Lecture 11: Piezoelectric Sensors & Actuators - …mech466/MECH466-Lecture-11.pdf · During normal operation, a piezoelectric material is either strained (to create an electric potential)

1

MECH 466Microelectromechanical Systems

University of VictoriaDept. of Mechanical Engineering

Lecture 11:Piezoelectric Sensors & Actuators

© N. Dechev, University of Victoria

2

Origin of direct and inverse piezoelectricity

Crystal properties of piezoelectric materials

Governing equations of piezoelectricity

Commonly used piezoelectric materials and their properties

Examples of piezoelectric sensors and actuators making use of cantilever beams

Examples of piezoelectric sensors and actuators making use of thin plates and membranes

Overview


There are many macro-scaled applications using piezoelectric materials. These include:(a) The ‘quartz resonator’ for use as a timing standard

- The frequency of the oscillator is determined by the cut and shape of the quartz crystal.

- Miniature encapsulated tuning forks which vibrate 32,768 times per second

3

Macro-Scale Piezoelectric Applications


(b) Sensors [1] based on ‘quartz resonators’ to measure physical phenomena such as: temperature, applied force (stress) and fluid density, among others.

(c) Ultrasonic transceivers for marine sonar.(d) Ultrasound systems for non-invasive biomedical

imaging.(e) The needles of record players(f) microphones

4

Macro-Scale Piezoelectric Applications


[1] E.P. Eernisse, R.W. Ward, R.B. Wiggins, “Survey of Quartz Bulk Resonator Sensor Technologies”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 3, May 1988

Direct Effect of Piezoelectricity- a mechanical stress on a material produces an electrical

polarization

Inverse Effect of Piezoelectricity- an applied electric field in a material produces dimensional

changes and stresses within a material.

In general, direct piezoelectricity and inverse piezoelectricity are both referred to as piezoelectric effects.

5

Definition of Piezoelectric Effect


The microscopic origin of piezoelectricity is the displacement of ionic charges within a crystal.

Symmetric (centrosymmetric) lattice structure does not produce piezoelectricity when deformed.

Asymmetric lattice structures will create an electric potential when deformed

6

Origin of Phenomena of Piezoelectric Effect


Unstrained Strained(no net charge change)

PositiveCharge Site

NegativeCharge Site

Unstrained Strained(charges cause potential change)

[ Diagrams - Chang Liu]

Piezoelectric effects are strongly dependent on the crystal orientation w.r.t. the strain/electric field.

In most cases, one particular orientation exhibits the strongest piezoelectric effect.

The direction of positive polarization is customarily parallel with the z-axis (i.e. the Poling axis is parallel to the z-axis)

The standard piezoelectric notation used is such that the x, y and z axes correspond to subscripts 1, 2, and 3, respectively.

7



[ Diagram from ‘Foundations of MEMS’, Chang Liu]

∆L

Therefore, if the electric field is applied parallel with the z-axis it is applied in ‘direction 3’.

Note: The resulting strain generated due to an electric field in direction 3, is parallel with the x-axis (direction 1).

Conversely, if a strain is applied in direction 1, the generated electric field will occur parallel to direction 3.

8



x

z

E

In its natural state, a piezoelectric material, such as quartz, is likely in a polycrystalline configuration with grains (domains) that are randomly oriented in various directions, as shown:

Since the domains are randomly oriented, the ‘net’ piezoelectric effect due to strain (or applied voltage) is zero.

9

Creation of Piezoelectric Materials


Magnified Image of Quartzite [Dept. of Geology and Geophysics, U. of Minnesota]

In order to create a ‘net’ piezoelectric effect, the material must be:

(a) a pure crystal (difficult to realize in most cases)

(b) the crystal domains must be brought into alignment

Poling: is a method aligning the crystal domains of piezoelectric materials.

During Poling, the material is exposed to a very strong electric field, and is simultaneously baked at an elevated temperature, which causes the domains to become aligned in the desired orientation.

This alignment (also known as polarization) is sensitive, and a material can become depolarized if it is subjected to extreme mechanical stress, electric fields or temperatures.

