technical report exp14at rev f · 2016-01-19 · technical report exp14at rev f title: e31 test...

Radiant Technologies, Inc.

2835B Pan American Freeway NE

Albuquerque, NM 87107

Tel: 505-842-8007

Fax: 505-842-0366

e-mail: [email protected]

www.ferrodevices.com

1

Technical Report

EXP14AT

Rev F

Title: e31 Test Fixture for Reference Piezoelectric Cantilevers

Date: May 21, 2015

Author: Joe Evans

Summary: A second version of Radiant’s e31 test fixture was recently completed. The modifications from

the first prototype allow more room for inserting and removing the sample cantilever. The slot

holding the cantilever is longer, giving it a firmer base. The foot has been re-designed to clamp

the cantilever more evenly and precisely at the edge of the shoe. A micrometer mechanism has

been added to the fixture to accurately set the vertical position of non-contact displacement

sensors above the cantilever tip. Since the cantilever under test can now be re-loaded and

clamped into exactly the same physical position and the displacement sensor probe can be re-

positioned to exactly the same vertical position above the cantilever tip each time, measurements

between loads are almost indistinguishable. Small decays in the butterfly loops of a new

cantilever as a function of the first few cycles can now be resolved from the test results. I made

measurements of Radiant’s 1µm-thick 4/20/80 PNZT. The new fixture yields a slightly higher e31

coefficient than with the initial version of the fixture, -13C/m2. I attribute this change to the

improvement of the micropositioner that holds the MTI photonic sensor wand and a change in the

way the foot clamps the cantilever. Radiant MOD 52/48 PZT 0.5µm-thick yielded an e31

coefficient of -19.3C/m2 at 7 volts.

The 2nd

prototype was demonstrated at the International Workshop on Acoustic Transduction

Materials and Devices (IWATMD 2015) at Penn State University last week. The display

continued into the International Conference on Electroceramics (ICE 2015) that followed the

IWATMD at the same location. I had the complete fixture along with sample cantilevers and an

MTI photonic displacement sensor so during lulls in the meetings I was able to program Vision to

run tests hours long and gather data I thought interesting. I also received recommendations from

attendees about the fixture and its applications.

The sections below will describe the test fixture, the e31 test procedure, the sample geometry

necessary to operate in the test fixture, and the results of the tests.

Radiant Technologies, Inc. 2

e31 Test Fixture

The e31 test fixture will allow Radiant’s tester customers to determine the e31 coefficient for their

films. The fixture configuration is below. The tester drives the cantilever capacitor with a

hysteresis measurement while capturing the displacement of the cantilever tip with a

displacement sensor. The results can be inserted into a derivation of the Stoney formula to

calculate e31.

The cantilever must fit a certain geometry to work inside the prototype. Bob Howard modeled

this geometry after my original “bender” design created back in 2001.

Fig. 1: e31 fixture aligned with test cantilever

The dimensions of the original test cantilevers from 2001 are below.

Fig. 2: Dimensions of the original test cantilever

75mm

5mm

20mm

4mm to 10mm

TE BE PZT

Drive

Return

Earth

Ground


The goal of the original procedure for fabricating cantilevers was to 1) make the cantilevers large

enough to handle by hand and 2) minimize the amount of photolithography required in their

construction. The procedure for the original cantilevers is listed below.

1. Coat a silicon wafer with global platinum bottom electrode.

2. Deposit the ferroelectric film globally.

3. Fabricate patterned platinum top electrodes.

4. Etch a single large square through the ferroelectric across the wafer to expose BE.

5. Dice the cantilevers with a saw. They will be 5mm wide and 75mm long.

6. The TE forms a long stripe 3mm wide by 5mm long over the global bottom electrode.

The fabrication process for these extremely simple structures requires only one precision mask,

the TE mask. Since it is over global bottom electrode, the TE mask needs no alignment mark to

the BE. The second masking for the PZT etch is not a precision alignment and does not need

alignment marks. The PZT etch exposes the BE platinum for contact and has a significant

amount of tolerance for misalignment. This masking step so simple it can be accomplished by a

placing a strip of metal or tape on the wafer by eye to act as a shadow mask during

photolithographic exposure.

