1

Physical Measurement Laboratory

Semiconductor and Dimensional Metrology Division

Nanoscale Metrology Group

MEMS Measurement Science and Standards Project

MEMS 5-in-1 RM Slide Set #4

Reference Materials 8096 and 8097The MEMS 5-in-1 Test Chips– Residual Strain Measurements

Photo taken by Curt Suplee, NIST

2

List of MEMS 5-in-1 RM Slide SetsSlide Set # Title of Slide Set

1 OVERVIEW OF THE MEMS 5-IN-1 RMs

2 PRELIMINARY DETAILS

THE MEASUREMENTS:

3 Young’s modulus measurements

4 Residual strain measurements

5 Strain gradient measurements

6 Step height measurements

7 In-plane length measurements

8 Residual stress and stress gradient calculations

9 Thickness measurements (for RM 8096)

10 Thickness measurements (for RM 8097)

11 REMAINING DETAILS

3

Outline forResidual Strain Measurements

1 References to consult

2 Residual strain a. Overview b. Equation used c. Data sheet uncertainty equations d. ROI uncertainty equation

3 Location of fixed-fixed beam on RM a. For RM 8096 b. For RM 8097

4 Fixed-fixed beam a. For RM 8096 b. For RM 8097

5 Calibration procedure

6 Measurement procedure

7 Using the data sheet

8 Using the MEMS 5-in-1 to verify measurements

4

• Overview1. J. Cassard, J. Geist, and J. Kramar, “Reference Materials 8096 and 8097 – The Microelectromechanical

Systems 5-in-1 Reference Materials: Homogeneous and Stable,” More-Than-Moore Issue of ECS Transactions, Vol. 61, May 2014.

2. J. Cassard, J. Geist, C. McGray, R. A. Allen, M. Afridi, B. Nablo, M. Gaitan, and D. G. Seiler, “The MEMS 5-in-1 Test Chips (Reference Materials 8096 and 8097),” Frontiers of Characterization and Metrology for Nanoelectronics: 2013, NIST, Gaithersburg, MD, March 25-28, 2013, pp. 179-182.

3. J. Cassard, J. Geist, M. Gaitan, and D. G. Seiler, “The MEMS 5-in-1 Reference Materials (RM 8096 and 8097),” Proceedings of the 2012 International Conference on Microelectronic Test Structures, ICMTS 2012, San Diego, CA, pp. 211-216, March 21, 2012.

• User’s guide (Section 3, pp. 51-75)4. J.M. Cassard, J. Geist, T.V. Vorburger, D.T. Read, M. Gaitan, and D.G. Seiler, “Standard Reference

Materials: User’s Guide for RM 8096 and 8097: The MEMS 5-in-1, 2013 Edition,” NIST SP 260-177, February 2013 (http://dx.doi.org/10.6028/NIST.SP.260-177).

• Standard5. ASTM E 2245-11e1, “Standard Test Method for Residual Strain Measurements of Thin, Reflecting Films

Using an Optical Interferometer,” September 2013. (Visit http://www.astm.org for ordering information.)

• Fabrication6. The RM 8096 chips were fabricated through MOSIS on the 1.5 µm On Semiconductor (formerly AMIS)

CMOS process. The URL for the MOSIS website is http://www.mosis.com. The bulk-micromachining was performed at NIST.

7. The RM 8097 chips were fabricated at MEMSCAP using MUMPs-Plus! (PolyMUMPs with a backside etch). The URL for the MEMSCAP website is http://www.memscap.com.

• Miscellaneous8. J. C. Marshall, “MEMS Length and Strain Measurements Using an Optical Interferometer,” NISTIR 6779,

National Institute of Standards and Technology, August 2001.

1. References to Consult

• Definition: The amount of deformation (or displacement) per unit length constrained within the structural layer after fabrication and before the constraint of the sacrificial layer (or substrate) is removed

• Purpose: To measure the strain present in parts of a microsystem before they relax after the removal of the stiff oxides that surround them during manufacturing

• Test structure: Fixed-fixed beam• Instrument: Interferometric microscope (or comparable instrument)• Method: The curved length of the fixed-fixed beam is determined from

five data points extracted from one data trace along the length of the fixed-fixed beam. The in-plane length of the fixed-fixed beam is also measured. The residual strain for the data trace is calculated given these measurements and taking into account offset and misalignment. The residual strain is the average of the residual strain values obtained from multiple data traces.

