perturbation on the tip. A third laser (blue) is reflected off the backside of the cantileverto report tip-sample force in a standard optical lever arm arrangement.

5.3 Results

The nascent ultra-stable AFM instrument has achieved an unprecedented level of tip-sample control in ambient conditions.

For example, the instrument has the newfound ability to hover an AFM tip over specific regions of interest with single-

Angstrom stability for time periods on the order of tens of minutes. We demonstrated this ability by using the backscattered

optical signals to measure and actively control the 3D position of an AFM tip 300 nm above the sample surface (Fig. 5.2).

For this demonstration, both backscattered lasers (red and green) were focused onto a silicon tip. We employed the 810-nm

(green) signal for feedback and the 845-nm (red) signal as an independent “out-of-loop” monitor of instrument stability [18].

Stabilities, determined from this out-of-loop monitor, were 26, 39, and 25 pm in x, y, and z, respectively (r.m.s.,

Df ¼ 0.01–10 Hz). Thus, we demonstrated simultaneous lateral and vertical tip control at atomic length scales (Fig. 5.2b).

Histograms of this data provided a complementary analysis and were well fit by Gaussians, with standard deviations of 28 and

26 pm in x and z, respectively. These reported stabilities represent the ultimate positional control between tip and sample that

can be achieved with our current apparatus, and include the uncertainty due to 3D pointing noise between the detection lasers.

Moreover, this direct measurement of tip position is independent of the traditional observable in AFM, cantilever deflection

(Fig. 5.1, blue). Thus, BSD provides a complimentary, local measurement of tip position that is independent of the tip-sample

force.

In addition to the precise 3D tip control, we also achieved a fivefold enhancement of the signal-to-noise ratio (S/N) in

imaging via slow stabilized scanning (Fig. 5.3). For conventional high resolution AFM imaging, the unwanted presence of

lateral drift necessitates fast scanning rates, restricting the ability to average the cantilever response before moving the tip to

the next pixel in the image. Here we demonstrate the potential to improve AFM image quality in real time through stabilized

slow scanning and real-time signal averaging. Specifically, we acquired three 30 � 30 nm2 images of a single 5-nm Au

nanosphere at increasing averaging times per pixel (0.2, 2, and 20 ms for Fig. 5.4b–d, respectively) in contact mode

(F � 200 pN). Improvement in image quality is visually apparent. Quantitatively, line scans through the center of each

image (Fig. 5.3d) revealed a fivefold reduction in the r.m.s. surface roughness over the center of the nanosphere. We note that

for many applications, real-time averaging is superior to post processing of the images; it does not require assumptions of

sample periodicity, symmetry, or image-to-image registration.

Finally, we designed an experiment to directly demonstrate atomic-scale tip-sample stability and registration. It is this

registration and stability, not resolution, that is the unique feature of the instrument. Resolution – the ability to differentiate

two neighboring objects – has been reported at the atomic scale in ambient conditions [19]; such resolution, however, is not

Fig. 5.2 Ultra-stable “hovering” an AFM tip 300 nm above a sample surface in room temperature air. (a) Tip position records versus time were

low-pass filtered to 10 Hz and offset vertically for clarity [x (red), y (blue), z (green)]. To yield the most accurate measurement of stability,

positions were determined by an “out-of-loop” monitor laser while the tip was actively stabilized with the other laser. (b) A scatter plot of the tip

position in the x-z plane from the 100 s record in (a). Histograms of the data projected onto the x and z axes were well fit by Gaussians with standarddeviations of 28 and 26 pm, respectively (Figure reproduced from Ref. [2] with permission)

5 A Precision Force Microscope for Biophysics 33

required to demonstrate atomic-scale stability and registration. Rather, what is needed is excellent localization precision

(i.e., the ability to determine the center of a single object). Localization precision always exceeds resolution. Indeed,

localization precision of 1/10th of a pixel and 1/100th of the resolution limit is common in optical microscopy [20, 21]. AFM

images are a convolution of tip and sample geometry. Thus, to demonstrate tip-sample stability, we tracked the center of an

object through a series of successive images.

Such image-based verification of stability and registration requires a stationary, unchanging object that can withstand

over an hour of continuous imaging; apparent motion could arise from instability of the object relative to the cover slip [17]

and from tip or sample degradation. To satisfy these requirements, we used single 5-nm diameter Au nanospheres, which are

known to be robust and incompressible [22], and imaged with silicon nitride tips at modest forces (~200 pN). We acquired

seven sequential images over 82 min. Images at the beginning, middle, and end of the time course are displayed in

Fig. 5.4a–c.

To track the nanosphere’s location with subpixel precision, we determined its center point using a 2D cross-correlation.

Specifically, we used the first image (Fig. 5.4a) as the kernel to analyze the subsequent six images. We fit the central 5 nm of

the cross-correlation to a 2D Gaussian and localized the peak with excellent precision [<10 pm (1/50th pixel)] in each axis

due, in part, to the high S/N of the images. From this analysis, we deduced the nanosphere’s location [e.g., xp ¼ 25.199

� 0.004 nm (peak � sfit)].

This precise cross-correlation analysis tracked the nanosphere’s location during 82 min of continuous imaging (Fig. 5.4e).

The precision of this control (and analysis technique) is further verified by small average deviations – 23 and 40 pm in x andy, respectively – of the nanosphere’s location from the linear fits. The residual lateral drift rates were a mere 4 and 5 pm/min

Fig. 5.3 Real-time signal averaging coupled with stabilized scanning improves signal-to-noise ratio in AFM images. (a–c) Sequential images of a

5-nm gold nanosphere taken with increased averaging. Specifically, the averaging times per pixel were 0.2, 2, and 20 ms for panels (a–c),

respectively. (d) Line scans through the center region of images [b (light purple), c (orange), and d (dark purple)] (Figure reproduced from Ref. [2]

with permission)

Fig. 5.4 Ultra-stable AFM imaging and residual drift analysis. (a–c) Images of a 5-nm gold nanosphere taken at times T ¼ 0, 41, and 82 min,

respectively. (d) The 2D cross-correlation between the first and last images. (e) Relative lateral position of the nanosphere plotted versus time

as determined by cross-correlation analysis [x (red), y (blue)]. From linear fits to the data (lines), we deduced residual lateral drift rates of 4 and

5 pm/min in x and y, respectively (Figure reproduced from Ref. [2] with permission)

34 G.M. King et al.

in x and y, representing a 250-fold reduction of the inherent instrumental drift rate and a 100-fold improvement over current

state of the art [10]. Indeed, these residual rates, achieved in air at room temperature, are close to those found in cryogenic

conditions (~1 pm/min, 8 K) [23]. Further, these rates represent an upper bound for the actual drift since the analysis assumes

a stationary object and no degradation of the tip or sample.

5.4 Conclusions

Precision measurements in SPM are currently confined to highly isolated non-biological research environments where

external perturbations are minimized via mostly passive means. In this paper, we demonstrated a robust and active ultra-

stable measurement platform based on generating a local differential laser-based reference frame for tip and sample position

detection. With an ultra-stable AFM, images can be obtained at high resolution while maintaining atomic-scale registration

between the tip and the sample during and after the scan. Hence, regions of interest can be identified in a scan and later

interrogated in detail. In addition to imaging, our ultra-stable SPM measurement platform allows for precision 3D tip

control. Thus, even when the tip is disengaged from the sample surface and the traditional SPM feedback mechanisms

(i.e. force, current) vanish, we maintain the ability to monitor the position and maneuver the tip with a high degree of

precision.

On a conceptual level, what we have developed is a robust optical “tripod” for AFMmeasurements. Our work extends the

full utility and precision of this widely used tool to a wide variety of real-world operating conditions. For example, we have

recently extended our ultra-stable AFM’s capabilities into room temperature fluid to study proteins in biologically relevant

conditions. We anticipate that the newfound capabilities of ultra-stable AFM will find applications in a variety of fields

ranging from fundamental studies in single molecule biophysics to tip-based nanofabrication.

Acknowledgments This work was supported by a Burroughs Wellcome Fund Career Award at the Scientific Interface (GMK) and a Burroughs

Wellcome Fund Career Award in the Biomedical Sciences (TTP), a National Research Council Research Associateship Award (GMK), an NIH

Molecular Biophysics Training Scholarship (ABC, T32 GM-065103), a Butcher Grant, the NSF (grant #: 0923544) and NIST. Mention of

commercial products is for information only; it does not imply NIST’s recommendation or endorsement, nor does it imply that the products

mentioned are necessarily the best available for the purpose. TTP is a staff member of NIST’s Quantum Physics Division.

References

1. Eigler DM, Schwizer EK (1990) Positioning single atoms with a scanning tunneling microscope. Nature 344:524–526

2. King GM et al (2009) Ultrastable atomic force microscopy: atomic-scale stability and registration in ambient conditions. Nano Lett 9:1451

3. King GM, Golovchenko JA (2005) Probing nanotube-nanopore interactions. Phys Rev Lett 95:216103

4. Piner RD et al (1999) “Dip-Pen” nanolithography. Science 283:661–663

5. Scheuring S, Sturgis JN (2005) Chromatic adaptation of photosynthetic membranes. Science 309:484–487

6. Pohl DW, Moller R (1988) “Tracking” tunneling microscopy. Rev Sci Instrum 59:840–842

7. Thomson NH et al (1996) Protein tracking and detection of protein motion using atomic force microscopy. Biophys J 70:2421–2431

8. Abe M et al (2007) Drift-compensated data acquisition performed at room temperature with frequency modulation atomic force microscopy.

Appl Phys Lett 90:203103

9. Horcas I et al (2007) WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev Sci Instrum 78:013705

10. Mokaberi B, Requicha AAG (2006) Drift compensation for automatic nanomanipulation with scanning probe microscopes. IEEE Trans Autom

Sci Eng 3:199–207

11. Proksch R, Dahlberg ED (1993) Optically stabilized, constant-height mode-operation of a magnetic force microscope. J Appl Phys

73:5808–5810

12. Sparks AW, Manalis SR (2004) Scanning probe microscopy with inherent disturbance suppression. Appl Phys Lett 85:3929–3931

13. Teague EC (1989) The National-Institute-of-Standards-and-Technology molecular measuring machine project – metrology and precision

engineering design. J Vac Sci Technol B 7:1898–1902

14. Moon EE, Smith HI (2006) Nanometer-precision pattern registration for scanning-probe lithographies using interferometric-spatial-phase

imaging. J Vac Sci Technol B 24:3083–3087

15. Moon EE et al (2007) Atomic-force lithography with interferometric tip-to-substrate position metrology. J Vac Sci Technol B 25:2284–2287

16. Nugent-Glandorf L, Perkins TT (2004) Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane

detection. Opt Lett 29:2611–2613

17. Carter AR et al (2007) Stabilization of an optical microscope to 0.1 nm in three dimensions. Appl Opt 46:421–427

18. Carter AR et al (2007) Back-scattered detection provides atomic-scale localization precision, stability, and registration in 3D. Opt Express

15:13434–13445

5 A Precision Force Microscope for Biophysics 35

19. Schimmel T et al (1999) True atomic resolution under ambient conditions obtained by atomic force microscopy in the contact mode. Appl Phys

A: Mater Sci Process 68:399–402

20. Gelles J et al (1988) Tracking kinesin-driven movements with nanometre-scale precision. Nature 331:450–453

21. Yildiz A et al (2003) Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization. Science 300:2061–2065

22. Vesenka J et al (1993) Colloidal gold particles as an incompressible atomic force microscope imaging standard for assessing the compress-

ibility of biomolecules. Biophys J 65:992–997

23. Stipe BC et al (1998) Single-molecule vibrational spectroscopy and microscopy. Science 280:1732–1735

36 G.M. King et al.

Chapter 6

Hydrodynamic Force Compensation for Single-Molecule Mechanical

Testing Using Colloidal Probe Atomic Force Microscopy

Gordon A. Shaw

Abstract The use of colloidal probes for mechanical testing of single molecules in an atomic force microscope (AFM)

provides an attractive alternative to conventional microfabricated AFM cantilever force sensors, in that they have a much

greater surface area available for specific binding to a target molecule. This is of particular importance for molecules have a

low binding probability or are sterically inhibited from binding in some way. There are, however, several features unique to

colloidal probe force measurements performed in a fluid environment, one of which is the presence of hydrodynamic forces

acting on the sphere at the tip of the cantilever as it moves through the fluid. This force must be subtracted from the total

measured force to isolate the molecular interaction of interest. Herein, a method is described to perform such a correction

based on Brenner’s equation, and the method is demonstrated on data from the mechanical testing of a single DNAmolecule.

6.1 Introduction

The atomic force microscope (AFM) allows force metrology to be performed in the force range from piconewtons to

micronewtons using a microfabricated cantilever spring as a force sensor. By measuring a displacement signal near the end

of the cantilever (most commonly from an optical lever system), and using Hooke’s law, the force applied at the end of the

cantilever can be determined for small displacements. The application of metrological principles to the accurate measure-

ment of force with the AFM has been ongoing [1, 2], with some emphasis being placed on the measurement of force using

colloidal probes [3]. These probes are a variant of the microfabricated AFM cantilever that have a micrometer-scale sphere

attached to the end, and are useful for probing a larger surface area than conventional AFM probes, the tips of which have

radii of curvature on the order of only 10 nm. Because of this larger surface area, viscous drag forces near the static fluid

layer at the interface between a fluid and solid surface are somewhat enhanced for colloidal probes relative to conventional

AFM probes. As a result, an effective strategy for subtracting the viscous drag force is required if the interaction between the

colloidal probe’s sphere and a surface is to be measured.

The viscous drag force on a colloidal probe as it approaches a surface can be modeled using Brenner’s equation for low

Reynold’s number fluids. At probe-surface separations that are small relative to the radius of the sphere [4],

FH ¼ 6p�b2U=a (6.1)

Where � is the viscosity of the medium, b is the radius of the sphere, U is the velocity at which the sphere moves relative to

the surface, and a is the separation between the sphere and surface at the closest point, as illustrated in Fig. 6.1. This

approximate solution has been used in two different methods as a way to calculate a force to calibrate the spring constant of

colloidal probe cantilevers, and shows reasonable agreement with other spring constant calibration methods [4]. Importantly,

the separation between the probe and surface must be large enough (approximately 150 nm for a gold-coated probe retracting

from a glass surface [5]) that forces associated with the electrochemical double layer are negligible for (6.1) to be useful.

G.A. Shaw (*)

Physical Measurement Laboratory, U.S. National Institute of Standards and Technology, Gaithersburg, MD, USA




37


6.2 Application to DNA Intrinsic Force Reference Molecule

In the particular case of molecular force spectroscopy, a chemically functionalized colloidal probe can be used to bind

one end of a molecule to be stretched. In the current case, this molecule is a 2,820 base pair double-stranded DNA molecule.

The molecule has been designed to be used as a force reference, and the force necessary to complete the half of the

molecule’s overstretch transition [6] is being calibrated in a fashion traceable to the International System of Units (SI).

The DNA is synthesized using pBR 322 as a template, and is terminated at its 50 ends with an amine, and a biotin group. The

amine-terminated end of the molecule is covalently affixed to an aldehyde-functionalized glass surface, and the remainder of

the surface is passivated with amine-terminated polyethylene glycol. A streptavidin-coated colloidal probe is then used to

bind the other end of the DNA molecule to allow the mechanical testing of individual DNA molecules. The force versus

extension curve for one such molecule is shown in Fig. 6.2. The force curve was measured using an Asylum MFP 3D AFM1

in phosphate buffered saline (PBS) at 29�C. Force was determined by multiplying the optical lever signal by cantilever

spring constant, the inverse optical lever sensitivity, and a correction term for colloidal probe geometry [6]. The inverse

optical lever sensitivity was determined by pressing the probe into a rigid surface at high enough forces that the contact

compliance is constant while simultaneously measuring the change in the optical lever signal voltage. The cantilever spring

constant was measured with a laser Doppler vibrometer by applying the thermal calibration method [8, 9].

At distances greater than 150 nm from the surface, the hydrodynamic forces dominate the force at the end of the colloidal

probe until the DNA molecule is stretched into its enthalpic regime. In the region where hydrodynamic force prevail, the

force displacement curve measured by the colloidal probe as it is retracted from the surface can be fit to

Ff ¼ Aþ B=ðsþ CÞ (6.2)

Where A, B, and C are adjustable parameters, and s is the probe surface separation. An optimized fit of this function to the

force curve in Fig. 6.2 is shown as a dashed line. The stretching force from the tethered DNA molecule must also be small in

the fitting regime. The worm-like chain model can be used to calculate the restoring force applied by a double-stranded DNA

molecule stretched from its randomly coiled equilibrium condition [6, 10]. Assuming a persistence length of 47.4 nm [10],

and a contour length of 968 nm calculated assuming a length of 0.342 nm/base pair and adding the length of the primers

attached to the ends of the molecule, the length of the force reference DNA molecule at 1 pN of force is 825 nm. Fitting to

regions in which the DNA is stretched to less than this length effectively minimizes the contribution of the DNA stretching

Fig. 6.1 Illustration of hydrodynamic force acting on a colloidal probe used for single molecule mechanical testing. The velocity and force vectors

illustrated show the case where the colloidal probe is being retracted away from the sample. In this case the hydrodynamic force acts in a direction

opposite the pulling direction. The force a single long polymer molecule exerts on the probe is denoted Fm

1NIST Disclaimer: This article is authored by employees of the U.S. federal government, and is not subject to copyright. Commercial equipment

and materials are identified in order to adequately specify certain procedures. In no case does such identification imply recommendation or

endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the

best available for the purpose.

38 G.A. Shaw

force to the hydrodynamic fit. In addition, at larger separations, the biotin-streptavidin complex attaching the DNAmolecule

to the colloidal probe ruptures, as evidenced by a sharp decrease in force after the end of the overstretch plateau has been

reached. This region of the force curve is used to increase the quality of the fit as well. Subsequently, the hydrodynamic force

can be reconstructed from the coefficients in (6.2) and subtracted from the force data, leaving the molecular force curve.

An uncorrected force curve, hydrodynamic fit, and corrected curve are shown in Fig. 6.2 as are the regions of the curve

used for the hydrodynamic fit. The portions of the curve used for fitting are also indicated. The hydrodynamic force acting on

the colloidal probe at the center of the overstretch plateau is approximately 17 pN, as determined from the curve fit in

Fig. 6.2a. This would seriously affect a measurement of the overstretch force, approximately 70 pN as measured at the center

of the overstretch plateau in Fig. 6.2b. There is significant low frequency noise at small probe surface separations; the effect

is atypically large for in this curve for the purpose of illustration, however it is important to note this effect when calculating

uncertainty. In addition, the curve shown is significantly different from other DNA overstretch data in the literature in

another way. The overstretch appears at a much smaller probe surface separation than would be predicted from its 968 nm

contour length. This is due to the pulling geometry. The DNA molecule examined in this curve is not attached to the nadir of

the colloidal probe, but is rather attached some distance up the side of the sphere, as is schematically illustrated in Fig. 6.1.

In addition, it is being pulled at an angle relative to the surface normal. These effects have previously been noted [10, 11],

however their correction is beyond the scope of the current paper. For the purposes of the hydrodynamic force subtraction, it

is important to check after this geometric correction to ensure that the area used for the hydrodynamic fitting is dominated by

hydrodynamic force and the tensile force on the molecule is less than approximately 1 pN, as described above.

6.3 Conclusion

A procedure for fitting and subtracting hydrodynamic forces from colloidal probe AFM single molecule mechanical testing

experiments is described. If applied correctly, the hydrodynamic correction helps to ensure accurate measurement of

molecular forces in this type of testing. Pitfalls can arise due to low frequency noise, and selection of the data used to do

the curve fitting necessary for the correction. Options for minimizing the impact of these issues on the force data are

outlined, but their contribution must still be considered if an uncertainty analysis is carried out.

References

1. Shaw GA, Kramar JA, Pratt JR (2007) SI-traceable spring constant calibration of microfabricated cantilevers for small force measurement.

Exp Mech 47:143–151

2. Kim M-S, Pratt JR, Brand U, Jones CW (2012) Report on the first international comparison of small force facilities: a pilot study at the

micronewton level. Metrologia 49:70–81

Fig. 6.2 Smoothed AFM force curves before (a) and after (b) subtraction of hydrodynamic force. The experimental data is shown as normal force

measured from cantilever deflection versus the separation between the nadir of the colloidal probe and the functionalized glass surface calculated

by subtracting the cantilever deflection distance from the change in stage position as the DNA is pulled. The location of zero separation is

approximate in these curves. The dashed line in (a) is the fit to the hydrodynamic function, and the fit regions used are marked with horizontalarrows

6 Hydrodynamic Force Compensation for Single-Molecule Mechanical Testing. . . 39

3. Chung K-H, Shaw GA, Pratt JR (2009) Accurate noncontact calibration of colloidal probe sensitivities in atomic force microscopy. Rev Sci

Instrum 80:065107-065107-13

4. Craig VSJ, Neto C (2001) In situ calibration of colloid probe cantilevers in force microscopy: hydrodynamic drag on a sphere approaching a

wall. Langmuir 17:6018–6022

5. Sheth SR, Leckband D (1997) Measurements of attractive forces between proteins and end-grafted poly(ethylene glycol) chains. Proc Natl

Acad Sci USA 94:8399–8404

6. Smith SB, Cui Y, Bustamante C (1996) Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA

molecules. Science 271:795–799

7. Edwards SA, Ducker WA, Sader JE (2008) Influence of atomic force microscope cantilever tilt and induced torque on force measurements.

J Appl Phys 103:064513-064513-6

8. Butt H-J, Jasche M (1995) Calculation of thermal noise in atomic force microscopy. Nanotechnology 6:1–7

9. Gates RS, Pratt JR (2012) Accurate and precise calibration of AFM cantilver spring constants using laser Doppler vibrometry (submitted)

10. Wang MD, Yin H, Landick R, Gelles J, Block SM (1997) Stretching DNA with optical tweezers. Biophys J 72:1335–1346

11. Ke C, Jiang Y, Rivera M, Clark RL, Marszalek PE (2007) Pulling geometry-induced errors in single molecule force spectroscopy

measurements. Biophys J 92:L76–L78

40 G.A. Shaw

Chapter 7

New Insight into Pile-Up in Thin Film Indentation

Kevin Schwieker, James Frye, and Barton C. Prorok

Abstract This work builds involves leveraging our recent thin film mechanics model on the discontinuous transfer of strain

from the film to the substrate. In applying this model with well-defined film and substrate properties we were able to

decouple the effects of elastic modulus and Poisson’s ratio mismatch in the indentation process. In doing so we identified

new insight in the processes of pile-up and strong evidence suggested a dependence on film thickness and ratios of film/

substrate of elastic modulus and Poisson’s ratio. Atomic force microscopy was employed to characterize the degree of pile-

up and correlate it with the above dependencies. We believe these efforts will enable the prediction of the degree of pile-up

and subsequently the removal of its influence in measuring thin film behavior.

7.1 Introduction

Indentation of materials on a macro and micro scale has been a cornerstone of determining mechanical properties, such as

hardness, of materials for the last century. During indentation, a tip with known geometric size and mechanical properties is

pressed into a material. Once loading is complete, the hardness of the indented material is then calculated from the maximum

load applied and the measured contact area from the remaining indent. As the experimentation method has progressed, there

has been a desire to make smaller and less intrusive indents on smaller and smaller scales. Over the last few decades

instrumented indentation on the nano-scale, nanoindentation, has gained attention as a method to extract the hardness and

Young’s modulus of a samples that require higher precision and much lower loads that can be applied by direct human

interaction.

With nanoindentation came the possibility to indent on a sample that consists of a thin layer, or film, of one material on

the surface of a different bulk material, or substrate. The interest in thin films comes from their use in a wide range of

material applications such as optical coatings, very large-scale integrated circuits, anti-corrosion, anti-wear and fuel cells.

Even when the applications are not centered on the mechanical behavior of the thin films, increasing their ability to

withstand processing, and durability during their lifetime is still needed. One current shortcoming of nanoindenting thin

films being widely researched is that as the film’s thickness decreases, the substrate starts to play more of a role in the

properties determined through indentation, even at very low penetration depths of the film. Recent authors [1–7] have

developed theoretical models based on both experimental and finite element analysis that attempt to extract the mechanical

properties of the film, independent of the substrate. While all of these models have their strengths, they also tend to only

work for certain material combinations; such as compliant films on hard substrates, or hard films on compliant substrates.

The goal of this research is to thoroughly review one of the more recent models to of been developed that takes a new

approach in describing the film and substrates composite behavior. This model, developed by Zhou et al. [6, 7] takes into

account that the transfer of energy across the film-substrate interface is not linear, but actually discontinuous; allowing it to

better describe the film’s behavior for a broader range of material combinations. A group of materials were selected for their

similar Poisson’s ratio, but varying Young’s modulus, to have a single thin film layer sputtered on them which also has a

similar Poisson’s ratio to the substrates. The samples were then nanoindented, comparing the Young’s modulus verses

indention depth to the behavior expected through the evaluated model.

K. Schwieker • J. Frye • B.C. Prorok (*)

Department of Mechanical Engineering, Auburn University, Auburn, AL 36849, USA




41


One substantial challenge to nanoindentation is the difficulty in accurately measuring the contact area during displace-

ment, due to how the material being indented can plastically deform around the indenter, causing a change in actual contact

area between the sample and tip, also known as erroneous contact area. If the material is soft it will tend to pile-up around the

indenter tip, causing an increase in contact area, leading to an overestimation of the material’s modulus, and hardness, as

there is more material providing elastic recovery. Harder materials have the tendency to translate their strain further away

from the tip, allowing for a greater volume of material to distribute the deformation, causing the area around the tip to sink-

in, reducing the contact area of the tip. The sink-in effect leads to an underestimation of the material’s modulus, and

hardness. A cross sectional schematic of both effects during indentation, and the resulting top-down view of the recovered

material after unload is shown in Fig. 7.1 [7].

The goal of this research is to thoroughly review one of the more recent models to of been developed that takes a new

approach in describing the film and substrates composite behavior. This model, developed by Zhou et al. [6, 7] takes into

account that the transfer of energy across the film-substrate interface is not linear, but actually discontinuous; allowing it to

better describe the film’s behavior for a broader range of material combinations. A group of materials were selected for their

similar Poisson’s ratio, but varying Young’s modulus, to have a single thin film layer sputtered on them which also has a

similar Poisson’s ratio to the substrates. The samples were then indented, comparing the Young’s modulus verses indention

depth to the behavior expected through the evaluated model. An interesting relationship was observed that may reveal new

information about Pile-up and sink-in and methods to mitigate their effects.

7.2 Experimental Procedure

For this work, a platinum film was simultaneously deposited on several substrates to investigate the influence of pile-up and

sink-in for different material combinations. Here the chosen materials all have identical Poisson’s ratio but different elastic

moduli. This enabled separation the Poisson’s ratio effect on pile-up and sink-in. Table 7.1 lists the materials and properties

employed.

The Pt film was simultaneously deposited onto the substrates by sputtering. A thin Ti film was first deposited to aid in

adhesion to the substrate. Table 7.2 lists the parameters employed.

The resulting platinum film was observed with SEM and found to have consistent coverage and excellent surface quality,

shown in Fig. 7.2. Table 7.3 shows that using the profilometer, the film thickness of each film-substrate combination was

measured in three locations and then averaged to determine the film thickness of 230 nm. As the platinum film had a good

surface quality with no disproportionally large protrusions over the film’s surface, this platinum film was determined to be

the best candidate for indentations.

Each Substrate was indented to assess their material properties before the Pt film was deposited. Twenty five indents were

made to determine an average value. The deposited PT film was than indented on each substrate using 25 indents per each

film/substrate combination.

Fig. 7.1 Schematics of the

pile-up and sink-in effect [7]

42 K. Schwieker et al.

7.3 Results and Discussions

The indentation results of the Pt film on the Cu substrate are given in Fig. 7.3 as an example. The solid circles are the average

experimental data while the solid squares are the elastic modulus of the film as extracted by the Zhou and Prorok model. This

was performed for each film-substrate combination with the results given in Table 7.4.

Table 7.1 Material selection

for the films and substratesFilms Substrates

Material E (GPa) n Material E (GPa) n

Al 70 0.35 In 11 0.44

Pt 168 0.36 Sn 50 0.36

Al (100) 63–70 0.35

Cu (100) 66–117 0.35

Ti 116 0.32

Pt 168 0.36

Si 178 0.28

Ta 186 0.34

Table 7.2 Sputtering

parameters of 230 nm Pt film

with Ti adhesion layer

Substrates Al, Si, Cu, In, Sn, Pt, Ti, Ta

Base pressure (Torr) 2.6 � 10�6

Magnetron type DC DC

Target material Pt Ti

Pre-sputtering power (W) 100 400

Pre-sputtering time (s) 15 25

Sputtering power (W) 100 400

Sputtering time (s) 800 25

Gas 1 (Ar) flow rate (sccm) 25 25

Gas 2 (O2/N2) flow rate (sccm) 0 0

Deposition pressure (mTorr) 4.7 4.7

Deposition temperature (�C) 23 23

Soak time (s) 0 0

Substrate holder rotation (%) 50 50

Ignition pressure (mTorr) 50 50

Expected film thickness (nm) 250 10

Actual film thickness (nm) 230 10

Fig. 7.2 Surface quality

of platinum film

7 New Insight into Pile-Up in Thin Film Indentation 43

The method indicates that the film properties can be extracted reliably. Probably the more interesting result is how the

pile-up and sink-in differed from substrate to substrate. Figure 7.4 gives scanning electron microscopy images of each indent

for the 230 nm thick Pt film at a maximum indent depth of 500 nm, or well past the film thickness.

Each substrate yielded a different degree of sink-in for the Pt film which can be isolated to the change in film/substrate

elastic modulus ratio. Furthermore in most cases, even though the indent depth was twice the film thickness the indent never

punched through the film (SI substrate the exception). Instead, the substrate was often the more compliant of the two in

yielded significantly causing s strong degree of sink-in. Case-in-point, it was noticed that the residual indention in the Pt-In

Table 7.3 Film thickness of sputtered platinum films

Substrate

Location 1

(nm)

Location 2

(nm)

Location 3

(nm)

Average

(nm)

SiO2 220 235 220 225

Si 235 236 231 234

Pt 210 235 214 220

Al 235 236 225 232

Ta 232 225 240 232

Ti 239 246 220 235

In 210 233 243 229

Sn 230 246 210 229

Cu 231 243 228 234

0

0.1

0.2

0.3

0.4

0.5

0

50

100

150

200

250

0 0.2 0.4 0.6 0.8 1

Poisson's R

atioM

odul

us (

GPa)

Normalized Displacement (h/t)

230nm Pt on Cu ExperimentalZ-P ModelFilm EFilm Alpha

Fig. 7.3 Indentation results of a 230 nm Pt film on a Cu substrate

Table 7.4 Determination of film properties on the various substrates

Substrate E0substrate nsubstrate E0

film nfilmIn 12 0.44 ? ?

Sn 42 0.36 163 � 5 0.36

Al 60 0.35 157 � 7 0.35

Cu 100 0.35 158 � 7 0.35

Ti 116 0.32 162 � 2 0.35

Pt 168 0.36 167 � 4 0.35

Ta 153 0.34 171 � 7 0.36

Si 178 0.28 166 � 2 0.36


surface was much smaller than that of the other materials, so another micrograph at 1,000 magnification was taken, Fig. 7.5.

In this micrograph there is a visible halo of deformation that spreads out wider than the readily identifiable indention shown

in Fig. 7.5a. It is believed that since the film is so much stiffer, that as the tip pushes down on the film, a larger area of the film

than that just below the tip begins to push down on the substrate; as demonstrated in Fig. 7.5b, c. Shortly after the tip contacts

the film’s surface, the film’s modulus as calculated through the Z–P model starts to rise toward its correct value, but once the

previously mechanism becomes dominate, there is more plastic deformation than expected, allowing for less elastic

recovery, so the film’s modulus starts to drop toward that of the substrate as the substrate becomes the driving force for

elastic recovery.

7.4 Conclusions

Instrumented indentation testing was used with the continuous stiffness method in order to evaluate nine different substrates,

with the same film. Once deposited, the platinum film was evaluated through SEM and was found that surface quality and

consistency were ideal for nanoindentation. The experimental data from indenting these samples was then compared to the

model, and the associated extracted film’s Young’s modulus and Poisson’s ratio to see to what degree they remain constant

through indentation. The Zhou–Prorok model is adept at predicting substrate effect behavior for plastically deforming

substrates, when sink-in is the dominating factor of erroneous contact area, not pile-up.

Fig. 7.4 Intents in the PT/substrate combinations for a 230 nm thick Pt film and a 500 nm maximum indent depth

7 New Insight into Pile-Up in Thin Film Indentation 45

References

1. Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation. J Mater Res 1:601–609

2. Hay J, Crawford B (2011) Measuring substrate-independent modulus of thin films. J Mater Res 26:727–738

3. King RB (1987) Elastic analysis of some punch problems for a layered medium. Int J Solids Struct 23:1657–1664

4. Pharr GM, Strader JH, Oliver WC (2009) Critical issues in making small-depth mechanical property measurements by nanoindentation with

continuous stiffness measurement. J Mater Res 24:653–666

5. Saha R, Nix WD (2002) Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater

50:23–38

6. Zhou B, Prorok BC (2009) A discontinuous elastic interface transfer model of thin film nanoindentation. Exp Mech 50:793–801

7. Zhou B, Prorok BC (2010) A new paradigm in thin film indentation. J Mater Res 25:1671–1678

8. McElhaney KW, Vlassak JJ, Nix WD (1998) Determination of indenter tip geometry and indentation contact area for depth-sensing indentation

experiments. J Mater Res 13:7

Fig. 7.5 Residual indents

in an Pt/In film/substrate

composite


Chapter 8

Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation

Jennifer Hay, Verena Maier, Karsten Durst, and Mathias G€oken

Abstract For materials which exhibit a power-law relationship between stress and strain rate, it is theoretically possible to

evaluate the exponent (m) which governs the relationship by means of instrumented indentation. However, in practice, tests

at small strain rates take so long that the results can easily be dominated by thermal drift. A new test method is developed in

which several constant strain rates are examined within a single indentation test by switching strain rates as the indenter

continues to move into the material. Switching strain rates within a single test overcomes the problem of long testing times

by examining large strain rates first and transitioning to smaller strain rates as the test proceeds. The new method is used to

test a sample of fine-grained nickel sold by NIST as a standard reference material for Vickers hardness. The strain-rate

sensitivity of this sample is measured to be m ¼ 0.021. This value is in good agreement with values obtained by others on

fine-grained nickel using both instrumented indentation and uniaxial creep testing.

8.1 Introduction

In many materials, the plastic stress that can be sustained depends on strain rate through a power-law relationship: higher

stresses are sustained with higher strain rates and vice versa. In a uniaxial tensile configuration, this relationship between

plastic stress, s, and strain rate, _eu is expressed as

s ¼ B� _emu ; (8.1)

where B* is a constant and m is the strain-rate sensitivity (SRS), which is always greater than or equal to zero. For materials

which manifest negligible strain-rate sensitivity, m is near zero, making s a constant. (Sapphire is an example of such a

material.) Materials with greater strain-rate sensitivity have greater values of m.Provided that hardness (H) is directly related to plastic stress, then hardness also manifests this same phenomenon, giving

the relation

H ¼ B_em: (8.2)

J. Hay (*)

Agilent Technologies, Inc., Nano-Measurements Operation, 105 Meco Ln., Suite 200, Oak Ridge, TN 37830, USA


V. Maier • K. Durst • M. G€okenDepartment of Materials Science and Engineering Institute 1: General Materials Properties, University Erlangen-Nuremberg,

Martensstrasse 5, Erlangen D-91058, Germany



47


In (8.2), B is a constant (though different in value from B* in (8.1)) and _e is the indentation strain rate, defined as the

loading rate divided by the load ( _P/P).1 The strain-rate sensitivity, m, has the same meaning and value in (8.2) as it does in

(8.1). Taking the logarithm of both sides of (8.2) and simplifying yields

lnðHÞ ¼ m � ln _eð Þ þ lnðBÞ: (8.3)

Thus, for many materials, there is a linear relationship between the logarithm of hardness and the logarithm of strain rate,

with the slope being the strain-rate sensitivity, m.Lucas and Oliver showed that the strain-rate sensitivity, m, could be evaluated by performing a series of indentations,

with each indentation performed using a different strain rate [1]. However, the approach of Lucas and Oliver is

problematic, because indentations at small strain rates take so long that the results can easily be dominated by thermal

drift. Recently, Maier et al. showed that all strain rates of interest may be executed within a single indentation test by

switching strain rates as the indenter continues to move into the material [2].