10

Creation of Piezoelectric Materials


During normal operation, a piezoelectric material is either strained (to create an electric potential) or is subjected to an electric potential (to create a strain).

However, care must be taken to operate the material within the parameters specified by the manufacturer.

Electrical depolarization can occur if a piezoelectric material is subjected to extreme electric fields (or voltages) which will cause it to lose (or significantly degrade) its piezoelectric effects.

Mechanical depolarization can occur if a material is excessively strained to the point where the crystal domains are significantly disturbed.

Thermal depolarization can occur if a material subjected to temperatures beyond the ‘Curie point’ of the material. A safe operational temperature is about half the Curie point temp.

11

Operational Limits of Piezoelectric Materials


Consider operation with the ‘direct piezoelectric effect’

If a material is strained, a charge will build up on opposite faces of the crystal:

You can think of a piezoelectric crystal like a ‘capacitor’ that generates charge on the upper and lower surfaces when you strain it, as shown in the diagram.

12

Actual Operation of Piezoelectric Materials


x

z

∆L

+ + + + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - -

+V *** as long as charge remains***

Piezoelectric ceramics tend to be very good insulators (i.e. poor conductors), so the charge will tend to remain on the upper and lower surfaces.

Continuing on with our ‘capacitor analogy’...

It is well known that there will be some finite amount of electric leakage of charge from one surface to another. (i.e. even capacitors will eventually loose their charge).

More importantly, if we try to do work with the developed potential (+V), buy connecting it to a load, current will flow to do the work. Therefore, the accumulated charge will drain, and the developed potential will drop.

13

Actual Operation of Piezoelectric Materials


The direct effect of piezoelectricity can be described by the general equation:

14

Governing Equations of Piezoelectric Effect


⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

333231

232221

131211

6

5

4

3

2

1

363534333231

262524232221

161514131211

3

2

1

EEE

TTTTTT

dddddddddddddddddd

DDD

εεε

εεε

εεε

EdTD ε+=Where: D - Electrical Polarization (C/m2) T - Stress Vector (N/m2) d - Piezoelectric Coefficient Matrix ε - Electrical Permitivity Matrix (F/m) (*Note: this is NOT strain*) E - Electric Field Vector (V/m)

The direct effect of piezoelectricity can be simplified down to the following equation, in the absence of an external electric field (i.e. E=0).

15



€

D = dT

€

D1D2

D3

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

=

d11 d12 d13 d14 d15 d16d21 d22 d23 d24 d25 d26d31 d32 d33 d34 d35 d36

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

T1T2T3T4T5T6

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

16© N. Dechev, University of Victoria

dESTs +=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

+

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

3

2

1

362616

352515

342414

332313

322212

312111

6

5

4

3

2

1

666564636261

565554535251

464544434241

363534333231

262524232221

161514131211

6

5

4

3

2

1

EEE

dddddddddddddddddd

TTTTTT

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

ssssss


The inverse effect of piezoelectricity can be described by the general equation:

Where: s - Strain Vector S - Compliance Matrix T - Stress Vector (N/m2) d - Piezoelectric Coefficient Matrix E - Electric Field Vector (V/m)



The inverse effect of piezoelectricity can be simplified to the following expression, if there is no additional mechanical stress present (i.e. T=0). Where strain is related the electric field by:

€

s = dE

€

s1s2s3s4s5s6

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

=

d11 d21 d31d12 d22 d32d13 d23 d33d14 d24 d34d15 d25 d35d16 d26 d36

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟

E1E2

E3

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥



The units of the piezoelectric constant, dij, are the units of electric displacement over the unit of the stress. Therefore:

Recall that:

Therefore the piezoelectric constant is a good way to measure the intensity of the piezoelectric effect, since we can think of it in terms of Columbs generated, per Newton applied.

€

V = Et

Where: V - Voltage E - Electric Field t - distance of interest through E

NColumb

mNmV

mF

TE

TDd ====

2

33 ][]][[

][][][ ε

ij

Si is symmetric and does not exhibit piezoelectricity.(Si: positive charge; bond electrons: negative change)

GaAs lattice is not symmetric and exhibits piezoelectricity.(However, GaAs has poor piezoelectric material properties)

19

Commonly Used Piezoelectric Materials


Crystal Structure of diamond and GaAs [Chang Liu]

ZnO- sputtered thin film- d33=246 pC/N

Lead zirconate titanate (PZT)- ceramic bulk, or sputtering thin film- d33=110 pC/N

Quartz- bulk single crystal- d33=2.33 pC/N

Polyvinylidene fluoride (PVDF)- polymer- d33=1.59 pC/N.