The cantilevers as fabricated on-wafer are diagrammed below. The cantilevers are disarticulated

by dicing. The dicing paths are shown as red dotted lines. Black and Gray lines are the top

electrode platinum pattern on each wafer. The cantilevers are large to allow physical handling

when placing them into and removing them from the e31 fixture.


Fig. 3: Dicing pattern for disarticulating cantilevers directly from a 100mm wafer

One such wafer recently completed by Naomi Montross in Radiant’s fabrication facility is

photographed in Figure 4. The cantilevers are still mounted on the dicing tape, forming the

outline of the 4-inch silicon wafer. The saw lines in the wafer are visible as is the reflection of

the camera in the exposed bottom electrode.

5mm

Dicing Line

15mm

5mm

5mm

Etched PZT


Fig. 4: Completed and diced test cantilever wafer for this experiment

The cantilevers slip into the shoe of the e31 fixture of Figure 5a. A foot at the end of a jack

screw clamps the end of the cantilevers into the foot from above. Bending only occurs outside

the shoe/foot clamp. A different shoe/foot combination will be provided for cantilevers made

with bulk materials that have an electrode on the bottom side of the cantilever. The front clamp

can be seen flush with the shoe block in Figure 5b.

Pogo pins in the foot provide electrical power to the piezoelectric capacitor on the cantilever top

surface. Pogo pins are spring mounted and extend out of an outer shell. They retract into the

shell when pressed. The pogo pins on the foot have approximately 0.5mm of play remaining

once the foot is pressed firmly down on the sample. The pins should make contact with the

electrodes without placing undue strain on the cantilever.

The e31fixture provides attachment points for several types of displacement sensors to measure

tip motion. The second prototype test fixture in Figure 5a and Figure 5b is shown without its

anodized black coating or its circuit board. This prototype is fitted with a special

micromanipulator to hold in place the sensor wand of an MTI Photonic sensor. The

micromanipulator is a new addition to the second e31 prototype and it works very well. Vertical

positioning is precise and there is no drift of the wand position. I have successfully run Vision

Test Definitions overnight with this latest version of the fixture using the micromanipulator

vertical positioning mechanism. We are working now with several other companies to provide a

range of sensor options with resolutions extending from a few nanometers to microns. Other

sensor types include LVDTs and laser vibrometers.

This particular MTI sensor has a maximum sensitivity of 0.5 micrometers per volt that will

measure down to 5 Ångstrom when connected to a Radiant Precision Premier II or Precision

Multiferroic. The cantilever tips I subsequently tested moved distances up to 12 microns which


were too far to use the higher resolution setting of this particular instrument. I switched to the

lower resolution setting of 5 micrometers per volt. In cases where the cantilever consists

completely of bulk ferroelectric or piezoelectric material, the cantilever tip may move more than

20 or 30 microns so even lower resolution instruments may be used.

Fig. 5a: Second generation e31 test fixture with cantilever and MTI Displacement Sensor


Fig. 5b: Close-up of the sample mounting foot, a cantilever,

and the sensor vertical adjustment mechanism.

Cantilever Design and Fabrication

The original design of the cantilevers will work for Radiant but not for most of our customers.

The reason is that the capacitor area of the original design is 1.5 cm2. This area is far too large

for most of our customers to yield functional capacitors that are not shorted. In our original 2002

experiment, only a few of these simple cantilevers yielded because of the large area. Given the

improvements in our process flow since that time, the most recent lot of cantilevers exhibited

very high yield. Nevertheless, the design of the cantilevers provided to our customers must allow

for small capacitor areas so customers with young programs can achieve functional devices. To

accomplish this, we will not use a global BE layer but instead provide a BE pattern arranged so

that the TE pad that electrically contacts the e31 boot is over a hole in the BE. With this

geometry, the only TE over BE will be outside the cantilever holder clamp. There will be no

parasitic capacitance in this design. All capacitance will contribute to actuator motion.