The protocol proposed by Maier et al. has a number of practical advantages. First, the testing time and thermal drift are

minimized by using fast strain rates when the applied force is small and slow strain rates when the applied force is large.

To understand this benefit, it is important to understand how a controlled-strain-rate experiment works. The force-

application rate required to maintain a given strain rate changes with applied force. For example, let us compare the

force-application rate required to achieve a strain rate of 0.01/s at 1 and 100 mN. Knowing the definition of strain rate

ð_e ¼ _P=PÞ, we calculate the necessary force-application rate for each situation ( _P) as the product of the desired strain rate

and the applied force. When the applied force is 1 mN, we have

_P ¼ 0:01=sec�1mN ¼ 0:01mN=sec:

When the applied force is 100 mN, we have

_P ¼ 0:01=sec�100mN ¼ 1mN=sec;

which is much faster. Though the same strain rate is achieved in both cases, the associated force rate is much higher in the

second case, because the applied force is much higher. Thus, it may take a prohibitively long time to examine a small strain

rate when the applied force is small, but that same small strain rate can be examined rather quickly when the applied force is

large. The protocol suggested by Maier et al. takes advantage of this reality by examining the largest strain rate at the

beginning of the test (when the applied force is small) and by examining progressively smaller strain rates as the applied

force increases. In this way, both testing time and thermal drift are minimized. The protocol of Maier et al. has been

implemented in a commercial test method; this article reports the results obtained with this new method on a nickel standard

reference material (SRM) produced by the U.S. National Institute of Standards and Technology (NIST).

The protocol of Maier et al. has a second important benefit: because all strain rates of interest are examined in every test, it

is possible to map out the spatial distribution of strain-rate sensitivity. Although this capacity was not exercised in this work,

Maier et al. measured local strain-rate sensitivity in and around a bond layer in roll-bonded aluminum.

8.2 Experimental Procedure

8.2.1 Sample

The sample tested in this work was a NIST standard reference material (SRM) for Vickers hardness. The sample consists of a

1.35 cm square test block of electrodeposited bright nickel, approximately 750 mm thick, on an AISI 1010 steel substrate,

mounted and highly polished in a thermosetting epoxy. A template certificate for this kind of sample can be found on the

1 Strictly, the term “indentation strain rate” refers to the displacement rate divided by the displacement ( _h/h). However, beginning with the

definition of hardness, it is easily shown that _h/h � 0.5( _P/P). Equation 8.2 holds true for either definition of strain rate, because the constant

difference between the two definitions (0.5) is simply absorbed into the constant B. Because the Agilent G200 NanoIndenter is a force-controlled

instrument, it is logistically easier to control _P/P than _h/h. Thus, in this work, the term “strain rate” refers to _P/P, unless specifically stated

otherwise.

48 J. Hay et al.

NIST website [3]. The qualities which make this sample ideal as a Vickers SRM also make it ideal for the present

demonstration. It has a smooth surface, is resistant to tarnish and corrosion, and has a small grain size. These qualities are

important, because ideally, changes in strain rate should be the only explanation for the observed changes in hardness.

Changes in hardness due to other factors such as surface layers, indentation size effect, and constraint influence can all

compromise the validity of the measured strain-rate sensitivity.

8.2.2 Equipment

An Agilent G200 NanoIndenter with a Berkovich indenter was used for all testing. The Continuous Stiffness Measurement

Option (CSM) was used in order to achieve hardness and elastic modulus as a continuous function of penetration depth [4].

8.2.3 Test Method

Twelve indentation tests were performed using the test method “G-Series XP CSM Strain-Rate Sensitivity.” This test

method allows the user to prescribe a penetration that must be achieved prior to strain-rate cycling. This initial penetration is

used to achieve a penetration depth that is large enough so that no further changes in hardness are expected due to indentation

size effect, surface inhomogeneities, tip anomalies, etc. Once this initial penetration has been achieved, the method

prescribes cycling between a test strain rate and a base strain rate. The test strain rate is executed in the first part of the

cycle, and the base strain rate is executed in the second part of the cycle. The return to the base strain rate after each test strain

rate provides a means for confirming that hardness is not changing with increasing penetration for any reason other than the

changing influence of strain rate. Figure 8.1 shows the strain-rate history for each indentation test on the Ni SRM.

8.3 Results and Discussion

The elastic modulus (E) of the Ni SRMwas measured to be 229 � 3 GPa, and the strain-rate sensitivity (m) was measured to

be 0.021 � 0.002. Table 8.1 is a survey of strain-rate-sensitivity values measured by others for fine-grained Ni.

Figure 8.2 shows the continuous elastic modulus during strain-rate cycling for one typical test. As expected, the modulus

did not change significantly during strain-rate cycling. Modulus is reported for each cycle by averaging the continuous

measurements which fall within 80–90% of the displacement range for the base-strain-rate segment of the cycle. In Fig. 8.2,

Fig. 8.1 Strain-rate cycling

imposed on the test sample.

The test strain rate is imposed

in the first part of the cycle.

The base strain rate is imposed

in the second part of the cycle

(For black-and-white copies,

the cycles are ordered from

left to right)

8 Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation 49

these measurements are plotted as green data points. The modulus value reported for each test is the average of the three

cycle-level results for that test. The average over all tests, 229 GPa, is 15% higher than the nominal value of 200 GPa for

pure nickel. One possible explanation for the discrepancy is that the Oliver-Pharr model for the contact area may

overestimate the true contact area. Because the calculation of elastic modulus by indentation goes as the inverse of the

square root of the contact area, an underestimation of the contact area leads to an overestimation of the modulus. Finite-

element simulations of indentations into a material with nickel-like properties could be used to further investigate this

explanation, because finite-element simulations allow a comparison between contact area determined by the Oliver-Pharr

model and contact are determined from the finite-element mesh.

Figure 8.3 shows the continuous hardness measured during strain-rate cycling for a typical test. (These data are from the

same test for which the modulus is plotted in Fig. 8.2.) The influence of changing strain rate is obvious. At each change, there

is a transient in the hardness response as the microstructure adjusts to the new rate. For each test strain rate, the hardness

values within 80–90% of the displacement range for the segment are averaged to report a single value of hardness; data

within this range for each cycle are plotted as black symbols in Fig. 8.3. Figure 8.4 shows Ln(H) vs. Ln(_e) for all 12 tests. Thelinearity of these results supports the hypothesis that this material is well described by (8.2). For each test, the strain-rate

sensitivity,m, is calculated as the slope of Ln(H) vs. Ln(_e). The value for strain-rate sensitivity obtained by averaging over all12 tests (m ¼ 0.021 � 0.002) is well within the range of SRS values that have been measured by others for fine-grained Ni

(Table 8.1).

A hardness value for each implementation of the base strain rate was also determined. For each base strain rate, the

hardness values within 80–90% of the displacement range for the segment are averaged to report a single value of hardness

for that segment; in Fig. 8.3, the included hardness values are plotted as green symbols. For all 12 tests, Fig. 8.5 shows

hardness associated with the base strain rate for each cycle. The lack of any trend in hardness with cycle number confirms

that hardness is not changing with depth when the same strain rate is applied.

Table 8.1 Survey of SRS (m) values measured by others on fine-grained Ni

Source Sample Method m

This work Ni Vickers SRM Indentation 0.021

Maier et al. [2] Nanocrystalline Ni Indentation 0.019

Maier et al. [2] Nanocrystalline Ni Uniaxial creep (compression) 0.016

Shen et al. [5] Nanocrystalline Ni Uniaxial creep (tension) 0.016–0.045

Dalla Torre et al. [6, 7] Nanocrystalline Ni Uniaxial creep (tension) 0.010–0.030

Wang et al. [8] Nanocrystalline Ni Uniaxial creep (tension) 0.019

Fig. 8.2 Modulus during

strain-rate cycling for one

typical test. Each vertical linemarks the beginning of a

different strain rate,

corresponding to those

identified in Fig. 8.1.

As expected, modulus is

not sensitive to strain rate

50 J. Hay et al.

8.4 Conclusions

An experimentally robust test method has been implemented for measuring strain-rate sensitivity by instrumented indenta-

tion. The method overcomes problems associated with long testing times by imposing small strain rates only when the

applied force is large. Using this method, the strain-rate sensitivity of a sample of nickel sold by NIST as a Vickers SRMwas

measured to be m ¼ 0.021. This value is in good agreement with values obtained by others on similar materials using both

instrumented indentation and uniaxial creep testing.

Fig. 8.3 Hardness during

strain-rate cycling. Sensitivity

to strain rate is evident. Blacksymbols denote data used to

calculate the hardness for each

test strain rate. Green symbolsdenote data used to calculate

the hardness for each base

strain rate

Fig. 8.4 Plot of ln(H) versusln(_e) for each of 12 tests.

Slope of ln(H) with respect

to ln(_e) for each test gives

the strain-rate sensitivity, m,for that test. Linearity of

these data demonstrates

that strain-rate sensitivity

for this material is well

modeled by (8.2)

8 Strain-Rate Sensitivity (SRS) of Nickel by Instrumented Indentation 51

References

1. Lucas BN, Oliver WC (1999) Indentation power-law creep of high-purity indium. Metall Mater Trans A Phys Metall Mater Sci 30(3):601–610

2. Maier V, Durst K, Mueller J, Backes B, Hoppel H, G€oken M (2011) Nanoindentation strain rate jump tests for determining the local strain rate

sensitivity in nanocrystalline Ni and ultrafine-grained Al. J Mater Res 26(11):1421–1430

3. NIST Certificate Standard Reference Material 1896a Vickers Microhardness of Nickel [cited 2011 October 10, 2011]. Available from: http://ts.

nist.gov/MeasurementServices/ReferenceMaterials/upload/1896a.pdf

4. Hay JL, Agee P, Herbert EG (2010) Continuous stiffness measurement during instrumented indentation testing. Exp Tech 34(3):86–94

5. Shen X, Lian JS, Jiang Z, Jiang Q (2008) High strength and high ductility of electrodeposited nanocrystalline Ni with broad grain size

distribution. Mater Sci Eng A487:410

6. Dalla Torre F, Van Swygenhoven H, Victoria M (2002) Nanocrystalline electrodeposited Ni: microstructure and tensile properties. Acta Mater

50:3957

7. Dalla Torre F, Sp€atig P, Sch€aublin R, Victoria M (2005) Deformation behavior and microstructure of nanocrystalline electrodeposited and high

pressure torsioned nickel. Acta Mater 53:2337

8. Wang YM, Hamza AV, Ma E (2006) Temperature-dependent strain-rate sensitivity and activation volume in nanocrystalline Ni. Acta Mater

54:2715

Fig. 8.5 Hardness measured

during the base-strain-rate

segment of each cycle. Lack

of any trend with cycle

number demonstrates that the

same hardness is measured

when the same strain rate

is applied, despite increasing

penetration

52 J. Hay et al.

http://ts.nist.gov/MeasurementServices/ReferenceMaterials/upload/1896a.pdf

http://ts.nist.gov/MeasurementServices/ReferenceMaterials/upload/1896a.pdf

Chapter 9

Frequency Multiplication and Demultiplication in MEMS

David B. Blocher, Alan T. Zehnder, and Richard H. Rand

Abstract In his 1927 paper in Nature, B. van der Pol described experiments in which an electrical circuit forming a

relaxation oscillator was externally forced with continuously varying frequency. The circuit’s response, he found, was

entrained to be only at whole submultiples of the forcing frequency, i.e. f/2, f/3, up to f/40. We describe similar results found

in an optically actuated MEMS limit cycle oscillator. Doubly supported beams are excited into self-oscillation in their first

mode of vibration by illuminating them within an interference field which couples absorption to displacement. While in limit

cycle oscillation, they are mechanically shaken out of plane with continuously varying frequency, and the limit cycle

response is seen to be entrained to multiples or submultiples of the forcing frequency f/3, f/2, f, 2f, up to 7f.

9.1 Introduction

Drawing on nano-fabrication technologies developed for microprocessors, in the last decades researchers have produced

micro-scale mechanical devices with applications such as switches [1], accelerometers, pressure sensors, projection displays

[2], temperature sensors [3], mass sensors [4–6], electrical filters [7, 8], and reference oscillators [9]. Such microelec-

tromechanical systems (MEMS) may be cheaply mass produced using techniques compatible with traditional electronics

fabrication, making them likely candidates for next generation sensors and actuators.

For some applications MEMS devices undergo quasi-static deflection, though many applications rely on the resonant

properties of the device. In order to achieve periodic motion, devices are typically driven electrostatically [9], piezoelectri-

cally [11] or thermo-optically [12] using an externally modulated drive. Self-sustained vibrations in the presence of

unmodulated drive have been reported in thermo-optical systems [13]. These self-oscillations, termed limit cycle (LC)

oscillations, are due to automodulation of thermal-stresses created by feedback between displacement and absorption. Self-

resonant systems may also use electrical feedback [14], and offer the promise of stand-alone cheap sensors since they do not

require expensive drive equipment to obtain periodic motion.

When an LC oscillator operating with frequency, fLCO, is externally driven at forcing frequency, fD, and forcing

amplitude, AD, the type of response depends on the strength of forcing and level of frequency detuning. For low drive

amplitudes with drive frequencies well separated from fLCO, the oscillator is unaffected by the drive. The frequency content

of the motion is mostly at fLCO with a small component at fD. For high drive amplitudes at frequencies close to fLCO the

frequency of the limit cycle is shifted to respond only at fD [15], and the limit cycle is said to be 1:1 entrained or locked.

Entrainment may also occur when the forcing frequency is near an integer multiple or demultiple of the limit cycle

frequency, i.e. n:1 subharmonic entrainment at fD ffi nfLCO or 1:n superharmonic entrainment at fD ffi (1/n)fLCO, where n

is an integer. In this case, the limit cycle frequency is shifted to the nearest multiple or submultiple of the drive frequency.

Observation of this phenomenon in an electrical circuit led Van der Pol to call the phenomenon frequency demultiplication

(or multiplication) [16]. A simplified model of subharmonic entrainment based on a one-dimensional flow with jumps

exhibited strong qualitative resemblance to Van der Pol’s original experiments [17]. Zalalutdinov et al. demonstrated 1:1

and 2:1 entrainment in a MEMS pillar [18], but to our knowledge superharmonic or higher order subharmonic entrainment

have not been demonstrated in a MEMS resonator.

D.B. Blocher (*) • A.T. Zehnder • R.H. Rand

Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA




53


In this work, we study entrainment of thermo-optically excited limit cycle oscillations in a doubly-supported MEMS

beam. Self-oscillating beams are driven at a variable frequency and amplitude, and the frequency of response characterized.

Entrainment is seen at fD:fLCO ratios as low as 1:7 and as high as 3:1. The presence of significant frequency noise reduces the

strength of locking, and asymmetry gives the region of locking considerable hysteresis.

In the following section we describe the fabrication of our devices, and the apparatus used to drive and detect their

motion. Next we outline the procedure used to obtain and entrain limit cycle motion. Finally we characterize frequency noise

and report entrainment results.

9.2 Experimental

Doubly supported beam resonators are fabricated out of single crystal silicon using an SOI process. It has been suggested

that large absorption contrast leads to strong coupling between displacement and heating and thus low critical power for self-

oscillation, Pcrit [19]. Thus, interference patterns are predicted using the code presented in Ref. [20] and wafer device

thickness and buried oxide thickness are selected to optimize absorption contrast in the final devices for low Pcrit. The wafer

is diced and fabrication proceeds on chips. Beams 2 mm wide and 7–40 mm long are patterned using photolithography and

defined with dry etching. Beams are released in a wet etch and critical point drying used to prevent stiction. Final device

thickness is measured to be 201 nm with 400 nm gap to substrate, and 1.6 mm undercutting (Fig. 9.1a). Data presented here

are for a 35 mm long beam. SEM and optical imaging indicates that it is post-buckled due to residual compressive stresses in

the device layer. The buckling amplitude is measured to be 286 nm using optical profilometry.

Devices are mounted on a piezoelectric disk, interferometrically driven under high vacuum (~10�7 mbar) and transduced

using a method described in Ref. [21]. An unmodulated HeNe laser is focused to a ~5 mm diameter spot at the center of the

beam. The beam-gap-substrate system forms a Fabry-Perot interferometer which couples laser absorption to out of plane

displacement. Motion of the beam through the interference field modulates the intensity of the reflected signal which is

measured in a high-speed photodiode and its frequency content determined on a spectrum analyzer (Fig. 9.1b). We can also

inertially drive the beam out of plane by applying a sinusoidal voltage across the piezo. At a threshold power of Pcrit ffi 225

mW, the beam is observed to spontaneously transition into limit cycle oscillation at its first mode frequency of 1.94 MHz.

Post-buckled beams are known to be amplitude-softening [22], i.e. their frequency of oscillation decreases with amplitude.

Increasing the laser power beyond Pcrit is seen to increase the amplitude of oscillation, decreasing the frequency down to

1.63 MHz at 3 mW laser power. Significant frequency instability is observed as sporadic motion of the resonant peak on the

spectrum analyzer, and 200 successive measurements of the frequency of undriven LC oscillation at 3 mW laser power give

a standard deviation in frequency of Df/f ~ 4 � 10�3.

In order to study entrainment, the laser power is increased beyond the threshold power for limit cycle oscillation, and

the self-oscillating devices are inertially driven. A function generator is used to create a swept sine wave which drives the

piezoelectric disk through a high frequency amplifier. The spectral content of the device motion may be observed on

the spectrum analyzer. A frequency counter is used to accurately track the forcing frequency. When entrained, a single stable

peak is seen at fD 6¼ fLCO.When not entrained, a noisy peak is seen at fLCO 6¼ fD and a second steady peak is usually seen at fD,

g 0

3.0

4.0

5.0

6.0

Gap

to S

ubst

rate

Absorption [%]

g 0+½λ

g 0 -

½λ

Image of device tested

a b

Top View yx

z

Diagram of experimental setup

z ySide View x

Gap toSubstrate

Thickness

SpectrumAnalyzer

Photo-Diode

Laser

Si

Si

SiO2

10 µm

Fig. 9.1 (a) Microscopic image of beam tested. (b) Absorption in a Fabry-Perot interferometer. Deflection of the beam from its initial gap to

substrate changes the amount of light absorbed. For high enough laser power, P > Pcrit, feedback leads to self-oscillation. Modulation of the

reflected signal is measured in a high speed photodiode and used to transduce motion

54 D.B. Blocher et al.

though it may disappear below the noise floor. The sweep rate is kept low enough (~0.2 %/s) that the drive frequency changes

roughly quasi-statically. The peak-to-peak voltage across the piezo is recorded and used as a measure of the drive amplitude,

AD. Note that due to the frequency dependent electrical andmechanical properties of the piezoelectric disk, this measure is not

directly related to the displacement amplitude. At high drive amplitudes and frequencies, distortion is seen and drive levels are

kept low enough at any given frequency so that the total harmonic distortion is less than 10%. The signal from the photodiode

is large enough to be picked up on an oscilloscope which may also be used to verify entrainment by triggering on the drive

signal and examining the photodiode (oscillator) signal.When the oscillator is phase locked to the drive, the photodiode signal

will appear as signal. When locking is lost, the oscillator phase will drift with respect to the drive, and the photodiode signal

will appear as high amplitude noise on the oscilloscope.

Due to the high level of frequency noise, the beam may jump in and/or out of entrainment for low forcing amplitudes,

causing entrainment to be an inherently statistical phenomenon. In order to study statistics for 1:1 entrainment, resonators

were also driven using the spectrum analyzer as the frequency source. In source mode, the spectrum analyzer band-pass

filters the response at the drive frequency, only displaying response at fD. When the limit cycle is entrained (fLCO ¼ fD), then

the return signal is not filtered out and a high response signal is measured. When entrainment is lost (fLCO 6¼ fD), then the

response signal is filtered out and the measured response is small. When using the spectrum analyzer as the source to study

1:1 entrainment, the measured response is a plateau whose end points show the frequency at which locking begins and is lost

(Fig. 9.2).


Using the spectrum analyzer as a frequency source, statistics of 1:1 entrainment are measured (Fig. 9.3). Due to high

frequency noise, for low drive amplitudes the limit cycle is only entrained part of the time even when fD � fLCO. Increasing

the drive amplitude increases the width of the entrainment region on any given sweep, sharpens the edges of the region of

entrainment and allows for strong locking – where the limit cycle is seen to be entrained at a given frequency on every

sweep. Note that the entrainment region depends on sweep direction due to asymmetry and hysteresis in the system. For

example, when sweeping up in frequency with AD ¼ 0.622 V, locking occurs when fD is 2 % below fLCO, but is maintained

up to 7 % above fLCO. Sweeping down, locking occurs when fD is 2 % above fLCO and is maintained down to 7 % below fLCO.

0.950.9 1 1.051.1

-30

-40

-50

-60

-70

-80

-90

-100

fD/fLCO

Ret

urn

Sig

nal [

dBm

]

ffree-downflock-down

ffree-up

flock-up

Fig. 9.2 Measured region of entrainment for AD ¼ 0.622 V drive amplitude. Upward sweep is in red and downward sweep in black. In source

mode, the spectrum analyzer filters for signal at fD only. When entrained, fLCO is locked to fD, leading to a large unfiltered return signal. When

entrainment is lost, the limit cycle returns to its unforced frequency, fLCO 6¼ fD, and the filtered return signal is small. Note the logarithmic scale –

due to nonlinearities in the transduction scheme, displacement is not linearly related to return signal, and calibrated displacement amplitude

measurements are impracticable

9 Frequency Multiplication and Demultiplication in MEMS 55

Using the function generator as a frequency source, and the spectrum analyzer to measure the response frequency, the

regions of superharmonic (Fig. 9.4), 1:1 and subharmonic (Fig. 9.5) entrainment are measured by tracking the resonant peak

of the response on the spectrum analyzer. Due to the time lag associated with the frequency measurement and finite sweep

speed, measured data points are slightly under-predicted. In addition, data is un-averaged leading to a jitter in the boundaries

of the entrainment region due to frequency noise.

Note that for the same forcing amplitude, AD, the width of the entrainment region is lower for higher order superharmonic

entrainment (Fig. 9.4). This is likely due to a combination of two factors. First of all, when superharmonically entrained at 1:n,

if the drive frequency, fD, increases by 1 Hz then the limit cycle frequency, fLCO, increases by n Hz. Thus a small width of

entrainment measured in terms of changes in fD is large when measured in terms of fLCO. In addition, the efficiency of energy

pumping decreases for increasing order of entrainment, transfer being most efficient when the frequency of response matches

the drive frequency. In the language of perturbation theory, 1:1 entrainment may be obtained with “soft” excitation where the

amplitude of excitation is the same order as the damping and nonlinear terms. However, sub- or superharmonic entrainment

require that the excitation be “hard,” i.e. scaled one or more orders higher than the damping and nonlinear terms [23].

0.90 0.95 1 1.05 1.100

10

20

30

40

50

60

70

80

90

100

0.90 0.95 1 1.05 1.100

10

20

30

40

50

60

70

80

90

100

a b

Per

cent

age

of T

ime

Ent

rain

ed

Sweep DownSweep Up

fD / fLCO fD / fLCO

0.622 V0.312 V0.156 V0.078 V

Fig. 9.3 Statistics for 1:1 entrainment at various drive amplitudes, AD. Asymmetry in the system causes results to differ when the drive frequency

is swept up (a) versus down (b)

0

2

4

6

8

10

12

14

16

1 2

1 3

1 4

1 5

1 6

1 7

V Pie

zo p

eak−

to−

peak

[V]

flock-up

ffree-up

flock-down

ffree-up

fD / fLCO

Fig. 9.4 Regions of superharmonic entrainment. The frequency dependent impedance of the piezo limits the achievable drive voltage at higher

frequencies due to distortion. Note that a logarithmic frequency scale is used so that for all superharmonics measured, the width of the entrainment

region is visible


Superharmonic entrainment of order 1:7 is only observed in our devices at the highest achievable drive amplitude, and 1:8

entrainment is not observed. See Fig. 9.6 for an oscilloscope trace of 1:4 superharmonic entrainment.

For subharmonic forcing, the width of entrainment at 3:1 appears to be slightly larger than for 2:1 at the same forcing

amplitude. This is likely due to the fact that for n:1 subharmonic entrainment, an increase in fD by 1 Hz leads to a (1/n) Hz

increase in fLCO, artificially increasing width of entrainment for subharmonic forcing when measured with respect to the

drive frequency. 4:1 and higher subharmonic entrainment is not observed. Measured by changes in fD or fLCO, the largest

region of entrainment is seen for 1:1 forcing. For 1:1, sub- and superharmonic entrainment, the width of the entrainment

region increases with AD as expected – stronger forcing can entrain the limit cycle at larger frequency detuning. Finally, we

note that the region of entrainment seems to decrease in frequency for higher amplitude of forcing, particularly for 1:1 and

subharmonic entrainment leading to a left-tilted V shape. It has been shown that an amplitude-hardening limit cycle

oscillator is constrained to the backbone curve when entrained, giving asymmetry in the region of entrainment with a

right-tilted V shape [18, 24]. In this work we see that the same is true for amplitude-softening LC oscillators, with the

direction of tilt switched – higher amplitudes of forcing may result in higher amplitude oscillations which push the oscillator

up the backbone curve, decreasing the frequency at which the oscillator entrains. However, a shift in the entrainment

frequencies for high amplitude forcing has also been demonstrated in models with no softening or hardening behavior [17].

Finally we note that 1:n superharmonic entrainment is seen to occur at frequencies slightly less than (1/n)fLCO. This may also

be related to the amplitude frequency relationship though more work is needed to determine the exact cause.

Fig. 9.5 Regions of 1:1 and subharmonic entrainment

1 5.00m 1.00V2 2 RUN

Drive2

1

Response

Vp-p(2) = 1.937 VVp-p(1) = 13.13 mVFreq (1) = 1.869MHz

v 600ns 500n

s

Fig. 9.6 Oscilloscope trace demonstrating 1:4 superharmonic entrainment. Note that during one forcing period, the resonator traverses four cycles

of motion. The small peak at the bottom of each response cycle is caused by nonlinearities in our detection method and does not represent changes

in the direction of motion of the device

9 Frequency Multiplication and Demultiplication in MEMS 57

9.4 Conclusion

In this paper we demonstrate subharmonic, superharmonic and 1:1 entrainment in an optically driven MEMS limit cycle

oscillation. The high level of frequency noise for the LC oscillator prevents strong locking for low forcing amplitudes,

though short term locking is observed. For higher forcing amplitudes, the limit cycle frequency is stabilized by strong

locking which can detune fLCO by up to 15 %. A shift towards lower frequency locking for higher forcing amplitudes is

observed which may be related to the amplitude-softening nonlinear stiffness of our device. Superharmonic entrainment at

1:7 is observed for the first time in a MEMS oscillator as well as 3:1 subharmonic entrainment. Sub- and superharmonic

entrainment may be of particular interest for applications as a replacement to distortion based frequency multipliers, or as

means to manipulate and control high frequency signals with lower frequency subharmonics.

Acknowledgements This work is supported under NSF grant 0600174 and was performed in part at the Cornell NanoScale Facility, a member of

the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS-0335765). This work

also made use of the Integrated Advanced Microscopy and Materials facilities of the Cornell Center for Materials Research (CCMR) with support

from the National Science Foundation Materials Research Science and Engineering Centers (MRSEC) program (DMR 1120296).

References

1. Rebeiz G (2003) RF MEMS: theory, design, and technology. Wiley, Hoboken

2. Senturia S (2001) Microsystem design. Springer, New York

3. Stokes N, Fatah R, Venkatesh F (1990) Self-excitation in fibre-optic microresonator sensors. Sens Actuat A Phys 21(3):369–372

4. Thundat T, Oden P, Warmac R (1997) Microcantilever sensors. Microscale Thermophys Eng 1(3):185–199

5. Ilic R, Czaplewski D, Craighead H, Neuzil P, Campagnolo C, Batt C (2000) Mechanical resonant immunospecific biological detector. Appl

Phys Lett 77:450–452

6. Waggoner P, Craighead H (2007) Micro- and nanomechanical sensors for environmental, chemical, and biological detection. Lab Chip

7:1238–1255

7. Lin L, Howe R, Pisano A (1998) Microelectromechanical filters for signal processing. J Microelectromech Syst 7(3):286–294

8. Reichenbach R, Zalalutdinov Z, Aubin K, Rand R, Houston B, Parpia J, Craighead H (2005) Third-order intermodulation in a micromechanical

thermal mixer. J Microelectromech Syst 14(6):1244–1252

9. Lee S, Demirci M, Nguyen C-C (2001) A 10-MHz micromechanical resonator pierce reference oscillator for communications. In: Digest of

technical papers, the 11th international conference on solid-state sensors and actuators (Transducers’01), Munich, Germany

10. Adams S, Bertsch F, Shaw K, Hartwell P, Moon F, MacDonald N (1998) Capacitance based tunable resonators. J Micromech Microeng

8(1):15–23

11. Jenkins D, Cunningham M, Velu G, Remiens D (1997) The use of sputtered ZnO piezoelectric thin films as broad-band microactuators. Sens

Actuat A Phys 63(2):135–139

12. Ilic R, Krylov S, Kondratovich M, Craighead H (2007) Optically actuated nanoelectromechanical oscillators. IEEE J Sel Top Quant Electron

13(2):392–399

13. Aubin K, Zalalutdinov M, Alan T, Reichenbach R, Rand R, Zehnder A, Parpia J, Craighead H (2004) Limit cycle oscillations in CW laser-

driven NEMS. J Microelectromech Syst 13(6):1018–1026

14. Feng X, White C, Hajimiri A, Roukes M (2008) A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator. Nat Nanotechnol

3:342–346

15. Rand R (2003) Lecture notes on nonlinear vibrations, version 45. Available online at http://hdl.handle.net/1813/79, Date of Access is March 1,

2012

16. Van der Pol B, Van der Mark J (1927) Frequency demultiplication. Nature 120(3019):363–364

17. Storti D, Rand R (1988) Subharmonic entrainment of a forced relaxation oscillator. Int J Non-Linear Mech 23(3):231–239

18. Zalalutdinov M, Aubin K, Pandey M, Zehnder A, Rand R, Craighead H, Parpia J, Houston B (2003) Frequency entrainment for

micromechanical oscillator. Appl Phys Lett 83(16):3281

19. Zalalutdinov M, Parpia J, Aubin K, Craighead H, Alan T, Zehnder A, Rand R (2003) Hopf bifurcation in a disk-shaped NEMS. In: Proceedings

of the 2003 ASME design engineering technical conferences, 19th biennial conference on mechanical vibrations and noise, Chicago,

pp 1759–1769

20. Sekaric L (2003) Studies in NEMS: nanoscale dynamics, energy dissipation, and structural materials. Ph.D. thesis, Cornell University

21. Carr D, Sekaric L, Craighead H, Parpia J (1999) Measurement of mechanical resonance in nanometer scale silicon wires. Appl Phys Lett

75(7):920–922

22. Eisley J (1964) Large amplitude vibration of buckled beams and rectangular plates. AIAA J 2(12):2207–2209

23. Nayfeh A, Mook D (1979) Nonlinear oscillations. Wiley, New York

24. Pandey M, Aubin K, Zalalutdinov M, Reichenbach R, Zehnder A, Rand R, Craighead H (2006) Analysis of frequency locking in optically

driven MEMS resonators. J Microelectromech Syst 15(6):1546–1554


http://hdl.handle.net/1813/79

Chapter 10

Characterizing Metal Insulator Transition (MIT) Materials

for Use as Micro-Switch Elements

Brent L. Danner and Ronald A. Coutu Jr.

Abstract Metal insulator transition (MIT) materials, or phase change materials (PCM) are material compounds that have

the ability to be either conductors or insulators. Vanadium dioxide (VO2) and germanium telluride (GeTe) exhibit such a

transition property. These materials have ferroelectric properties as well as a variable resistivity. The ability to vary the

resistance of a single material is useful when designing integrated circuits on the micro scale. By varying the temperature or

the electric field across these materials, we are able to change the resistivity within a portion of a line. This can in turn be

used to create a switch within a wire. In order to measure these changing properties, we developed novel surface

micromachined test structures capable of using a variety of MIT materials. By varying the electric field or the thermal

gradient across an area of the wire segment, we were able to adjust the resistivity of the material. Therefore, by tailoring the

properties of specific portions of a conductor, we were able to control current flow in a circuit without needing a

micro-mechanical or a microelectronic device.

10.1 Introduction

The ability to control the flow of current in a wire without using a mechanical component provides a possibility for more

robust switching capability. The research done involving metal insulator transition (MIT) materials has been focused on

using vanadium dioxide (VO2) and germanium telluride (GeTe) as the switching components. This is due to VO2 being an

insulator at room temperature with a monoclinic crystalline phase and a metal with a tetragonal crystalline phase when

thermally or electrically activated [1]. Bouyge et al. began using VO2 in reconfigurable microwave systems and was able to

create a variable resistivity of three to five orders of magnitude using an electric field across the VO2 wire segment [2]. Using

two metallic electrodes to create the electric field across the material, transition times from an insulator state to a metallic

state were achieved in a few hundred nano-seconds [3]. While this method of varying resistivity has a great potential in the

future capability of tuning RF devices, it isn’t always practical to insert multiple electrodes in compact micro devices. MIT

materials also have the ability to switch phases when a thermal gradient is placed across the material. This transition was

found to occur constantly at 340 K in VO2 [1, 3, 4]. The changing of the material is caused by a combination of electronic

and lattice degrees of freedom within the molecules of VO2 [5]. After reaching the transition temperature, VO2 can switch at

times less than 100 ns [6]. Germanium telluride (GeTe) has also been used as an MIT material. Using Joule heating, GeTe

can be transitioned from an amorphous to a crystalline phase [7]. Unlike the low temperature transition of VO2, GeTe has a

crystallization temperature of greater than 423 K [8]. Due to the stability of these states, this material can be used in phase-

change memory cells [7]. These chalcogenide materials can also shift phases using both thermal and electrical stimulation.

Phase change memory can be created and tuned using different doping levels of the chalcogenides and by altering the alloy

stoichiometry [9]. Much of the testing done on these phase change materials (PCM) has been done on sapphire substrates in

order to reduce the leakage current into the substrate [2, 3, 10]. Through this research, using PCMs as micro-switches on a

silicon substrate is investigated.

B.L. Danner • R.A. Coutu Jr. (*)

Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA




59


10.2 Design/Modeling

Varying the resistivity of a wire in a microstructure provides the ability to change the total length of a wire, and therefore its

inductance. Making this change in a fast, controlled manner can be extremely useful in the micro world. By running several

wire segments of MIT material as part of a single wire and adjusting the resistivity in select sections, it is possible to select

which wire segment the current flows through.

Two designs were used to vary the resistivity across the MIT materials. The first option used a single MIT wire segment

capable of being placed on a thermal electric stand. The second option incorporated a single MIT wire segment placed

between two metallic pads. With a biased applied to the pads, an electric field is created across the MIT material, changing

its resistivity.

The first design utilizes various lengths and widths of PCM wires in order to test a broad range of their capabilities.

Previous studies have tested VO2 with lengths between 150 and 1,000 mm [2]. Using this as a starting point, tests were done

on wire segments with lengths ranging from 200 to 2,000 mm. All segments were also created in widths of 20 and 40 mm.

These baseline dimensions were also used in testing GeTe wires. Figure 10.1 shows the layout of a micro structure used to

test each of the different PCMs.

The second design was used to test the varying resistivity in MIT materials when an electric field was placed across them.

In order to accurately compare the results from both the thermal and electrical tests, the same size wires were used in each

design. Electrical contact pads were placed above and below the MIT wire and connected to the two parallel plates, one on

each side of the wire. These plates ran nearly the entire length of the MIT material in order to fully transition as much of the

material as possible from an insulator to a conductor. In order to avoid creating large fringing fields from the parallel plates

to the test pads at the end of the wire, the plates were fabricated with a 10 mm gap between the pads. Other structures with

various spacing between the capacitor plates and the test pads where created to measure the effect of these fringe fields

generated in between the two.

