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Characterizing Ferroelectric Materials

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Radiant Technologies, Inc. Characterizing Ferroelectric Materials Joe T. Evans, Radiant Technologies, Inc. March 7, 2011 www.ferrodevices.com Based on the tutorial at ISAF-ECAPD ‘10
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Page 1: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.

Characterizing FerroelectricMaterials

Joe T. Evans,Radiant Technologies, Inc.

March 7, 2011www.ferrodevices.com

Based on the tutorial at ISAF-ECAPD ‘10

Page 2: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.2

Tutorial Outline

• Introduction

• A device model for non-linear capacitors

• Instrumentation theory

• Definitions of tests

• Fatigue and Imprint

• Conclusion

Page 3: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.3

Radiant Technologies, Inc.

• Radiant Technologies pursues thedevelopment and implementation of thinferroelectric film technology.– Test Equipment: Radiant supplies ferroelectric

materials test equipment world-wide.

– Thin Films: Radiant fabricates integrated-scaleferroelectric capacitors for use as test references andcommercial products.

Page 4: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.4

The Presenter• Joe T. Evans, Jr.

• BSEE – US Air Force Academy in1976

• MSEE – Stanford University in1982

• Founded Krysalis Corporation and built the firstfully functional CMOS FRAM in 1987

– Holds the fundamental patent for FRAM architecture

• Founded Radiant Technologies, Inc in 1988.

Page 5: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.5

An Excellent Hysteresis Loop

• This loop is nearly “perfect”. Most loops are not. Afterthis presentation, you should be able to discern thedifference upon inspection.

-10

0

10

20

30

40

50

60

70

80

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 6: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.6

What is this?

• Is this loop as good as the previous loop?

-10

0

10

20

30

40

50

60

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

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 7: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.7

What is this?

• Real clean. This one is easy.

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 8: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.8

A Harder One

-20

-10

0

10

20

30

40

50

60

-4 -3 -2 -1 -0 1 2 3 4

Pola

rizat

ion

(µC

/cm

2)

Voltage

• Quite a few papers include loops that look like this.

Page 9: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.9

Is this Ferroelectric?

0

250

500

750

1000

1250

1500

1750

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 10: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.10

What Happened Here?

0

10

20

30

40

50

60

70

80

90

100

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 11: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.11

• In electrical engineering, a fundamental approachto understanding a system is to break it intocomponents and model each component.

– Each component responds independently to thestimulus.

– The output of a component is either the input to anothercomponent or is summed with the outputs of othercomponents to form the response of the device.

Modeling Nonlinear Capacitance

Page 12: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.12

• According to Joe:– Linear capacitance– Non-linear capacitance– Remanent polarization– Remanent and nonremanent leakage– Remanent and nonremanent small signal capacitance– Reverse bias diode electrode interfaces– Left-overs

The Components

Page 13: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.13

A Mathematical ToolThe hysteresis loop is polarization responding to appliedvoltage: P(V). Its derivative with respect to voltage is

δP/δV => (δQ/δV)/Area

Which equals Large Signal Capacitance per Unit Area.RT17 Normalized C(V)

-80

-60

-40

-20

0

20

40

60

80

-12 -9 -6 -3 0 3 6 9 12

Vdrive

RT17 Hysteresis

RT17 nC(V)

3500Å 20/80 PZT

RT17 Hysteresis

-80

-60

-40

-20

0

20

40

60

80

-12 -9 -6 -3 0 3 6 9 12

Vdrive

RT17 Hysteresis

3500Å 20/80 PZT

Page 14: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.14

Normalized CVThe normalized CV [nCV] has the formula

δP/δV => (δQ/δV)/Area

and has the units of

µF/cm2

when the derivation is performed on the polarization units of

µC/cm2.

Page 15: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.15

Integration

• Some measurements determine capacitance.– Small signal capacitance vs. Voltage

• Mathematical integration will convert the capacitance to itsequivalent polarization contribution at each voltage.

• This is the inverse operation to the normalized CV functionfrom the previous slide.