Fig. 6a: Proposed capacitor structure for the commercial e31 fixture. The blue rectangles are both top electrode platinum.

These geometries will require a more complex mask layout. At least three and possible five

layers will be involved in fabrication so alignment marks and a photolithographic printer will be

required. For those customers with the appropriate resources, we will simply provide them with

the GDSII files so they can create their own masks. For those without the sophisticated processes

necessary to recreate these patterns on wafer, we can provide the bottom electrode wafers for

them to deposit their films. If the customers cannot do top electrodes, Radiant can receive the

wafers back and deposit/pattern top electrodes on those wafers. Radiant can then pattern the

wafers with photoresist for the piezoelectric film etch. The wafers must be sent back to the

customers for the ferroelectric etch so Radiant does not have to deal with modifications to its

waste stream for any toxic materials in customer films. Radiant can dice the final wafers and

send them back to the customers for testing. Of course, there may be other combinations of

services that Radiant supplies in between these two extremes. The fabrication services that

Radiant will provide coupled with the improved electrode geometries should make it possible for

even the smallest university material science program to make, test, and publish results from their

piezoelectric films.

One aspect of the dicing is that the length and width of the cantilever dimensions shown in the

diagrams represent dimensions before dicing. The width of the trench in the shoe of the fixture

will hold a cantilever very slightly more than 5mm wide (5.1mm). Therefore, dicing exactly on

5mm lines between the cantilevers will 1) ensure that the cantilevers fit snugly in the foot of e31

fixture and 2) ensure that the cantilevers can be replaced in the exact same position each time to

ensure reproducibility in the results. Measurement reproducibility is the bane of piezoelectric

measurement. It is the reason Radiant took so long to develop such a fixture. We had to find

fixture/sample geometry that would minimize variances between re-loadings. This new fixture

can be shipped to the other side of the world and be correct on the first measurement made out of

the shipping container.

An exciting characteristic of the design of this fixture is that a variety of top electrode geometries

can be used. The active capacitor area of the top electrode in the new mask geometry will occur

only where TE crosses over BE. This arrangement will allow us to make parallel-plate capacitor

actuators with a wide range of areas. The bottom electrode can be eliminated altogether to allow

75mm

5mm

25.4mm

4mm to 10mm Bending Moment (42mm)

Sensor Sample Point

Etched

Electrical Contact Points

Clamp


the testing of actuators with interdigitated electrodes. For parallel-plate actuator capacitors, the

“hole” in the bottom electrode platinum prevents the formation of parasitic capacitance that does

not contribute to actuator motion. For the capacitor shown in Figure 6a, all charges measured

during a hysteresis/butterfly loop will be generated in the active actuator area. Direct comparison

of charge to displacement will be possible allowing calculation of the g piezoelectric coefficient.

Figure 6b below shows a capacitor constructed with interdigitated electrodes and another with a

long but super narrow top electrode.

Fig. 6b: Other possible cantilever configurations.

In Figure 6, the active area of the piezoelectric capacitor is the blue portion of the top electrode

that overlays bottom electrode. It is much shorter and narrower than the cantilever itself. It has a

smaller capacitor area than if the top electrode covered the entire cantilever and thus it has a

much higher chance of yielding functionality, especially with thin films. This will make possible

the piezoelectric characterization of very thin piezoelectric or ferroelectric films which cannot

support large capacitor areas. The bending motion for smaller capacitors may be tiny but this

small motion will be amplified by the long length of the silicon cantilever beyond the end of the

actuator capacitor. This amplified motion will be visible to laser vibrometers which have

resolutions down to 20pm or less. On the other hand, as already described, some cantilevers with

large-area actuator capacitors will move as much as 12 to 20 microns, allowing the use of low

cost low resolution displacement sensors. A major attribute of the e31 fixture will be its ability to

test a variety of actuator geometries at a variety motion scales.

Area = 1mm2

Area = 100µm2


In summary:

1. The e31 fixture will accept cantilevers with a variety of actuator designs.

2. The 75 millimeter length of the cantilever amplifies the piezoelectric response of thin

films to the point that even films only a few hundred Ångstroms thick will still be

measurable.