An electric field was then generated across the MIT wire in order to change the resistivity of the material. Using various

voltages and different gaps between the capacitor plates, a variety of electrical field strengths were tested. The first order

magnitude of these fields was calculated using

E ¼ V

d; (10.1)

where V is the voltage applied across the parallel plates and d is the distance between the plates. Previous studies used

voltages between 10 and 20 V, but the distance between capacitor plates was not given [1, 3]. These designs were created

with distances of 80 and 100 mm. This gap, along with the ability to vary the voltage across the plates, allows for a broad

range of electrical fields to be tested.

Figure 10.2 is a model of the MIT wire between two parallel plates with 100 mm spacing between the plates and 10 mmspacing between the plates and the test pads. Similar to the thermal test structures, a volt meter was used to measure the

resistance across the MIT wire. The resistivity was measured using a four point probe. This value is then used to predict

the resistance of the wire segment using

R ¼ rLA

; (10.2)

where R is the resistance, L is the length of the MIT wire, A is the cross-sectional area of the wire, and r is the resistivity of

the material. By measuring the resistance while varying the voltage applied to the parallel plates, the transition of the MIT

Fig. 10.1 Layout of

thermally varied resistivity

60 B.L. Danner and R.A. Coutu Jr.

material was observed. While any electric field across any material will have some impact on the resistivity, the drastic

variance in the resistivity that MIT materials exhibit makes them unique.

Vanadium witness samples were oxidized in the O2 plasma asher in order to determine the appropriate length of time

required to fully oxidize the wires. In order to create the vanadium dioxide desired, the test samples were oxidized in the O2

plasma asher at 250 W for 45 min. One sample was not oxidized and used as the baseline resistivity of sample.

Witness samples of both VO2 and GeTe were used to model the resistance of the PCMwires at room temperature. Using a

four point probe, the sheet resistance of these materials was measured. Since all of our samples are much longer and wider

than they are thick, sheet resistance is an appropriate way of finding the resistivity of the thin film. A surface profilometer

was then used to measure the thickness of the deposited material. The VO2 wire segments had an average thickness of

199 nm and the GeTe segments had an average thickness of 202 nm. The resistivity of the material can be found using

r ¼ RSt; (10.3)

where r is the resistivity of the material, Rs is the measured sheet resistance, and t is the thickness of the thin film. The

average resistivity of the thin GeTe film was calculated to be 5.71 � 10�4 O-mm. The resistivity of VO2 ashed for 10 min in

the O2 plasma asher was calculated to be 1.67 � 10�6 O-mm. Figure 10.3 shows the resistivity of GeTe, VO2, and vanadium

on the witness samples at room temperature. Variances in the measured resistivity can be attributed to the localized heating

of the samples due to current flow in the four point probe. Using (10.2), the resistance of a MIT wire segment with a length of

200 mm and a width of 20 mm is 28.5 kO for GeTe and 83.5 O for VO2. This resistance at room temperature serves as a

baseline for the full range of switching capabilities of these materials.

The novel test structures designed here enable testing of various MIT materials while using the same design. Both designs

allow for the substitution of different MIT materials into the wire section and provide the ability to vary the temperature and

electric field enough to elicit the transition from an insulator to a conductor. Therefore, using only two masks, these designs

can be fabricated to test the varying resistance in any material.

Fig. 10.2 Layout

of electrically varied

resistivity

1.E−03

1.E−04

1.E−05

Log

10R

esistivi

ty (

Ω−μ

m)

1.E−06

Time (min)

GeTe

Vanadium

VO26 min O2plasma ashed

VO210 min O2plasma ashed

1 2 3 4 5 6 7

Fig. 10.3 Resistivity

measurements obtained

using a four point probe

10 Characterizing Metal Insulator Transition (MIT) Materials for Use as Micro-Switch Elements 61

10.3 Fabrication

The test structures were microfabricated on a 100 Silicon wafer. Testing the capabilities of these materials on a relatively

inexpensive and readily available substrate provides the eventual opportunity to use MIT switches on a large scale in

microelectromechanical systems (MEMS). Both the thermal and electrical test structures were designed using the electronic

design automation software tool L-Edit. Consideration in the design was taken to ensure that the structures were easily

testable and manufacturable in AFIT’s class 1000 cleanroom.

Using L-Edit to layout the design, a positive tone mask was fabricated using a Heidelberg mPG 101 Mask Maker. Several

samples were microfabricated using VO2. Using a 99.99 % pure vanadium (V) target, approximately 200 nm were sputter

deposited onto the wafer. Careful consideration was taken to ensure the vanadium layer was not too thick, preventing the

ability to do a liftoff. Using photolithography, the PCM wires were patterned onto two layers of photoresist on the Si

substrate as seen in Fig. 10.4b. Liftoff was used to form the MIT wire segments allowing for a uniform fabrication process

for all materials. The vanadium wires were then placed in an O2 plasma asher to create VO2.

Additional samples were fabricated using GeTe. Using RF sputtering deposition, a 200 nm film was deposited onto the Si

wafers. Using liftoff, various wire length segments were created with the GeTe. After the liftoff, small “wings” could be seen

on the top edges of the wire segments due to the conformance of the GeTe film prior to liftoff. The thin film of GeTe in

Fig. 10.5 shows the porous nature of the wire segment. The vacancies in the film can cause electron scattering when

measuring the resistance of the PCM wires.

After all of the MIT wire segments were plasma ashed to remove surface contaminants, test pads and parallel plate

capacitors were deposited on top of them. Using an EVG 620 mask aligner and a second positive tone mask, the samples

Fig. 10.4 (a) MIT material sputter deposited, (b) MIT wire patterned using photolithography and liftoff, (c) evaporation deposition of gold, and

(d) patterned gold contacts using photolithography and liftoff

Fig. 10.5 SEM photograph of GeTe thin film


were exposed to UV light and developed. A 20 nm layer of titanium (Ti) was then evaporated onto all of the samples as an

adhesive layer for the gold. A 280 nm thick gold layer was then evaporated on top of the Ti, as seen in Fig. 10.4c. Gold was

chosen for the metal parts of the test structure because of its low resistivity. The gold was then patterned using liftoff, shown

in Fig. 10.4d. Figure 10.6 shows a SEM picture of the finished electrically variable resistivity test structure.

10.4 Testing

The first test was done by placing the vanadium, vanadium dioxide, and germanium telluride samples on a thermal electric

stand in order to create a thermal gradient across the material. Figure 10.7 shows the thermal test structure under the SEM.

The samples were then heated from 30�C up to 80�C (the max temperature of the thermal stand). Using a digital multimeter

connected to hair tip probes and then .1 mm tungsten probes, the resistance was measured over each of the wires. Using

(10.2), the resistivity of each of the samples was calculated. Figure 10.8 shows the resistivity of the control sample plotted as

a function of temperature.

Using the hair tip probes, the GeTe resistivity increased starting at 50�C. Over a 30�C range, the resistivity was increased

by an order of magnitude. The VO2 wire resistivity remained consistent across the entire range of the thermal gradient. This

is due to only the surface of the thin film being oxidized in the plasma asher and can be seen in the comparison of the

vanadium and VO2 resistivity’s as the temperature was increased. The resistivity of the wires at room temperature varies

from the model due to inconsistencies in the geometry of the wires. The “wings”, formed by using liftoff as a fabrication

technique, add additional area to the wire segments. The porous nature of the thin film also contributed to the resistivities

being different. The interface between the MIT wire and the gold test pads also add a measurement bias to the resistance.

The second test was conducted on each of the wires using a variable electric field. Figure 10.9 shows the resistivity

change as a higher voltage was applied to the parallel plates for GeTe. The resistivity of each of the wires increased three to

five orders of magnitude from 37 to 45 V. When the voltage applied to the parallel plates exceeded 50 V, clipping occurred

and the resistance could no longer be measured.

The VO2 wire segments were tested using voltages on the parallel plate capacitor from 0 to 200 V. The shorter wires saw

minimal changes in the resistivity across the wires. The baseline resistivity changes of the vanadium followed closely with

that of the VO2 wires. This is attributed to the thin film of the wire only being oxidized on the surface, causing only a fraction

of the material to transition from an insulator to a metal. The wires with a length of 10,000 mm saw an increase in resistivity

near an order of magnitude with a 20 V bias applied to the plates. Due to the large length of the wire, there was a greater

oxidized area of the material. This allowed for more of a transition to occur in the thin film and therefore an increase in the

resistivity of the wire segment. Figure 10.10 shows the resistivity of the wire segments as the voltage was increased across

the parallel plates for vanadium and VO2.

Using the electric field test structures, the AC response, at 1 kHz, of the 10,000 mm PCM wires was measured. For the

VO2 samples, with a zero volt bias across the parallel plates, the AC response mirrored that of the input. When the electric

field was charged with a 110 V bias, the amplitude of the output signal was decreased by 20 % and a 7 V DC offset was added

Fig. 10.6 SEM photograph

of electrical test structure


to the signal. In the vanadium wire segments, the amplitude of the AC signal when 0 V were applied to the parallel plates was

only 35 % of the input signal. However, when 5 V were applied to the plates, the amplitude of the output signal again

matched that of the input signal with an additional 600 mV DC offset. With 110 V across the plates, the vanadium wire

segments caused a slight decrease in the amplitude, while only incurring a DC offset equal to half that of the VO2 samples.

Figure 10.11a, b shows the AC response for the VO2 wire segments. Figure 10.11c–e shows the AC response for the

vanadium wire segments.

2.6E-06 1.E-02

1.E-03

1.E-04

1.E-05

1.E-0630 40 50 60 70 80

2.4E-062.2E-062.0E-061.8E-061.6E-061.4E-061.2E-061.0E-06

VO2 20W600L

VO2 40W600L

V 20W600L

V 40W600L

V 20W2000L

Temperature (�C) Temperature (�C)

VO2 20W2000L

Res

istiv

ity (

Ω-μ

m)

Log

10 o

f R

esistivi

ty(Ω

-μm

)

30 40 50 60 70 80

20W600Lhairtip probe



20W2000Ltungsten tip

20W600Ltungsten tip

a b

Fig. 10.8 (a) Resistivity of vanadium and VO2 with varying temperatures, and (b) resistivity of GeTe with varying temperatures

1.E+00

Log

10 o

f R

esistivi

ty(Ω

−μm

) 1.E-02

1.E-04

1.E-06

0 5 10 15 20 25 30 35 40 45 50

Vo1tage Applied to Parallel Plates (V)

MIT Transition

20W200L20W200L40W200L20W200L40W2000L

Fig. 10.9 Varying resistivity of and GeTe using an electric field

Fig. 10.7 SEM photograph of thermal test structure


10.5 Conclusions

The resistivity of the MIT material can be altered by applying a thermal gradient or an electric field across the wire segments.

The GeTe wires were changed from a conductor to an insulator by applying a bias across the parallel plate capacitor. The

resistivity increased over three orders of magnitude with the introduction of the electric field. The lattice structure of the

GeTe films becomes amorphous with the introduction of a 35 V bias across the parallel plates. Short thin film VO2 wires saw

minimal changes in resistivity due to only the surface of the wire segment being oxidized. The resistivity of long VO2 wires

increased an order of magnitude when a 25 V potential was placed across the parallel plate capacitor. These changes in the

PCM wires allow for the creation of micro switches without a mechanical component.

10.6 Recommendations

The adaptability of these test structure designs and fabrication processes allow for a variety of MIT materials to be tested.

Comparison of the switching capability of these different materials will provide the ability to fabricate high quality micro

switches without a mechanical component. Measuring the switching times of both testing methods using different MIT

1.E-04

5 10 15 20 25 30 50 60 70 80 100

150

175

20040

1.E-05

MIT Transition

Voltage (V)

V 20W 200L

Log 1

0Res

istiv

ity(Ω

-μm

)

VOZ 20W 200L

VOZ 20W 2000L

VOZ 20W 10000L

VOZ 20W 10000L

V 40W 200L

V 20W 2000L

1.E-06

Fig. 10.10 Varying resistivity of vanadium and vanadium dioxide with an increasing potential across the parallel plates

Fig. 10.11 AC response across 10,000 mm (a) and (b) vanadium wires and (c–e) VO2 wires


materials will be the focus of future investigations. When testing the capabilities of VO2, use reactive sputtering with

vanadium and oxygen in order to compare the resistivity differences between a pure VO2 wire and a vanadium wire with a

VO2 thin film on the surface. The variance in resistivity of MIT wires using localized heating should be explored. Test the

full range of RF capabilities of the MIT wires.

Acknowledgements The authors are thankful to the AFIT cleanroom technicians, Mr. Rich Johnston and Mr. Tom Stephenson, for their support

in the fabrication of these devices.

Disclaimer The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air

Force, Department of Defense, or the U.S. Government.

References

1. Givernaud J, Champeaux C, Catherinot A, Pothier A, Blondy P, Crunteanu A (2008) Tunable band stop filters based on metal-insulator

transition in vanadium dioxide thin films. Presented at 2008 IEEE MTT-S international microwave symposium digest, Atlanta

2. Bouyge D, Crunteanu A, Orlianges JC, Passerieux D, Champeaux C, Catherinot A, Velez A, Bonache J, Martin F, Blondy P (2009)

Reconfigurable bandpass filter based on split ring resonators and vanadium dioxide (VO2) microwave switches. Presented at Asia-Pacific

microwave conference 2009 (APMC 2009), Singapore

3. Crunteanu A, Dumas-Bouchiat F, Champeaux C, Catherinot A, Pofhier A, Blondy P (2007) Microwave switching functions using reversible

metal-insulator transition (MIT) in VO2 thin films. Presented at European microwave conference, 2007, Germany

4. Cavalleri A, Toth C, Siders CW, Squier JA, Raksi F, Forget P, Kieffer JC (2001) Femtosecond structural dynamics in VO2 during an ultrafast

solid-solid phase transition. Phys Rev Lett 87(23):237401

5. Schilbe P, Maurer D (2004) Lattice dynamics in VO2 near the metal-insulator transition. Mater Sci Eng A 370(1–2):449–452

6. Dumas-Bouchiat F, Champeaux C, Catherinot A, Crunteanu A, Blondy P (2007) Rf-microwave switches based on reversible semiconduc-

tor–metal transition of VO2 thin films synthesized by pulsed-laser deposition. Appl Phys Lett 91(22):223505

7. Di Ventra M, Pershin YV (2011) Memory materials: a unifying description. Mater Today 14(12):584–591

8. Chen M, Rubin KA, Barton RW (1986) Compound materials for reversible, phase-change optical data storage. Appl Phys Lett 49(9):502

9. Lelmini D, Lacaita AL (2011) Phase change materials in non-volatile storage. Mater Today 14(12):600–607

10. Stotz M, Fritze S, Downar H, Wenger J (1999) Thermally controlled coplanar microwave switches. Presented at 29th European microwave

conference, vol 2, Munich, 5–7 Oct 1999


Chapter 11

Stiction Failure in Microswitches Due to Elasto-Plastic

Adhesive Contacts

Ling Wu, Jean-Claude Golinval, and Ludovic Noels

Abstract Undesirable stiction, which results from the contact between surfaces, is a major failure mode in micro-switches.

Indeed the adhesive forces can become so important that the two surfaces remain permanently glued, limiting the life-time of

the MEMS. This is especially true when the contact happens between surfaces where elasto-plastic asperities deform

permanently until the surfaces reach plastic accommodation, increasing the surface forces. To predict this behavior, a micro

adhesive-contact model is developed, which accounts for the surfaces topography evolutions during elasto-plastic contacts.

This model can be used at a higher scale to study the MEMS behavior, and thus its life-time. TheMEMS devices studied here

are assumed to work in a dry environment. In these operating conditions only the Van der Waals forces have to be considered

for adhesion. For illustration purpose, an electrostatic-structural analysis is performed on a micro-switch. To determine the

degree of plasticity involved, the impact energy of the movable electrode at pull-in is estimated. Thus the maximal adhesive

force is predicted using the developed model.

11.1 Introduction

The inherent characters of MEMS such as the large surface area-to-volume ratio, smooth surfaces, small interfacial gaps and

small restoring forces, make them particularly vulnerable to stiction which is one of the most common failure mechanism of

MEMS [1]. Stiction happens when two components entering into contact permanently adhere to each-other because the

restoring forces are smaller than the surface forces (capillary, van der Waals (VDW) or electrostatic). This can happen either

during the fabrication process at etching (release stiction) or during normal use (in-use stiction).

To improve the reliability ofMEMS, models are required in order to predict and avoid in-use stiction failure. Amulti-scale

model can predict at the lower scale the adhesive contact forces of two rough surfaces, and thus can integrate these curves on

the surface of the finite elements as a contact law at the higher scale [2, 3]. The authors recently proposed [4] a model

predicting the micro adhesive-contact curves, i.e. the adhesive-contact force vs. the surface separation distance, for two

interacting micro-surfaces. This analytical model, accounting for elastic deformations of the asperities, and for van derWaals

forces, is based on classical adhesion theories [5–10] and can be easily integrated in the multiscale framework [2, 3].

Although the two-scale framework [3] based on the elastic micro-model [4] has been shown to predict accurate results for

elastic materials in dry environment [3], in order to extend the applicability of the method to other environments, the micro-

model requires enhancements, and in particular its extension to the elasto-plastic behavior of the asperities. As a first step

toward this end, this paper presents an improved model for the single elastic–plastic asperity-plane interaction problem.

When elastic–plastic rough surfaces interact, each asperity will be affected differently due to the statistical nature of the

asperity distribution on the surfaces: higher asperities will experience plastic deformations first. Due to the plastic behavior,

L. Wu

Aerospace and Mechanical Engineering Department, University of Liege, Chemin des Chevreuils 1, B4000 Liege, Belgium

School of Aeronautics, Northwestern Polytechnical University, 710072 Xi’an, China


J.-C. Golinval • L. Noels (*)

Aerospace and Mechanical Engineering Department, University of Liege, Chemin des Chevreuils 1, B4000 Liege, Belgium




67




the contact force on deformed asperities is lower than in the elastic case for the same contact interference (distance between

undeformed profiles), while the adhesive force increases due to the change of the asperity profile. Because of the combination

of these two phenomena the pull-out force – maximum attractive forces or the minimum compressive forces between the two

interacting surfaces – is higher than that between two pure elastic contacting rough surfaces. Another qualitative difference

with elastic surfaces is the difference of behavior under cyclic loading: after repeated contacts, the distribution of asperities

heights and the tip radii of the higher asperities change [11], until plastic accommodation or shakedown [11]. This induces a

“contact hardening” [13] and the pull-out force increases until accommodation, unless in-use stiction happens first.

To account for the elasto-plastic behavior, the authors [14] have developed a micro-model able to predict stiction for

elastic–plastic rough surfaces by first considering the problem of a single elasto-plastic asperity interaction and thus the

generalization to the interaction of rough surfaces. The single asperity/plane contact problem is modeled using semi-

analytical models [15–17] which evaluate the deformed asperity profile during hysteretic loading/unloading without

considering the adhesion effect. Assuming adhesion will not affect the plastic deformations, which is not the case for

extremely soft materials as gold [18], we can consider the Maugis theory [7] completed by Kim expansion [8] to evaluate the

adhesion forces during the unloading phase [4] from the tip radius evolution during loading process. As amain difference with

previous models [15–17], adhesion forces are evaluated taking into account the effect of the non-constant asperity curvature

resulting from elasto-plastic deformations, which conducts to an accurate prediction of the pull-out forces [14]. In this model

only van der Waals forces are considered, which is a realistic assumption below 30% humidity [1]. The interaction of two

rough surfaces is achieved by considering a usual statistical distribution of asperities [5, 6], however, contrarily to the elastic

case, the distribution of asperities heights and the asperity profiles of the higher asperities change due to the plastic

deformations. These changes, and the resulting adhesive-contact forces, are evaluated using the single asperity model. As a

result, micro adhesive-contact curves of two interacting elasto-plastic rough surfaces can be predicted in an analytical way

during loading and unloading.

The purpose of this paper is to predict the reliability of a micro-switch by considering the effect of repeated interactions

between the movable/substrate electrodes. For illustration purpose a one-dimensional model is considered and contact

occurs between two Ruthenium (Ru) films. We also show that unloading curves change after repeated interactions until

reaching accommodation. Thus, the pull-out force can be predicted in terms of the pull-in force and of the cycles number,

opening the way to a stiction-free design.

The organization of the paper is as follows. In Sect. 11.2, the micro-model for elasto-plastic adhesive-contact is

summarized. First the single elasto-plastic asperity/plane interaction model with no adhesion effect is described. Then,

the adhesion forces are evaluated from the deformed asperity profile taking into account the effect of the non-constant

asperity curvature resulting from elasto-plastic deformations. Finally the micro adhesive-contact curves of two interacting

elasto-plastic rough surfaces are deduced. This model can then be used in Sect. 11.3 to study the micro-switch reliability. In

particular the effect of cyclic loading on the pull-out force, and thus on the stiction risk, is predicted.

11.2 Micro-model for Elasto-Plastic Adhesive-Contacts

In this section, the single elasto-plastic asperity/plane interaction model with no adhesion effect is first described before

evaluating the adhesion forces from the deformed asperity profile. Then, using a statistical distribution of asperities heights

accounting for the changes in asperity profiles and heights due to the plastic deformations, the micro adhesive-contact curves

of two interacting elasto-plastic rough surfaces can be predicted.

11.2.1 Single Asperity Elasto-Plastic Contacts

Let an asperity of tip radius R, Young modulus E, and yield stress SY, interacts with a rigid plane at an interference distance d,positive in case of contact and negative otherwise, see Figs. 11.1a, b, defined as the distance between the original profile of

the asperity tip and the plane. When the plane starts interacting with the asperity during loading, the critical yield

interference dCP is defined as the interference at which the asperity starts yielding and can be expressed as [15–17]

dCPR

¼ pCvSY2E

� �2(11.1)

68 L. Wu et al.

In this expression Cv is a coefficient that depends on the Poisson ratio v, and that can be evaluated from Cv ¼ 1.295e0.736v,

e.g. [16]. As, with our assumption, the asperity starts yielding at positive interference, there exists a corresponding critical

contact radius aCP, Fig. 11.1a, and a critical contact force FCP, respectively evaluated as

aCP ¼ffiffiffiffiffiffiffidCPR

r(11.2)

FCP

R¼ 2

3pCvSYdCP (11.3)

During the loading phase, assuming the interference goes beyond the critical interference dCP, the asperity is subject to

permanent plastic deformations that depend on dmax, the maximal interference reached. After unloading, the asperity

exhibits a permanent reduction of the asperity height dres, and a modified asperity tip radius Rres, see Fig. 11.1c, that were

curve-fitted from finite element numerical simulations [17]

dresdrmax

¼ 1� dCPdrmax

� �0:28" #1� dCP

drmax

� �0:69" #(11.4)

Rres

R¼ 1þ 1:275

SYE

� �0:216 dmax

dCP� 1

� �(11.5)

11.2.2 Single Asperity Elasto-Plastic Adhesive Contacts

In Maugis theory [7], the inter-atomic attraction effect is modeled using a Dugdale assumption: within a critical value of

separation z0, two surfaces are attracted with a constant force per unit area s0, while if the separation z exceeds z0, theadhesive traction vanishes. The associated adhesive energy readsϖ ¼ s0z0. Maugis theory for the interaction of two elastic

asperities characterized by two Young modulii E1 and E2, two Poisson ratios v1 and v2, and by two tip radii R1 and R2, is

based on the definition of a transition parameter

l ¼ 2s0ffiffiffiffiffiffiffiffiffip�oK2

R3

q whereK ¼ 4

3

1� v12

E1

þ 1� v22

E2

� ��1

andR ¼ R1R2

R1 þ R2

(11.6)

are respectively the equivalent modulus and initial tip radius of two interacting asperities, or the initial radius of an asperity

interacting with a plane. The transition parameter defines a solution ranging from JKR regime [5] – soft materials with a

large contact curvature surface and with a high surface energy – to the DMT regime [6] – hard materials with a reduced

contact curvature and with a low surface energy. This solution provides, for a given interaction d, the adhesive contact forceFn, the interacting contact radius a and the adhesive-contact radius c on which adhesive forces apply, see Fig. 11.1a. The

system of equations is written in terms of the non-dimensional values

A ¼ aK

p �oR2

� �1=3; �Fn ¼ Fn

p�oR; D ¼ d

K2

p2 �o2R

� �1=3and m ¼ c

a(11.7)

Fig. 11.1 Definition of single asperity interference [14]

11 Stiction Failure in Microswitches Due to Elasto-Plastic Adhesive Contacts 69

and reads

1 ¼ lA2

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1

pþ m2 � 2� �

arctanffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1

ph iþ 4l2A

3


parctan


p� mþ 1

h i(11.8)

D ¼ A2 � 4lA3


p(11.9)

�Fn ¼ A3 � lA2ffiffiffiffiffiffiffiffiffiffiffiffiffiffim2 � 1

pþ m2 arctan


ph i(11.10)

This set of equations is completed by the interference evaluation

d ¼ a2

R� 8s0

3K

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2 � a2

p(11.11)

Kim et al. [8] extended Maugis-Dugdale solution to the non-contact regime when a ¼ 0 and c 6¼ 0, see Fig. 11.1b, see [4]

for details. Practically, this expansion has to be considered when l <0.938.

Although this adhesive theory is based on Hertz contact model, and thus assumes an elastic behavior, we proposed [14] to

apply this theory on the permanently deformed asperity profile. As during the unloading the behavior remains elastic, at the

exception of extremely soft materials, Maugis theory completed by Kim extension constitutes a good approximation.

However, we proposed to account for a non-constant asperity radius in terms of the interference, see Fig. 11.1c, and to

perform the adhesive-contact theory on the assumed elastically deformed asperity, which has an effective tip radius Reff at a

contact interference d � dres. This is motivated by the fact that Maugis theory assumes a uniform asperity radius to apply

Hertz theory although this case is only met at the limit case d ¼ dres. The following expression has been proposed [14]

Reff

R¼ Rres

R� 1:275 1� c1ð Þ SY

E

� �0:216 dmax

dCP� 1

� �1� e

c2d�dres

dmax�dres

1� ec2

0@

1A (11.12)

In this expression, c1 and c2 are functions that have to be determined by inverse analysis from finite-element results.

Using the simulations performed for Ru [19], we proposed [14]

c1 ¼ 0:22þ 0:6242e�0:092

drmax

dCP and c2 ¼ 10

1þ drmax 10dCP=ð Þ2 � 5 (11.13)

Because of the elasto-plastic behavior happening during contacts, the theory developed here results in different adhesive-

contact forces during loading FnL(d) and unloading Fn

U(d). During the loading phase, once dCP is reached, the maximum

interference is identical to the current one (dmax ¼ d) and the deformed profile can be evaluated from (11.4) and (11.5).

Thus, the loading force FnL(d) is evaluated from Maugis solution by solving the system (11.8), (11.9), (11.10), and (11.11),

with as input for R the effective radius (11.12), and as input for d the effective value d � dres, where dres increases during thewhole loading process. During unloading however, the residual (dres) and maximal (dmax) interferences reached remain

constant. The adhesive-contact force during unloading FnU(d) is computed from the Kim extension [8] of Maugis theory [7],

with as input for R the effective radius (11.12), and as input for d the effective value d � dres. Contrarily to the loading

process, the effect of adhesion needs to be considered at the intermediate pull-out stage, which is achieved by using the Kim

extension [8].

The elastic–plastic adhesive contact of a micro sphere was studied for Ruthenium (Ru) in [19]. Ru has the advantage of

not exhibiting plastic deformations under adhesive effects only. Material properties and the initial asperity tip radius are

reported in Table 11.1. To demonstrate the accuracy of the proposed method, Fig. 11.2 compares the predicted adhesive-

contact forces to the FE results for the loading and unloading adhesive-contact forces at three maximum interferences dmax

successively equal to 17, 34 and 51 nm. It is seen that an excellent agreement is obtained for the three loading conditions.

70 L. Wu et al.

11.2.3 Rough Surfaces Interaction

Greenwood and Williamson ‘asperity-based model’ [9] is applied to simulate the rough surface/plane interaction. A rough

surface is described by a collection of spherical asperities with identical end radii R, whose heights h have a statistical

distribution

’ðhÞ ¼ 1

ssffiffiffiffiffiffi2p

p exp�h2

2s2s

� �(11.14)

where ss is the standard deviations in asperity heights. The contact of two rough surfaces can be represented by the contact

between an equivalent rough surface and a smooth plane [10]: if the two initial contacting rough surfaces have respectively

the asperities end radii of R1 and R2, the equivalent radius is defined by (11.6), and if the standard deviation in asperity

heights are ss1 and ss2, the equivalent rough surface is defined by the standard deviation in asperity heights ss ¼ (ss12 +

ss22)1/2. The interaction between two rough surfaces is also characterized by the distance d between the two rough surface

mean planes of asperity heights, and by N, the surface density of asperities. All these values can be identified from the study

of the surfaces topography, and, in particular, depend on the surface RMS roughness Rq, see [3] for details.

The surface loading and unloading forces, respectively FnTL and FnT

U can now be evaluated by integrating on the surface

the effect of each asperity, for which the interference reads d ¼ h � d, using the framework described in Sect. 11.2.2.

Toward this end, non-dimensional values are defined

�FnT ¼ FnT

p �oR; �d ¼ d

ffiffiffiffiffiffiffiffiffiffiffiffiffiK2

p2 �o2R

3

rand ss ¼ ss

ffiffiffiffiffiffiffiffiffiffiffiffiffiK2

p2 �o2R

3

rð11:15Þ

Table 11.1 Properties

of Ru filmsR [mm] 4

E [GPa] 410

v [�] 0.3

SY [GPa] 3.42

z0 [nm] 0.169

ϖ [J/m2] 1

ss [nm] 7.78

Rq [nm] 7.81

N [mm�2] 10

Fig. 11.2 Comparison of

the single asperity model

with finite element results

for Ru


which allows writing

�FnT ¼ N

�ssffiffiffiffiffiffi2p

pð�Fn Dð Þe�

Dþdð Þ22�ss2 dD (11.16)

It bears emphasize that as asperities enter into plasticity for different surface distances, the effective profile is different for

each asperity. Details on the integration (11.16) are provided in [14].

11.3 Cyclic Loading of a Micro-switch

A one-dimensional model of micro-switch is considered, see Fig. 11.3. In this model, a potential difference U is applied

between a movable electrode and a substrate electrode covered by a dielectric layer of thickness td and permittivity ed. Themovable electrode is attached to a spring of stiffness per unit area KS, and is initially at a distance d0 from the substrate.

The switch is supposed to work in vacuum, permittivity e0, so the damping effect of a squeeze film is neglected. Typical

values for SiN dielectric are reported in Table 11.2. Contact is assumed to occur between two Ru surfaces, for which typical

topography values are reported in Table 11.1. Ru films of thickness ts are deposited on the movable electrode, and also on a

part of the substrate.

From these data, the pull-in voltage and the impact energy can be computed in terms of the stiffness KS. This computation

has been performed in [14], and in this application we consider an impact energy of EI ¼ 0.5 J/m2. This impact energy per

unit surface of the contacting area affects the plastic deformations of the asperities and thus the adhesion-contact forces.

Indeed, once an impact occurs, the energy EI is converted into elastic and plastic deformations energies. The asperities

loading process finishes once all the energy has been converted. The energy for elastic wave propagation is neglected in this

work; however the elastic energy in the Ru film is accounted for. With these assumptions, the distance de between the two

rough surfaces mean planes of asperity heights reached at the end of the impact process is deduced from

EI ¼ð1

de

FnTLðdÞdd þ FnT

L deð Þ� �2ts

2E(11.17)

Once the distance de has been computed, the deformed profile of the asperities is known, and the unloading process can be

studied. In particular, the adhesive contact forces FnTU are evaluated from (11.16) in terms of the distance d > de.

Fig. 11.3 1D micro-switch

application

Table 11.2 Properties

of the micro-switchd0 [mm] 2

td [mm] 0.15

e0 [pF/m] 8.854

ed / e0 [�] 7.6

ts [nm] 180

72 L. Wu et al.

These two steps characterize one loading/unloading cycle. To study cyclic loading, the same analyses have to be

performed with updated asperities profiles. Indeed, after the first cycle, the profile of the surface is modified as only higher

asperities entered into contact and exhibited plastic deformations. History is tracked by keeping after each loading the

function dmax(h) of the maximal interference reached for an asperity of initial height h. From this function the profile change

of an asperity of initial height h can be known to evaluate its effect on the loading/unloading forces (11.16). Thus, the

reliability of the micro-switch can be studied by considering the effect of repeated interactions between the movable/

substrate electrodes. Indeed, the unloading curves change after repeated interactions until reaching accommodation, as

illustrated on Fig. 11.4, where the unloading curves after 1, 2, 3 and 10 cycles are reported. From this figure it appears that

the pull-out force after accommodation can be predicted, opening the way to stiction-free design. On this figure the elastic

solution is also reported, and is shown to underestimate the pull-out force. Also the loading curve is represented.

11.4 Conclusions

In order to predict stiction in MEMS structures, a possible approach is to consider a multi-scale framework. If at the higher

scale a finite element analysis can be considered, it requires an adhesive-contact law to be integrated on the interacting

surfaces.

The definition of this adhesive-contact law constitutes the micro-scale problem. In this paper, this adhesive contact-

distance curve of two interacting elasto-plastic rough surfaces was established using a semi-analytical analysis. First the

deformed profile of the asperity is evaluated from literaturemodels, which uncouple the plastic deformation from the adhesive

effect. This assumption usually holds except for materials suffering from jump-in induced plasticity, as for gold, for which

the sole adhesion effect can lead to plastic deformations. Then, we useMaugis-Kim adhesive theory to evaluate the adhesive-

contact forces. In order to account for the deformed shape of the asperity, assumed as spherical in the Hertz contact of the

Maugis theory, we propose to evaluate an effective asperity radius which depends on the interference. With this method, we

can predict the loading/unloading hysteresis curves of a single elastic–plastic asperity interacting with a rigid plane. Finally a

statistical model of asperity height is considered to study the interaction of two elasto-plastic rough surfaces.

The predictions of this model are illustrated by considering the cyclic loading of a 1D micro-switch application. It is

shown that the repeated loading of a MEMS switch changes the structure of the contacting surface due to the plastic

deformations. Thus, with time, the contact surfaces become smoother, increasing the adhesion effect. This effect should be

considered at the design stage to avoid in-use stiction.

Fig. 11.4 Cyclic loading of the 1D micro-switch


References

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experiments in microelectronics and microsystems (EuroSimE), Linz, Austria, April 2011, pp 1–6

3. Wu L, Noels L, Rochus V, Pustan M, Golinval J-C (2011) A micro-macroapproach to predict stiction due to surface contact in microelec-

tromechanical systems. J Microelectromech Syst 20(4):976–990

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1–113502-10

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6. Derjaguin B, Muller V, Toporov Y (1975) Effect of contact deformation on the adhesion of elastic solids. J Colloid Interface Sci 53

(2):314–326

7. Maugis D (1992) Adhesion of spheres: the JKRDMT transition using a Dugdale model. J Colloid Interface Sci 150(1):243–269

8. Kim K, McMeeking R, Johnson K (1998) Adhesion, slip, cohesive zones and energy fluxes for elastic spheres in contact. J Mech Phys Solids

46(2):243–266

9. Greenwood J, Williamson J (1966) Contact of nominally flat surfaces. Proc R Soc Lond A Math Phys Eng Sci 295(1442):300–319

10. Greenwood J, Tripp J (1971) The contact of two nominally flat rough surfaces. Proc Inst Mech Eng 1847–1996 185(1970):625–633

11. Jones R (2004) Models for contact loading and unloading of a rough surface. Int J Eng Sci 42(17–18):1931–1947

12. Williams J (2005) The influence of repeated loading, residual stresses and shakedown on the behaviour of tribological contacts. Tribol Int 38

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14. Wu L, Golinval J-C, Noels L. A micro model for elasto-plastic adhesive-contact in micro-switches. Tribol Int (submitted)

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74 L. Wu et al.

Chapter 12

Simultaneous Measurement of Force and Conductance Across

Single Molecule Junctions

Sriharsha V. Aradhya, Michael Frei, Mark S. Hybertsen, and Latha Venkataraman

Abstract Measurement of electronics and mechanics of single molecules provides a fundamental understanding of

conductance as well as bonding at the atomic scale. To study the mechanics at these length scales, we have built a

conducting atomic force microscope (AFM) optimized for high displacement and force resolution. Here, we simultaneously

measure conductance and force across single Au-molecule-Au junctions in order to obtain complementary information

about the electronics and structure in these systems. First we show that single-atom Au contacts, which have a conductance

of G0 (2e2/h), have a rupture force of about 1.4 nN, in excellent agreement with previous theoretical and experimental

studies. For a series of amine and pyridine linked molecules which are bound to Au electrodes through an Au-N donor-

acceptor bond, we observe that the rupture force depends on the backbone chemistry and can range from 0.5 to 0.8 nN. We

also study junctions formed with molecules that bind through P-Au and S-Au interactions. We find that both the conductance

signatures and junction evolution of covalent S-Au bond (thiolate) and a donor-acceptor S-Au bond (thiol) are dramatically

different. Finally, we perform density functional theory based adiabatic molecular junction elongation and rupture

calculations which give us an insight into the underlying mechanisms in these experiments.