2a. Residual Strain Overview

6

wherer residual strainrt residual strain obtained from trace “t”rcorrection relative residual strain correction termL in-plane length of fixed-fixed beamL0 length of the fixed-fixed beam when no applied axial-

compressive forcesLc length of the curved fixed-fixed beamLe′ effective length of the fixed-fixed beamt thickness

2b. Residual Strain Equation

nrcorrectiort LLL 1/ 00

3/rdrcrbr

22220 )/(12/)/(12 tLLLLLLLL ececc

(for one trace)

where

7

2c. Data Sheet Uncertainty Equations

2)(

2222)(

22222222

samprepeatcorrectionlineardriftshsrepeat

certnoiseRavexresxcalzresLW

rcuuuuu

uuuuuuuuu

• Residual strain combined standard uncertainty, ucr, equation

where uW due to variations across the width of the fixed-fixed beam uL due to measurement uncertainty of L uzres due to the resolution in the z-direction of the interferometer uxcal due to the calibration uncertainty in the x-direction uxres due to the resolution in the x-direction of the interferometer as

pertains to the five data points chosen along the beam uRave due to the sample’s surface roughness unoise due to interferometric noise ucert due to the uncertainty of the value of the step height standard

used for calibration urepeat(shs) due to the repeatability of measurements taken on the step

height standard

• Continued….

where udrift due to the amount of drift during the data session ulinear due to the deviation from linearity of the data scan ucorrection due to the uncertainty of the correction term urepeat(samp) due to the repeatability of similar residual strain measurements

• The data sheet (DS) expanded uncertainty equation is

where k=2 is used to approximate a 95 % level of confidence.8

2c. Data Sheet Uncertainty Equations

2)(

2222)(

22222222

samprepeatcorrectionlineardriftshsrepeat

certnoiseRavexresxcalzresLW

rcuuuuu

uuuuuuuuu

rcrDS uUU 2

9

Effective value for RM 8096 due to:1. Debris in the attachment corners2. Undercutting of the beam3. Multiple SiO2 layers

Effective value for RM 8097 due to:1.Kinks in cantilevers2.Undercutting of the beam3.Non-rigid support

2c. Data Sheet Uncertainty Equations

3rdrcrb

r

nrcorrectiort L

LL

1

0

0

3

|| rtnrcorrectiotcorrectionu

3dcorrectionccorrectionbcorrection

correction

uuuu

where

nrcorrectio

10

UROI expanded uncertainty recorded on the Report of Investigation (ROI)

UDS expanded uncertainty as obtained from the data sheet (DS)

Ustability stability expanded uncertainty

2d. ROI Uncertainty Equation

22stabilityDSROI UUU

11

3. Location of Fixed-Fixed Beam on RM Chip (The 2 Types of Chips)

• RM 8097– Fabricated using a polysilicon

multi-user surface-micromachining MEMS process with a backside etch

– Material properties of the first or second polysilicon layer are reported

– Chip dimensions:

1 cm x 1 cm

• RM 8096– Fabricated on a multi-user

1.5 µm CMOS process followed by a bulk-micromachining etch

– Material properties of the composite oxide layer are reported

– Chip dimensions:

4600 µm x 4700 µm

Lot 95 Lot 98

12

3a. Location of Fixed-Fixed Beam on RM 8096

12Locate the fixed-fixed beam in this group given the information on the NIST-supplied data sheet

For RM 8096

Structural layer composite oxide

Wffb (µm) 40

Lffb (µm) 200, 248, 300, 348, and 400

t (µm) ≈2.743

Orientation 0º

Quantity of beams

3 of each length (or 15 beams)

Top view of a fixed-fixed beam

13

3b. Location of Fixed-Fixed Beam on RM 8097

Locate the fixed-fixed beam in this group given the information on the NIST-supplied data sheet

Top view of two fixed-fixed beams

For RM 8097

Structural layer poly1 or poly2

Wffb (µm) 16

Lffb (µm) 400, 450, 500, 550, 600, 650,700, 750, and 800

t (µm) ≈2.0 (for poly1) and ≈1.5 (for poly2)

Orientation 0º (for poly1 and poly2) and 90º (for poly1)

Quantity of beams

3 of each length and each orientation (or 54 poly1 and 27 poly2 beams)

Lot 95

Lot 98

14

4a. Fixed-Fixed Beam (For RM 8096)LEdge 1 Edge 2

y

x

a

bc

d

e

exposed silicon to be etched (design layers include active area, contact, via, and glass)

metal2 (m2) dimensional marker

etch stop (n-implant encompassing active area)

e΄

a΄

Top view of a fixed-fixed beam

15

4b. Fixed-Fixed Beam (For RM 8097)

Top view of a p2 fixed-fixed beam (Lot 95)

Data along Trace a′, a, e, or e′

These “tabs” are not present in the residual strain group on Lot 98.(The original intent was to keep the same anchor designs as used in the Young’s modulus group, but these tabs make it more difficult to locate traces a′, a, e, and e′.)

16

• Calibrate instrument in the z-direction– As specified for step-height calibrations

• Calibrate instrument in the x- and y-directions– As specified for in-plane length calibrations

5. Calibration Procedure

17

• Seven 2D data traces are extracted from a 3D data set

• For Traces a, a, e, and e– Enter into the data sheet

• The uncalibrated values (x1uppert and x2uppert) for Edge 1 and Edge 2– To find xupper

» The x value that most appropriately locates the upper corner of the transitional edge is called xupper or x1uppera for Edge 1 with Trace a

• The values for n1t and n2t

– The maximum uncertainty associated with the identification of xupper is ntxrescalx» If it is easy to identify one point, nt = 1» For a less obvious point that locates the upper corner, nt > 1