3. Customers with sophisticated tools and processes will be able to design and test their own

cantilever and actuator architectures.

4. Other customers will be able to acquire from Radiant the standard mask layout (Figure 6)

for a standardized cantilever architecture, acquire their own masks, and fabricate their

own devices.

5. For those customers with less sophisticated processing capabilities, Radiant will fabricate

and sell prepared bottom electrode wafers.

6. Some researchers that can fabricate films but have no photolithography or metal

deposition capabilities, Radiant will perform the process steps they cannot.


Test Procedures There are two test procedures to be executed with Radiant’s e31 fixture. The first is an indirect

measurement where the tester executes a hysteresis measurement on the capacitor of the test

cantilever while simultaneously capturing the displacement of the cantilever tip using any one of

several types of displacement sensors. The cantilever motion and voltage will be inserted into a

formula to derive the e31 coefficient. The basis for the calculation will be the Stoney formula.

The year 2009 marked the 100th anniversary for the derivation of this formula by George Gerald

Stoney describing the bending motion of a cantilever caused by a thin film on its surface. Stoney

developed this equation to describe the effects of changes of temperature where the two materials

have different coefficients of thermal expansion. More recently, several researchers have

published treatments of the Stoney formula for use in deriving e31 from piezoelectric actuations as

opposed to temperature changes. For calculations in this document, I will use two different

published treatments to determine the e31 of a Radiant test cantilever and compare the results.

As a matter of historical perspective, George Gerald Stoney was the son of

George Johnstone Stoney. George Johnstone Stoney was a physicist who in the

1870’s was the first to propose a fundamental unit for electrical charge. He

named it the electron in 1891. The electron particle was found by J. J. Thompson

of the Cavendish Laboratory in 1897. I visited the site of the Cavendish

Laboratory during one of my visits to England. Alas, it is now but a sign on a

university office building. To continue, the senior Stoney in 1881 proposed a

unification of physics built around electric charge and mass to calculate the

fundamental scales. Nine years after Stoney named the electron, Max Planck in

1900 proposed the quantization of energy of which the electron is but one form.

Einstein’s astounding revelations came five years later in 1905. Modern physics

began with Einstein and Planck. Planck’s approach with his constant is now

considered the proper method for unifying physics at all scales versus Stoney’s

proposal but it is interesting to find that none of these famous scientists operated

in a vacuum. Was Planck influenced by Stoney’s prior work on unification or did

both build from someone else’s work? No matter. Radiant’s e31 fixture has four

degrees of separation from Einstein, three from Planck, and two from the

discovery of the electron!

The second type of test that can be executed with the e31 fixture is the direct d31 measurement.

This is accomplished by forcing the cantilever tip to move while recording the charge generated

by the piezoelectric capacitor as it is stressed. For this purpose, the center crossbar of the test

fixture is configured to hold a linear piezoelectric actuator to move the cantilever tip.

The tester will capture the charge generated by the capacitor when the cantilever is displaced

when the linear motor is commanded to move a certain distance. The displacement sensor will

measure how far the tip displaces to eliminate the effect of backlash in the motor. The charge

measurement and the displacement along with the geometry of the cantilever can be used to

derive d31 for the piezoelectric film. I have not yet researched methods for this mathematical

derivation. That will be a future development project for the test fixture.


Fig. 7: The 2

nd prototype after black anodization with the piezoelectric linear displacement motor

mounted under the cantilever tip.

The printed circuit board mounted on the pedestal connects the sample to the tester using coaxial

cables. The bottom socket is for a banana plug so the fixture can be grounded to the tester earth

ground.


Experimental Results

I connected the e31 fixture to a Precision LC II and inserted an MTI displacement probe into its

collar. I inserted two types of test cantilevers (Figure 4) into the fixture. One consisted of 1µm-

thick 4/20/80 niobium-doped PZT. The other consisted of 0.5µm 52/48 PZT with the same

1.5cm2 electrode configuration. I used the low resolution channel of the MTI2032RX with a

resolution of -10.3 µm/volt for the scale factor.