12.1 Introduction

Understanding the physical properties of single molecule junctions is of fundamental importance to nanoscale electronics

[1–7]. While the electrical and thermal properties of a variety of organic molecules bound to metal electrodes have been

probed [6–14], measurements of rupture forces of single metal-molecule-metal junctions are new [15–19]. Mechanical

information at these length scales can help address a multitude of untested predictions regarding the interplay between

structure, mechanics and electronics of these junctions. In particular, probing the relation between mechanical and electronic

properties of single molecule circuits provides a deeper understanding of the structure-conductance relation in these systems.

The force signature for particular bond rupture events occurring during junction formation and evolution are probed in these

measurements, similar to the more established conductance signatures for a variety of known molecular backbones and

linker group combinations. However, conductance data alone is often insufficient to fully explain the complex, atomic

processes that control the evolution of the junction structure, in particular under stress. In this respect, force measurements

can potentially be used to determine bond rupture forces, junction stiffness, and their relation to the loading rate, that has

been demonstrated for biomolecular systems [20, 21].

Here, we use a modified atomic force microscope (AFM) to form single molecule junctions between an Au substrate and

an Au-coated cantilever (Fig. 12.1). The simultaneously measured conductance and force between the AFM tip and substrate

are analyzed to determine bond rupture forces [17, 18]. We analyze force data to obtain bond rupture forces from a large,

statistically significant set of individual measurements. We first show that the force required to break an Au-Au bond is

S.V. Aradhya • M. Frei • L. Venkataraman (*)

Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA


M.S. Hybertsen

Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA



75



1.4 nN, based on over 31,000 individual measurements and in good agreement with previous published results [22–24].

We then show that for single molecule junctions, the N-Au bond-rupture force depends on the molecular backbone, and

varies from 0.8 nN for 4,40 bipyridine to 0.5 nN in 1,4 diaminobenzene [17]. We then compare the conductance and rupture

forces of single molecule junctions formed by alkane backbones terminated with four different linker groups: amine,

methylsulfide, diphenylphosphine and thiol [18]. For the first three, which bind to Au through a donor-acceptor bond, we see

clear conductance signatures, with junctions rupturing under 0.6–0.8 nN stress. In contrast, junctions with thiol linkers

undergo multiple plastic deformation events during elongation, indicative of structural rearrangements. However, we find

that these events have an average rupture force that is smaller than the 1.4 nN observed for the rupture force of a single Au

atom contact. These results show that the rupture of an Au-S covalently bonded junction, which would most likely occur at

an Au-Au bond, does not require a force of 1.4 nN contrary to what is commonly assumed. Finally, we perform density

functional theory (DFT) calculations for adiabatic junction elongation trajectories. Chemical trends in the maximum

sustained force determined from these calculations agree well with the experimental results for rupture forces.

12.2 Experimental Methods

A schematic representation of the AFM setup is shown in Fig. 12.2a. The conductive AFM consists of a modified AFM head

(Veeco Multimode), external adder and filter circuits (SRS), as well as a homebuilt cantilever holder. A constant bias is

applied between an Au coated cantilever (TAP300, BudgetSensors) and an Au substrate placed on top of a single-axis

piezoelectric positioner with a built-in position sensor (Mad City Labs). The resulting current is converted to a voltage with a

current amplifier (Keithley 428). Data collection and control of the piezoelectric positioner are done by means of a data

acquisition board (National Instruments, PXI-4461) driven by a customized program using Igor software (Wavemetrics

Inc.). The AFM cantilever coated with a 5 nm Chromium adhesion layer and 100 nm of Au (99.999% purity, Alfa Aesar)

served as one electrode. An Au substrate (mica with 100 nm Au layer, 99.999% purity, Alfa Aesar) served as the second

electrode. The cantilever and substrate were UV/ozone cleaned prior to use. Force was determined by measuring the

deflections of a laser spot focused on the back of the cantilever, collected on the detector. The detector signal was calibrated

to yield the force data, using the thermal power spectrum method [23, 25]. For the simultaneous conductance and force trace

measurements, the substrate approached the cantilever tip until a set conductance larger than 5 G0 was measured to ensure

that the Au-molecule-Au junction from the previous measurement was completely destroyed. The sample was withdrawn at

a rate of 18 nm/s and the current and force versus position data was recorded at a sampling frequency of 100 kHz. All

position determinations were based on measurements with the built-in position sensor within our custom piezoelectric

positioner. This position sensor was calibrated both by the manufacturer and by us using laser interference measurements.

We found the absolute values of the measured displacements to be accurate to within 5%.

We simultaneously measure the conductance and force of molecular junctions by repeatedly forming and rupturing Au

point contacts between the tip and substrate of the AFM (Fig. 12.2a). Simultaneous measurements of cantilever deflection

relate to the force applied across the junction. The AFM is operated in ambient conditions at room temperature. Conductance

is measured by applying a constant bias of 25 mV between the tip and substrate, and measuring the resulting current. For

each measurement, an Au point-contact is first formed between the substrate and cantilever. It is then pulled apart and

Fig. 12.1 Illustration of

stretching and breaking

of a single molecule junction

between the AFM cantilever

and the substrate. Chemical

structure of the linker groups

and molecular backbones

measured in this study are

shown along with arrowsof size proportional to their

respective measured rupture

forces

76 S.V. Aradhya et al.

broken, while conductance and force are recorded as a function of sample displacement. This process is repeated thousands

of times to obtain large data sets of conductance and simultaneously acquired force versus junction elongation. Before

adding any molecule to the substrate, at least 1,000 conductance and force traces were collected to ensure that no

contamination was present in the setup. Individual conductance traces for an Au point-contact show stepwise decrease in

conductance until a single atom contact is formed with a conductance of G0 ¼ 2e2/h, the quantum of conductance

(Fig. 12.2b). The simultaneously acquired force traces show a characteristic saw-tooth pattern (Fig. 12.2b) indicating two

distinct force regimes: gradual linear increases due to elastic (reversible) elongations and sharp drops due to permanent

deformations of the junction. Upon further stretching, the single atomic gold wire breaks and the conductance exhibits a

tunneling signature when no molecules are present, while the cantilever displacement changes abruptly. When

measurements are carried out in an environment of molecules, an additional conductance step is frequently observed at a

molecule-dependent conductance value below 1 G0 along with an additional abrupt change in the force trace. The full trace

of force versus elongation presents a rich dataset describing the mechanical evolution of these junctions under stress. In this

study, we focus on the force associated with the breaking of a single atomic Au contacts or an Au-molecule-Au junctions.

This can be determined by analyzing the change in the cantilever deflection at the location where the 1 G0 or the molecular

conductance step ends and the junction breaks.

To extract statistically significant characteristics from the evolution of junction conductance and force as a function of

sample displacement, we construct two-dimensional (2D) histograms from the conductance and force traces, setting the origin

of the displacement axis at the point where either the 1 G0 conductance step or the molecular conductance step breaks. This

well-defined position on the x-axis is determined individually for each trace, using an automated algorithm. A fraction of the

traces do not show a conductance plateau at G0 or a plateau corresponding to a molecular junction. It is likely that the absence

of the G0 or the molecular conductance plateau means that a single-atom point contact or a single molecule junction was not

formed during that particular measurement. Therefore, these traces were not used for further analysis, as they do not contain

the bond rupture event of interest. The statistical occurrence of the junction of interest varies with the case, but a statistically

significant and unbiased data set results in each case. Each data point on the digitized conductance (force) trace was thus

assigned a conductance (force) coordinate (along the y-axis) and a position coordinate (along the x-axis). Two-dimensional

conductance histograms were then generated without further analysis. For the two-dimensional force histogram, we also set

the force at the new zero-displacement position to zero force by subtracting an offset from the entire force trace. This

realigned all force traces to a common point such that each force and displacement value was now determined relative to the

value at the end of the conductance step in each trace. After this realignment, thousands of force traces were added to generate

a two-dimensional force histogram. A statistically averaged force profile is obtained from this histogram from the peak of a

Gaussian that is fit to vertical sections at every displacement bin.

Figure 12.3a, b shows two-dimensional conductance and force histograms, respectively, constructed from over 31,000

traces measured without any molecules present and using 20 different tip/sample pairs. Insets to Fig. 12.3a, b show a

sample conductance and simultaneously acquired force trace, respectively, to illustrate where the zero in displacement is set.

The conductance is plotted on a logarithmic axis, whereas the force and the position (x-) axes use linear bins in these plots.

Negative displacements are events that occur before the end of the 1 G0 plateau while positive corresponds to data beyond the

Fig. 12.2 (a) Schematic of the modified conductive atomic force microscope. An Au point contact is formed between a Cr/Au-coated cantilever

and an Au-coated substrate with the relative separation controlled by a piezo. The force acting on the junction is detected by optically measuring

the deflection of the cantilever. (b) Sample conductance (red) and force (blue) data showing the evolution and rupture of an Au point contact, at abias of 25 mV and a piezo displacement speed of 18 nm/s. Step-wise decreases in conductance are accompanied by sudden jumps in the force

12 Simultaneous Measurement of Force and Conductance Across Single Molecule Junctions 77

end of the plateau. These histograms are generated from traces where the G0 step can be identified with our automated

algorithm. Approximately 80% (31,033 out of 39,000) of the measured traces exhibit a clearly identifiable 1 G0 step and are

included. Figure 12.3a shows clear peaks at integer multiples of G0 occurring at negative displacements, and almost no counts

at positive displacements, since zero displacement is set at the point when the G0 contact breaks.

The 2D force histogram, created from the same set of traces, (Fig. 12.3b) shows a trend in the force that is increasing with

increasing displacement, just prior to the clear sharp drop at zero displacement. The force required to break the G0 contact can

be determined from the magnitude of this drop. The force profile is effectively an averaged force trace for the single atom

contact rupture event. It shows a clearly defined drop of 1.4 � 0.2 nN at zero displacement, as illustrated in Fig. 12.3b,

corresponding to the breaking force of a single Au-Au bond. This value is in good agreement with published experimental and

theoretical results [22–24], validating our 2D analysis method. We note here that this result is from a statistically significant

data set of about 31,000 traces, providing a robust and unbiased determination of the single Au-Au bond breaking force.

12.3 Single Molecule Measurements

We apply this same technique to compare the bond rupture force in single molecule junctions. We study seven molecules

chosen to represent (a) four different molecular backbones (butane, hexane, benzene and bipyridine), each with a nitrogen

termination, and (b) four linker groups (Amine [NH2], thiomethyl [SMe], thiol [SH] and diphenylphosphine [DPP]), each

attached to similar saturated backbones (of 4 or 5 carbon atoms). The chemical names (and abbreviations used in the

following discussion) for the molecules are: (a) 1,4 diaminobenzene (BDA), (b) 4,40 bipyridine (BP), (c) 1,6-hexanediamine

(C6A), (d) 1,4-butanediamine (C4A) (e) 1,4-bis(methylsulfide) butane (C4SMe), (f) 1,5 bis-(diphenyl-phosphino)pentane

(C5DPP), and (g) 1,4-butanedithiol (C4SH). Each compound is obtained from commercial sources, and used without further

purification. Conductance is determined by measuring current through the junction at a constant applied bias of 25 mV for all

molecules, except 75 mV for C6A and for BP. The molecules are deposited onto the Au substrate either by evaporation or by

addition of a dilute concentration of molecule in the solvent 1,2,4-tricholorobenzene (TCB). Both the conductance and force

results are independent of the deposition method. Over 10,000 individual conductance and simultaneously acquired force

traces are collected with multiple tip/sample pairs for each molecule and these are analyzed by generating 2D histograms, as

detailed above, to characterize the molecular breaking force.

Figure 12.4a shows a 2D conductance histogram for C4A where the origin in the displacement axis is set at the end of the

molecular conductance step. Logarithmic bins for the conductance (y-) axis and linear bins for the displacement (x-) axis are

chosen for image clarity. The measured traces that show a molecular conductance step were selected using an automated

algorithm for both conductance and force analysis. Insets of Fig. 12.4a, b show conductance and simultaneous force data for

one particular junction breaking event, out of the over 3,500 individual measurements used to construct the 2D histograms.

A clear feature is seen in the conductance histogram at 9 � 10�4 G0, which gives us the most probable conductance of an

Fig. 12.3 (a) Two-dimensional conductance histogram constructed from over 31,000 traces. All traces are aligned such that the end of the plateau at

1 G0 is at zero along the displacement axis. A large number of counts is visible at integer multiples of G0. Inset: Sample conductance trace aligned to

zero displacement at the end of the 1 G0 plateau. (b) Two-dimensional force histogram constructed from simultaneously acquired force traces.

The force profile (black curve) is overlaid and shows a clear jump at zero displacement. The rupture force of 1.4 nN for a single atomic contact is

determined by extrapolating the fit of the force profile (dotted line). Inset: Force trace acquired simultaneously with conductance trace shown in the

inset to panel (a), aligned at the 1 G0 break


Au-C4A-Au junction. This peak extends over a displacement of about 0.15 nm, indicating that molecular junctions can be

elongated over this distance prior to the final rupture.

Every molecule, except C4SH, shows characteristic conductance features due to the selective binding of the N, SMe or

DPP linker to undercoordinated Au atoms [26, 27]. Particularly, BP shows two characteristic conductance peaks (a ‘high-G’

and a ‘low-G’ peak) that occur at distinct junction elongation distances [28–30]. In this work, we probe the rupture from the

low-G peak, which corresponds to a geometry where the molecule bridges the two Au electrodes vertically [30]. Except

C4SH, for which we do not find any well-defined conductance, we note that the conductance peak positions (corresponding

to the most frequently measured conductance, see Table 12.1) are in good agreement with previously published data

collected in solution using the scanning tunneling microscope-based break junction technique [27, 30]. This further validates

our measurement and molecule deposition techniques. Furthermore, the clear conductance signature seen for all these

molecules allows us to measure specific single Au-molecule-Au junction rupture events unambiguously. In each case, except

the thiolate (SH) linker, it is also known that the binding mechanism is the (N, P or S)-Au donor-acceptor interaction [26, 27,

30–33]. In Table 12.1, we show bond rupture forces determined from 2D force histograms for six molecules considered here,

except C4SH. We see that in all these cases, the Au-molecule-Au junction ruptures at a force smaller than that of an Au-Au

bond, indicating that rupture occurs at the respective donor-acceptor bonds consistent with earlier work [16, 27, 33].

Specifically in the amine linked molecules, by comparing the measured rupture forces for C4A and C6A we see first that for

these two alkanes with 4 and 6 carbons in the backbone, the rupture forces are very similar. Additionally, we see that the

force required to break the N-Au bond in the conjugated molecule, BDA, is considerably smaller than in C4A and C6A,

which are fully saturated.

For the thiol (SH) linker, there are multiple bonding scenarios for an Au-S covalent bond, many possible locations for the

adsorption of the H atom on the electrodes and also a possibility of forming an Au-SH donor-acceptor bond [34]. In our

conductance results of C4SH, we see a qualitatively different behavior from those of the other three linkers. We see a

multitude of conductance features over a wide range of conductance spanning from just below G0 to the experimental noise

floor. This fact reflects previous studies [35, 36] which have explained such observations based on the many possible binding

mechanisms and geometries accessible to thiol linkers. Figure 12.5a, c demonstrates the lack of any clear conductance feature

in individual measurements of C4SH, in comparison to measurements with C4SMe, in our experiments. This precludes the

unambiguous assignment of the displacement at which the junction ruptured in each trace, which is essential in constructing a

2D conductance or force histogram. We therefore focus the analysis on the force traces, and use an alternate approach, based

on identification of all sharp drops in individual force traces with an automated algorithm. Each force drop corresponds either

to a structural rearrangement in the junction or junction rupture. Each such event can be associated with the conductance of the

junction immediately prior to the abrupt jump in force. One key difference between the 2D force analysis technique used

above and this alternate force event identification method is that the former relies on the identification of events through

conductance and therefore does not bias the results towards larger force values that are more easily identified.

Fig. 12.4 (a) Two-dimensional conductance histogram of C4A constructed from over 3,500 traces with a molecular conductance step. Features

representing a sequence of Au contacts clearly appear at integer multiples of G0. A molecular signature can be clearly seen at 9 � 10�4 G0. Inset:

A sample conductance trace showing a G0 and molecular plateau with zero displacement set to the end of the molecular plateau. (b) The two-

dimensional force histogram for C4A is constructed from the simultaneously acquired force traces of the same set of traces used to construct the

conductance histogram. The average force profile (black curve) shows a clear drop at zero-displacement, which gives a statistically determined

breaking force for the N-Au bond of ~0.6 nN. Inset: The simultaneously acquired force trace aligned after the molecular step is shown


Table 12.1 Comparison of most frequently measured conductance and rupture force for molecular junctions with a nitrogen termination having

different backbones (rows 1–4) and saturated backbones having different linker groups (rows 4–6)

No. Molecule Chemical structure

Conductance

(G0)

Bond rupture force (nN)

Expt. DFT

1 1,4 benzenediamine (BDA) 6 � 10�3 0.5 0.46

2 4,40 bipyridine (BP) 1 � 10�4 0.8 1.00

3 1,6 hexanediamine (C6A) 1 � 10�4 0.6 –

4 1,4 butanediamine (C4A) 9 � 10�4 0.6 0.84

5 1,4-bis(methylsulfide) butane (C4SMe) 1 � 10�3 0.7 0.84

6 1,5 bis-(diphenyl-phosphino)-pentane (C5DPP) 7 � 10�4 0.8a 1.4b

Rupture forces predicted by DFT adiabatic trajectory simulations of representative junctions are also listed for quantitative comparisonaExperiments with C5DPP showed evidence of significant fluctuations in force over the course of individual molecular conductance signaturesbDFT calculations for butane with dimethylphosphine links [33]

Fig. 12.5 Sample conductance (red) and force (blue) traces for C4SMe (a) and C4SH (c). The double headed arrows indicate a 0.2 nm

displacement. 2D histograms showing each identified force drop event and its corresponding conductance value for C4SMe (b – 51,000 events)

and C4SH (d – 121,000 events). The conductance bin size is 30 bins per decade, and the force bin size is 0.04 nN


In Fig. 12.5b, d we show the two-dimensional histograms correlating the change in force for each force event against the

associated conductance immediately prior to the force event from all measured traces for C4SMe and C4SH. Each count in

this 2D histogram represents a force and conductance value of an individual trace, as determined by the automated

algorithm. We see first that both histograms show a large number of force events at a conductance value around 1 G0.

These force events correspond to rearrangement and the final breaking of a single-atom gold contact. Second, for C4SH

(Fig. 12.5d), we find numerous force events spread along the conductance axis from just below 1 G0 to the experimental

conductance noise floor of about 2 � 10�5 G0. For C4SH, we find that 75% of all measured traces exhibit force events with a

conductance below 1 G0. Furthermore, from this selected subset, we find that each trace has an average of 2.7 force events.

This is a direct indication that junctions formed with the S-Au bond undergo substantial rearrangements with varied atomic

structure that sustain a broad range of conductance values. In contrast, the C4SMe data (Fig. 12.5b) shows that almost all

force events below 1 G0 occur within a narrowly defined conductance range [33]. Of all the measured traces, 40% show force

events for a conductance below 1 G0, and of this subset, each trace has an average of 1.5 force events. Thus although some

structural rearrangement might occur in SMe terminated molecular junctions, they are not accompanied by large changes in

conductance. This agrees with previous DFT based junction elongation simulations that show shifts in attachment point for

the donor-acceptor bond with modest changes in junction conductance [33]. Finally, the C4SH data also shows a significant

number of force events with conductance values within our experimental noise; a large number of force events occur at a

conductance that is too low to measure in this set-up. This could be due to the formation of molecular dimers or due to

pulling out of chains of gold atoms, as has been seen in simulations [37–40].

12.4 Discussion

We have used DFT-based calculations to simulate the junction elongation [40, 41] process and to understand the trends in the

rupture forces for the molecules studied here. Representative junction structures are developed with similar orientation and

link bonding for comparisons. Each Au tip and surface were modeled with an Au pyramid (20 atoms each) with (111)

surfaces with the tip atom on the top pyramid moved to an adatom site on one facet resulting in a blunt, three atom tip [33].

Here we focused on the portion of the trajectory where the junction was elongated from a local energy minimum through the

inflection point and finally probed the dissociated structure after one bond ruptures. The back layer of Au atoms in each

pyramid was held fixed with a bulk lattice parameter of 4.08 A. All other degrees of freedom were relaxed until all forces

were less than 0.005–0.01 eV/A for each junction structure. The junction was elongated in steps of 0.05–0.1 A by increasing

the separation between the pyramids along the z direction and then fully optimizing the geometry. Density functional theory

total energy calculations and geometry optimization were performed with the VASP package [42], using the projector

augmented wave approach which naturally included scalar relativistic effects for Au [43, 44] and the generalized gradient

approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [45] for the exchange-correlation density functional. The

model junction was placed in a hexagonal supercell (a ¼ 2.0 nm, c ¼ 3.5 nm) and the basis set for solution of the Kohn-

Sham equations was determined by a 400 eV cutoff.

The qualitative features of the calculated energy and force curves of an adiabatic junction trajectory are demonstrated in

Fig. 12.6a. In this case the calculations were performed by pulling on a C4SMe junction (Fig. 12.6b). Under the application

of increasing force due to junction elongation, the total energy increases from its local minimum value. Finally, a maximum

sustained force value (here ~0.8 nN) is reached. In these junction structures, the link bonds are not identical. One of the two

undergoes most of the elongation and after the maximum sustained force that link bond length rapidly increases,

corresponding to bond rupture. The calculated values listed for the maximum sustained force in Table 12.1 represent

model structures for each junction with similar backbone orientation, giving a good basis for assessing chemical trends.

They do generally represent a single adiabatic junction elongation trajectory. However, our previous studies [33] have

shown that small changes in junction structure (attachment point or molecule orientation) can lead to ~0.1–0.2 nN variations

in the maximum sustained force. More generally, we can also expect that diverse junction structures are sampled in the

experiments, including variations in Au-linker bond orientation in the junction and relative to the pulling direction

(Fig. 12.6c–f).

With due considerations for the variations in junction structures as well as the fluctuations due to temperature and

mechanical vibrations encountered in experiments, there is a good agreement between the DFT calculations of maximum

sustained force and experimental rupture forces. For the phosphine links (C5DPP in the experiments), calculations suggested

a substantially larger maximum sustained force. The typical maximum sustained force for the Au-P donor-acceptor bond

was around 1.4 nN for butane with the dimethylphosphine linker and there were clear indications that the stress is sufficient

to rearrange the local Au atomic arrangement near the link bond [27, 33]. However, the selectivity of the link bonding motif,


to specific undercoordinated Au atomic sites, still results in the well-defined conductance plateaus. In phosphine linked

junctions, modest steps in conductance are often observed in individual experimental traces that may correspond to

rearrangement. Qualitatively, the DFT-based simulations are consistent with the measurements, but the relatively low

measured average rupture force has not been explained. One possibility is that constraints in full junction formation (bonds

to substrate and tip, accommodating the bulky tertiary phenyl groups) result in structures where the donor-acceptor bonds are

weaker than optimal. The rearrangement of the local Au atomic structure may also be significant.

For junctions with S-Au linkage, DFT based calculations have indicated that selected scenarios support a maximum

sustained Au-S bond force in excess of 1.5 nN [41, 46]. More strikingly, detailed molecular dynamics simulations of thiol

linked junction evolution show a rich series of rupture/rearrangement events with the molecule removing one or more Au

atoms in the final, ruptured state [37–40]. Also, the position and resulting effects of the hydrogen from the SH can lead to

drastic changes in force and conductance values [40, 41, 46, 47]. The experimental behavior of conductance and force

trajectories for C4SH junctions, summarized in Fig. 12.5c, d, are consistent with a sustained force that is sufficient to drive

substantial rearrangement of the local structure during elongation. However, most of these events occur with a change in

force that is substantially less than the average force required to rupture the Au point contact. This does not imply that they

do not break at the Au-Au bond. Molecular dynamics simulations illustrate that junctions formed with Au-S links can result

in contact structures that have varied geometries. In contrast to the idealized structure (Fig. 12.6c), the terminal Au atom

could be on the side of an electrode structure (Fig. 12.6d), the constraints on junction formation with two distinct link bonds,

one to each electrode, can result in an angle between the backbone and the pulling direction (Fig. 12.6e), and the

coordination of the Au atom to which the S is bonded can be altered (Fig. 12.6f). A key factor is the strength of the Au-S

bond relative to the softness of the Au resulting in local rearrangement under stress [37–40]. Our calculated adiabatic

trajectories for selected scenarios illustrate that the maximum sustained force can be both larger and smaller than the

nominal Au single point contact rupture force, depending on the structure. A broader-based survey of structure as well as

investigation of the role of thermal fluctuations and solvent interactions will be essential to fully understand the measured

rupture forces in cases like thiol bonded junctions with strong bonds to Au. The occurrence of these non-ideal evolution

scenarios is supported by our experimental results for conductance and force of C5DPP and C4SH single molecule junctions.

In summary, we demonstrated an experimental approach to simultaneously measure force and conductance data for

single molecular junctions, developing and establishing a new, two-dimensional histogram method to statistically evaluate

thousands of individual measurements. This method leads to an experimentally determined average breaking force of a

single Au-Au bond of 1.4 nN, based on over 31,000 individual measurements. Using a set of N terminated molecules, we

showed that the electronic structure of the molecular backbone alters N-Au bond strengths considerably, as can be seen both

in the calculations and measurements: 1,4-benzenediamine binds most weakly to Au atoms, while the pyridine-gold bond

exhibits the largest breaking force among the molecules considered here. We then presented measurements for four different

chemical linker groups connected to saturated backbones. Analyzing this data using the 2D conductance and force

Fig. 12.6 (a) Calculated total energy (top) and force (bottom) curves from an adiabatic trajectory calculation for C4SMe, shown as a function of

displacement. Bar shown at right indicates the asymptotic value. This calculation demonstrates the typical qualitative features of single-molecule

junctions with donor-acceptor interactions. (b) Snapshot of the C4SMe junction structure near the local energy minimum. (c–f) Illustrations of

possible contact structures in single-molecule junctions formed with C4SH. Scenarios include: (c) H atom remains on the S, (d) Au atom is not at

the apex of the electrode, (e) junction is formed at an angle, and (f) Au atom coordination is altered due to chain formation


histograms, we have shown that amine, methylsulfide, and diphenylphosphine linkers break in a molecular junction with a

most probable breaking force of about 0.6, 0.7, and 0.8 nN respectively, indicating rupture at the donor-acceptor linkage. In

the case of thiol linkers, we compiled force and conductance data from individual traces, since we did not observe a well-

defined molecular conductance signature. Correlating the occurrence of force events with conductance, we find that C4SH

junctions on average have more force events per trace than C4SMe. This observation supports the notion that a strong

covalent sulfur-gold bond drives more significant rearrangement of these molecular junctions. By combining simultaneous

measurement of force and conductance with statistical analysis and DFT simulations we obtain a quantitative insight into the

electronics and mechanics of single-molecule junctions. In the future, these results can help us understand and engineer

molecular electronic devices with varied functionality.

Acknowledgements This work was supported by the National Science Foundation (Career Award CHE-07-44185) and by the Packard

Foundation. A portion of this work was performed using facilities in the Center for Functional Nanomaterials at Brookhaven National Laboratory

and supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.

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Chapter 13

High Speed Magnetic Tweezers at 10,000fps

with Reflected Hg-Lamp Illumination

Bob M. Lansdorp and Omar A. Saleh

Abstract The magnetic tweezer is a simple and stable single-molecule manipulation instrument. However, the standard

probe-tracking methods have typically failed to reach the high resolution (�0.3 nm) needed to measure motor protein

stepping. In this paper we present a novel illumination geometry, based on an inverted microscope with Hg lamp

illumination, that aims to push the resolution of magnetic tweezers to their ultimate thermal limits. Using a metal-coated

coverslip and motorized magnets, we convert a standard inverted microscope into a high-resolution magnetic tweezers

instrument. Our novel optical geometry reduces the restrictions on magnet design inherent to transmission-based illumina-

tion, and does not require fiber-optic coupling. We introduce a high-speed CMOS camera as the optical detector, and

demonstrate how an improvement in temporal resolution directly impacts the spatial resolution.

13.1 Introduction

Single molecule experiments measure the motion of a probe particle in order to deduce the properties of single molecules

such as DNA. In the case of optical and magnetic tweezers, the resolution of particle tracking is limited both by the

instrumental error and by the fundamental thermal limit caused by Brownian motion of the probe particle. For certain

applications, it is desirable to improve the instrumental resolution of particle tracking towards the thermal limit.

Following [1], we have identified the frame rate of the particle-imaging camera as a key factor limiting the instrumental

resolution. High-speed CMOS cameras can overcome the limitations of low frame-rate CCDs, but these cameras require

new illumination strategies to obtain sufficient light. We present a new illumination geometry that pushes magnetic tweezers

towards the thermal limit of maximum instrumental resolution.

13.2 A Novel Illumination Geometry

Although micron-sized beads scatter light in all directions, they scatter orders of magnitude more strongly in the forward

direction than back (see Fig. 13.1). Thus, it is desirable from an experimental point of view to utilize forward scattered light

to maximize the signal intensity.

To collect forward-scattered light from magnetic beads using a standard inverted microscope (Nikon Eclipse TE2000-U)

with epi-illumination, we employ a novel reflective geometry. On the return journey through the sample, forward-scattered

photons are collected by the objective (see Fig. 13.2b).

B.M. Lansdorp (*)

Graduate Student, Materials Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA


O.A. Saleh

Professor, Materials Department and Biomolecular Science and Engineering Program, University of California Santa Barbara,

Santa Barbara, CA 93106, USA



85


By placing a lens into the illumination optical path, we change the positions of the F-iris and A-iris conjugate planes.

We find that by tuning the focal length of the lens and the flowcell thickness, we can retain independent control over the

field-stop and collimation with the existing two irises.

Although a fiber-coupled Hg lamp has recently been used for high-speed particle tracking in 2D [1], a fiber might

interfere with our magnets. Our geometry collects the maximum amount of light while simultaneously providing added

flexibility to design magnets independently of optics.

Fig. 13.1 A polar plot of Mie scattering function (Taken from [2]). For 1mm sized beads, the forward-scatter intensity is three orders of magnitude

more intense than backscatter

Fig. 13.2 Novel illumination geometry inverts F and A irises. (a) Conventional RICM illumination. (b) Novel illumination geometry with added lens

86 B.M. Lansdorp and O.A. Saleh

The advantages of our design include: high intensity forward-scatter collection, minimization of backscatter on first pass

through sample by forming a conjugate image of an iris after reflection, and flexibility to design magnets independently of

optics.

13.3 Optics Design

We characterize our novel optical geometry, which is based on a single lens placed in a filter cube, in two steps. First, we

vary the lens focal length and measure the position of the resulting F-iris conjugate plane. Second, we vary the thickness of

the flowcell to find a configuration that brings the A-iris in focus.

In the first optimization, we place a range of Thorlabs lenses (f¼50mm, 75mm, 100mm, 125mm, 150mm, 200mm,

400mm) into the filter cube (see Fig. 13.3) and find that placing a 125mm lens into the filter cube results in no measurable in-

focus F-iris conjugate plane within the allowed travel range of the objective. We hereby deduce that f¼125mm results in a

nearly infinity-conjugate F-iris, and therefore nearly collimated light when the F-iris is closed down to a small hole.

In the second part of our optimization, we aim to find the location of the A-iris conjugate plane when a lens of f¼125mm

is inserted. To accomplish this goal, we construct a number of flowcells with various thicknesses and fill them with air (n¼1),

water (n¼1.33), and immersion oil (n¼1.515), and manually defocus the microscope to find the best-focus position of the

A-iris. Given the schematic representation of our experiment shown in Fig. 13.4, we can write the following two equations

which describe the position of the various focal planes:

h0 ¼ hA þ s1:515

n

� �(13.1)

and:

X ¼ hA þ 1:515

n

� �2tmeas � sð Þ (13.2)

To correct for the index of refraction mismatch,

tmeas ¼ ðh0 � hRÞ n

1:515

� �(13.3)

The results of this experiment are shown in Table 13.1. In the ideal experiment, s¼0 and the A-iris is in-focus after

passing through the sample. For each flowcell, given the actual A-iris position, we can make a prediction for the ideal

flowcell thickness such that s¼0 and the A-iris is in focus.

tideal ¼ tmeas þ ðhR � hAÞ n

1:515(13.4)

Fig. 13.3 A standard filter

cube that allows easy

placement of an

additional lens

13 High Speed Magnetic Tweezers at 10,000fps with Reflected Hg-Lamp Illumination 87

From Table 13.1 is it clear that a flowcell thickness of approximately 46mmwill result in an in-focus A-iris which can then

act as a field-stop. Effectively, by adding an f¼125mm lens and manufacturing a 46mm flowcell, we have reversed the A and

F irises. The A-iris is now a field-stop and the F-iris controls collimation.

X

h_0

100X objective

to tube lensand CCD

from A iris

h_A

St

Fig. 13.4 A schematic

illustrating the relative

positions of the A iris

conjugate plane and the

coverslips

Table 13.1 Experimental measurements of best-focus surfaces

Exp n h0 (mm)

hR for reflective

surface (mm)

hA for A-iris

(mm) tideal (mm)

1 1 202 107 165 51.0

2 1 192 121 172 44.9

3 1 186 131 180 43.1

4 1.33 200 156 206 44.0

5 1.33 201 138 187 43.1

6 1.33 201 141 194 46.6

7 1 200 121 175 47.5

8 1 201 125 179 47.5

9 1 205 125 180 48.4

10 1 206 128 181 46.6

11 1 203 112 167 48.4

12 1.33 202 138 190 45.8

13 1.33 208 141 193 45.8

14 1.33 206 144 196 45.8

15 1.33 205 154 204 44.0

16 1.515 202 161 210 43.1

17 1.515 208 164 214 44.0

18 1.515 210 156 204 42.2

19 1.515 208 151 201 44.0

20 1.33 209 100 156 49.3

Average – – – 46


13.4 Flowcell Manufacture

To manufacture a flowcell with the requirements mentioned above, we sandwiched steel shims of thickness 38mm (Small

Parts) between an Al-coated reflective coverslip (Deposition Research Lab, Inc) and a # 1 coverslip. We sealed the perimeter

of our flowcell using parafilm strips cut to approximately 1mm width using a razor blade, and left the sandwich on a hotplate

with a steel weight on top at 120∘C for 5min to seal the flowcell. Unfortunately, the result in Fig. 13.5b was measured to be

93mm instead of the nominal 46mm, which we attribute to burrs on our shims and insufficient time on the hotplate. We did

manufacture one flowcell with height of 46mm by placing it on a 145∘C hotplate for 15min, and found that the A-iris was

indeed in focus. By optimizing the manufacturing process, we expect to more reliably make accurate flowcells in the future.

13.5 Resolution Limits in Single Molecule Experiments

There are two main sources of noise in video-based particle tracking: Brownian motion of the probe particle during the

exposure time, and instrumental error in determining the probe particle position. The fundamental resolution of a thermally-

limited particle-tracking instrument [3] due to Brownian motion is:

s2SMMðtÞ ¼2kBTak2t

1þ 2akt

e�kta � a

2kte�2kta � 3a

2kt

� �(13.5)

where ktether is the tether stiffness, t is the averaging time, kBT is the thermal energy and a is the drag coefficient for the probe

particle. This thermal limitation affects both optical and magnetic tweezers, but magnetic tweezers may hold some

advantages over optical tweezers since the surface-bound tethers can be made very short and stiff, whereas dumb-bell

optical tweezers experience difficulty trapping beads that are closer together than the diffraction limit.

In the case of video-tracking, the instrument error can be reduced by using specialized reflective beads [4] or more simply

by using a high bandwidth camera and down-sampling. We have employed the latter approach, in combination with a high-

speed CMOS camera.