Page 16: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.16

Linear Capacitance

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Pola

rizat

ion

(µC

/cm

2)

Voltage

• Q = CxV where C is a constant

Page 17: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.17

0

1

2

3

4

5

6

7

8

9

10

11

12

-4 -3 -2 -1 -0 1 2 3 4

1nF Linear Capacitor

uF/c

m^2

Voltage

Derivative of Linear Capacitance

• C is a constant slope so the derivative of linear capacitanceis simply a vertical offset on the nCV plot.

Page 18: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.18

Capacitance vs Frequency• Capacitance is about separation of charge!

– Electrons are fast (light speed!).– Atoms are slow!– Domains are real slow!

Capacitance

Domains

Nuclei

Electrons Frequency

Page 19: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.19

Non-linear Capacitance

• When the electric field begins to move atoms in the lattice,the lattice stretches, changing its spring constant.Capacitance goes down with increasing voltage

-40

-30

-20

-10

0

10

20

30

40

-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

Radiant 9/65/35 PLZT[ 1700A ]

Pola

rizat

ion

Volts

Page 20: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.20

The Derivative

A non-linear capacitor has decreasing capacitance as the appliedvoltage increases.

0

1

2

3

4

5

6

7

8

9

10

-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

nCV of 9/65/35 PLZTuF

/cm

^2

Volts

Page 21: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.21

0

1

2

3

4

5

6

7

8

9

10

-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

nCV of 9/65/35 PLZTuF

/cm

^2

Volts

Linear Capacitance Component

Linear vs. Non-linear Capacitance

This device has both linear and non-linear capacitance. The linearcapacitance is the vertical offset of the nCV plot so that the non-linearcapacitance does not reach zero.

Page 22: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 22

Math Model for Non-remanentCapacitance

Non-remanent capacitance is the sum of linear capacitance (C•V) plusa non-linear capacitance which decreases with increasing voltage. Thenon-linear capacitance may be adequately modeled with a Gaussiandistribution with a mean of zero volts.

Eq(1)

•PNR is the non-remanent component.

•Pnlc is the polarization contributed by the non-linear capacitance.

•The rate at which the non-linear capacitance decreases with voltage isset by the variance parameter σ.

[ ]linearnon

V

nlclinearLNR ePVCP−

⎟⎟

⎜⎜

⎥⎥⎦

⎢⎢⎣

⎡+•= 2

2

2

22

1 σ

πσ

Page 23: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.23

Remanent Polarization• The PUND test is a familiar measurement:

• Any matched pair of switched and non-switched pulses may besubtracted from each other to get the remanent (spontaneous)polarization.

Drive Voltage

Time

PresetPulse

DelayPeriod

±Vmax

PositiveSwitched

Pulse

PositiveUnswitched

Pulse

NegativeSwitched

Pulse

NegativeUnswitched

Pulse

Page 24: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.24

Remanent Hysteresis• The same measurement may be made using half-hysteresis

loops instead of pulses:

• The difference between the switching and non-switching measurementswill give the Remanent Polarization vs Voltage function loop.

Switching Non-switching

1/2Period

Page 25: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.25

Switching and Non-switching half loops:Switching & Non-switching Loops

0

10

20

30

40

50

60

70

0 1 2 3 4 5Volts

uC/v

m̂2

SwitchingNon-switching

Remanent Hysteresis

Page 26: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.26

• PUND: P*r - P^r = dP = Qswitched• Hysteresis: Switching - Non-switching = Remanence

• Note in the graph that the non-switching measurement was moved toalign with the top of the switching measurement.

Remanent Hysteresis Calculation

-10

0

10

20

30

40

50

60

70

0 1 2 3 4 5Volts

uC/v

m̂2

SwitchingDifferenceNon-Switching

RemanentHalf Loop

Remanent Hysteresis

Page 27: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.27

• The test may be executed in both voltage directions and the two halvesjoined to show the switching of the remanent polarization that takesplace inside the full loop.

Remanent Hysteresis

-40

-30

-20

-10

0

10

20

30

40

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Remanent Hysteresis[ Type AB WHITE ]

Pola

rizat

ion

(µC

/cm

2)

Voltage

Unswitched - Logic 0 Switched - Logic 1 Remanent

Page 28: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.28

Remanent vs. Normal Hysteresis

-30

-20

-10

0

10

20

30

-4 -3 -2 -1 0 1 2 3 4

1 Second Hyst vs 1 second Rhyst[ Radiant Type AB White, 9V preset ]

Pol

ariz

atio

n

Voltage

+4V 1s Rhyst: Polarization (µC/cm2) -4V 1s Hyst: Polarization (µC/cm2)

+4V 1s Hyst: Polarization (µC/cm2)

• The remanenthysteresis is in blue.