Three 2-second hysteresis loops with their associated butterfly loops for the 1µm PNZT are in

Figure 8. Reproducibility is excellent.

Fig. 8: Sequential butterfly loops without re-loading for 1µm PNZT

Six 1-second monopolar actuator motions of the PNZT taken from the same test definition

execution by Vision are in Figure 9.

-30

-20

-10

0

10

20

30

-20 -15 -10 -5 0 5 10 15 20

4/20/80 Bipolar and M onopolar Uniformity[ EXP14AT e31 Fixture ]

Po

lari

za

tio

n (

µC

/cm

2)

& M

icro

ns

V o l tage

advPx1 20V 2s B ipolar: Polarizat ion (µC/cm2): 2 advPx1 20V 2s B ipolar: Polarizat ion (µC/cm2): 4 advPx1 20V 2s B ipolar: Polarizat ion (µC/cm2): 6

advPx1 20V 2s B ipolar: Polarizat ion (µC/cm2): 2 advPx1 20V 2s B ipolar: Polarizat ion (µC/cm2): 4 advPx1 20V 2s B ipolar: Polarizat ion (µC/cm2): 6


Fig. 9: Sequential monopolar loops without re-loading for 1µm PNZT

The red dashed line represents a calculation of the displacement of the cantilever from its

maximum to its landing point at the end of the test. The red line has a magnitude of 15.5µm at 20

volts.

Figures 10 and 11 show the same measurements for the 0.5µm-thick 52/48 film.

0 .0

2 .5

5 .0

7 .5

10 .0

12 .5

15 .0

17 .5

20 .0

0 .0 2 .5 5 .0 7 .5 10 .0 12 .5 15 .0 17 .5 20 .0

4/20/80 Bipolar and M onopolar Uniformity[ EXP14AT e31 Fixture ]

Po

lari

za

tio

n (

µC

/cm

2)

& M

icro

ns

V o l tage

ad vPx1 20V 1s M o n o : P o l ari zat i o n (µC/cm 2): 1 ad vPx1 20V 1s M o n o : P o l ari zat i o n (µC/cm 2): 2 ad vPx1 20V 1s M o n o : P o l ari zat i o n (µC/cm 2): 3

ad vPx1 20V 1s M o n o : P o l ari zat i o n (µC/cm 2): 4 ad vPx1 20V 1s M o n o : P o l ari zat i o n (µC/cm 2): 5 ad vPx1 20V 1s M o n o : P o l ari zat i o n (µC/cm 2): 6


Fig. 10: Sequential butterfly loops without re-loading for 0.5µm 52/48

-20

-15

-10

-5

0

5

10

15

20

-7 .5 -5 .0 -2 .5 0 .0 2 .5 5 .0 7 .5

52-48 Bipolar and M onopolar Uniformity[ EXP14AT e31 Fixture ]

Po

lari

za

tio

n (

µC

/cm

2)

& D

isp

lac

em

en

t

V o l tage

ad vPx1 7V 2s B i p o l ar: P o l ari zat i o n (µC/cm 2): 2 ad vPx1 7V 2s B i p o l ar: P o l ari zat i o n (µC/cm 2): 4 ad vPx1 7V 2s B i p o l ar: P o l ari zat i o n (µC/cm 2): 6

ad vPx1 7V 2s B i p o l ar: P o l ari zat i o n (µC/cm 2): 2 ad vPx1 7V 2s B i p o l ar: P o l ari zat i o n (µC/cm 2): 4 ad vPx1 7V 2s B i p o l ar: P o l ari zat i o n (µC/cm 2): 6


Fig. 11: Sequential monopolar loops without re-loading for 0.5µm 52/48

The red dashed line represents a calculation of the displacement of the cantilever from its

maximum to its landing point at the end of the test. The red line has a magnitude of 17.9µm at 7

volts.