13.6 Particle Tracking Error

To determine the instrumental resolution of our system, we measured the position of 1.05mm superparamagnetic beads stuck

to a glass coverslip surface as a function of time at 10,000fps using a high-speed CMOS (Phantom v7.3). The z-position of

particles is determined by comparing particle images to a calibration image (shown in Fig. 13.6b). We measure a per-frame

z-axis resolution of 7nm per frame at 10,000fps (see Fig. 13.7).

We note that the higher-order fringes present in a previously conducted low-speed experiment Fig. 13.6a were not present

in the high-speed experiment because the imperfect flowcell thickness resulted in imperfect collimation and blurred the

higher order fringes. We expect to be able to improve the collimation and approach our previously attained per-frame

resolution of approximately 2nm.

Fig. 13.5 Schematic and experimental flowcell with well-defined thickness. (a) Schematic. (b) Inverted view of experimental flowcell


We expect the total particle tracking error of our magnetic tweezer to be a combination of the thermal noise (Eq.13.5) and

the per-frame instrumental resolution:

s2total ¼ s2SMM þ s2instr (13.6)

We can predict the total noise in our instrument when a double-stranded DNA tether of length 50nm is pulled upwards with a

force of 0.56pN by a 530nm radius magnetic bead (resulting in a ¼ 1:4� 10�4pN s/nm after the Faxen’ correction [5], and

kz¼0.12pN/nm for a worm-like-chain [6]). The instrumental noise dominates for a low frame-rate CCD, but a high-speed

camera approaches the thermal limit (see Fig. 13.7).

13.7 Conclusion

Wehave demonstrated a novel illumination geometry that pushes the resolution of ourmagnetic tweezer to 0.35nm at 10Hz.We

expect to further improve our instrumental resolution by optimizing the flowcell manufacturing process and the resulting

calibration images of our beads.We expect that ourmagnetic tweezerswill soon reach the thermal limit for short and stiff tethers.

Fig. 13.6 A comparison of calibration images used to determine bead z position. A piezo objective is used to step in increments of 100nm per

pixel in the vertical direction. A calibration using a microfabricated reference yielded 163nm/pixel for the CCD and 148nm/pixel for the HS-

CMOS. (a) 1.05mm beads with 4f optics using 635nm LED illumination with CCD detection at 60fps and 163nm/pixel. (b) 1.05mm beads with

546nm Hg emission line and hs-CMOS detection at 10,000fps and 148nm/pixel. (c) Partially melted 2.5mm diameter Polystyrene reference bead

and 1.05mm diameter superparamagnetic microspheres

10

5

1

0.5

0.10.0001 0.001 0.01 0.1 1

Time [s]

Alla

n D

evia

tion

s [n

m]

Fig. 13.7 Allan deviation measured experimentally at 10,000fps (red dots) and 60Hz (green dots). The theoretical thermal noise (black line)results in predictions for the total noise at 10,000fps (red dashed line) and 60Hz (green dashed line)


Acknowledgements We gratefully acknowledge S. Pennathur and T. Wynne for lending us their hs-CMOS camera, A. Weinberg for

manufacturing parts, and F. Freitas for reviewing this manuscript. B.L. acknowledges support from an NSERC PGS-D fellowship.

References

1. Otto O, Czerwinski F, Gornall JL, Stober G, Oddershede LB, Seidel R, Keyser UF (2010) Real-time particle tracking at 10,000fps using optical

fiber illumination. Opt Express 18(22):22722–22733

2. Prahl S (2012) Mie scattering calculation. http://omlc.ogi.edu/calc/. Accessed 29 Feb 2012

3. Lansdorp BM, Saleh OA (2012) Power spectrum and allan variance methods for calibrating single-molecule video-tracking instruments. Rev

Sci Instrum 83(2):025115

4. Kim K, Saleh OA (2009) A high-resolution magnetic tweezer for single-molecule measurements. Nucleic Acids Res 37(20):e136

5. Sch€affer E, Nørrelykke SF, Howard J (2007) Surface forces and drag coefficients of microspheres near a plane surface measured with optical

tweezers. Langmuir 23(7):3654–3665

6. Bouchiat C, Wang MD, Allemand JF, Strick T, Block SM, Croquette V (1999) Estimating the persistence length of a worm-like chain molecule

from force-extension measurements. Biophys J 76(1):409–413


http://omlc.ogi.edu/calc/

Chapter 14

Etching Silicon Dioxide for CNT Field Emission Device

Nathan E. Glauvitz, Ronald A. Coutu Jr., Peter J. Collins, and LaVern A. Starman

Abstract Carbon nanotube (CNT) based electron field emission devices may have an advantage over metal Spindt tip style

designs due to the ability to create a highly localized electric field at the extremely small diameter tip of the CNT. The primary

objective for this work is to create a robust micro structure to support low voltage field emission from the CNTs in a gated

device. This paper will discuss the micro fabrication techniques used to etch 2–4 mm thick thermal oxide layers on silicon

substrates. A chrome layer is deposited by electron beam evaporation to make the gate layer of the triode device and act as an

etch mask. The metal layer is then coated with photoresist, patterned with hole openings ranging from 8 to 12 mm in diameter

and wet etched in acid through to the SiO2 layer. Different dry etch chemistries combined with wet etching are used to study

the effect on the SiO2 sidewall. The shape and slope of the SiO2 sidewall and gate opening play a vital role in fabricating a

robust triode device that doesn’t easily short out when the CNTs are grown later in the process.

14.1 Introduction

There are many applications for CNTs to be used in electronic devices such as field emission (FE) tips in vacuum electronics,

field emission displays [1], or space charge neutralization for satellites [2, 3]. Under vacuum conditions and high local

electric fields, electrons can tunnel out of a solid high aspect ratio material into a vacuum as describe by Fowler-Nordheim

theory [4]. The physical and electrical properties of CNTs make them nearly ideal FE tips. For power limited applications,

low operating voltage and low leakage currents are highly desired device performance characteristics. In CNT vacuum

electronics, lower electron extraction potentials can be achieved via three general methods: reduce the anode and cathode

gap, optimize the CNT growth length and CNT spacing to reduce the screening effects, or use a triode type configuration

where a gate extraction electrode is positioned very close to the emitter tips. The latter method of creating a gate opening in

close proximity to the CNT tip will be the focus of this work; specifically the oxide layer sidewall geometry of the hole

openings to provide the robust structure to support a thin film metal gate. The close proximity of the gate allows lower

extraction potentials to cause electron tunneling from CNT tips into vacuum.

The most common techniques used to micromachine an oxide layer in a top-down device fabrication method to create

gated FE device are plasma etching, wet etching [5], or a combination of plasma and wet etching [6]. In this work, a radio

frequency (RF) parallel plate reactive ion etch (RIE) plasma system is used to initially dry etch the oxide layer followed by a

brief wet etch in a buffered oxide etch (BOE). Through the use of RIE, etch parameters can be modified to control the

undercut of the gate and the slope of the sidewall. Reduced undercut of the gate allows the use of thicker oxide layers and

tighter hole packing densities compared to a wet etch only method. Also, since CNTs can have a rapid growth rate in the

thermal chemical vapor deposition (T-CVD) system, a thicker oxide allows for some flexibility in the growth duration.

Once the substrate is exposed through the oxide, single mask or multiple mask step techniques can be used to pattern

the CNT catalyst material in the holes. In single mask techniques, the gate metal and oxide layer is etched, and the same

photoresist layer is then used for metal lift off after catalyst deposition. Single mask techniques have the advantage of

self-alignment where the catalyst is naturally centered in the emission hole site. Wong et al. used a single mask technique for

catalyst deposition along with a plasma pretreatment process on the catalyst layer which caused the CNTs to grow in a

N.E. Glauvitz • R.A. Coutu Jr. (*) • P.J. Collins • LaVern A. Starman

Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA




93


convex-shape [5]. The method pursued in this work is a top-down fabrication approach where an additional mask step is used

to center the catalyst metal in the emission hole site. Proper positioning of the catalyst metal is an essential step in the

fabrication of these gated FE devices since poor alignment can result in increased gate leakage current. Excessive CNT

growth length is another problem seen in gated FE devices. Longer than desired CNTs can create an electrical short from the

substrate to the gate and potentially cause the device to fail. In this work, the oxide sidewall geometry and undercut of the

gate metal was studied to mitigate those potential gate leakage problems in the triode design. The barrier layer, catalyst metal

thickness, catalyzation and growth times were then used to control the CNT diameter, spacing, and length to achieve uniform

growth [7–9].

14.2 Device Fabrication

Field emission devices fabricated here consist of three structural layers, a wafer substrate, an oxide insulator layer, and a

metal extraction gate. The fabrication steps numbered in Fig. 14.1 begin with highly doped n-type silicon (100) wafers

purchased from Ultrasil Corporation with thermally grown oxides. Wafers with 2, 3, and 4 mm oxide thicknesses were

selected in order to compare the field emission characteristics of the devices which will be presented in later work.

Figure 14.1 (1) shows a 220 nm chromium gate layer was deposited on the oxidized wafers in an electron beam evaporator.

The wafers were then cleaved into 12 mm � 12 mm squares so the samples could be loaded into the T-CVD system. Devices

were fabricated using standard photolithography techniques, four mask steps, and were thoroughly cleaned between each

photo masking step. The first mask step shown in Fig. 14.1 (2) defined the area of the chrome gate electrode. Similarly, the

second mask in Fig. 14.1 (3) was used to protect an area larger than the chrome gate and the SiO2 layer was etched in BOE

(7:1) to create a large oxide mesa and an outer surface contact area to the sample substrate. In Fig. 14.1 (4) samples were

coated again with resist and the third mask is used to pattern the hole openings in the gate metal which were etched with

chromium etchant. Circular hole patterns 8 mm in diameter were linearly packed with 18 mm array spacing, resulting in

127,008 emission sites covering an area of approximately 0.43 cm2. Coving the same area, hole sizes of 10 and 12 mmdiameter openings were also fabricated and consisted of 108,676 and 65,520 emission sites respectively. Kapton tape was

then used to cover the exposed outer edge of the oxide mesa and silicon substrate, protecting those areas during the following

RIE etch.

In Fig. 14.1 (5), the SiO2 etch parameter study was conducted with a Trion Phantom III RIE system. The RIE power, gas

etchants, flow rates, and process pressure were modified to achieve the desired etch depth and SiO2 sidewall profiles. Etch

study results are presented in the next section.

After the RIE process, the remaining thin oxide layer at the bottom of the hole openings was removed in a heated BOE

solution, shown in Fig. 14.1 (6). The complete removal of the oxide to the silicon surface in the hole openings across the

Si substrate

SiO2

Chrome

Ti + Fe layers

CNTs

Gate

After RIE

After BOE

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Si substrate

SiO2

Ti + Fe layers

CNTs

After RIE

After BOE

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Oxide Mesa

Gate metal hole

Fig. 14.1 Fabrication steps to form gated CNT field emission device began with (1) deposition of chrome gate metal, (2) defined gate area, (3)formed oxide mesa, (4) defined gate metal holes in chrome layer, (5) etched SiO2 in RIE, (6) etched in BOE to clear remaining oxide to substrate,

(7) deposited patterned Ti and Fe in holes, and (8) the final device after CNT growth in the T-CVD system

94 N.E. Glauvitz et al.

entire array was closely monitored to minimize undercut of the gate metal and to ensure a clean substrate surface area for

later CNT growth. An oxide free substrate surface for CNT growth is needed because it provides the electrical contact point

to the base of the CNTs. Also a clean uniform silicon surface should promote a more uniform CNT growth. Then a 220 A

titanium barrier layer was deposited by e-beam evaporation on the samples. A final photoresist pattern in Fig. 14.1 (7) was

then used to center the catalyst in the holes. A 75 A layer of iron was deposited via RF sputtering for the CNT catalyst

material. Samples were soaked in acetone and briefly placed in an ultrasonic bath to lift-off the unwanted iron and

photoresist. The lift-off procedure was a critical step in the fabrication process and this is where a limited undercut of the

gate metal was beneficial. In the ultrasonic bath, chrome at the edge of the hole openings would break off on the samples that

had too much undercut from the BOE step.

CNTs were grown on samples in the T-CVD system which consists of a one inch diameter quartz tube positioned

horizontally through a heater, a mechanical rough pump, mass flow controllers, flowmeter, and feedstock gasses. A complete

description of the T-CVD CNT growth process can be found in previous work [9]. Earlier work in Ref. [9] studied the effects

of barrier layer and catalyst layer thicknesses on the resulting CNT carpet growths. For gated devices fabricated here, the

growth time was reduced to 30–40 s in durations due to the close proximity of the gate metal on the oxide.

14.3 Silicon Dioxide Etch and Device Results

The objective of this etch study was to optimize the underlying oxide to form a robust support structure for the extraction

gate. Both dry plasma reactive ion etching and wet etching of the oxide layer were used to achieve a robust oxide support.

All samples etched in the RIE used a patterned chrome layer as the etch mask. Etch parameters in the Trion Phantom III

system were systematically modified and the resulting etches were studied to select the optimal conditions to be used on the

final devices. The Trion RIE system is configured with a 600 W maximum, 13.56 MHz solid state RF generator. Table 14.1

lists the RIE etch parameters used and the resulting SiO2 etch rates.

Effects of RIE power, chemical etchant, flow rates, and process pressure were studied in a scanning electron microscope

(SEM) to achieve the desired SiO2 sidewall profiles and etch depth. Relatively low RIE powers of 100–150 W with CF4etchant or CF4 with a small percentage of O2 were tested. Sample A, etched with the parameters listed in Table 14.1 was

accomplished as the baseline etch and utilized the suggested parameters in the Trion publication [10]. Shown in Fig. 14.2 are

SEM images of Sample A after the 2 mm oxide layer was partially etched through after 38.3 min in the RIE. An SEM image

of a single hole shown in Fig. 14.2a was taken at a 45� angle to highlight the bottom oxide surface roughness and a small

amount of oxide undercut of the chrome mask. A close-up view of the cleaved edge in Fig. 14.2b shows roughly a quarter

micron undercut of the chrome mask and provides another perspective of the surface roughness from the micro-mask formed

on the oxide layer. This initial etch yielded more undercut than desired and a relatively slow etch rate. The observed etch rate

of Sample A was over six times slower than the Trion reported etch rate [10]. The difference between the two rates is likely

Table 14.1 Reactive ion etch parameters tested and the resulting etch rates

Sample Power (W)

Pressure

(mTorr)

CF4 flow

(sccm)

O2 flow

(sccm)

Etch rate

(nm/min)

A 100 150 45 5 23.5

B 100 150 40 – 14.8

C 100 100 40 – 17.6

D 100 25 40 – 45.9

E 125 25 40 – 66.1

F 125 25 40 4 78.3

G 125 50 40 4 77.0

H 125 50 40 6 71.8

I 125 50 40 8 71.4

Ja 125 25 40 – 61.3

125 50 – 100

K 150 50 40 6 80.1

L 150 25 40 – 84.0

M 150 12 25 3 86.3aAccomplished 200 s CF4 followed by 90 s O2 plasma; series repeated ten times

14 Etching Silicon Dioxide for CNT Field Emission Device 95

due to several factors such as differences in the oxide material composition or RIE system configurations. Thermally grown

oxides have reported slower etch rates than phosphosilicate glass or CVD SiO2 when using CF4 based etch chemistry [11].

Another factor that could have contributed to the difference in etch rates was the amount of reactants flowed through the

chamber and the utilization factor. Samples etched here had very low utilization factors since the exposed oxide area was

small and the etch rate was so slow. The etch reaction in the holes was likely inhibited by excessive flow of the reactant

species and contributed to the observed slower etch rate.

The flow of CF4 was then reduced slightly to 40 sccm after the initial run and the effects of the process pressure were

studied using only CF4. Samples B, C, and D shown in Fig. 14.3 had a 2 mm thick oxide layer and were etched for 26.7 min

using 100 W of RIE power under different pressure conditions. The top images taken at a 45� angle in Fig. 14.3 show a

portion of a hole etch while the bottom images show the cross section edge of the oxide etch and chrome mask. Sample B and

C were etched with the pressure set at 150 and 100 mTorr respectively. The higher pressure etches with CF4 only resulted in

slower etch rates (14.8–17.6 nm/min) without the addition of oxygen, but the amount of undercut was reduced. Sample C

processed at 100 mTorr had close to vertical SiO2 sidewalls. While Sample D, the 25 mTorr etch shown in Fig. 14.3, etched

nearly three times faster and created a 68� sloped sidewall relative to the silicon surface. The sidewall appeared to be formed

from a combination of the oxide layer and redeposited material from the RIE process. This lower pressure etch of Sample D

clearly eliminated any undercut issues of the chrome mask but it did cause a small trench effect where the RIE etch occurred

more rapidly along the edge of the mask. The reduced process pressure delivered more ion energy to the surface which

increased the reaction rate of the oxide layer. To further increase the reaction rate, the power must be increased.

The RIE power was then adjusted to 125W on the next six samples to obtain a faster etch rate. Sample E in Fig. 14.4 is the

result of 125 W, 25 mTorr, 40 sccm of CF4, after 38 min in the RIE. The oxide sidewall angle on a cleaved sample measured

approximately 69� from the horizontal plane and was seen only on the top half of the oxide. This etch resulted in the clean

removal of the top half of the oxide thickness, while the lower half of the oxide contained spires of oxide below the micro-

mask layer. The micro-masking effect in the center of the hole opening is fairly dense when there is no oxygen present during

the etch. With the addition of 10%, 15%, or 20% oxygen to the etch chemistry and a slight increase in process pressure;

Samples G, H, and I in Fig. 14.4 had a reduction in the sidewall slope, a visual reduction of the micro-mask surface density,

and no undercut of the chrome gate metal. Sample H appeared to have the most vertical oxide sidewalls and virtually no edge

effect trenching. The last image in Fig. 14.4; Sample J was made in an effort to increase the oxide sidewall slope and reduce

the amount of micro-masking through a series of alternated etches. A 200 s pure CF4 etch followed by a 90 s O2 plasma clean

were performed and the sequence was repeated ten times. By cycling through the CF4 and O2 plasmas, the clear etch depth

increased only slightly and the sidewall slope improved by approximately 4� over Sample E.

The final three RIE etches were performed at 150 W on samples with 4 mm oxide layers. In Fig 14.5, the cleaved

edge of Sample K and Sample M show a portion of the hole etch after RIE. This view after the RIE etch is presented to

illustrate the increased clear etch depth above the micro-mask layer achieved on Sample M through the reduction of etchant

flow and lower process pressure. Additional RIE parameter modifications could be performed in an attempt to eliminate

the micro-mask layer but previously accomplished etches have produced the desired oxide sidewalls to move onto the

BOE step.

Based on the RIE etch results above, several samples were continued in the fabrication process and etched in heated BOE.

The heated BOE solution etched the oxide at approximately 200 nm/min and was used to clear the remaining oxide at the

Fig. 14.2 SEM image (a) of a single hole on Sample A was taken at a 45� view after RIE illustrates the oxide surface roughness and undercut on

the chrome mask. Image (b) is a view of the side of a hole opening on the cleaved edge shows nearly a quarter micron undercut of the chrome mask

and the small micro-mask layer on the surface of the partially etched oxide


bottom of the holes to the substrate surface. As the BOE step preformed an isotropic removal of the oxide from the hole

openings, samples with shorter durations in BOE consequently had better support structures for the gate metal. Figure 14.6a

shows Sample H after RIE. Sample H was then etched in heated BOE for 90 s. Figure 14.6b shows Sample H again after

successful metal lift-off of the iron catalyst and proved the oxide layer is very robust with only minor damage to the gate

metal. Sample E in Fig. 14.6c shows the partial etch of the oxide after 60 s in heated BOE. Sample E initially shown in

Fig. 14.4 after RIE, possessed a sloped sidewall from the low pressure CF4 only etch. After the short time in BOE, any

remnant of the sloped sidewall is gone leaving a near vertical oxide wall in the hole. The trench effect from the RIE is clearly

visible after BOE, as shown in Fig. 14.6c where the region near the mask edge has opened up to the substrate while the center

of the hole is yet covered with a thin oxide layer. The required wet etch time to clear away the remaining oxide layer in the

center of the hole caused more undercut of the gate oxide than desired and degraded the oxide support of gate metal.

Fig. 14.4 SEM images taken at a 45� angle illustrate the sidewall profile and micro-masking which occurred for some of the 125 W etched

samples. Sample E was etched with CF4 only, while Samples G, H, and I were etched at a higher pressure and had the addition of 10%, 15%, or

20% of O2 respectively. Sample J was made by alternating pure CF4 and O2 plasmas

Fig. 14.3 SEM images of Samples B, C and D show a portion of an etch hole at a 45� view (top), a cleaved edge view (bottom) which shows

examples of the measured etch depth on the samples and the oxide surface structure


The most robust samples fabricated were produced with the RIE configured at 125W, 50 mTorr pressure, 40 sccm of CF4,

6 sccm of O2 and required less than 2 min in heated BOE. Samples that were etched more than 2 min in the BOE solution had

portions of the chrome gate over the hole openings break off during the catalyst metal lift-off process. Sample I was etched

in BOE for 2 min after the RIE step. Shown in Fig. 14.7 is Sample I as a completed device after a 30 s CNT growth phase.

The CNTs in the emission hole sites grew very uniformly across the sample with a few exceptions. The measured gate

resistance to the substrate on the sample was in the kO range, not an open. The low gate resistance is likely due to

Fig. 14.5 SEM images of a hole etch on the cleaved edge of Sample K and M are shown to highlight the improved clear etch depth to the micro

mask layer achieved on Sample M by reducing the etchant flow and process pressure

Fig. 14.6 Sample H shown in image (a) after RIE produced nearly vertical sidewalls and a reduced amount of micro masking compared to the

other etches. In image (b) is Sample H after 90 s in heated BOE and iron catalyst deposition in the center of the hole, it held up very well to

the metal lift-off. While Sample E, shown in Fig. 14.4 after RIE, began with the sloped side walls and now shows almost vertical oxide walls in

(c) after 60 s in BOE

Fig. 14.7 Top view (left) of Sample I after 30 s CNT growth and close-up view (right) at a 45� angle show a near vertical oxide sidewall creating a

small overhang of the chrome gate


contamination found in a few hole combined with the occasional excessive CNT length found at sites. Other problem sites

were due to the photoresist patterning used for catalyst deposition and then metal lift-off. Improperly masked holes allowed

iron catalyst metal to be deposited at the base of the oxide layer and resulted in CNTs that grew tens of microns long.

14.4 Conclusions

In this effort, robust gate structures were fabricated for CNT field emission devices through the use of RIE and wet etching of

a thermal oxide layer. The patterned layer of evaporated chrome was used as the RIE etch mask and later as the gate

extraction electrode for the device. Through the series of RIE and wet etches, a favorable RIE configuration of 125 W,

50 mTorr pressure, 40 sccm of CF4, and 6 sccm of O2 was found. Further refinement of the RIE parameters and reduced flow

of the etch gasses would likely produce an improved oxide etch. It was important to minimize the undercut of the gate during

the buffered oxide etch and that was achieved by performing the initial RIE duration to reach just above the silicon surface.

By the addition of some oxygen to etch chemistry, a cleaner hole etch was achieved and was preferred over the CF4 only etch

which produced the increased oxide sidewall slope. Future work will include further design refinement of the triode

structures, field emission data collection, and analysis to maximize the emission current density of the devices.

Acknowledgements The authors would like to thank the Air Force Research Laboratory (AFRL) Propulsion Directorate for their assistance, use

of their resources and facilities, especially the sputtering and T-CVD systems. The authors also thank the technical support and dedicated work of

AFIT’s own cleanroom staff, Rich Johnston and Thomas Stephenson.

Disclaimer Theviews expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air

Force, Department of Defense, or the U.S. Government.

References

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nanotubes grown by chemical vapor deposition. Appl Phys Lett 88(26):263504

2. Velasquez-Garci LF, Akinwande AI (2007) A MEMS CNT-based neutralizer for micro-propulsion applications. Paper presented at the 30th

international electric propulsion conference, Florence, 17–20 Sep 2007

3. Aplin KL, Kent BJ, Song W, Castelli C (2009) Field emission performance of multiwalled carbon nanotubes for a low-power spacecraft

neutraliser. Acta Astronaut 64(9–10):875–881

4. Fursey G (2005) In: Brodi I, Schwoebel P (eds) Field emission in vacuum microelectronics. Kluwer Academic/Plenum Publishers, New York

5. Wong YM, Kang WP, Davidson JL, Choi BK, Hofmeister W, Huang JH (2006) Fabrication of aligned convex CNT field emission triode by

MPCVD. Diamond Relat Mater 15(2–3):334–340

6. Williams LT, Kumsomboone VS, Ready WJ, Walker MLR (2010) Lifetime and failure mechanisms of an arrayed carbon nanotube field

emission cathode. IEEE Trans Electron Dev 57(11):3163–3168

7. Srivastava SK, Vankar VD, Kumar V (2007) Effect of catalyst film thickness on the growth, microstructure and field emission characteristics

of carbon nanotubes. Paper presented at physics of semiconductor devices. IWPSD 2007. International workshop on 16–20 Dec 2007,

Bombay, India

8. Wang Y, Luo Z, Li B, Ho PS, Yao Z, Shi L, Bryan EN, Nemanich RJ (2007) Comparison study of catalyst nanoparticle formation and carbon

nanotube growth: support effect. J Appl Phys 101(12):124310–124310-8

9. Crossley BL, Glauvitz NE, Quinton BT, Coutu RAJ, Collins PJ (2011) Characterizing multi-walled carbon nanotube synthesis for field

emission applications. In: Marulanda JM (ed) Carbon nanotubes applications on electron devices. In Tech Education and Publishing, Croatia,

pp 105–126

10. Crockett A, Almoustafa M. Plasma delayering of integrated circuits. M. Trion Technology, Tempe, Arizona, and Vanderlinde, W. Laboratory

for Physical Sciences, College Park, MD, USA http://www.triontech.com/pdfs/Plasma%20Delayering%20of%20Integrated%20Circuits%

20V4%20080%E2%80%A6.pdf still available 7/25/2012

11. Madou M (2002) Fundamentals of microfabrication: the science of miniaturization, 2nd edn. CRC, Boca Raton. ISBN 0-8493-0826-7


http://www.triontech.com/pdfs/Plasma%20Delayering%20of%20Integrated%20Circuits%20V4%20080%E2%80%A6.pdf

http://www.triontech.com/pdfs/Plasma%20Delayering%20of%20Integrated%20Circuits%20V4%20080%E2%80%A6.pdf

Chapter 15

Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity

Benjamin Klusemann, Alain Franz Knorr, Horst Vehoff, and Bob Svendsen

Abstract In this contribution experimental and theoretical investigations of sheet metal mesocrystals with coarse texture

are performed. One focus of this work is on size effects due to a lack of statistical homogeneity. The overall mechanical

response is then strongly influenced by the orientation of the individual grains. For this purpose a crystal-plasticity-based

finite-element model is developed for each grain, the grain morphology, and the specimen as a whole. The crystal plasticity

model itself is rate-dependent and accounts for local dissipative hardening effects. This model is applied to simulate the

thin sheet metal specimens with coarse texture subjected to tensile loading at room temperature. Investigations are done

for body-centered-cubic Fe-3%Si and face-centered-cubic Ni samples. Comparison of simulation results to experiment

are given.

15.1 Introduction

The relation between microstructure, material properties and mechanical response is a basic issue of research in material

science and material mechanics. From the modeling point of view, a common concept used to account for the effect of the

microstructure on the material behavior is that of a representative volume element (RVE). This concept is based on

the assumption of scale separation between the microstructural and macrostructural lengthscale. If the characteristic size

of the system (e.g., sheet thickness) approaches that of the microstructure (e.g., grain size), however, such scale separation is

no longer given and one must resort to other means of representing the effect of microstructural heterogeneity on the system

behavior. As the macrostructural lengthscale approaches the microstructural one, the degree of material heterogeneity

increases, and the local microstructural behavior may deviate significantly from the average macrostructural behavior [e.g.,

10, 17]. In this case, the model has to account for the microstructural details such as orientation details of the grain structure

[e.g., 18] or phase distribution [e.g., 13, 23]. In the extreme case, the microstructural and macrostructural lengthscales are of

the same order of magnitude, and one must resort to numerical modeling of the microstructure with the help of, e.g., the

finite-element method [e.g., 4, 14, 19, 28]. In the case of polycrystalline materials, for example, such finite-element models

are often constructed with the help of, e.g., optical and/or EBSD data on the grain morphology. In specimens with more than

one grain over the thickness, the common method of projecting the two-dimensional EBSD information uniformly in the

third dimension will generally lead to incorrect results [e.g., 26]. If the specimen is one grain thick, however, such an

optical-/SEM-/EBSD-based approach should be reasonable. For such a specimen a number of size effects are expected

to influence its mechanical properties. These effects have been known for years and are still the subject of active research

[e.g., 5, 6, 9, 12].

The overall mechanical response is strongly influenced by the orientation of the individual grains if the number of grains

over the thickness is fairly small [5]. In the case of thin sheets the mechanical properties in a given cross section are

increasingly dominated by each individual grain as reported in [7]. Due to the different orientations of the grains located in

the sheet plane, the deformation is no longer uniform even under homogeneous loading conditions. This heterogeneity and

B. Klusemann (*) • B. Svendsen

Material Mechanics, RWTH Aachen University, Aachen, Germany


A.F. Knorr • H. Vehoff

Chair of Material Science, University of Saarland, Saarbr€ucken, Germany



101


the size-dependence of deformation give rise to size effects [e.g., 8]. To understand and predict the behavior of such

specimens correctly, simulation and experiment have to be compared locally, e.g., within individual grains in a polycrystal-

line specimen. For this purpose, detailed local experimental information is necessary [7].

The purpose of the current work is the investigation and modeling of so called oligocrystals which are specimens

consisting of one or more coarse-textured layers over their thickness. As example a body-centered cubic Fe-3%Si and a face-

centered cubic pure Ni sheet metal sample are investigated. The Fe-3%Si sample has been investigated experimentally by

Henning and Vehoff [7, 8]. These samples are grown in such a way that there is only one grain over the thickness, and grain

boundaries are perpendicular to the sample surface. The modeling is carried out with the help of crystal-plasticity and the

finite-element method [CPFEM: e.g., 5, 18, 19]. Related previous experimental and modeling work to oligocrystals includes

for example that of [21], who investigated grain interaction in an Al oligocrystal with columnar grains subject to plane strain

channel die extrusion. In addition, [28] examined plastic localization and surface roughening in an Al oligocrystal. Statistical

size effects also relevant to the current work have been investigated by F€ul€op et al. [5] in ultra-thin (0.1–0.5 mm) Al

oligocrystals. On the other hand, [24] investigated the behavior of a Cu oligocrystal characterized by multiple grains over the

thickness during plane strain compression. The discrepancy between experiment and simulation results noted by them was

attributed among other things to a lack of information about the grain morphology in the thickness direction.

The paper is structured in the following fashion. First the single-crystal model is given. After this experimental and

simulation results for an Fe-3%Si and an pure Ni oligocrystal are presented. The work ends with a summary.

15.2 Single-Crystal Model

Let sa; na, and ta: ¼ na � sa represent the glide direction, glide plane normal, and direction transverse to the glide direction

in the glide plane, of the ath glide system, respectively. As usual, (sa; ta; na) represent an orthonormal system assumed

constant with respect to the intermediate local configuration as determined by the inelastic local deformation FP. As usual,

the evolution of the intermediate local configuration and FP is modeled by the large-deformation form

_FP ¼ LPFP ¼X

a_ga sa � FT

Pna (15.1)

in the case of glide-based large-deformation crystal plasticity. Here, g1; g2; . . . represent the glide-system shears whose

evolution is modeled here via the power-law form

_ga ¼ _g0tatda

��m0

dirðtaÞ (15.2)

in terms of the Schmid ta :¼ sa �Mna and Mandel M stresses. Here, dirðtaÞ ¼ ta=jtaj is the shear-rate direction, _g0represents a characteristic glide shear-rate, m0 is the strain-rate exponent, and tda is the dissipative slip resistance whose

evolution is modeled by the interaction form

_tda ¼X

bhdab j _gbj (15.3)

[e.g., 1]. Here, the saturation model

hdab ¼ qab h0 ð1� tdb=tds0 Þ

n0; a; b ¼ 1; 2; . . . ; (15.4)

[e.g., 2] is assumed for the components of the hardening matrix, with qab ¼ 1:0 ð1:4Þ for a ¼ b ða 6¼ bÞ the components of

the matrix of hardening-rate ratios [e.g., 1] for the bcc case, h0 the initial hardening rate, tds0 the saturation value of tdb, and n0the hardening rate exponent. For the fcc case the components of the matrix of hardening-rate ratios qab are given by qab ¼1:0 ð1:4Þ for a same glide plane as b (a other glide plane as bÞ. The current model is completed by the linear elastic

constitutive relation

SE ¼ CEEE (15.5)

102 B. Klusemann et al.

for the elastic second Piola-Kirchhoff stress SE determining the Mandel M � SE and Kirchhoff

K ¼ FESEFTE (15.6)

stresses, the former in the context of small elastic strain. Here, CE is the constant elasticity tensor, EE ¼ 12ðFT

EFE � IÞrepresents the elastic Green strain, and FE :¼ FF�1

P is the elastic local deformation as usual.

The algorithmic formulation of the model combines explicit update at the integration-point level combined with implicit

update at the finite-element/structural level for satisfaction of the boundary conditions. The resulting mixed algorithm has

been implemented into the commercial program ABAQUS via the user material (UMAT) and user element (UEL)

interfaces. The simulations to be discussed below were all carried out in ABAQUS/Standard. To ensure reliable and robust

numerical results, adaptive time-step-size control is employed for the explicit update of inelastic model quantities used at the

integration-point level. In particular, this latter is based on the magnitude of the inelastic velocity gradient jLPj related to thecorresponding approximation of the algorithmic flow rule for FP. The critical value of this parameter for stability is

determined empirically via one-element tests. For more details, the interested reader is referred to [11].

15.3 Results for Fe-3%Si

For theexperimental investigationof [7], a test sampleof approximately5 mmwidth and15 mmlengthwas laser-cut froma larger

Fe-3%Si sheet of thickness 1 mm consisting of a single layer of grains having amean diameter of about 2 mm. The specimenwas

subject to simple tension under quasi-static loading conditions (10� 3 s�1). During the test, sample geometry, grain morphology,

and the local lattice orientation were measured at selected total strain states (0%, 1.5%, 4%, 10%, 19.5%) in the tension direction.

The experimental results from [7]with respect to the orientation gradient and change in specimen shape and grainmorphology are

shown in Fig. 15.1. The orientation gradient [e.g., 8, 25] is ameasure of the local (maximum)mismatch between the orientation of

a given point and that of its neighbors. More precisely, this is a measure of the change in lattice orientation between two

neighboring (regularly-spaced) measurement points in the plane of the EBSD measurements. To calculate these, let Ri andRiþ1

represent the orientation of two adjacent points in either the i¼ x or i¼ y direction in the plane. Then

Dyi : ¼ minQ2Gc

arccos1

2ðRi �QRiþ1 � 1Þ

� �� (15.7)

represents the orientation gradient at i modulo crystal symmetry transformations, i.e., elements of the crystal symmetry

group Gc (here cubic). The values of Dyx and Dyy determine in turn the measure

Dy1 ¼ maxfDyx;Dyyg (15.8)

of maximal local orientation gradient and so the OG mapping. In the experimental case, Ri and Riþ1 are determined directly

from the EBSD data. In the model case, Ri and Riþ1 in (15.7) and so (15.8) are determined by the spatial distribution of the

elastic local rotation RE.

The 3D model specimen in Fig. 15.2 was obtained from the 2D experimental information of the undeformed sample via

direct extrusion of the specimen shape and grain morphology into the third dimension. This represents a possible source of

discrepancy between the experimental and simulation results to be discussed below. Transition regions on either end of the

actual specimen consisting of elastic isotropic material have been introduced in order to transmit the tension boundary

conditions more accurately to the more complex specimen boundary [29]. As input data for the simulation the measured

EBSD data is used as initial orientation. The orientation in every grain is assumed to be homogeneous.

Room-temperature values for the material parameter in the single-crystal model assumed for the simulations are shown in

Table 15.1 which are taken from [14]. Here it is assumed that slip in Fe-3%Si occurs in h111i direction on the f110g and

{112} planes. Further it is also assumed that the material parameters for {110} and {112} systems are equal and that these

systems do not interact. To model this, the corresponding coupling terms in the hardening matrix qab are set to zero.