• The uncalibrated values for ya and ye

– Determine the uncalibrated endpoints

6. Measurement Procedure

t indicates the data trace (e.g., a, a, e, or e)

xres = uncalibrated resolution in x-direction4/)( '' uppereuppereupperaupperaave 1x1x1x1x1x

4/)( '' uppereuppereupperaupperaave 2x2x2x2x2x

18

6. Measurement Procedure (continued)

eupperaupper 1x1x1x eupperaupper 2x2x2x

y

x

cal

cal

y

x1tan

ea yyy

Trace a΄

Trace e΄

(x1uppera΄, ya΄) (x2uppera΄, ya΄)

(x1uppere΄, ye΄) (x2uppere΄, ye΄)

Edge 2Edge 1Δy

Δx2

Δx1

α1

α2

Lmeasa΄

Lmease΄

αLmeas

Lalign

• Determine the misalignment angle, • Use the two outermost data traces (a and e)

'''' eaea 2n2n1n1n 1 1xx if , then and

and if , then and'''' eaea 2n2n1n1n 2 2xx

19

6. Measurement Procedure (continued)

• For Traces b, c, and d• Eliminate the data values at both ends of the

trace (i.e., less than x1ave and greater thanx2ave)

• Divide the remaining data into two data sets• Choose 3 representative data points

(sufficiently separated) within each data set.

• Enter into the data sheet five points:(x1F, z1F), (x2F, z2F), (x3F, z3F) = (x1S, z1S), (x2S, z2S), (x3S, z3S)

• x1F is slightly larger than x1ave

• (x2F, z2F) is located near an inflection point• (x3F, z3F) = (x1S, z1S)

x3F is at or near the x-value with the max or min y-value• (x2S, z2S) is located near an inflection point• x3S is slightly smaller than x2ave

z

x1F x3F= x1S x3Sx2F x2S

x1avex2ave

Data Derived from Trace b, c, or d

(x1F, z1F)

(x2F, z2F)

(x3F, z3F) = (x1S, z1S)

(x2S, z2S)

x(x3S, z3S)

20

6. Measurement Procedure (continued)• Account for the misalignment angle, , and the x-calibration

factor• The v-axis is used to measure the length of the beam• x1ave, x1F, x2F, x3F = x1S, x2S, x3S, and x2ave

become f, g, h, i, j, k, and l, respectively, along the v-axis

Trace a΄

Trace e΄

Edge 2Edge 1

gh

i

jk

lLoffset/2

Loffset/2

x3F calx = x1S calxx2S calx

x3S calx

x2F calx

x1F calx x2ave calx

α

L

Lalign

f=x1ave calx

v

• L=Lalign + Loffset = l – f + Loffset

• Endpoints: v1end = f – Loffset/2 v2end = l + Loffset/2

f=x1avecalxg=(x1Fcalxf)cos+fh=(x2Fcalxf)cos+fi=(x3Fcalxf)cos+fj=(x2Scalxf)cos+fk=(x3Scalxf)cos+fl=(x2avecalxf)cos+f

21

6. Measurement Procedure (continued)• Two cosine functions are used to model the out-of-plane shape of the beam

to obtain the curved length, Lc

• Plot the data with the model using the following equations:

• If the data doesn’t match the plot, try one or more different data points

FF

F1F sAz

gi

ivwsAz

3cos

1cos

F1

F3F1F w

zzsA

To find w1F, consult ASTM E 2245s = 1 (for downward bending beams)s = 1 (for upward bending beams)

To find w3S, consult ASTM E 2245

1cos

3S

1S3SS w

zzsA

SS1

S3S3S sAz

ik

kvwwsAz

cos where i < v < v2end

where v1end < v < i

22

Consult the reference (NISTIR 6779) for a derivation.

nrcorrectiort LLL 1/ 00

3/rdrcrbr

22220 )/(12/)/(12 tLLLLLLLL ececc

(for one trace)

where

6. Measurement Procedure (continued)

23

• Find Data Sheet RS.3– On the MEMS Calculator website (Standard Reference Database 166)

accessible via the NIST Data Gateway (http://srdata.nist.gov/gateway/) with the keyword “MEMS Calculator”

– Note the symbol next to this data sheet. This symbol denotes items used with the MEMS 5-in-1 RMs.

• Using Data Sheet RS.3– Click “Reset this form”– Supply INPUTS to Tables 1 through 5– Click “Calculate and Verify”– At the bottom of the data sheet, make sure all the pertinent boxes say

“ok.” If a pertinent box says “wait,” address the issue and “recalculate.”

– Compare both the inputs and outputs with the NIST-supplied values

7. Using the Data Sheet

24

• If your criterion for acceptance is:

whereDr positive difference between the residual strain value

of the customer, r(customer), and that appearing on theROI, r

Ur(customer) residual strain expanded uncertainty of the customerUr residual strain expanded uncertainty on the ROI, UROI

8. Using the MEMS 5-in-1To Verify Residual Strain Measurements

22)()( rcustomerrrcustomerrr UUD

• Then can assume measuring residual strain according to ASTM E2245 according to your criterion for acceptance if:– Criteria above satisfied and– No pertinent “wait” statements at the bottom of your Data Sheet RS.3