I tested the mechanical reproducibility of this second version of the e31 fixture by running six

loops in a row on a single sample. I removed and replaced the sample back into the fixture every

second loop. To remove the sample, I had to move the MTI sensor tip so that after reloading the

sample I had to execute another calibration the MTI. The vertical micrometer on this fixture

allowed me to reposition the displacement sensor to the same position each time. The result is

that the sample measurements were absolutely reproducible. Of note is that this sample was

brand new and had seen only three cycles prior to this test. At this point in its life, it will decay

on each new cycle. That property is visible in Figure 12. The first loop of the test has the

maximum value at Vmax. For each subsequent loop, the displacement value of Vmax decreased

slightly. The decrease occurred whether the cantilever remained in the fixture (even tests) or was

re-loaded (odd tests).

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7

52-48 Bipolar and M onopolar Uniformity[ EXP14AT e31 Fixture ]

Po

lari

za

tio

n (

µC

/cm

2)

& D

isp

lac

em

en

t

V o l tage

ad vPx1 7V 1s M o n o : Po l ari zat i o n (µC/cm 2): 1 ad vPx1 7V 1s M o n o : Po l ari zat i o n (µC/cm 2): 2 ad vPx1 7V 1s M o n o : Po l ari zat i o n (µC/cm 2): 3

ad vPx1 7V 1s M o n o : Po l ari zat i o n (µC/cm 2): 4 ad vPx1 7V 1s M o n o : Po l ari zat i o n (µC/cm 2): 5 ad vPx1 7V 1s M o n o : Po l ari zat i o n (µC/cm 2): 6


Fig. 12: Two loops each from three loads: green = 1

st load, blue = 2

nd re-laod, and red = 3

rd re-load

The blue loops were from the first load. The green loops were from the second load. The red

loops were from the third load.

-5

0

5

10

15

20

-20 -15 -10 -5 0 5 10 15 20

Re-load uniformity of AdvP on e31 Fixture - 4/20/80[ EXP14AT e31 Fixture ]

Mic

ron

s

V o l ts

adv Px1 20V 2s C2: Sensor Value adv Px1 20V 2s C1: Sensor Value adv Px1 20V 2s B2: Sensor Value

adv Px1 20V 2s B1: Sensor Value adv Px1 20V 2s A2: Sensor Value adv Px1 20V 2s A1: Sensor Value

16.5

17.0

17.5

18.0

18.5

19.0

16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0

Mic

ron

s

Vol ts

advPx1 20V 2s C2: Sensor Value advPx1 20V 2s C1: Sensor Value advPx1 20V 2s B2: Sensor Value

advPx1 20V 2s B1: Sensor Value advPx1 20V 2s A2: Sensor Value advPx1 20V 2s A1: Sensor Value


Calculating e31

To convert the tip displacement to an e31 value, I turned to two published equations: one by

Mazzalai at EPFL and the other by Kanno at the University of Kobe.

The e31 equation according to Mazzalai, Balma, Chidambaram, Jin, and Muralt (EPFL)

[International Symposium on Applications of Ferroelectrics - ISAF, Prague, Czech Republic;

07/2013] is

Y = Young’s modulus of the silicon (substrate) in Gigapascals ( silicon = 169GPa)

= Poisson’s ratio for the silicon (substrate) [silicon = 0.064]

tSi = Thickness of the silicon substrate in centimeters (usually 550µm for Radiant

wafers)

tp = Thickness of the piezoelectric film in centimeters (not shown)

V = Volts applied to piezoelectric capacitor

cf = Ratio of capacitor width to cantilever width (0.6 for Radiant cantilevers)

x1 = Distance from clamp point to the end of the piezoelectric capacitor in meters.

x2 = Distance from clamp point to the displacement sensor.

(x2) = Vertical displacement of the cantilever at x2 in meters.

To find the assumed-to-be-uniform stress (in N/m2 = Pa) in the volume of an actuator below the

top electrode, multiply the e31 value by the applied electric field [V/ tp in meters].

For the reference cantilever in the e31 fixture,

x1 = 3.96cm

x2 = 4.24cm

Note: all dimensions entered into the equation should be in meters and the result will be in units

of C/m2.