In the following the deformation behavior and the evolution of the orientation gradient between experiment and simulation

are investigated. For sake of comparison and to understand the influence of the assumed hardening law better simulations have

been carried out neglecting all hardening. In the initial stages of loading where little or no hardening can have occurred, this is

not unreasonable and allows a check of the initial conditions of the model independent of the hardening modeling.

15 Modeling of Sheet Metals with Coarse Texture via Crystal Plasticity 103

Fig. 15.2 FE-model of the Fe-3%Si tensile specimen. Individual grains are numbered for reference in the sequel

Fig. 15.1 Orientation gradient (OG) Dy1 during tensile loading of Fe-3%Si oligocrystal determined experimentally at (from top to bottom)1.5 %, 4 %, 10 %, and 19.5 %, total strain [7]. The OG results are superimposed on the current specimen geometry and grain morphology in

contour form (red line used as approximation of shape change). Points in the specimen where EBSD data was not obtained or too poor to determine

the OG distribution are shown in black

Table 15.1 Material parameter values assumed for bcc Fe-3%Si. In particular, the elastic constant values are from [20], and the other paramters

have been determined in [14]. Glide-system parameter values are assumed to be equal for both glide-system families {110} and {112} considered

in this work

cE11 [GPa] cE12 [GPa] cE44 [GPa] td0½MPa� _g0 [s�1] m0 h0 [MPa] tds0 ½MPa� n0

222 135 120 161 10�3 20 243.9 1,137 0.48


First we turn to a comparison of experimental and simulation results for change in specimen shape and grain morphology

as shown in Fig. 15.3. As shown by the comparison of grain boundary motion for the results where hardening is neglected,

generally the simulation underestimates the amount of grain deformation in the grains to the left of grains 13 and 14, and

overestimates it in grains 13, 14 and 15. Discrepancies such as those seen in grains 13 and 14 are significantly enhanced by

incipient specimen-level deformation localization and shear-band formation, in particular in the case of ideal viscoplasticity.

It is interesting to note that grain 14 had already the highest Schmid factor at the start of the deformation [14]. Comparing the

simulation results including hardening to the results neglecting hardening suggests that, up to 4%, little or no deviation

between the simulation results is visible. These results agree as well with experiment up to this point. After this point,

however, the effect of including hardening becomes quite apparent. In particular, hardening results in a reduction in the

prediction of the amount of grain deformation, something particularly apparent in the grains to the left of grain 13, but also in

grains 13, 14 and 15. The grain boundary morphology is also well predicted, even at large deformation only a deviation in the

contraction of grain 15 and 16 is observed.

Next we turn to the investigation of the orientation gradient. The experimental results shown in Fig. 15.1 as well as the

simulation results in Fig. 15.4 are only depicting the orientation gradient inside each grain due to the fact that the initial

orientation gradient over the grain boundaries (misorientation) is much larger than the orientation gradient during loading.

Again the simulations are performed for neglecting and including hardening. Consider first the simulation results neglecting

hardening. As for the deformation results a localization of the gradient can be observed for grain 13, 14 and 15. It can be

seen from these results that the simulation neglecting hardening cannot predict the correct tendency for the OG in the

experiment. Again up to 4% deformation a similar orientation gradient can be observed for the simulations neglecting and

including hardening, however, afterwards no correlation is anymore visible. In contrast the simulation results including

hardening predicts for example the band-like distribution of high OG at the boundary between grains 1 and 4 (and perhaps

grain 5 as well where data is missing) as seen in the experiment. As well, the homogeneous lattice orientation, i.e., lack of

an OG, in the middle of grains 4 and 8 in the experiment is also seen in grains 4, 5 and 8 in the model. Further, the

development of higher OGs in grain 9 near its boundary with grain 13, as well as in grains 13 and 15 near their common

boundary, is present in the model results. On the other hand, the OG band in grain 15 parallel to its boundary with grain 16

is missing, as is the OG in grain 17 near its boundary with grain 15. In addition, the experimental and model OG

distributions in grain 16, especially near the boundary with grain 14, are different. Then again, the development of OG

bands in grain 11 near its boundaries with grains 8 and 12, although much more diffuse than in the experiment, is present.

In summary, the simulations including hardening of the bcc Fe-3%Si sample were able to predict the experimental results

with respect to the deformation behavior and the orientation gradient evolution quite good.

Fig. 15.3 Comparison of experimental (red thin line) and simulation (black thick line) results of Fe-3%Si oligocrystal for the specimen geometry

and grain morphology at (a) 1.5 %,(b) 4 %, (c) 10 %, (d) 19.5 %, total strain in the tension direction for simulations neglecting (left) and including(right) hardening


15.4 Results for Ni

An investigation of a face-centered cubic metal was done on an 99.99%-pure nickel sample. A test sample of approximately

18 mmwidth and 50 mm length was cut by spark erosion from a larger sheet of 2 mm thickness. After the annealing process

(first 24 h at 1,350∘C then further 24 h at 1,425∘C) the average specimen thickness is reduced to 0.5 mm and grains have a

mean diameter of about 1 mm, which implies the achieved single grain layer condition. Due to the annealing process also

width and length of the test sample have been reduced to 16.5 and 48.5 mm, the thickness varied linear from 0.3 to 0.6 mm

from left to right.

The specimen was subject to simple tension under quasi-static loading conditions (10� 3 s�1). During the test, the sample

geometry, grain morphology, and the local lattice orientation were measured at certain total strain states (0%, 1%, 2%, 4%,

6%) in the tension direction.

The 3D model specimen of the pure Ni sample in Fig. 15.5 was obtained via extrusion of the specimen shape and grain

morphology into the third dimension from the 2D experimental information of the undeformed Ni sample. Transition

regions on either end of the actual specimen consisting of elastic isotropic material have been introduced in order to transmit

the tension boundary conditions more accurately. As input data for the simulation the measured EBSD data is used as initial

orientation with the orientation in every grain assumed to be homogeneous.

In the case of face-centered cubic pure nickel it is known that the deformation occurs on 4 {111} planes in 3 < 110 >directions. The material parameter for these slip systems are identified on experimental data from [22] for [111] single

crystal tensile data for room-temperature and quasi-static loading conditions (_e0 ¼ 8:3 � 10�4 s�1). For the model identifica-

tion a single crystal in the simulation is rotated into the [111] direction and therefore the axes of the crystallographic system

have to be rotated by the euler angles ff1 ¼ cos 1ffiffi3

p ; F ¼ p4; f2 ¼ 0g. The tensile load is applied into x-direction which

results initially in six active slip systems. The identification is done using LS-OPT in conjunction with ABAQUS by fitting

the stress-strain curves. The optimization techniques rely on response surface methodology (RSM) [15], a mathematical

method for constructing smooth approximations of functions in a design space. The approximations are based on results

Fig. 15.4 Comparison of modeling results for the orientation gradient (OG) Dy1 of Fe-3%Si oligocrystal at total deformation states of (from topto bottom) 1.5%, 4%, 10%, and 19.5% in the tension direction for simulations neglecting (left) and including (right) hardening


calculated at numerous points in the multi-dimensional design space. In this study, the material parameters are the design

variables, and the model together with the data determines the objective function of the corresponding optimization problem.

The shear-rate sensitivity, m0 is assumed to be 20 and reference shear rate _g0 to be 10� 3 s�1 for the current case of quasi-

static loading conditions which is in accordance to [27]. The identified parameters are shown in Table 15.2. Here it has to be

noted that the material parameters are only fitted for crystal orientation of [111]. However, it is known that Ni shows

significant different stress-strain curves for different orientations [e.g., 3, 15] depending on the fact whether the crystal is

showing single or double slip. Of course, this represents one possible source of discrepancy between the experimental and

simulation results.

During the experiment the applied displacement and corresponding reaction force were continuously recorded. The

results are shown in Fig. 15.6. The reference area used to calculate the first Piola-Kirchhoff stress is the initially smallest

cross-section of the specimen given by A0 ¼ 1.544mm. The simulation results were obtained in the same way. However, in

contrast to the experiment the specimen was continuously loaded in the simulation. It can be observed that the initial yield

point in the experiment is lower compared to the results in the simulation which might be related to the fact that the material

parameters used in the simulation are obtained from [111] single crystal data. After 4% total strain the simulation

underestimates the required force for the specified displacement. This might due to the evolution of geometrically necessary

Table 15.2 Identified hardening parameter values for pure nickel based on the experimental data from [22] for an [111] single crystal

cE11 [GPa] cE12 [GPa] cE44 [GPa] td0½MPa� _g0 [s�1] m0 h0 [MPa] tds0 ½MPa� n0

246 147.3 124.7 8.65 10� 3 20 427.9 900 14.77

experimentsimulation

2 4 6 800

50

150

100

200

strain[%]

firs

t Pio

la-K

irch

hoff

str

ess

[MPa]

Fig. 15.6 Comparison of experimental and simulation results for first Piola-Kirchhoff stress (P ¼ FA0

with A0 ¼ 1.544 mm) in loading direction

over strain ( Dll0 with l0 ¼ 49.5 mm) for pure Ni oligocrystal

Fig. 15.5 Model of the pure Ni tensile specimen


dislocations (GNDs) in the specimen which strengthen the material. The influence of including these GNDs in the simulation

for additional hardening is on-going research and will be studied with help of the experimental obtained orientation gradient.

Next we investigate the development of the specimen geometry and grain morphology. Exemplarily the results for 4%

total strain are compared between experiment and simulation in Fig. 15.7a. In general, it can be observed that the simulation

is able to predict the specimen geometry and grain morphology for 4% total strain quite well. However, from these results it

is very difficult to see where the main activity occurs. Therefore the total slip of the {111} glide system family is shown in

Fig. 15.7b. It can be observed that the main deformation occurred in grain D (for labeling see Fig. 15.5). Furthermore a

relative high activity can be seen in grain A, B and at the boundary of grain D to grain C. This is related to the fact that in this

region the specimen is slightly smaller in width and thickness compared to regions more on the right of the specimen. Figure

15.7c shows a micrograph from light microscopy after the shear band is visible which occurs at � 6% total strain (cp.

Fig. 15.6). Although in the simulation failure is not considered, the total slip indicates where the highest deformation is

present. This can be seen as an indicator where a shear band would be most likely start. From the simulation results it would

be most likely that a shear band could occur in the region of grain D, C and E. In the experiment the shear band was observed

in grain D and C which at least for grain D this could be anticipated by the simulation.

In summary, these first exemplary simulation results of the face-centered pure Ni sample show that the simulation was

able to predict the general behavior correctly, however, certain deviations occur which might be related to the fact that only

[111] single crystal data were considered for the material parameter identification. Further a failure model has to be included

to be able to predict the shear band.

Fig. 15.7 (a) Comparison of experimental (red line) and simulation (black line) results for the specimen geometry and grain morphology at 4 %

total strain in the tension direction. (b) Total slip for {111} glide system family at 6 % total strain projected on deformed geometry. (c) Micrograph

from light microscopy of the specimen after shear band occur at � 6 % total strain


15.5 Summary and Outlook

The current work has focused on the modeling and simulation of the behavior of two thin metal sheets, one consisting of a

single layer of large grains of Fe-3%Si (bcc) and one consisting of a single layer of large grains of pure Ni (fcc). Since such

material are highly heterogeneous, they are modeled with the help of single-crystal plasticity for each grain in the specimen

and the finite-element method for the grain morphology and specimen as a whole. The single-crystal model is rate-dependent

and accounts for (local) dissipative hardening effects.

The predictions of the model are compared with experimental results of thin sheets of Fe-3%Si and pure Ni loaded

incrementally in tension. For the Fe-3%Si sample the specimen geometry and grain morphology and the development of the

orientation gradient were analyzed. Two modeling cases were examined and compared with each other. In the first case, all

hardening was neglected, resulting in ideal viscoplastic behavior of the grains. Initially, reasonable agreement is obtained;

but as one can imagine, further loading and increasing deformation leads to significant hardening. As such, neglecting all

hardening results in overestimate of the deformation in favorably oriented grains and to corresponding mismatch with

experiment. Including hardening leads to quite good agreement. For the pure Nickel sample the stress-strain curve were

compared between simulation and experiment which showed some deviations. Further, the specimen geometry and grain

morphology were exemplary investigated as well as the strain field. In general the simulation showed the same tendency as

obtained in the experiment. However, certain deviations occur which might be related to the fact that only [111] single

crystal data were considered for the material parameter identification.

Besides dissipative hardening, the effects of additional strengthening due to grain size and misorientation distributions, as

well as that of additional hardening due to GND development in the specimen, on the deformation behavior will be

investigated in the future. Further a failure model has to be included to be able to predict the occurrence of the shear band in

the experiment which will be on-going work.

Due to the fact that with Fe-3%Si and pure Nickel representatives of body-centered-cubic and face-centered-cubic

materials were investigated, the next step would be the investigation of the third important crystal system, the hexagonal

closed packed system.

Acknowledgements Financial support of this work from the German Research Foundation (DFG) under contracts Sv 8/8-2 and VE 132/24-2 is

gratefully acknowledged.

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(2):457–464


Chapter 16

Evaluation of Mechanical Properties of Nano-structured

Al6061 Synthesized Using Machining

Paresh S. Ghangrekar, H. Murthy, and Balkrishna C. Rao

Abstract This work focuses on the synthesis of nano-structured Al6061 using machining under plane strain and evaluation

of its mechanical properties. It discusses an unusual application of the machining process by using it as a severe plastic

deformation (SPD) process to develop nano-structured or ultra-fine grained materials. Chips obtained from this process show

higher hardness than the bulk material which is in agreement with results reported in existing literature. Chips with minimum

curvature have been obtained using restricted contact tool and extrusion-machining processes. Hardness of the straight chips

obtained by the stated methods, though higher than the bulk material, was less than the hardness of the curled chips obtained

from conventional orthogonal machining. Furthermore, hardness of the chips obtained using tool with restricted contact

length of 0.6mm showed lesser variation. Hence they were used to prepare samples for the tensile test. A novel method was

used to prepare small test specimens from chips to measure tensile strength. Specimens made from the chips had higher

ultimate tensile strength (53%) and yield strength (85%) than that of bulk material. Improvement in strength was

accompanied by a reduction in ductility (58%) for chips as compared to bulk material. It was observed that for both the

chip and the bulk material, the reduction in gauge length leads to lower values of Young s modulus showing size effect.

16.1 Introduction

Materials with ultra-fine grained microstructure have appealing properties when compared to those of conventional

materials [1, 2]. The role of large strain deformation in microstructure refinement has been reported in the past by Embury

and Fisher [3] and Langford and Cohen [4]. Equal channel angular pressing/extrusion (ECAP/E), high pressure torsional

straining (HPT) and accumulative roll bonding (ARB) are some of the traditional severe plastic deformation (SPD)

processes. Enhancement in mechanical properties of nano-structured materials obtained from ECAP and HPT processes

have been observed by many researchers. But these traditional SPD processes have disadvantages as follows. They require

multiple passes to get large strains and some high strength metals and alloys are difficult to deform in this manner due to

constraints imposed by the forming equipment, tools and dies [5, 6]. Further, application of traditional SPD processes for

these materials is also restricted by the production-cost being above $100 per pound [7].

Machining has been used in recent years as an SPD process. Figure 16.1 shows the schematic of a typical machining

process. A wedge shaped tool is fed orthogonally against a stationary workpiece at a low cutting speed (Vo). This ensures

both low-temperature condition at the tool-chip interface region and condition of plane-strain. Intense plastic deformation on

the shear plane oriented at an angle (b) with the surface of the workpiece results in a shaving (or chip) that possesses an ultra-fine grain structure. The rake angle (a) of the tool determines the direction of chip flow as it is formed and the clearance angle

provides a small clearance between tool flank and newly generated machined surface. During machining, the cutting edge

of the tool is positioned at a certain distance below the original work surface. This corresponds to the undeformed chip

thickness (to). As the chip is formed along the shear plane, its thickness increases to tc. The ratio of to to tc is called

chip thickness ratio (rc) and is usually less than 1. A state of plane strain (2-D) deformation prevails when the tool edge is

P.S. Ghangrekar • H. Murthy (*)

Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India


B.C. Rao

Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600036, India



111


perpendicular to the cutting velocity (Vo) and the undeformed chip width (aw) is large compared to the undeformed chip

thickness (to). As opposed to traditional SPD processes, it is possible to impose shear strains ranging between 1 and 10 in a

single pass of the tool during the machining process [5]. The unconstrained nature of the machining process also enables the

creation of nano-crystalline materials with enhanced hardness values from a wide range of metals and alloys [5]. Hence it is a

big source of shavings or chips that are nano-structured with enhanced properties. These chips can be up cycled as advanced

materials. Furthermore, machining is economical vis-a-vis traditional SPD processes.

Precipitation heat treatable aluminum alloys like Al6061-T6 are widely used in aerospace and automotive sectors because

of their high strength to weight ratio. It has been observed that the presence of the second phase particles (precipitates)

accelerates grain refinement during the plastic deformation process [8]. Shankar et al. [8] have utilized this grain refinement

with precipitation to obtain a nano-structured aluminum 6061-T6 alloy through the machining process. This paper discusses

the mechanical properties of straight chips obtained from machining under controlled conditions.

16.2 Machining as Severe Plastic Deformation Process

16.2.1 Experimental Setup and Preliminary Tests

Large-strain cutting operations under plane-strain conditions were performed on a Deckel CNC milling machine.

A schematic of this setup is presented in Fig. 16.2. To ensure orthogonal conditions while cutting the work-piece, a fixture

has been fabricated for aligning the cutting tool. Rectangular plates made of solution treated aluminum 6061-T6 alloy were

machined to create nano-structured chips. Each of these plates having dimensions of 100 � 50 � 3mm was solution treated

at 550 ∘C for 10 h prior to the machining operation. The cutting tool is made of High Speed Steel (HSS) with a rake angle of

5∘. Tests have been conducted with the 5∘ tool since this falls between the extremes of positive and negative rakes.

Orthogonal machining tests were carried out with 0.3 mm depth of cut at a low cutting speed of 517 mm/min.

Shavings or chips obtained had thicknesses in the range of 1.23–1.58 mm. To obtain scratch-free specimens for

measuring hardness, chips were polished successively with finer abrasive materials including the final 0.1mm microid

diamond compound with aerosol spray. The production of longer chips entailed use of longer rectangular plates (150 mm).

16.2.2 Methods to Produce Straight Chips

Attempts were made to procure chips with minimum curvature or straight chips so that they could be used to prepare samples

for measuring the tensile strength of the nano-crystalline Al6061-T6 alloy. To produce chips with minimum curvature, it is

necessary to understand the mechanism of chip curl. Available literature on the reasons for chip curl seem to indicate that the

chip curl mechanism is related to the two zones of deformation in orthogonal cutting. These are described as the primary

deformation zone in which the chip is formed and the secondary deformation zone in which there is severe deformation of

the chip material due to large frictional forces between the chip and the rake face of the tool. Furthermore, at the tool-chip

interface there exist two zones which exhibit different frictional characteristics: the sticking zone and sliding zones [9]. Sizes

of these zones and the contact tool could have a bearing on the curvature of the chips.

Cuttingtool

Workpiece

Chip

V0

t0

tc

Shear plane

β

α

aw

Fig. 16.1 Schematic of a

typical machining process. Vo

is the cutting velocity, aw is

the undeformed chip width, tois the undeformed chip

thickness, tc is the chipthickness, b is the shear

plane angle and a is the

rake angle [5]

112 P.S. Ghangrekar et al.

Jawahir [10] presented the impact of restricting tool contact on breaking chips effectively and found that there is a

possibility of obtaining straight chips during machining in some cases. For a range of materials machined orthogonally,

Worthington and Redford [9] have provided experimental evidence that chips are formed with minimum curvature when the

zone of sticking friction is equal in length to that of the restricted contact. Jawahir [10] also showed that within the range

investigated, sticking length varies linearly with chip thickness. Experiments have been conducted to produce straight chips

using restricted contact machining. Figure 16.3a shows the machining operation under restricted contact condition between

the tool and chip. Here, h is the restricted contact length; hn is the natural contact length; V0 is the cutting velocity and a is the

primary rake angle. Rectangular plates made of aluminum 6061-T6 having dimensions of 150 � 50 � 3 mm were solution

treated before machining. The 5∘ rake angle tools with restricted contact lengths of 0.6 and 0.8mm have been used for

cutting. It resulted in the production of chips with minimum curvature which were suitable for preparation of tensile test

specimens. The depth of cut and cutting speed are similar to those used for preliminary tests with the conventional tool.

Extrusion machining is also useful in obtaining straight cips. As shown in Fig. 16.3b, a fixture was made of High Speed

Steel (HSS) with a groove for guiding the chip generated from the machining process. The groove was designed to procure a

chip with thickness and width similar to that of the chip obtained by the unconstrained machining process. This arrangement

represents a combination of extrusion and machining processes. Extrusion-machining experiments have been carried out

with the 5∘ rake angle tool under machining conditions similar to the preliminary tests. In this case as well, the curvature was

reduced. Representative chips obtained from different machining tests are shown in Fig. 16.4. It clearly indicates the

production of straighter chips using restricted-contact tools and extrusion-machining. The thicknesses of chips with

minimum curvature are in the range of 1.05–1.1 mm whereas those from conventional orthogonal machining operation

are slightly higher, i.e. 1.23–1.5 mm.

The chips have been polished unto 0.1 mm for carrying out metallographic tests. Subsequently, they were etched with

Keller’s reagent [11] to reveal their microstructure.In all the cases shown in Fig. 16.5, the microstructure clearly reveals flow

lines which are characteristic of a continuous lamellar structure resulting from plastic shear.

Fixture fortool alignment

Workpiece

52mm

40mm

135mm

Fig. 16.2 Schematic of the

Deckel milling machine used

for machining

hn h

Restricted contactlength tool

Conventional tool

Workpiece

Chip

V0

Slot to insert toolGroove to guide a chip

a bFig. 16.3 (a) Schematic to

depict machining with

restricted contact tool. h is the

restricted contact length, hn isthe natural contact length and

Vo is the cutting velocity [10]

(b) Fixture for implementing

extrusion-machining

16 Evaluation of Mechanical Properties. . . 113

16.3 Mechanical Properties of Chips

16.3.1 Hardness Tests

The chips obtained were polished unto 0.1mmmicroid diamond compound with aerosol spray for performing micro-hardness

tests on the samples. The results of the hardness tests on two specimens obtained from different large strain machining

processes are presented in Table 16.1. The hardness values of the straighter chips are less than those of chips obtained by the

conventional orthogonal machining process. Moreover, the chips machined by using a tool of 0.6 mm restricted contact

show less variation in their hardness values when compared to those obtained using both the 0.8 mm restricted contact tool

and the extrusion-machining process. The deviation in hardness values of the chips obtained from extrusion-machining

might be because, the groove made in the fixture does not allow the chip to flow freely. Furthermore, the resisting force

offered by the groove might vary from one location to another during the flow of the chip. Thus, the chips obtained from

machining with a tool of 0.6 mm restricted contact has been used to study the mechanical properties. Specimens made out of

bulk material as well as chips were peak-aged at 175∘ for 8 h to study the effect of peak-aging on hardness and tensile

properties. Table 16.2 shows the effect of peak-aging heat treatment on hardness values of bulk and chip material. It has been

observed that peak-aging on bulk material improves it’s hardness by about 30% and peak aging of chip obtained from bulk

material shows negligible effect on hardness values.

16.3.2 Tensile Testing

16.3.2.1 Preparation of Small Tensile Test Specimens

The chips obtained using the tool with restricted contact length of 0.6mm were used in tensile tests since they show lesser

variation in hardness values as discussed in the previous section. A portion of the chip, which was nearly straight, was cut out

from the raw chip to prepare a given tensile test specimen. The raw chips have two surfaces, one of them being smoother

Fig. 16.4 Chips obtained from: (a) conventional orthogonal machining; (b) and (c) machining using tools with restricted contact lengths of 0.6

and 0.8 mm respectively; (d) extrusion-machining

Fig. 16.5 Microstructure of chips obtained from: (a) and (b) machining using tool with restricted contact lengths of 0.6 and 0.8 mm respectively;

(c) extrusion-machining


when compared to the other. Both the surfaces should be smooth for tensile test specimens so that there is no crack initiation

due to surface defects. This can be achieved by polishing. Small size of the chip makes this polishing difficult. Special care

has been taken while polishing the raw chips having small curvature. This is shown in Fig. 16.6a where the middle portion on

the lower side of the chip requires more polishing compared to the extreme portion on lower side. Hence chips have been

polished up to 0.4 mm thickness with a tolerance of 0.01 mm such that the rough portion as seen in Fig. 16.6a is avoided.

Fabrication of the tensile test specimens from polished chips itself is quite challenging. The small size of the tensile

specimen limited the use of techniques such as electric discharge machining (EDM) for fabrication. Hence manual polishing

was employed to prepare test specimens. In this regard, steel templates have been prepared to match the dimensions of the

tensile test specimen shown in Fig. 16.7. The straight portion of the chip (polished up to 0.4 mm thickness) has been placed

between two properly aligned templates and clamped in machine vice (Fig. 16.6a). Then the specimen was prepared to the

required dimensions by filing and polishing it slowly with a tolerance limit of 0.01 mm throughout the gauge length. During

the preparation, dimensions of the specimen were checked frequently to keep variation of width within 0.01 mm throughout

the gauge length. A typical tensile test specimen is shown in Fig. 16.6b. For comparison, tensile test specimens have also

been prepared from solution treated Al6061 bulk material. Moreover, some specimens made from bulk solution treated

Al6061 and chips obtained from solution treated Al6061 have been peak-aged prior to tensile tests to study the effect of

peak-aging on tensile strength.

Table 16.1 Results of micro-hardness tests for chips obtained from different machining processes using

Vicker’s indenter at 50 gm load. Twenty indentations were taken for each sample. Hardness of the bulk

material was 85.4 � 2.8 Average values are reported along with standard deviation

Large-strain process

Hardness values

(HV or kg/mm2)

Sample 1 Sample 2

Conventional orthogonal machining 143.4 � 2.4 138.8 � 2.6

Machining with 0.8 mm restricted tool 128.7 � 7.9 136.9 � 5.1

Machining with 0.6 mm restricted tool 137.0 � 4.2 134.7 � 4.9

Extrusion-machining 121.2 � 7.7 124.9 � 9.2

Table 16.2 Results of micro-hardness tests for bulk material and chips obtained from 0.6mm restricted

contact machining process using Vicker’s indenter at 50 gm load. Twenty indentations were taken

for each sample. Both samples were tested before and after peak-aging to observe the effect of further

peak-aging on hardness. Average values are reported along with standard deviation

Specimen

Hardness values

(HV or kg/mm2)

Without peak-aging With peak-aging

Bulk 85.4 � 2.8 111.2 � 2.5

Chip 137.0 � 4.2 134.7 � 4.9 133.9 � 3.3 136.1 � 2.9

Chip Polished chip

1.1 mm

28 mm

0.4 mm

Template

Polished chip

a b c

Fig. 16.6 (a) Polishing chips with minimum curvature to obtain straight chips. (b) Arrangement of steel templates and polished aluminum chip for

specimen preparation. (c) Photograph of the small tensile test specimen


16.3.2.2 Tensile Stress-Strain Tests

An INSTRON tensile testing machine has been used to conduct the tests on small tensile test specimens, at a moderate

displacement rate of 0.96 mm/min. Typical tensile stress-strain curves for representative specimens made from bulk material

and chips are shown in Fig 16.8a. It can be seen that the chips have lower ductility when compared with that of the bulk

material by approximately 58%.Yield stress and ultimate tensile stress values for solution treated Al6061 bulk, peak-aged

Al6061 bulk, chips obtained from solution treated Al6061 andpeak-aged chips obtained from solution treated Al6061 are

presented inTable 16.3 and Fig. 16.8b. To ensure repeatability, five specimens were prepared for each of the four conditions

and subsequently tested. For each condition, Table 16.3 reports the average of five stress values along with the standard

deviation. Following observations could be made from these results:

• The ultimate tensile strength of the chips shows about 53% increase compared to that of the bulk material.

• The yield strength of the chips shows about 85% increase compared to that of bulk material.

• Peak-aging treatment on the bulk material improves its tensile strength by 30%. But, peak-aged chips have approximately

same tensile strength as that of chips without peak-aging.

5 5 58 5

3

R10.625

All dimensions are in mm

0.4

Fig. 16.7 Dimensions of a given tensile test specimen

0 0.02 0.04 0.06 0.080

100

200

300

400

500

Strain

Stre

ss (M

Pa)

bulkchip from bulkpeak−aged bulk peak−aged chip

Bulk Peak−aged bulk Chip Peak−aged chip0

100

200

300

400

500

Material (solution treated Al6061)

Stre

ss,

σ, (

in M

Pa)

σyield

σultimate

a b

Fig. 16.8 (a) Tensile stress-strain curves for smaller specimens made out of solution treated Al6061: comparison between bulk material and chip

with and without peak-aging; (b) Yield stress and ultimate tensile stress values from tensile tests on small specimens


• Peak-aging of bulk material increases yield strength by about 51%. However, peak-aged chips show negligible

improvement in yield stress when compared to that of non-peak-aged chips.

Kim et al. [12] have investigated post-aging behavior of equal channel angular pressed Al6061 and found that post-aging

treatment on nano-structured material improves ultimate tensile strength only by about 10%. Similar slight improvement in

the tensile strength of peak-aged chips compared to the non-peak-aged type may not be visible here because of the 5% error

in area of gauge section and this possibility needs to be investigated further.

Young’s modulus values were calculated for all the specimens and were found to be in the range of 21–25 GPa which is

well below the values for larger samples of Al6061 material (i.e. 70 GPa). Sergueeva et al. [13] have studied the effect of

gauge length and sample size on measured properties during tensile testing. It has been proved experimentally that as gauge

length and sample size decrease, the Young’s modulus also decreases while the tensile strength remains constant. Similarly

in our studies, Young’s modulus measured for Al6061 sample with gauge length of 8mm is in the range of 21–25 GPa, which

is 64–70% below the Young’s modulus specified in literature. Therefore, to corroborate the effect of gauge length and

sample size, another specimen with larger dimensions (i.e. gauge length¼ 40 mm, gauge thickness¼ 3 mm and gauge width

¼ 2.5 mm) made out of the bulk material was tested. In this case, the tensile strength was observed to remain same for the

larger specimen with a Young’s modulus value of 70 GPa. Accordingly, this size effect needs further investigation.

16.4 Conclusion

Ultra-fine grained Al6061 alloy has been obtained using machining as a severe plastic deformation (SPD) process. The

hardness of the chip obtained exceeds that of the bulk material indicating the impact of a finer grain structure on yield

strength. This research has demonstrated the possibility of obtaining chips with minimum curvature using restricted contact

tool and the extrusion-machining processes. Flow lines typical of large strain deformation are seen in the continuous chips

obtained in all the machining processes. Hardness of the straight chips obtained by the stated methods, though higher than

that of the bulk material, is less than the hardness of curled chips obtained from conventional orthogonal machining.

Furthermore, hardness of chips obtained using a tool with restricted contact length of 0.6 mm shows lesser variation.

Therefore, a 0.6 mm restricted contact tool was used to create samples for the tensile tests. It was observed from the results of

the tensile test that the strength of Al6061 chips is higher than solution treated bulk Al6061 with a 53% increase in ultimate

tensile strength and 85% increase in the value of yield stress. The peak-aging heat treatment on bulk material resulted in a

30% increase in ultimate tensile strength and 51% increase in yield strength. In contrast, chips from solution treated Al6061

show negligible change in tensile strength and yield strength after the peak-aging heat treatment. This shows that if we use

machining as an SPD process, we get much better improvement in strength as compared to peak-aging. The improvement in

strength was accompanied by a reduction in ductility by 58% for chips obtained from solution treated bulk material vis-a-vis

bulk material. Moreover, this work has also reported the influence of specimen size on Young’s modulus. It has been shown

that Young’s moduli for smaller specimens is 60–70% lesser than those for larger specimens.

Acknowledgements Authors would like to thank the following laboratories at IIT Madras for providing facilities for the experimental work:

Manufacturing Engineering Section (Mechanical Engineering Dept.), Physical Metallurgy Laboratory (Metallurgy and Material Science Dept.)

and Structures Laboratory (Civil Engineering Dept.). Authors would also like to thank Frontier life line pvt. ltd., Chennai for permitting us to use

their INSTRON 3345 tensile testing machine.

Table 16.3 Yield stress and ultimate tensile stress values from tensile tests on small specimens. Bulk

material is solution treated Al6061. Five specimens were tested under each condition. Average values are

reported along with standard deviation

Specimen Yield stress (MPa) Ultimate stress (MPa)

Bulk material 223 � 45.0 284 � 43.5

Chip obtained from bulk material 413 � 43.6 435 � 41.1

Peak-aged bulk material 335 � 16.6 368 � 12.0

Peak-aged chips obtained from bulk material 418 � 13.8 430 � 17.2


References

1. Gleiter H (1989) Nanocrystalline materials. Prog Mater Sci 33:223–315

2. Siegel RW (1986) Creating nanophase materials. Sci Am 275:74–79

3. Embury JD, Fisher RM (1966) The structure and properties of drawn pearlite. Acta Metall 14(2):147–159

4. Langford G, Cohen M (1969) Strain hardening of iron by severe plastic deformation. Trans ASM 62:623–638

5. Swaminathan S, Shankar MR, Lee S, Hwang J, King AH, Kezara RF, Rao BC, Brown TL, Chandrasekar S, Compton WD, Trumble KP (2005)

Large strain deformation and ultrafine grained materials by machining. Mater Sci Eng A 410–411:358–363

6. Swaminathan S, Shankar MR, Rao BC, Compton WD, Chandrasekar S, King AH, Trumble KP (2007) Severe plastic deformation (spd) and

nanostructured materials by machining. J Mater Sci 42:1529–1541

7. Briesen H, Fuhrmann A, Pratsinis SE (1998) Electrically assisted aerosol reactors using ring electrodes. In: Duenwu H, Beaucage G, Burns G,

Mark JE (eds) Nanostructured powders and their industrial applications. Proceedings of materials research society symposium, San Francisco,

vol 520. pp 3–14, 1998

8. Shankar MR, Chandrasekar S, Compton WD, King AH (2005) Characteristics of aluminum 6061-t6 deformed to large plastic strains by

machining. Mater Sci Eng A 410–411:364–368, 2005

9. Worthington B, Redford AH (1973) Chip curl and the action of the groove type chip former. Int J Mach Tool Des Res 13:257–270

10. Jawahir IS (1988) The tool restricted contact effect as a major influencing factor in chip breaking: An experimental analysis. Ann CIRP Manuf

Technol 37(1):121–126

11. ASTM Standard (2007) Volume E407. ASTM International, West Conshohocken

12. Kim JK, Kim HK, Park JW, Kim WJ (2005) Large enhancement in mechanical properties of the 6061 al alloys after a single pressing by ecap.

Scr Mater 53:1207–1211

13. Sergueeva AV, Zhou J, Meacham BE, Branagan DJ (2009) Gage length and sample size effect on measured properties during tensile testing.

Mater Sci Eng A 526:79–83


Chapter 17

Hardening Behaviour of Thin Wires Under Loading

with Strain Gradients

Ying Chen, Mario Walter, and Oliver Kraft

Abstract Based on the work of Fleck et al., the influence of strain gradients on the deformation behaviour of metals in small

dimensions has been studied intensively. However, since almost 20 years comparable torsion experiments have never been

repeated. In this work, the deformation behaviour of Au and Al (containing 1 wt.-% Si) wires with diameters ranging from 15

to 40 mm was investigated in both tension and torsion, using a self-developed test facility. Size effects were observed in the

torsion tests as in the classical experiments, performed by Fleck and co-workers. However, thermal treatments of the wires in

combination with grain structural analysis show clearly that the microstructure of the wires plays an important role when

comparing the as-received and the annealed state with fine and coarse grains, respectively. Moreover, a variation of the

deformation velocity within the tests on AlSi1 wires showed an additional influence on the strength level in tension and

the size effect in torsion.