Diagram of a ‘Sputtering System’ for depositing piezoelectric materials onto wafers, [Chang Liu]



Table 7.2 Properties of Selected Piezoelectric Materials[From ‘Foundations of MEMS’, Chang Liu]

Material Relativepermitivity(dielectricconstant)

Young’smodulus

(GPa)

Density(kg/m3)

Couplingfactor (k)

Curietemperature

(oC)

ZnO 8.5 210 5600 0.075 **

PZT-4(PbZrTiO3)

1300-1475 48-135 7500 0.6 365

PZT-5A(PbZrTiO3)

1730 48-135 7750 0.66 365

Quartz(SiO2)

4.52 107 2650 0.09 **

Lithiumtantalate(LiTaO3)

41 233 7640 0.51 350

Lithiumniobate(LiNbO3)

44 245 4640 ** **

PVDF 13 3 1880 0.2 80


Issues with Piezoelectric Materials

Curie temperature- temperature above which the piezoelectric property will be lost.

Material purity- the piezoelectric constant is sensitive to the composition of the

material and can be damaged by defects.

Frequency response- most materials have sufficient leakage and cannot “hold” a DC

force. The DC response is therefore not superior but can be improved by materials deposition/preparation conditions.

Bulk vs thin film- bulk materials are easy to form but can not integrate with MEMS

or IC easily. Thin film materials are not as thick and overall displacement is limited.

23

Bi-Layer Bending Configuration:

Where: Ap and Ae are the cross-section areas of the piezoelectric and the elastic layer, Ep and Ee are the Young’s modulus of the piezoelectric and the elastic layer, and tp and te are the thickness of the piezoelectric and the elastic layer


Example of Piezoelectric Cantilever Beam

2))(())((4

))((21

epeeppeeppeepp

eeppeplong

ttEAEAEAEAIEIE

EAEAttsr ++++

+=

24

Diagram of Bi-Layer Beam:







Cr/AuSi3N4

ZnOSi3N4

Cr

27

A patch of ZnO thin film is located near the base of a cantilever beam, as shown in the diagram below. The ZnO film is vertically sandwiched between two conducting films.

The length of the entire beam is l. It consists of two segments: A and B. Segment A is overlapped with the piezoelectric material while segment B is not. The length of segments A and B are lA and lB, respectively.

If the device is used as a force sensor, find the relationship between applied force F and the induced voltage.


Example #2: ZnO Piezoelectric Force Sensor

28

Axis 3 of the deposited ZnO is normal to the front surface of the substrate it is deposited on. A transverse force would produce a longitudinal tensile stress in the piezoelectric element (along axis 1), which in turn produces an electric field and output voltage along axis 3.

The stress along the length of the piezoresistor is actually not uniform and changes with position. For simplicity, we assume the longitudinal stress is constant and equals the maximum stress value at the base. The maximum stress induced along the longitudinal direction of the cantilever is given by:

Where the stress component is parallel to axis 1.

According to Equation 2, the output electric polarization in the direction of axis 3 is:

The overall output voltage is then:

with Tpiezo being the thickness of the piezoelectric stack.


Example #2: Solution

beambeam IFltIMt 2/)2/(max,1 ==σ

max,1313 σdD =

beam

piezobeampiezopiezo I

tFlttDtEV

εε 23

3 === d31

Please read the article titled: “The Daintiest Dynamos” for homework.

The article is available for download in the “Supplementary Notes” area on the Mech 466 web-site.

We will discuss this interesting proposed concept next class.

Specifically, we will look at the proposed solution, the benefits, and the problems.


Homework:

Documents

Lecture 11: Piezoelectric Sensors & Actuators - …mech466/MECH466-Lecture-11.pdf · During normal operation, a piezoelectric material is either strained (to create an electric potential)