Plugging in the fixed geometry values, the equation reduces to

Mazzalai Test Volts Tip Displacement e31

1µm 4/20/80 PNZT 20 15.5µm -13.13 C/m2

0.5µm 52/48 PZT 7 7.9µm -19.32 C/m2

Below I calculate e31 using the equation published by Kanno, Kotera, and Wasa of Kyoto

University. [Sensors and Actuators A 107 (2003) 68–74]

Since s11S

is the compliance of silicon which is the inverse of the Young’s modulus, the equation

can be re-written as

HS = Thickness of the silicon substrate

L = Length of the cantilever

V = Volts applied to the capacitor

= Tip displacement

Yielding the simple equation:

Kanno’s predictions are below.


Kanno Test Volts Tip Displacement e31

1µm 4/20/80 PNZT 20 15.5µm -7.35 C/m2

0.5µm 52/48 PZT 7 7.9µm -10.7 C/m2

The calculated e31 values for Mallazai and Kanno are very different by almost a factor of 2. Note

that there is a difference in the stress generated by the thin film between these two equations. The

Mazzalai equation assumes that the piezoelectric capacitor stops short of the displacement sample

point (the difference between x1 and x2) while the Kanno equation assumes that the capacitor

extends the entire length of the L. Kanno also assumes that the capacitor is the same width as the

cantilever. Below I will adjust the Kanno equation for these differences in geometry and compare

results.

Analysis Compare the two equations:

Mazzalai

Kanno

The Mazzalai equation has two extra terms than does the Kanno equation:

(1- )cf

which corrects the e31 value if the capacitor is not as wide as the silicon cantilever and

x1(2x2 – x1)

which corrects e31 if the capacitor does not extend all the way to the test point. The second term

reduces to

x12

if the capacitor extends all the way to the displacement sensor which is the identical term to

Kanno’s

L2.

The Mazzalai cf term increases e31 if the piezoelectric capacitor is not as wide as the cantilever

itself. This makes sense. Consider if the capacitor were only 1 micron wide while the cantilever


is 5 mm wide (as it is for our test sample). That 1µm-wide capacitor could not bend the

cantilever up nearly as far as does our 3mm-wide capacitor.

The only term in Mazzalai not in the Kanno equation is ¸which is the Poisson ratio for silicon.

The Poisson ratio is the ratio of how the width of the material reduces if its thickness increases

due to an applied force. This value should be in the equation so Mazzalai is probably more

precise. However, the value Mazzalai gave for silicon is only 0.064 which means that Mazzalai

corrects e31 by a value of only 7%. Putting all of factors together yields a correction factor of

0.56406. Applying these geometric corrections to Kanno yields the following comparison:

Kanno Mazzalai Kanno Kanno (adjusted)

1µm 4/20/80 PNZT -13.13 -7.35 -13.13

0.5µm 52/48 PZT -19.32 -10.7 -19.13

The Kanno and Mazzalai interpretations of the Stoney equation are not the only possibilities. Dr.

Jan Smits, an IEEE Fellow for MEMs, has observed that more complex models may be needed to

account for the stress created in the cantilevers by the electrodes of the capacitors. Over time and

with the help of the community, Radiant can offer in Vision a variety of electromechanical

models for the cantilevers to provide ever more accurate estimations. The structure of Vision is

such that new formulas can be easily added to the Library and evaluated by the community.

Vision The Advanced Piezo Task in Vision already provides the tools for capturing the displacement of

the cantilever tip simultaneously with the capacitor polarization. Radiant need only add a Data

Filter task to the Vision Library that will automatically calculate e31 from measurements made by

the Advanced Piezo Task. The user enters the geometry and material property parameters into

the filter menu. During execution, Advanced Piezo passes its measurements results to the e31

Filter Task for the calculation to take place. The e31 Filter Task should be able to pass its results

to the Single Point Filter Task so users create Branch-Loop Test Definitions that will measure and

plot e31 as a function of voltage, frequency, and/or temperature.