17.1 Introduction

From many experiments like torsion tests on small wires [1], micro-beam bending test [2] or also indentation tests [3, 4] it is

known, that gradients in plastic strain, resulting from multi-axial loading conditions, show a significant influence on the

hardening behaviour of metallic materials. When strain gradients are present, it has been found that the hardening scales

inversely with a characteristic length in which plastic deformation occurs and thus, leading to increasing flow stresses with

decreasing component sizes. Accordingly, it can be argued that the impact of strain gradients on themechanical behaviour has

to be taken into account by a mathematical description of the deformation behaviour of metals in small dimensions [5–11].

However, the interplay between material parameters like grain size and the sample size with and without the occurrence of

strain gradients, as well as the influence of testing parameters like the strain rate on the deformation behaviour has to be

studied. In this context, carefully conducted tensile and torsion experiments on small-scaled Au and AlSi1 wires,

accompanied by a thorough characterization and control of the microstructure of the investigated specimens, were performed

in order to separate the impact of the strain gradient and the microstructure on the commonly observed size effects.

17.2 Experimental Issues

Both, the tensile tests and the torsion tests were performed using a self constructed high resolution micro testing facility

based on a small tabletop testing machine (Zwick Z2.5, Ulm, Germany). To measure the torsion moment during twisting a

specimen, a wire is clamped under a low axial pre-load between a load cell and a rotation table. At a defined height, a stiff

cross-beam is glued to the wire. At this beam, two load cells (high-resolution atomic force microscope tips, supplied by

Y. Chen (*) • M. Walter • O. Kraft

Karlsruher Institut f€ur Technologie – Institut f€ur Angewandte Materialien, Hermann-von-Helmholtz-Platz 1,

Eggenstein-Leopoldshafen 76344, Germany




119


Kleindiek, Reutlingen, Germany) are positioned opposing each other with well defined equal distances to the specimen in a

symmetrical configuration. By using the rotation table, the specimen is twisted in the direction of the positioned load sensors.

Since the movement of the cross-beam is inhibited, as illustrated in Fig. 17.1, the torsion moment can be determined directly

as a function of the torque angle. As the inner moment is equal to the outer moment, the torsion momentMt is obtained from:

Mt ¼ Md left þMd right ¼ aFleft þ aFright (17.1)

where a is the distance between the centre of the wire and the load cell, Fleft and Fright are the measured forces, andMd left and

Md right the corresponding torsion moments.

This measuring principle allows applying and measuring torsion moments even in the nNm-range. A more detailed

description of the test set-up as well as the general capability of the measurement system is given in [12, 13].

To investigate the mechanical behaviour of metals in small dimensions under both uniaxial (without gradients) and multi-

axial (with gradients) load conditions, wires from pure Au (diameter D ¼ 15, 25 and 40 mm; purity >99.99%; supplied by

Haeraeus, Hanau Germany) were tested at room temperature RT in the ‘as received’ state as well as in a specified recrystallized

state in tension (initial gauge length l0 ¼ 30 mm; strain rate de/dt ¼ 3.34 � 10�5, 3.34 � 10�4, and 3.34 � 10�3 s�1) and

torsion (initial gauge length l0 ¼ 50 mm; rotation angle rate d’/dt ¼ 0.086, 0.172 and 0.345 rad/s). The heat treatments were

carried out using a high vacuum tube furnace and for the micro structural investigations, a dual beam workstation Focused Ion

Beam (FIB) and Scannin Electron Microscope (SEM) from FEI was used. Additionally, AlSi1 wires (Al 1 wt.-% Si, diameter

D ¼ 17.5 and 40 mm; supplied by Haeraeus) were investigated in the ‘as received’ state under equal test conditions.

17.3 Results

The microstructure of the Au wires in the ‘as received’ state is found to be fine grained (Fig. 17.2), with almost identical

average grain size d for all diameters, ranging from d ¼ 0.54 via 0.64–0.7 mm with increasing specimen diameter.

Due to the fabrication process by presumably cold drawing, a comparable high dislocation density may be assumed.

In combination with the comparable microstructure, the general deformation behaviour in tension of wires with different

diameters is also almost identical (Fig. 17.3 – right). However, it can be observed, that both the uniform elongation and the

elongation at fracture are increasing with increasing diameter. An influence of the deformation velocity on the strength of

Fig. 17.1 Schematically

illustration of the measuring

principle

120 Y. Chen et al.

the Au wires was not found, but on the uniform elongation and elongation at fracture – both values increase with increasing

de/dt as exemplified for the wires with D ¼ 15 mm (Fig. 17.3 – left).

In torsion, the twist rate in general shows no influence on the deformation behaviour of wires with equal diameters

(Fig. 17.4 – left). However, in contrast to tension, a significant size effect can be observed for 15 mm wires compared to 25

and 40 mm wires. The deformation behaviour of the thicker wires is almost identical as illustrated in Fig 17.4 – right.

To investigate the material behaviour concerning the influence of strain gradients for the full recrystallized state

(i.e. coarse grains, low dislocation density), the three different wires were annealed. Different conditions were chosen to

achieve similar deformation behaviour in tension, particularly at lower strains (e < 1%, compare Fig. 17.6 – left). The

resulting micro structures are shown in Fig. 17.5. One can see, that the wires reveal almost the same number of grains within

a cross section and thus, an increasing average grain size with increasing wire diameter. In this case, a size effect in torsion

can be observed as illustrated in Fig. 17.6 – right. Comparable to the ‘as received’ state, an impact of the deformation

velocity on the strength level in both tension and torsion was not observed.

Comparable to the Au wires, AlSi1 wires reveal also a fine grained micro structure in the ‘as received’ state. The average

grain size is slightly smaller with 0.33 mm for the wires with D ¼ 17.5 and 0.38 mm for the wires with D ¼ 40 mm,

respectively. However, in contrast to the investigations on the noble metal, a significant influence of the deformation rate on

the strength was found during the tests on AlSi1 wires – in tension (Fig. 17.7) as well as in torsion (Fig. 17.8 – right).

Furthermore, it was again observed in tension, that both the uniform elongation and the elongation at fracture is increasing

with increasing de/dt.

Fig. 17.2 FIB micrographs of Au wires in the ‘as received’ state

Fig. 17.3 Deformation behaviour of Au micro wires (‘as received’ state – related micrographs see Fig. 17.2) in tension. Left: results of

investigations to the strain rate dependency. Right: results of investigations to the size dependency

17 Hardening Behaviour of Thin Wires Under Loading with Strain Gradients 121

Fig. 17.4 Deformation behaviour of Au micro wires (‘as received’ state – related micrographs see Fig. 17.2) in torsion. Left: results of

investigations to the twist rate dependency. Right: results of investigations to the size dependency

Fig. 17.5 FIB micrographs of Au wires in the full recrystallized state

Fig. 17.6 Deformation behaviour of Au micro wires (full recrystallized state – related micrographs see Fig. 17.5). Left: almost identical

stress–strain progress for e < ca. 1%. Right: results of investigations to the size dependency in torsion

Although the 40 mm wire shows a higher strength in tension compared to the 17.5 mm wire (Fig. 17.8 – left), a size effect

is clearly observable in torsion – even when comparing the thicker wire tested with the highest twist rate and the smaller wire

tested with the lowest twist rate (Fig. 17.8 – right).

17.4 Discussion

The results presented here reveal that strain gradients obviously affect the strength of polycrystalline metals in small

dimensions. However, as mentioned above the microstructure of the investigated specimens, as well as the test conditions

have a strong impact on the observed size effect. When comparing the results of the investigations on the Au wires, one may

argue that in the fully recrystallized state the size effect in torsion may not be solely attributed to the strain gradients but is

Fig. 17.7 Deformation behaviour of AlSi1 micro wires (‘as received’ state) in tension. Left: results of investigations to the strain rate dependencyfor wires with D ¼ 17.5 mm. Right: results of investigations to the strain rate dependency for wires with D ¼ 40 mm

Fig. 17.8 Deformation behaviour of AlSi1 micro wires (‘as received’ state) in tension and torsion. Left: results of investigations to the size

dependency in tension. Right: results of investigations to the size dependency in torsion

17 Hardening Behaviour of Thin Wires Under Loading with Strain Gradients 123

also related to the grain size (Fig. 17.9 – right). Surprisingly, the influence of the grain size is not seen in tension. This is

shown in Fig. 17.9 – left, where the yield strength, determined as flow stress at 0.2% plastic strain, is plotted versus the

inverse square root of the grain size in the wires. For the tension tests, no influence of the grain is observed.

In contrast, in the ‘as received’ state for both Au and AlSi1, the strain gradients lead to a significant size effect.

In particular for wires smaller than 25 mm, the strength in torsion increases strongly. For these wires, the characteristic

length of the microstructure, with fine grains and high dislocation density, is much smaller than the wire diameter. Therefore,

it is quite surprising that the wire diameter seems to govern the strength and not the internal length. On the other hand, it is

feasible that the wires are quite inhomogeneously deformed during processing and that, as a result, the strength varies within

the wires leading to different observations in tension and torsion. As these findings are not conclusive, more wires with

different annealing conditions and diameters of less than 15 mm will be tested in the future.

References

1. Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42(2):475–487

2. St€olken JS, Evans AG (1998) A microbend test method for measuring the plasticity length scale. Acta Mater 46:5109–5115

3. McElhaney KW, Vlassak JJ, NixWD (1998) Determination of indenter tip geometry and indentation contact area for depth sensing indentation

experiments. J Mater Res 13:1300–1306

4. Ma Q, Clarke DR (1996) Size dependent hardness of silver single crystals. J Mater Res 10:853–863

5. Ashby MF (1970) The deformation of plastically non-homogeneous materials. Philos Mag 21:399

6. de Borst R, M€uhlhaus H-B (1992) Gradient dependent plasticity: formulation and algorithmic aspects. Int J Numer Methods Eng 35:521

7. Gao H, Huang Y, Nix WD, Hutchinson JW (1999) Mechanism-based strain gradient plasticity – I. Therory. J Mech Phys Solids 47:1239

8. Nix D, Gao H (1998) Indentation size effects in crystalline materials: a law for strain gradient plasticity. J Mech Phys Solids 46:411–425

9. Fleck NA, Hutchinson JW (1993) A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids 41:1825–1857

10. Fleck NA, Hutchinson JW (1997) Strain gradient plasticity. Adv Appl Mech 33:295–361

11. Dunstan DJ, Ehrler B, Bossis R, Joly S, P’ng KMP, Bushby AJ (2009) Elastic limit and strain hardening of thin wires in torsion. Phys Rev Lett

103:155501

12. Walter M, Kraft O, Klotz M (2011) European patent no. 1903326

13. Walter M, Kraft O (2011) A new method to measure torsion moments on small scaled specimens. Rev Sci Instrum 82(3):035109

Fig. 17.9 Hall–Petch behaviour for the annealed Au wires in tension and torsion, plotting the flow stress at 0.2 % plastic strain versus the inverse

square root of the grain size

124 Y. Chen et al.

Chapter 18

Mapping the Histology of the Human Tympanic Membrane

by Spatial Domain Optical Coherence Tomography

Corey Rutledge, Michael Thyden, Cosme Furlong, John J. Rosowski, and Jeffery Tao Cheng

Abstract The tympanic membrane is one of the major structures of the ear that aids in the hearing process, giving humans

one of the five major senses. It is hypothesized that sound induced displacements of the membrane, which allow humans to

hear, are directly related to the membrane’s medial layer which is comprised of a network of collagen fibers. Limitations in

available medical imaging techniques have thus far inhibited the further study of these fibers. In this paper we detail an

imaging system that we developed with the capability to quantitatively and noninvasively image the internal structures of

biological tissues in vitro through spatial domain optical coherence tomography (OCT). By utilizing spatial OCT, we can

correlate the characteristics of internal collagen fibers to sound induced displacements in the tympanic membrane. This will

eventually lead to improved modeling of the middle-ear and a better understanding of hearing mechanics.

18.1 Background

The hearing process contains a complex network of physical structures acting with the nervous system to allow humans to

perceive sound in the environment. One of themajor structures in this process is the tympanic membrane (TM), which is a thin

film of tissue that converts pressure waves in the air into mechanical vibrations and transmits them to the middle-ear. The TM

is comprised of three layers with the outermost and innermost layers providing protection for the medial layer, also known as

the lamina propria. The lamina propria is composed of collagen fibers arranged in a pattern that resembles that of a spider web.

These collagen fibers are responsible for the major mechanical properties of the TM as a whole, and are essential in sound

transmission to the middle-ear. Figure 18.1 shows an image of the theoretical orientation of collagen fibers in the TM.

While the existence of these collagen fibers in the TM is known, current imaging techniques have not been able to

quantitatively detail their structure and orientation. This is mainly because of limitations in available optical systems

to image internal structures. Most optical techniques are only capable of surface measurements and fewer still can generate

three-dimensional representations of the shape data gathered. To overcome these limitations, we have developed a spatial

domain optical coherence tomography imaging system that is capable of imaging internal structures present in biological

tissues. By post-processing these images we can create three-dimensional representations of the internal collagen fiber

structures present in the lamina propria of the TM.

C. Rutledge (*) • M. Thyden

Mechanical Engineering Department, Center for Holographic Studies and Laser micro-Mechatronics, Worcester Polytechnic Institute,

100 Institute Road, Worcester, MA 01609, USA


C. Furlong



Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA

J.J. Rosowski • J.T. Cheng

Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, Boston, MA 02114, USA



125



18.2 Methodology

Optical coherence tomography (OCT) is a rapidly growing imaging technique that has been used to characterize biological

tissues and structures [2]. Spatial OCT follows the basic principles of white-light interferometry. In our experimental setup,

we selected a light source with a wavelength that can penetrate tissue at a sufficient depth to enable imaging of internal

structures of tissue. A 720 nm infrared light source was used. This light source was directed into a beam splitter, which split

light into object and reference beams. By use of mirrors, both of the beams were recombined resulting in either constructive

or deconstructive interference. This yielded fringe patterns when the optical path length difference between the object and

reference beams was less than the coherence length of the light source. Our light source is characterized by a coherence

length of 20 mm. Figure 18.2 is an image of the experimental setup that was developed.

To acquire 3D information on a sample, our system required the ability to scan a sample in the axial direction. To do this,

we used a piezo-electric positioner with 100 mm traveling distance and sub-nanometer resolution as well as a custom made

LabVIEW program to send a linear voltage ramp to our piezo. This allowed us to capture the intensity modulations resulting

from interference fringes over the full coherence length of our light source for each individual pixel in an image. A theoretical

intensity modulation through the depth of a tissue is shown in Fig. 18.3. As seen in this figure, intensity modulation increases

as the three principal layers of the tympanic membrane are scanned.

An experimentally acquired intensity modulation is shown in Fig. 18.4. The maximum of the intensity modulation was

isolated by applying a Hilbert transform to the intensity modulation to generate an envelope over the signal. This envelope

defines the peak of the intensity modulation and the vertical location of a geometrical feature within a sample. By gathering

the maxima of the intensity modulation for each pixel in the field-of-view of a set of stacked images, these locations can be

used to generate three-dimensional tomographic images of a tissue.

Acquiring intensity modulations required the use of several software packages. As stated earlier, LabVIEW was used to

send a linear voltage to our piezo-electric positioner. All image acquisition was synchronized in LaserVIEW, which is an in-

house developed software package designed specifically for interferometric holography measurements. The interferogram

allows for live viewing of the sample being imaged, and video files containing images in .llvid format can be recorded.

LaserVIEW also allows for specification of camera frame rate and exposure time, which was essential to determining

distance between images and total time for our voltage ramp. All image processing and data analysis was conducted in

MATLAB 2011b, including analysis of video files created in LaserVIEW to create three dimensional tomographic images.

Accuracy and resolution of our system were characterized by measurements of NIST traceable gauge blocks. By imaging

these blocks, we were able to successfully image step sizes on the order of 100 nm with a resolution of 5 nm at the maximum

field of view on the order of 1.37 � 1.72 mm.

18.3 Representative Measurements

For our experimental procedure, a chinchilla TM was first imaged. The membrane was partially dissected, with the

epidermal layer removed and the lamina propria exposed. This allowed sufficient access to the collagen fibers for imaging.

The field of view used for the chinchilla TM imaging was 0.87 � 0.65 mm. After successfully gathering data from the

Fig. 18.1 A depiction of the

fibers in the lamina propria

of the TM oriented around

the malleus and umbo [1]

126 C. Rutledge et al.

chinchilla TM, we next moved to a human TM. The human TM was that of the left ear of a 52 year old male. For this

experiment, a field of view of 0.75 � 0.75 mm was used. Images were gathered starting next to the umbo and in the radial

direction to acquire structural data as distance from the umbo increased. The goal was to determine information on the

collagen fiber size as well as to determine if the density of collagen fibers changed as distance from the umbo increased.

From analysis of acquired images of the chinchilla TM lamina propria, we were able to determine that the diameter of

collagen fibers was approximately 5 mm (see Fig. 18.5). Additionally, we found that a 135 � 135 mm location could contain

between 15 and 20 collagen fibers. It was also clear from our results that the fiber orientation changed. This led us to believe

that the density of collagen fibers changed as distance from the umbo increased. These measurements correlate with data

reported in the literature [3].

Fig. 18.2 Spatial OCT experimental setup

Fig. 18.3 Intensity modulations as different layers of the TM are scanned [1]

18 Mapping the Histology of the Human Tympanic Membrane by Spatial. . . 127

0

10

20

30

mic

rom

eter

s40

50

60-60 -40 -20 0

Amplitude

20 40 60

Fig. 18.4 Intensity modulation with generated envelope for an individual pixel in the axial direction. Measurements performed on a human TM

Fig. 18.5 Spatial OCT image of the lamina propria of a chinchilla and corresponding interferogram. The field of view is 0.87 � 0.65 mm

0-10-20-30-40-50

800 700 600 500 400

y axis (microns)

x axis (microns)

dept

h (m

icro

ns)

dept

h (m

icro

ns)

300 200 100 00

100

200300

400500

600

700

800

0-20-40

800700

600500

400300

200100 0 0

100 x axis (microns)

y axis (microns)

200

300

400

500

600

700

800

Fig. 18.6 Spatial OCT image for the human TM lamina propria. The field of view is 750 � 750 mm

Figure 18.6 shows spatial OCT images of the human TM lamina propria. The images were taken approximately half way

from the umbo to the outer edge of the TM. The donor was known to have mild tympanosclerosis, which could be an

indication as to why inconsistencies exist in the fiber size. By specifying 135 � 135 mm sections of the OCT images, fiber

sizes were identified as varying from 1 to 15 mm in diameter. Between 10 and 15 collagen fibers could be seen in

135 � 135 mm locations throughout the images in Fig. 18.6. Figure 18.7 shows a representation of the lamina propria for

a human TM generated through spatial OCT. Eight spatial OCT images were stitched together that were gathered

horizontally across the TM. The anatomical characteristics and fiber orientation of the TM can be clearly observed.

18.4 Conclusions

Spatial domain optical coherence tomography can be a very effective means to image the internal structure of the tympanic

membrane. Through analysis of OCT generated TM images, the collagen fiber size and density throughout the tympanic

membrane can be determined. Because of the difference in collagen fiber density throughout the TM, it is very likely that

TM displacements relate to the structure and orientation of the collagen fibers [4]. Future research will attempt to correlate

TM displacements at a location under a specific frequency to the anatomical characteristics of the TM generated through

spatial OCT.

References

1. Lim DJ (1995) Structure and function of the tympanic membrane: a review. Acta Oto-Rhino-Laryngol Belg 49:101–115

2. Chan A, Duker JS, Ko TH, Schuman JS, Fujimoto JG (2006) Ultrahigh resolution optical coherence tomography of retinal pigment epithelial

tear following blunt trauma. Arch Ophthalmol 124:281–283

3. Jackson RP, Chlebicki C, Krasieva TB, Puria S (2008) Multiphoton microscopy imaging of collagen fiber layers and orientation in the tympanic

membrane. Proc SPIE 2842:1–7

4. Cheng JT, Aarnisalo AA, Harrington E, del Socorro Hernandez-Montes M, Furlong C, Merchant SN, Rosowski JJ (2010) Motion of the surface

of the human tympanic membrane measured with stroboscopic holography. Hear Res 263(1–2):66–77

Fig. 18.7 Spatial OCT representation of a TM lamina propria cross-section. The field of view is 0.75 � 6 mm, which represents the stitching of

eight different measurements

18 Mapping the Histology of the Human Tympanic Membrane by Spatial. . . 129

Chapter 19

Opto-Mechanical Characterization of a MEMS Sensor

for Real-Time Infrared Imaging

Everett Tripp, Frank Pantuso, Lei Zhang, Ellery Harrington, and Cosme Furlong

Abstract MEMS technology has led to the development of new uncooled infrared imaging detectors. These MEMS

detectors consist of arrays of bi-metallic cantilevered beams that deflect linearly as a function of temperature associated

with infrared radiation from the scene. The main advantage of these detectors is the optical readout system that measures the

tilt of the beams based on the intensity reflected light. This removes the need for electronic readout at each of the sensing

elements and reduces the fabrication cost and complexity of sensor design, as well as eliminating the electronic noise at the

detector. The optical readout accuracy is sensitive to the uniformity of individual pixels on the array. The hypothesis of the

present research is that direct measurements of the change in deflection will reduce the need for high pixel uniformity.

Measurements of deflection change for a vacuum packaged detector with responsivity of 2.4 nm/K are made with a Linnik

interferometer employing the four phase step technique. The interferometer can measure real-time, full-field height

variations across the array. In double-exposure mode, the current height map is subtracted from a reference image so that

the change in deflection is measured. A software algorithm locates each mirror on the array, extracts the measured deflection

at the tip of a mirror, and uses that measurement to form a pixel of a thermogram in real-time. A blackbody target projector

with temperature controllable to 0.001 K is used to test the thermal resolution of the imaging system. The minimum

temperature resolution is below 250 mK.

19.1 Background

AMEMS uncooled infrared imaging detector consists of an array of bi-metallic cantilevered beams that deflect proportional

to infrared radiation from the scene. One material needs to be an efficient infrared absorber. The difference between

coefficients of thermal expansion between the two materials needs to be as large as possible to maximize the deflection of the

beam with respect to temperature at the scene. An electronic signal can be measured through a change in capacitance

between the tip of the cantilever and the substrate. The electronic readout is complicated and costly to manufacture.

Additionally, the electronic signal introduces additional noise from heat.

Optical readout systems provide an alternative. The second of the two metallic layers is an efficient reflector of visible

light. Light is reflected off of the array of cantilevers. The intensity of the reflected light detected by a camera corresponds to

the tilt of the mirror and thus to the temperature. Compensation arms of the sensing element deflect at a rate proportional

to the substrate temperature. This is situated so that the compensation arm opposes rotation of the sensor arm. Net deflection

is then only proportional to temperature changes at the scene. Noise can be controlled by adjustments to the optical system

and the design of the detector can be simplified. An image of an individual array element is shown in Fig. 19.1 [1].

E. Tripp (*) • E. Harrington • C. Furlong




F. Pantuso • L. Zhang

Agiltron Incorporated, 15 Presidential Way, Woburn, MA 01801, USA



131


Manufacturing errors exist across the array. Ideally, every pixel will have the same tilt at the same temperature.

Nevertheless, the thin layers of the structure can become rotated or rounded. As a result of these distortions, the intensity

of reflected light with respect to temperature is not uniform across the array. This limits the potential temperature resolution

of the readout system.

19.2 Methodology

Holographic techniques can be used to compensate for the nonuniformity in the array. The use of interferometry to produce

full-field, non-contact, real-time holograms of a MEMS opto-mechanical array has been demonstrated [2]. This is done with

four-phase step interferometry to measure the optical phase of the array. In double exposure holography, a reference phase

map is measured in an unloaded state. Additional images are subtracted from the reference image so that only changes in

optical phase due to loading are measured. The measurements are real-time, full field, and non-contact.

The IR absorbing side of a MEMS opto-mechanical detector is mounted at the focal point of a long wave infrared imaging

lens. The reflective side of the array is focused on the object path of a Linnik interferometer with 4� magnification.

The MEMS detector is housed in a vacuum-sealed package. The array is viewed through an optical window. This introduces

an additional optical path length difference greater than the coherence length of the LED illumination source. Interference

between the two paths will not occur as a result. A compensation window of the same material and thickness as the optical

window is placed in the reference path to correct for the optical path length difference. A piezo-electric transducer moves the

reference mirror of the interferometer through the four phase step positions. Figure 19.2 is an image of the experimental

setup [3].

LaserView is in-house developed software designed specifically for interferometric holography measurements. The

software syncs the camera shutter signal with the signal to the positioner so that one interferogram is captured at each phase

position. The software calculates optical phase and modulation from the interferograms. A reference image can be captured

at any time to display the double exposed phase map. When a temperature load from the scene is applied, the mirrors of the

array tilt. The change in phase due to this tilt is visible in the double-exposed phase map.

Because the mirrors tilt, mirror response is at a maximum at one edge of each mirror. An algorithm is used to calculate a

value that represents the real-time height change associated with each mirror. Measurements are made with modulation only

on the surface of the mirrors. A threshold modulation value is set so that the image can be segmented into regions based on

mirror location. A median value is calculated at a location offset from the centroid of the mirror. These values are placed at

the respective centroids. All other pixels have no value. The total number of pixels is reduced to eliminate the gaps. The

result is a thermogram of the heat distributions as measured by the readout system on the detector. A differential blackbody

projector with temperature controllable to 0.001 K produces uniform scenes of known temperature. The blackbody target

is used to test the resolution of the readout system. The imaging system with the blackbody calibration setup is shown

in Fig. 19.3.

Fig. 19.1 Bimetallic MEMS cantilever layout [1]

132 E. Tripp et al.

19.3 Results

Real-time images are produced with the optical readout system. Because of the magnification of the interferometer, only

40 � 40 mirrors or approximately 2% of the entire array area is observed by the camera at once. Consequently, the spatial

resolution of the calculated thermograms is 40 � 40 pixels. Images appear pixelated. The frame rate of the readout system

nearly matches the frame rate of the camera itself. Figure 19.4 is a thermogram of the blackbody at 35�C. The blackbodyprojector produces uniform scenes of known temperature. A number of sequential images are captured of the uniform scene

so that spatial and temporal noise of the measurements can be calculated. The average responses of the array at two different

temperatures are used to calculate the pixel responsivity. Noise Equivalent Differential Temperature (NEDT) is the point at

which the measurement signal and the signal noise are equivalent. This provides an estimation of the temperature resolution.

NEDT is then the noise in nm divided by the response in nm/K. With real-time temporal averaging, the mean response of the

mirrors in the array is 1.5 nm/K with a noise of 0.33 nm for an NEDT of 220 mK. This is greater than the target value of

100 mK.

Fig. 19.2 Interferometric

readout system

Fig. 19.3 Imaging system

with blackbody calibration

setup

19 Opto-Mechanical Characterization of a MEMS Sensor for Real-Time Infrared Imaging 133

Figure 19.5a is a thermogram of three fingers as generated by the algorithm from the optical phase map and modulation

image. The temperature differential between the finger nails and the skin is noticeable. The temperature difference is

600 mK. Figure 19.5b is a thermogram of a portrait if a human face. Temperature differences between hair, clothing, and

eyes are noticeable. The temperature difference between the skin and the eyes is 800 mK.

19.4 Conclusions

Double exposure holography eliminated spatial noise in the measurements due to detector non-uniformity. The optical phase

measurements introduce noise from positioner non-linearity and camera noise. This noise is propagated by the median value

selection algorithm. The noise introduced by the holographic system is greater than the reduction in spatial noise from the

use of holography. Reduction in noise of the holographic measurements either through improvements to the existing system

or alternative holographic approaches will allow the system to achieve an NEDT lower than the target value of 100 mk.

References

1. Erdtman M, Simelgor G, Radhakrishan L, Zhang L, Liu Y, Emelie P, Salerno J (2010) Photomechanical imager FPA design for

manufacturability. In: Proceedings of the SPIE, Infrared technology and applications XXXVI, Orlando, FL USA 7660:766017–766017-8

2. Dobrev I, Balboa M, Fossett R, Furlong C, Harrington E (2011) MEMS for real-time infrared imaging. In: Proceedings of the SEM, MEMS

and nanotechnology, Uncasville, CT USA 4:119–125

3. Tripp E (2012) Interferometric optical readout system for a MEMS infrared imaging detector. MS thesis, Mechanical Engineering Department,

Worcester Polytechnic Institute

Fig. 19.4 Thermogram

of blackbody target at

temperature of 35�C

Fig. 19.5 Example

thermograms of (a) fingers

with temperature differential

of 600 mK between the nail

and skin and (b) a portrait with

temperature differential of

800 mK between the eyes and

the skin

134 E. Tripp et al.

Chapter 20

Global Digital Image Correlation for Pressure Deflected Membranes

Jan Neggers, Johan Hoefnagels, Francois Hild, Stephane Roux, and Marc Geers

Abstract Bulge testing is known for its ability to quantify the mechanical behavior of homogeneous thin membranes.

In this method the measured quantities are related to the averaged stress and strain using bulge equations that only exist for a

very limited set of membrane geometries. A novel 3D Digital Image Correlation (DIC) method is proposed to directly

measure the strain and curvature fields without using any closed form approximation of the deformation kinematics.

Importantly, for membranes under pressure, the stress is directly related to the curvature.

20.1 Introduction

Thin films, which often have one dimension smaller than the intrinsic micro-structural length scale of the material, are

regularly applied in micro-electronic devices or integrated systems [1]. Typically, these films exhibit a so-called size effect,

which means that the thin film material response is different from their bulk counterparts [2]. Therefore, experimental

methods that can characterize these thin films in the same form as they are produced and used are invaluable. An important

experiment in this class is the bulge test.In a bulge test a thin film or membrane is deflected using a pressurized medium. From the pressure and deflection at the

apex of the bulge, the stress-strain response is calculated by means of analytical descriptions of the membrane deformation,

called the bulge-equations [3]. There exist bulge-equations for circular, square, and, rectangular membranes, typically

derived from plate theory [4]. These bulge-equations work very well within the assumptions of the plate theory. However,

the limits are not always obviously fulfilled especially considering the membrane boundary [5]. Additionally, the results are

sensitive to experimental inaccuracies like sample variations, sample misalignment, temperature variations.

In this article a new bulge test method is proposed that does not use any a priori assumed description of the membrane

deformation, which relies on a single spot measurement. Instead, a full-field surface profile of the membrane at each

deformation increment is measured. From this profile, the full-field membrane strain is calculated using Digital Image

Correlation (DIC). Moreover, the full-field curvature is calculated from the profile, which is directly related to the membrane

stress. The proposed methodology results in a direct measurement of the stress and strain on the part of the membrane of

interest, i.e., the complex deformation at the boundary can be excluded from the measurement.

To prove this new method, it is benchmarked against a virtual experiment. This virtual experiment is a simulated

representation of a real experiment. In this synthetic environment, none of the experimental inaccuracies exist, and thus it

allows for a thorough evaluation of the methodology as if performed on a perfectly executed experiment. Moreover, also

virtual measurement noise can be injected in various ways to evaluate the robustness of the methodology to experimental

inaccuracies.

J. Neggers (*) • J. Hoefnagels • M. Geers

Department of Mechanical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ, Eindhoven, Netherlands


F. Hild • S. Roux

LMT Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud Paris, 61 avenue du President Wilson, 94235 Cachan Cedex, France



135


20.2 Virtual Experiment

The reference experiment is the deflection of a 100 nm thick Silicon Nitride (Si3N4) membrane with “in-plane” dimensions

of 1�6 mm, which is also used as a reference configuration in [5, 6], and results in a plane-strain stress state in the center of

the membrane, and a membrane with dimensions of 1 � 1 mm, which results in a biaxial stress state in the center of the

membrane. In the experiment, a 3D pattern is applied to the membrane using 80–500 nm Ag particles, and the deflection of

the membrane is measured with an optical profilometer that has an “in-plane” pixel size of 380 nm [6]. The membrane is

deflected by pressurising a liquid “ethanol” on the back side of the membrane incrementally to a pressure of 1 bar.

The virtual experiment consists of a Finite Element Method (FEM) simulation using (50,000) 3D 4-node bilinear Mindlin

shell elements (Fig. 20.1). This large number of elements is used to improve the interpolation from the FEM discretization to

the pixel discretization that represents the optical profilometer data. In the simulation a pure elastic material model, with a

Young’s modulus of E ¼ 235 GPa and a Poisson’s ratio of n ¼ 0.27, is used in the large displacements formulation to

represent the material properties of Si3N4. The three displacement nodal Degrees Of Freedom (DOF) are used to artificially

deform a real picture of an undeformed membrane with a particle pattern (Fig. 20.2). The resulting data is similar to the data

normally obtained from a real experiment but with some differences: (1) there is no measurement noise in the data, only

interpolation errors, which are very similar to the pixel discretization of a optical profilometer camera, (2) the displacement-,

strain-, and stress-fields are known before analysing the data, and they can be used as a reference to quantify the accuracy of

the data-analysis.

20.3 Global DIC

To obtain the displacement field from the virtual experiment data a “global DIC” method is developed. The implementation

uses the same reasoning as previous “global DIC” implementations [7, 8]. In particular, the ability to resolve 3D displacement

fields, as a function of a 2D position vector, which is required for any profilimetric type measurement. The method is based on

Fig. 20.1 The deformed shape of the two virtual experiments, i.e., (a) the square membrane, (b) the rectangular membrane. Note that the out of

plane deformation is amplified by the micrometer scale of the z-axes, and that the visible grid does not represent the actual mesh grid, which would

be too fine to show in such an image

x [µm]

y [µ

m]

−100 −50 0 50 100

−50

0

50

z [µ

m]

1

2

3

4

−100 −50 0 50 100

−50

0

50 56

58

60

x [µm]

y [µ

m]

z [µ

m]

−100 −50 0 50 100

−50

0

5045

46

47

48

49

50

x [µm]

y [µ

m]

z [µ

m]

a b c

Fig. 20.2 A real picture of a pattern on top of a membrane is used as a reference image f(x) (a), which is deformed using the FEM displacement

field from the rectangular membrane (b) and the square membrane (c), thereby creating the deformed images g(x). Both combinations of f(x) andg(x) are then used in the correlation procedure

136 J. Neggers et al.

the conservation of the squared height difference of the topography between a deformed surface profile g(x) and a referencesurface profile f(x) integrated over the considered domain

�2 ¼ð½ f ðxÞ � gðxþ uxyðxÞÞ þ uzðxÞ�2dx ¼

ðrðxÞ2dx; (20.1)

where x is an in-plane coordinate vector, uxy the in-plane displacement, uz the out-of-plane displacement, r(x) the residualfield, and � the global residual that is minimized in the global DIC procedure. The displacement field is parametrized as a

sum of shape functions ’n(x) that act over the entire region of interest and are weighted with a discrete set of DOF un

uðxÞ ¼Xn

un’nðxÞei; (20.2)

where i ¼ { x, y, z} and the basis functions ’n(x) are polynomials dependent on the in-plane coordinate x ¼ xex þ yey

’n ¼ xaðnÞybðnÞ: (20.3)

Note that each basis function (of degree [a, b]) can be applied in three position directions, associated with three degrees of

freedom. The purpose of using this type of shape functions is because a C1 continuity on the displacement field is enforced,

which is important for the accuracy of the curvature calculation. The smoothness of the displacement fields may lead to an

incorrect conclusion that there was no error in the method. However, this particular global DIC implementation effectively

filters out any measurement noise in one step, leaving smooth displacement data and allows for the validation of the assumed

kinematic hypothesis.

The curvature tensor k is calculated as the gradient of the normal vector n

kðxÞ ¼ r � nðxÞ; (20.4)

which in turn is the gradient of the position field z (corrected for rotations)

nðxÞ ¼ rzðxÞjjrzðxÞjj : (20.5)

Since the curvature of a membrane is only defined in the tangential plane, components of the curvature are extracted using

two orthogonal membrane tangent vectors, i.e., tx and ty, where tx is the vector tangent to the membrane normal to the eydirection, and ty is the vector tangent to the membrane normal to the ex direction, resulting in the curvature fields

kxxðxÞ ¼ txðxÞ � kðxÞ � txðxÞ; (20.6)

kyyðxÞ ¼ tyðxÞ � kðxÞ � tyðxÞ; (20.7)

Similarly, the strain is calculated by using the Green-Lagrange strain tensor E ¼ 12ðruÞ þ ðruÞt þ ðruÞt � ðruÞ� �

, from

which two strain components are extracted

exxðxÞ ¼ txðxÞ � EðxÞ � txðxÞ; (20.8)

eyyðxÞ ¼ tyðxÞ � EðxÞ � tyðxÞ; (20.9)

For the rectangular membrane the plane-strain membrane stress in the center of the membrane can be related to the

curvature using the hoop equations [5]

sxx ¼ P

t kxx; (20.10)

20 Global Digital Image Correlation for Pressure Deflected Membranes 137

where P is the applied pressure to deflect the membrane and t the membrane thickness. For the square membrane the

deformation shape in the center of the membrane can be considered to be axisymmetric. Consequently, the principal stresses

are related to the principal curvatures, which are in this case aligned with the global ex and ey directions [9]

sxx ¼ P

2t kyy; (20.11)

syy ¼ P

t kyy1� kxx

2kyy

� �: (20.12)

Since these two curvatures are equal in the center of the membrane, the two corresponding stresses are also equal at that

location.

20.4 Results

Figures 20.3 and 20.4 show the measured displacement fields for the center area of both square and rectangular membranes.

For the rectangular membrane, six DOFs with corresponding shape functions are used,

’1 ¼ x0y0ez; ’2 ¼ x1y0ex;

’3 ¼ x0y1ey; ’4 ¼ x2y0ez;

’5 ¼ x3y0ex; ’6 ¼ x4y0ex;

−100 −50 0 50 100

−50

0

50

−1

−0.5

0

0.5

1

x [µm]

Ux

[µm

]

y [µ

m]

−100 −50 0 50 100

−50

0

50−2

−1

0

1

2

x 10−3

x [µm]

Uy

[µm

]

y [µ

m]

−100 −50 0 50 100

−50

0

50

54

55

56

57

x [µm]

Uz

[µm

]

y [µ

m]

−100 −50 0 50 100

−50

0

50

r [n

m]

−40

−20

0

20

40

x [µm]

y [µ

m]

a b

c d

Fig. 20.3 The components of the correlated displacement field (a–c) and the correlation residual field (d) for the center part of the rectangular

membrane


and for the square membrane, 14 DOFs are used,

’1 ¼ x0y0ez; ’2 ¼ x1y0ex; ’3 ¼ x0y1ey; ’4 ¼ x0y2ez;

’5 ¼ x2y0ez; ’6 ¼ x0y3ey; ’7 ¼ x1y2ex; ’8 ¼ x2y1ey;

’9 ¼ x3y0ex; ’10 ¼ x0y4ez; ’11 ¼ x2y2ez; ’12 ¼ x4y0ez;

’13 ¼ x0y5ey; ’14 ¼ x5y0ex:

This is a very limited set of degrees of freedom, which is useful to limit noise and interpolation errors. However, more can be

added to allow for unknown kinematics, e.g., rigid body translations, sample misalignment.

Each simulation consisted of many increments, however, only eight increments at regular pressure intervals are used for

the analysis. The image correlation method was robust enough to correlate the displacement field between the coarse

increment steps, without finding a false minimum. Figure 20.5 shows the stress-strain response in tx the direction for both therectangular and square membrane. Both membranes show an expected linear relationship between stress and strain, the

corresponding stiffnesses are related to the Young’s modulus and Poisson’s ratio

Eb ¼ E

1� n¼ 2G; (20.13)

Ep ¼ E

1� n2¼ 2G

1þ n: (20.14)

Note that for both virtual experiments the same solution strategy is applied, while the membrane deformation paths are

different. This provides means to extract not only the Young’s modulus but also the Poisson’s ratio, if a membrane is inflated

that is shaped such that it has both a locationwhich biaxially deforms and a locationwhich deforms in plane-strain. The simplest

example of such a sample would be a substrate with two membranes, close to each other such that they can be measured in

parallel. The two elastic properties can be extracted from the biaxial modulus Eb and the plane-strain modulus Ep using,

E ¼ 2Eb � E2b

Ep; (20.15)

−100 −50 0 50 100

−50

0

50−0.5

0

0.5

x [µm]

Ux

[µm

]

y [µ

m]

−100 −50 0 50 100

−50

0

50

−0.4

−0.2

0

0.2

0.4

x [µm]

Uy

[µm

]

y [µ

m]

−100 −50 0 50 100

−50

0

50

44

45

46

47

x [µm]U

z [µ

m]

y [µ

m]

−100 −50 0 50 100

−50

0

50

r [n

m]

−60

−40

−20

0

20

40

x [µm]

y [µ

m]

a b

c d

Fig. 20.4 The components of the correlated displacement field (a–c) and the correlation residual field (d) for the center part of the squaremembrane

20 Global Digital Image Correlation for Pressure Deflected Membranes 139

n ¼ Eb

Ep� 1: (20.16)

This has been done for the current virtual experiments and the corresponding elastic modulus of E¼ 236 GPa and Poisson’s

ratio of n ¼ 0.27 are in good agreement with the material properties which were used in the simulation.

20.5 Conclusion

A custom version of global Digital Image Correlation has been developed to cope with the 3D nature of the surface

profilometry data, where the gray-level is interpreted as a z-position. The newly-developed 3D global DIC method yields

full-field displacement maps of the bulging membrane and utilizes a long wavelength discretization basis to force a smooth

and continuously differentiable measured displacement field. This makes it possible to calculate the membrane curvature

field from the double derivative of the position field with high accuracy.

Both the displacement measurement and the curvature calculation procedure have been tested on simulated finite element

experiments. The results from these studies give confidence that the method can be used to capture the three-dimensional

displacement fields and curvature fields of bulge membranes without using any a priori knowledge of the kinematics,

relieving the need for the bulge equations with its associated assumptions. The method will be further developed to be able to

capture full-field stress and strain maps, the details of which are still under development.

References

1. Nix WD (1989) Mechanical properties of thin films. Metall Trans A 20A:2217–2245

2. Gruber PA, B€ohm J, Onuseit F, Wanner A, Spolenak R, Arzt E (2008) Size effects on yield strength and strain hardening for ultra-thin Cu films

with and without passivation: a study by synchrotron and bulge test techniques. Acta Mater 56:2318–2335

3. Xiang Y, Chen X, Vlassak JJ (2005) Plane-strain bulge test for thin films. J Mater Res 20(9):2360–2370

4. Vlassak JJ, NixWD (1992) A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films. J Mater Res 7

(12):3242–3249

5. Neggers J, Hoefnagels JPM, Geers MGD (2012) On the validity regime of the bulge equations. J Mater Res 27(9):1245–1250

6. Neggers J, Hoefnagels JPM, Hild F, Roux S, Geers MGD (2012) A global digital image correlation enhanced full-field bulge test method.

Procedia IUTAM Full-field measurements and identification in solid mechanics (submitted)

7. Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis from digital images: application to Portevin-Le Chatelier bands.

Exp Mech 46:141–157

8. Hild F, Roux S, Guerrero N, Marante ME, Florez-Lopez J (2011) Calibration of constitutive models of steel beams subject to local buckling by

using digital image correlation. Eur J Mech A/Solids 30:1–10

9. Hsu FPK, Liu AMC, Downs J, Rigamonti D, Humphrey JD (1995) A triplane video-based experimental system for studying axisymmetrically

inflated biomembranes. IEEE Trans Biomed Eng 42:442–445

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

1.5

2

2.5

measured square membraneEb = 323.1 GPa

measured rectangular membraneEp = 254.5 GPa

estimated uniaxial responseE = 236.0 GPa,n = 0.27

Strain [%]St

ress

[G

Pa]

FEMGDIC

Fig. 20.5 The stress-strain

response for the center spot of

the square membrane and the

rectangular membrane, each

conforming to Hooke’s law


Chapter 21

Design and Development of Internal Friction and Energy Loss

Measurement on Nanocrystalline Aluminum Thin Films

T.-C. Hu, F.-C. Hsu, M.-T. Lin, C.-J. Tong, and Y.-T. Wang

Abstract A technique developed for studying the internal friction and energy loss of nano-scale thin metal films on

substrate is presented. The test microstructure was designed on the triangular cantilever beam and fabricated by the standard

C-MOS processes, which can improve stress distribution non-uniform problem of conventional cantilever beam. The

thickness of deposited film on its surface could reduce to several nanometers. Nanocrystalline Al thin film with thickness

of sub-micrometer and nanometer were performed to observe its internal friction and energy loss response under dynamic

frequency response of the cantilever beam structure generated by electrostatic force within vacuum pressure. The results

show the measurement system used here can accurately measures the energy loss of thin film. The internal friction

measurement results provided evidence for the grain boundary motion and dislocation motion in the nanoscale thin films.

Moreover, the length scale dependence on loss mechanism of tested films was observed.

21.1 Introduction

Metal films used in manufacturing or packaging technologies are deposited in sequence. Metal films applied in IC and micro

electro-mechanical system, MEMS, structures are stacked layer on layer, attached directly to each other. Each fabrication

step may involve a different temperature, so the entire structure is subjected to temperature changes throughout the complete

process. Whether the processing temperature is raised or dropped, the mechanical stresses due to the mismatch of thermal

expansion coefficients of different directly contacting materials can be easily produced. Sometimes these stresses will

become very large [1], and may result in mechanical failure in the device.

In MEMS applications, a moving part is always involved. Metal films deposited onto the moving part can be subjected to

dynamic loads. In the miniaturized structure the operating frequency may reach megahertz or gigahertz. Bulk machines were

never designed to operate at such high frequencies because of restriction within that dimension. Therefore, the dynamic

mechanical properties and responses of thin metal films are more critical, especially energy loss.

As mention above, it is important to understand the mechanical properties of small scale materials. There are many testing

methods for obtaining information about thin film mechanical properties, such as wafer curvature and nano-indentation

[2–5]. Most results only discuss quasistatic properties using those methods. Thus, measurement and analysis of the dynamic

properties of thin films must establish alternate measurement criteria. This study presents results using a resonant system for

determining the energy loss mechanism of thin Al films.

T.-C. Hu • F.-C. Hsu • M.-T. Lin (*) • C.-J. Tong • Y.-T. Wang

Graduate Institute of Precision Engineering, National Chung Hsing University, 250, Kuo-Kuang Rd.,

Taichung, Taiwan 40227, Republic of China




141


21.2 Experimental Detail

Paddle sample with uniform stress distribution cantilever beam has been used to carry very thin Al films because of metal

films can’t support itself in such small thickness. Sample dimensions have designed 20 � 20 mm of the frame, 5 � 5 mm of

the square, and 3 mm of tapered beam length which with vary width. There is a thin (40 mm) section (the uniform stress

beam) between the frame of the chip (250 mm thick, the thickness of the Si wafer from which it was fabricated) and the thick

paddle plate (also 250 mm). Because of their relative stiffness, all of the bending in the assembly occurs in the thin section.

All test samples were fabricated through the standard C-MOS processes which already proposed in previously research

[6, 7]. Traditional Si wafer that usually use to fabricate memory, CPU, GPU and so on, their requirement of the resistivity

about several tens Ohm-cm. But the paddle sample with such resistivity will not directly measure the energy loss and internal

friction information due to bare Si paddle sample use the existing measurement, therefore high doping Si wafers are use

to collocate paddle capacitance measurement which as well designed in previously research [8]. Polycrystalline Al films

with thickness ranges from 0.03 to 0.25 mmwere deposited from 5 N Al target onto the top surface of bare Si paddle samples.

The Al film deposited using pulse DC sputter system with 200 W deposit power at 5 � 10�3 torr deposit pressure which

balance by 10 sccm argon flow.

Test system in this work is designed to eliminate mechanical contact entirely, relying on electrostatic force instead.

Bending force has been designed generate by excitation which connects from waveform generator to drive electrode

underneath square plate. Excitation has two different kind exciting voltages, sweep frequency volts and constant frequency

volts. Sweep frequency excitation is used to finding out the resonance of paddle sample after complete fabrication in

resonance experiment. Constant frequency excitation is used to build stable amplitude before paddle sample free vibration

after suddenly turned off the excitation. Free decay is a common method that use to measure energy loss and internal friction

information. When the paddle samples have a bend due to the excitation work, displacement current will has the

corresponding change through the coupling capacitor. The changes in displacement current also immediately receive by

lock-in amplifier and recorder by Labview program. The lock-in amplifier output signal can be make a plot of output voltage

against experiment time then use Fast Fourier Transform, FFT, to analysis the frequency component in the response.

Environment pressure is the main factor in the decay rate experiment; therefore all capacitance measurement was located in

high vacuum chamber to reduce affect due to environment gas. When measure the decay rate due to bare Si paddle sample

with a thin Al film on the surface, the decay rate was indicated the total response not Al film alone. So, before measure the

Ai/Si component the decay rate of bare Si paddle sample is must be obtained firstly. Then, further compare and calculate

both results of bare Si sample without and with Al films, the internal friction in pure Al film can be extract from total

response by (21.1). Qf�1 is represents internal friction in thin metal film, QSi

�1 is the internal friction of Si alone, Qc�1 is the

internal friction in Al/Si component that is a weighted average of the internal friction in the substrate thickness, film

thickness, Qf�1 and QSi

�1 respectively. ESi and Ef are respectively representing the Young’s modulus of Si substrate and Al

film. Thickness of Si beam and Al film has been expressed in tSi and tf. All measurement was operating at the same pressure

in order to can get rid of the effect due to gas damping in follow calculation.

Q�1f ¼ tSi

3tf� ESi

EfQ�1

c �Q�1Si

� �(21.1)

21.3 Results

First, bare Si paddle samples were mounted into the capacitance measurement to find out the resonance of paddle sample.

An AC excitation applies on the drive electrode with various frequency excitation frequencies, the excitation sweep range

from 50 to 300 Hz. The lock-in amplifier output versus experiment time has plotted in Fig. 21.1, the FFT power spectrum

also translated and plotted in Fig. 21.2. Maximum peak in the FFT power spectrum is expressing the resonance of tested

paddle sample, in this result the resonance is indicated 233.37 Hz. According to the resonance of paddle sample (which

finding out in resonance experiment), the excitation on drive electrode was setting on a constant frequency that could help

paddle sample build stable amplitude before turned off the excitation. Once the AC excitation suddenly turned off, the stable

vibrate amplitude is starting decay (the free decay vibrate frequency also nearly the resonance). Continuously recorder the

lock-in amplifier output until the paddle sample stop vibration, then make a plot versus time as Fig. 21.3. Figure 21.3 is

the free decay result use one of bare Si paddle samples, and use exponential decay function to fitting the signal envelope, the

142 T.-C. Hu et al.

2.6

2.4

2.2

2

1.8

Lock

in o

utpu

t(V

)

1.6

1.4

1.2

1

0 500 1000 1500 2000

Time(sec)

2500 3000 3500 40000.8

Max Amplitude= 2.4647VTime=835.907sec

Fig. 21.1 The lock-in amplifier output versus experiment time use sweep frequency excitation in nitrogen at 6.8 � 10�5 torr. The scan range is

from 50 to 350 Hz

900

800

700

600

500

400

300

200

100

00 50 100 150 200 250

Frequency (Hz)

300 350 400 450 500

Pow

er

Frequency = 233.3726HzPower = 794.4649

Fig. 21.2 FFT power spectrum for bare Si paddle sample that translate from Fig. 21.1

21 Design and Development of Internal Friction and Energy Loss Measurement. . . 143

decay rate in Fig. 21.3 was indicated 0.00498 s�1. The decay rate of bare Si paddle sample that measured in nitrogen at

6.8 � 10�5 torr between 0.0044 and 0.0056 s�1. The corresponding logarithmic decrement has calculated in 1.8 � 10�5 to

2.2 � 10�5, those results indicated only have very slight different in each bare Si paddle sample.

The Al films follow deposited on the paddle sample full surface after finish the bare Si paddle sample measurement.

By various deposit time the Al film thickness have well control. All thickness of Al films will directly measured from focus

ionic beam, FIB, cross-section images. We make the 30, 60, 100, and 200 nm Al films respectively deposited on the bare Si

paddle sample those already measured in last procedure. All paddle samples with Al film also need re-finding out the new

resonance because of the Al film will change the beam stiffness and the square mass. The re-measure resonance results

indicated the depositing Al film onto bare Si paddle sample top surface will lead to the resonance has slight change

(increase), only 0.6 Hz delta frequency of paddle sample carry the thickest Al film. Figure 21.4 presents the delta frequency

of each bare Si paddle with different thickness Al film on the surface. It is clearly to see the delta frequency increasing with

Al film thickness.

According to the new resonance of Al/Si component, the excitation on the drive electrode need adjust to the same value

and re-build stable vibration amplitude. Waiting for a while until the response stable and suddenly turned off the excitation

again. Continuously record and plotted response then fitting signal envelope by exponential decay function (shows as

Fig. 21.5). Make a comparison between bare Si paddle sample with and without Al film, the decay rate due to paddle sample

with Al films significant larger than (increase from 0.00498 to 0.0224 s�1) paddle sample without film. The corresponding

logarithmic decrement also has calculated in 3.05 � 10�5. Summarize the logarithmic decrement due to bare Si sample and

after deposit Al films in one plot (show as Fig. 21.6). The black data points in Fig. 21.6 represent the logarithmic decrement

due to four different bare Si samples, the results also indicated the Si paddle sample almost have similar logarithmic

decrement at the same environment pressure. Gray data points express the logarithmic decrement use Si paddle sample has

Al film on the surface. The results clearly present the logarithmic decrement increase near linearly with Al film thickness in

addition very significant. Compare the delta resonance and delta logarithmic results, when the deposit film thickness has

been reduced lower than 200 nm, the change in resonance is difficult observe but easily observed from logarithmic

decrement change. Further extract the internal friction in pure Al film from total response by (21.1), the internal friction

around between 6.5 � 10�3 and 8.8 � 10�3. The relationship between internal friction in Al film and film deposited

thickness has been plotted in Fig. 21.7. Internal friction in Al films are inverse proportional to the film thickness except for

2.3

2.2

Decay function = 0.3279* e(-0.00498t)+ 1.79562.1

2

1.9

1.8

lock

in o

utpu

t(V

)

1.7

1.6

1.5

1.4

1.31400 1600 1800 2000 2200

t(sec)2400 2600 2800 3000 3200

Fig. 21.3 Free decay results of bare Si paddle sample, the excitation has suddenly turned off at 1,500 s, which measured in nitrogen at

6.8 � 10�5 torr

144 T.-C. Hu et al.

the thinnest one. The thinnest Al film only 30 nm thick and the micro structure image do not observed significant grain

structure. The result indicated the structure still have island structure and not yet link to a grain, so the internal friction would

slight smaller than the film with very small grain size. Once the films show the grain structure, the internal friction goes down

with grain size goes up.

Fig. 21.4 The relationship between delta frequency and deposited Al film thicknesses

2.3

2.2

2.1

2

1.9

1.8

lock

in o

utpu

t(V

)

1.7

1.6

1.5

1.4

1.3300 400

t(sec)500 600 700 800 900

Decay function =0.32026*e(-0.0224t)+1.7942

Fig. 21.5 Free decay result of Si paddle sample with Al metal film on the surface, excitation suddenly turned off at 400 s, which measured in

nitrogen at 6.8 � 10�5 torr


21.4 Conclusions

In this paper, we proposed a uniform stress distribution test sample to correlate the high vacuum capacitance measurement.

We also successfully measured the energy loss and internal friction information in Al thin films that thickness has been

reduced less than 100 nm. We found the internal friction in Al films seem not depend much on the Al film thickness. Internal

friction in the thinnest Al film slight smaller than the maximum internal friction because of the film still stay island structure

not yet cluster to the grain structure. In the 60 nm Al film, very small grain structure has been observed that due to the

independent island already link each other. With the thickness growth, the grain size also become larger and larger that

induces the internal friction in Al film goes down. Therefore, fewer grain boundaries in the Al film will reduce the grain

boundary relaxation also can reduce the energy loss when the Al film under free vibration.

Fig. 21.6 Comparison of logarithmic decrement between bare Si paddle sample and deposited Al film on the paddle sample surface

Fig. 21.7 The internal friction in Al film versus deposited thicknesses

146 T.-C. Hu et al.

References

1. Nix WD (1989) Mechanical properties of thin films. Metall Mater Trans A 20:2217–2245

2. Flinn PA (1991) Measurement and interpretation of stress in copper films as a function of thermal history. J Mater Res 6:1548–1501

3. Vinci RP, Zielinski EM, Bravman JC (1995) Thermal strain and stress in copper thin films. Thin Solid Films 262:142–153

4. Keller RM, Baker SP, Arzt E (1998) Quantitative analysis of strengthening mechanisms in thin Cu films: effects of film thickness, grain size, and

passivation. J Mater Res 13:1307–1317

5. Suresh S, Nieh TG, Choi BW (1999) Nano-indentation of copper thin films on silicon substrates. Scr Mater 41:951–957

6. Tong CJ, Cheng YC, Lin MT, Chung KJ, Hsu JS, Wu CL (2010) Optical micro-paddle beam deflection measurement for electrostatic

mechanical testing of nano-scale thin film application to MEMS. Microsyst Technol 16:1131–1137

7. Cheng YC, Tong CJ, Lin MT (2011) Measurement of static and dynamic mechanical behavior of micro and nano-scale thin metal films: using

micro-cantilever beam deflection. Microsyst Technol 17:721–731

8. Tong CJ, Lin MT (2009) Design and development of a novel paddle test structure for the mechanical behavior measurement of thin films

application for MEMS. Microsyst Technol 15:1207–1216


Chapter 22

Detection of Damage of Epoxy Composites Using Carbon

Nanotube Network

S. Cardoso, C. Mooney, R. Pivonka, V.B. Chalivendra, A. Shukla, and S.Z. Yang

Abstract A detailed experimental study is conducted to understand damage initiation and growth in epoxy particulate

composites using a multi-wall carbon nanotube (MWCNTs) conductive network under two different loading conditions:

(a) quasi-static shear and (b) fracture. Two different particulates (a) Cenospheres (aluminum silicate hollow spheres), and

(b) carboxyl-terminated butadiene acrylonitrile copolymer (CTBN) rubber of three different volume fractions (10%, 20%

and 30%) and mass fractions (10phr, 20phr and 30phr) respectively are used in thermoset epoxy resin composites. First,

MWCNTs are well dispersed in an epoxy matrix using ultrasonication, and later the above particulates are added and shear-

mixed into the solution to prepare composites. A v-notch rail shear specimen configuration for shear experiments, and single

edge notch tension (SENT) configuration for fracture are considered in this experimental study. A four-point probe

methodology along with high-resolution data acquisition is employed to capture electrical-resistance response of network

changes associated with non-linear deformation, damage initiation and growth within composites under said loading

conditions. It is identified from experiments that the electrical response associated with the above mechanisms is quite

different with the addition of particulates compared to that of epoxy with no particulate.

22.1 Introduction

Carbon nanotubes (CNTs) have been at the forefront of materials research since their conception from the buckminsterful-

lerene [1, 2]. With a vast wealth of studies performed to determine the mechanical, electrical and other properties of CNTs,

the potential for various applications have and are currently being explored [3–6]. To date, a wide range of different material

types with the inclusion of CNTs have been considered under various loading conditions such as tensile, compressive and

impact. Many of the noted studies are performed on polymer systems for their ease of manipulation and growing application

base. Qian et al. investigated the apparent changes in mechanical strength of polystyrene with carbon nanotube addition

when under tensile load [7]. Ultimately, it was determined that the nanotubes themselves are far stronger than the matrix in

which they resided, and were capable of yielding an increase in break stress of up to 25% with a CNT loading of 1% wt.

Similar studies have been performed under differing loading conditions.

Carbon nanotubes are also capable of acting as a sensory network when properly dispersed into a medium. Recently,

Heeder et al. investigated the use of CNTs as a sensory network in detecting damage within epoxy composites under static

and dynamic loading conditions [8, 9]. Employing a four circumferential ring measurement technique, samples were loaded

under quasi-static compression and Split-Hopkinson pressure bar (SHPB) impact. The samples also contained other

particulate additives, such that the damage associated with varying content fractions of additive could be monitored and

compared.

Though fracture studies pertaining to composites are readily available in literature today, there is little to the authors’

knowledge of fracture investigations using CNTs as a sensory network [10–12]. The same holds true for CNT embedded

composites under pure shear conditions [13–15]. The present study is concerned with the evolution of damage occurring

S. Cardoso • C. Mooney • R. Pivonka • V.B. Chalivendra (*)

University of Massachusetts Dartmouth, 285 Old Westport Rd., North Dartmouth, MA 02747, USA


A. Shukla • S.Z. Yang

University of Rhode Island, 75 Lower College Road, Kingston, RI 02881, USA



149


within specimen under the foregoing conditions. The purpose is to use a CNT sensory network for the detection and analysis

of damage within the process zone of fracture specimen, and along the loading plane of pure shear specimen. In addition,

each of these cases is performed on nanocomposites containing particulate additives, in order to determine the effect of the

additive on the evolution of damage. Fracture testing is performed on samples of plain epoxy, and those with an addition of

carboxyl-terminated butadiene acrylonitrile copolymer (CTBN) rubber at a given weight fraction (10phr, 20phr and 30phr).

Similarly, the shear study is performed on similar sample types. Specimen containing cenospheres (aluminum silicate

hollow spheres) will also be considered in shear to compare the effects of rigid and elastomeric particulates. Similar to the

rubber case, three volume fractions of rigid particulates (10%, 20% and 30%) will be used.

22.2 Materials and Experimental Procedure

Epoxy and hardener were selected to facilitate easy fabrication. Bisphenol-A epoxy resin (Buehler Epothin 20-8140-128)

was chosen for its ease of casting. The resin is accompanied by a hardener counterpart (Buehler Epothin 20-8142-064).

CNTs were obtained from NanoLab Inc. They are 95% or higher purity, have an outer diameter of 30 � 15 nm, lengths of

5–20 microns with specific surface area of 200–400 m2/g. CVC Thermoset specialties HYPRO 1300X13 Polymer was

chosen as the CTBN rubber component. Cenospheres (hollow aluminum silicate spheres) with a diameter range of

10–300 mm and a wall thickness of one-tenth of the diameter were also used.

Only a general outline of the procedure is presented for completeness; however the readers can refer to reference [9] for

additional information and more specific details. Pre-determined amounts of resin and CNT are mechanically combined and

shear mixed. 0.3% wt. of CNTs is used for fracture while 0.2% wt. of CNTs is used for shear. The required amount of CNTs

was determined separately, in attempt to optimize the sensory network. Carbon nanotubes are dispersed using a combination

of ultrasonication and shear mixing techniques. A separate extensive study was conducted to identify the amount CNTs and

the duration of sonication that provides the best dispersion without damaging the CNTs or reducing the overall conductivity

of the fabricated material. For applicable cases, particulate additives are added to the mixture in pre-measured quantities, and

the solution is vacuumed to remove trapped gasses. Finally the hardener is added to complete the mixture, which is then

vacuumed briefly before being poured into pre-prepared rotating molds. Sheets are cast from the mixture and allowed to

cure, from which samples of a specific geometry are made. Figure 22.1 illustrated the nominal dimensions for (a) Fracture

and (b) shear specimen. Electrical leads are fixed to each sample with conductive silver epoxy, and the gripped ends are

insulated to ensure that current is not transferred from the sample to the machine. Resistance is monitored using a high-

resolution electrometer based four point/four circumferential ring probe system. Here, the resistance change is simply

calculated by dividing the difference in resistance with respect to the static resistance by the static difference. This quotient is

multiplied by a factor of 100 for a percentage scenario. SENT samples are gripped using standard tensile fixtures on a screw-

driven material testing machine, while shear samples are gripped using a v-notch rail shear fixture with the same machine.

The geometry and test configuration used for the shear investigation are outlined in by ASTM standards (ASTM 7078).

a b25.40 mm

101.60 mm

31.75 mm 15.88 mm

57.15 mm 3.18 mm

90°

0.30 mm

6.35 mm

3.00 mm

Fig. 22.1 Geometry for (a) fracture and (b) shear specimen

150 S. Cardoso et al.


22.3.1 Fracture Results

Carbon nanotube embedded SENT specimens of the following compositions were loaded under opening mode conditions:

epoxy without additive, 10phr, 20phr and 30phr CTBN rubber. To adequately determine the damage as it occurs within the

process zone the electrical leads were fixed in very close proximity to the machined crack tip in four point configuration,

wherein the resistance changes recorded reflects damage as it evolves within this small zone. The change in crack tip

opening displacement (CTOD) is used as a common reference for analysis of the electro-mechanical response of the system.

CTOD is measured directly by the Tracy method (1976) from images taken using a high resolution camera outfitted with

magnifying lenses. For consistency, data collection was performed only until the first sign of crack propagation for all cases.

In order to have complete confidence in the experimentally obtained results, several experiments were performed for each

material case. For the sake of brevity and convenience for making comparisons, only a single representative result from each

material group is presented. Figure 22.2 illustrates these representative results on a common set of axes. In the following

passages, each result is discussed in detail.

The electro-mechanical response of plain epoxy containing 0.3% wt. of CNTs is shown in Fig. 22.2. Initially, there is very

little change in the measured resistance, meaning that there is no significant damage mechanism occurring. After the initial

portion, a linear increase in resistance is found. Volume dilatation occurs within this stage of the specimen loading, pulling

apart carbon nanotubes in the loading direction. A change in the slope on the increasing resistance curve denotes another

change in the conductive network. As the specimen is continuously loaded, the matrix is manipulated, reducing overall

resistance within the process zone. All epoxy samples underwent fast fracture prior to large changes in CTOD.

Also presented in Fig. 22.2 is the electro-mechanical response of 0.3% wt. CNT embedded epoxy containing 10phr

rubber reinforcement. The specimen initially shows little response, explained by the same reasoning as for the epoxy case.

A second stage of damage is a linearly increasing resistance of constant slope. The same mechanisms occurring within plain

epoxy are also occurring here. A final stage of damage finds a slightly reduced slope in the increasing resistance trend.

Macro-scale changes in the matrix are driving the response. Given the relatively low content of rubber existing within the

sample, the material still fails under brittle fracture without any indication of crack propagation.

20phr composites experience minimal resistance change during the earliest stage of loading. This is shown in Fig. 22.2.

The same reasoning from previous discussions applies here. Another segment of the material deformation is characterized

by a linear increase in resistance of constant slope, again a result from the separation of CNTs. Following the second damage

stage, the material undergoes further deformation resulting in another resistance increase. Previous discussions concerning

the mechanisms behind the reduction in slope are still applicable for the 20phr case. The 20phr specimen still fails under a

brittle fracture with no crack propagation.

The response of epoxy composites containing 0.3% wt. CNTs and 30phr rubber is also shown on Fig. 22.2. 30phr also

exhibits a short stage of minimal recorded changes. Another damage stage is denoted by a fairly linear increase in resistance.

15

Epoxy

10phr

20phr

30phr

10

5

0

-5

-10

-15

Δ CTOD (mm)

Res

ista

nce

Cha

nge

(%)

0 0.05 0.1 0.15 0.2 0.25 0.3Fig. 22.2 Comparison

of electro-mechanical

response in fracture

22 Detection of Damage of Epoxy Composites Using Carbon Nanotube Network 151

The mechanisms explained previously remain unchanged for the 30phr case. With increasing CTOD, the third stage of

damage reflects a resistance drop at a constant rate. There are several contributors to this net effect. Large scale manipulation

of the matrix, and high concentrations of rubber enabling overall thinning are the reasons for such a drop. A final stage,

ending just prior to crack propagation, is characterized by another increase in resistance. With a drastic amount of damage

existing in the process zone, micro-cracks form rapidly yielding breakage in the sensory network. 30phr specimen did not

observe a brittle failure.

22.3.2 Shear Results

V-notch rail shear methodology is used to example the following composites under pure shear loading conditions: plain

epoxy without particulate inclusion, 10phr, 20phr and 30phr rubber, 10%, 20% and 30% cenospheres. The damage

mechanisms associated with pure shear loading will be obtained for each item in this broad spectrum of materials ranging

from high fractions of rigid particulates to high fractions of elastomeric particulates. At the present time, only the extremes

of the particulate cases (30phr rubber and 30% cenospheres) have been studied. Electrical leads are placed in a four

circumferential ring configuration such that the inner probes are separated by the plane on which shear is induced. The

measured voltage is therefore across the shear plane. For the case of rubber embedded samples, data collection is ended at

the first indication of sample failure. A representative result from each case in presented for discussion.

Figure 22.3 contains the electro-mechanical response of epoxy containing 0.2% wt. CNT and 30% volume of

rigid cenosphere particulate. Heavy rigid particle loading causes the resulting composite to be brittle in nature, as shown

by the linear stress–strain relationship. It appears that the 30% fraction of cenospheres reduces the overall potential for

damage detection of the sensory network. In all, very little resistance change is recorded throughout the specimen loading.

In this region, as the specimen undergoes shear deformation, the CNTs re-orient themselves in such a manner that no net

change is recorded. The slight inflection observed at the end of the resistance curve denotes the beginning of a second

damage. In this case, the bonds between particles and matrix are broken. This interfacial separation distorts the conductive

network.

A representative response of epoxy containing 30phr rubber reinforcement is presented in Fig. 22.4. Several damage

stages are present for the elastomeric composite case. First, a stage exhibiting minimal response is observed, again meaning

that the CNTs have been continuously re-oriented. A second stage of damage exhibits a dropping resistance trend as

the stress within the body is at its highest. The rubber particles are a blunting force for micro-crack formation and growth

within the matrix, allowing the network to be more conductive. Finally, the response shows an exponentially increasing

resistance until the first sign of failure is detected. Having sustained high stress, drastic amounts of damage are now

present in the measured region. This increasing amount of damage makes electron transfer far more difficult for the sensory

network.

30

25

20

15

10

5

0

Strain (%)

Res

ista

nce

Cha

nge

(%)

Str

ess

(MP

a)

0

1

-1

2

3

4

5

0 1 2 3 4 5 6 7

Fig. 22.3 Electro-mechanical

response of epoxy with 30%

cenospheres in shear


22.4 Conclusion

Fracture testing was performed with emphasis on recording damage within the process zone for composites incorporating

10phr, 20phr and 30phr CTBN rubber. It was found that each material type saw a short region where little response was

recorded and no significant mechanism was acting within the measured zone. Epoxy, 10phr and 20phr samples all exhibited

the same general trend of increase due to volume dilatation and matrix changes. 30phr specimen saw several stages of

damage, each with its own explanation.

Shear testing was performed in a v-notch rail shear configuration on epoxy composites separately toughened with rubber

(10phr, 20phr and 30phr) and rigid particles (10%, 20% and 30% cenospheres). Only 30% cenosphere and 30phr rubber

results are presently available. Samples containing 30% rigid reinforcement had little response due to CNT re-orientation.

A slight increase in resistance is also recorded due to drastic damage. 30phr rubber toughened epoxy still endures a long

stage of damage where resistance is fairly static. A clear drop in resistance is also recorded, due to the prevention of micro-

cracks. Severe damage finally yields a large scale resistance increase.

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7. Qian D, Dickey EC, Andrews R, Rantell T (2000) Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites.

Appl Phys Lett 76:2868–2870

8. Heeder NJ, Shukla A, Chalivendra V, Yang S, Park K (2011) Electrical response of carbon nanotube reinforced nanocomposites under static

and dynamic loading. Exp Mech. doi: 10.1007/s11340-011-9488-x

9. Heeder N, Shukla A, Chalivendra V, Yang S (2012) Sensitivity and dynamic electrical response of CNT-reinforced nanocomposites. J Mater

Sci 47:3808–3816

10. Kinloch AJ, Shaw SJ, Tod DA, Hunston DL (1983) Deformation and fracture behavior of a rubber-toughened epoxy: 1. Microstructure and

fracture studies. Polymer 24:1341–1354

11. Kinloch AJ, Shaw SJ, Tod DA, Hunston DL (1983) Deformation and fracture behavior of a rubber-toughened epoxy: 2. Failure criteria.

Polymer 24:1355–1363

12. Kim BC, Park SW, Lee DG (2008) Fracture toughness of the nano-particle reinforced epoxy composite. Compos Struct 86:69–77

20

18

16

14

12

10

8

6

4

2

0

0

-20

20

40

60

80

100

120

20 2510 150 5S

tres

s (M

Pa)

Strain (%)

Res

ista

nce

Cha

nge

(%)

Fig. 22.4 Electro-mechanical

response of epoxy with 30phr

rubber in shear

22 Detection of Damage of Epoxy Composites Using Carbon Nanotube Network 153

http://dx.doi.org/10.1007/s11340-011-9488-x

13. Hussain AK, Adams DF (2004) Experimental evaluation of the Wyoming-modified two-rail shear test method for composite materials.

Exp Mech 44(4):354–364

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Documents

MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimental and Applied Mechanics