The e31 Filter Task should offer at least the Mazzalai and Kanno equations as options for

calculating e31. We may add other formulas to the task as we investigate this subject further. We

will certainly get customer feedback on optimizing the calculation.

The programmability of Vision allows sophisticated measurements to be made unattended by the

researcher. The plot below is one of nested butterfly loops of the 52/48 cantilever made at the

IWATMD meeting.


Fig. 13: Nested butterfly loops for the 52/48 cantilever measured with 10 second periods.

The cantilever is well behaved.

Other Tests Radiant has been developing PAINT and DLTS tasks for Vision. In these impulse-type tests, a

pulse is applied to the sample, the voltage returns to zero, and the tester listens for echoes from

the sample. When applied to a cantilever in the e31 fixture, the cantilever rings at its resonant

frequency.

-1

0

1

2

3

4

5

6

7

8

9

10

-7 .5 -5 .0 -2 .5 0 .0 2 .5 5 .0 7 .5

Displacement vs Volts0.5 um 52/48 PZT on 75mmx5mm Cantilever

Mic

ron

s

P e r iod (m s )

adv P 8V 75m s : S ens or V al: 1 adv P 8V 75m s : S ens or V al: 2 adv P 8V 75m s : S ens or V al: 3 adv P 8V 75m s : S ens or V al: 4 adv P 8V 75m s : S ens or V al: 5 adv P 8V 75m s : S ens or V al: 6 adv P 8V 75m s : S ens or V al: 7

adv P 8V 75m s : S ens or V al: 8 adv P 8V 75m s : S ens or V al: 9 adv P 8V 75m s : S ens or V al: 10 adv P 8V 75m s : S ens or V al: 11 adv P 8V 75m s : S ens or V al: 12 adv P 8V 75m s : S ens or V al: 13 adv P 8V 75m s : S ens or V al: 14


Fig. 14: Non-switching pulse and ringing of the 52/48 cantilever.

Like the nested butterfly loops of Figure 13, the impulse response of the cantilever can be

measured versus voltage.

0.0

2.5

5.0

7.5

0

2

0

2

4

0 10 20 30 40 50 60 70

Im p u lse R e sp o n se fo r 4 m s 4 V P u lse[ 0.5um 52/48 Cantilever ]

Po

lari

za

tio

n (

µC

/cm

2)

Mic

ron

sD

riv

e V

olt

s

Pr oc. Hys t Pr oc. Dis p Dr ive Voltage


Fig. 15: Non-switching pulse and ringing of the 52/48 cantilever.

Dynamic models of cantilever motion will be more complex than derivatives of the Stoney

equation which is a static model. Nevertheless, dynamic measurements of the

cantilever/piezoelectric capacitor combination may yield more information about the films and

the effects of the electrodes and passivation layers on the performance of the actuators.

Conclusion The second version of the e31 fixture is acceptable for distribution to customers. The GDSII files

for that mask set are still to be created but should be available by the be. Radiant should prepare

inventory of pre-fabricated BE wafers for the cantilevers for inventory. The possibility of using

wafers thinner than the 500µm-thick standard prime wafers should be explored.

Experimental results with two different compositions produce e31 results that indicate that the

Kanno and Mazzalai equations are equivalent to within 6% of each other when geometry is taken

into account . Both formulas can be placed as options in a Vision filter task to estimate e31 from

the measurement results made by Vision’s Advanced Piezo Task. More formulas may be added

as we get feedback from researchers.

-2

-1

0

1

2

3

4

5

10 15 20 25 30 35 40 45

Cantilever Displacement after 4ms 4.9V Pulse0.5 um 52/48 PZT on 75mmx5mm Cantilever

Mic

ron

s

P e r iod (m s )

U P 8V 75m s : 1 U P 8V 75m s : 3 U P 8V 75m s : 5 U P 8V 75m s : 7 U P 8V 75m s : 9

U P 8V 75m s : 12 U P 8V 75m s : 14 U P 8V 75m s : 16 U P 8V 75m s : 18 U P 8V 75m s : 20

technical report exp14at rev f · 2016-01-19 · technical report exp14at rev f title: e31 test...

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