• The standardhysteresis loop is inred.

• The Vc of theremanent loop liesoutside that of thenormal loop. Why?(Hint: the reason ispurely mathematical.)

• The Vc of theremanent loop is thetrue coercive voltage.

Page 29: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.29

The Derivative

• The nCV of the remanent polarization loop rests on the X-axis because it has no capacitance on its re-trace.

0

50

100

150

200

250

300

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

nCV of Remanent Hysteresis Loop[ Type AB ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Remanent

Page 30: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.30

The Perfect Capacitor• A perfect capacitor combines non-linear capacitance with

remanent polarization. The blue line is the standard loop.

-1

0

1

2

3

4

5

6

7

8

9

10

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

Remanent Hysteresis[ 1u 4/20/80 PNZT ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Switched - Logic 1 Remanent

Page 31: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 31

Math Model for RemanentPolarization

Remanent polarization may be adequately modeled as a normaldistribution of small discrete remanent polarization units where each unithas its unique switching voltage threshold.

•PR is the remanent polarization.

•PS is the maximum switchable spontaneous polarization.

•The width of the switching peaks in the nCV is set by the σ parameters.

( ) ( )

⎟⎟⎟

⎜⎜⎜

+

⎟⎟⎟

⎜⎜⎜

⎟⎟⎟

⎜⎜⎜

⎥⎥

⎢⎢

⎡−

⎥⎥

⎢⎢

⎡= −

+

+

+

2

2

2

2

2

2

2

2

12

2

1 σ

πσ

σ

πσ

cc VVVV

sR eePP

Page 32: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 32

Math Model for RemanentPolarization

• Define the remanent polarization as consisting of small units ofpolarization where each has its own switching threshold whichdefines where it sits under either of the ±distribution curves in Eq(2).

• PS is the sum of all remanent polarization units.

• All of PS fits under one distribution curve but can be dividedbetween the two distribution curves by the action of applied voltages.

P

V

P

Distribution after negative Vsat

Distribution after positive Vsat

Page 33: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 33

Math Model for RemanentPolarization

• When a voltage increases under a portion of one or the other of thedistribution curves, any polarization units under that curve at thatvoltage at that time will switch polarity, that is, jump to the otherdistribution curve.

• PR is the difference of the population of polarization units under eachdistribution curve.

P

VDistribution after negative Vsat followed by voltage < +Vc

+Distribution Envelope-Distribution Envelope

Page 34: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 34

Math Model for RemanentPolarization

• It is possible using custom voltage profiles to create uniquedistributions of remanent polarization units between the two curves.

• As an example, given a ferroelectric capacitor with symmetricalswitching in both directions having the following parameters:

σ = 0.5vVc = 2v,

99% of the remanent polarization will switch between 0.5v and 3.5v.

• Applying the following voltage sequence, [-5,+2.5,-1.5] will leavethe remanent polarization distribution looking as below:

P

V

Page 35: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 35

Hysteresis in other Properties

• It is reasonable to assume that the remanent polarizationstate will affect other properties of the capacitor, givingthose properties hysteresis as well.

• This is true for small signal capacitance and DC leakage.

• The effect of remanent polarization on these two propertiesare described in the following panels.

Page 36: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.36

Hysteresis in Small SignalCapacitance

• The small signal capacitance versus bias voltage isdetermined by measuring the sample capacitance with alow amplitude signal at a series of bias voltages.

– Theoretically, the signal amplitude should be small enough that itdoes not disturb the state of the capacitor.

• While this is a noble effort, it cannot be ignored that theremanent polarization modulates the small signalcapacitance.

• The state of the remanent polarization must be managedduring measurements of small signal capacitance.

Page 37: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 37

Small Signal vs Large Signal

• The ferroelectric hysteresis measurement is defined at Radiant as a“large signal” measurement of the polarization properties of the sample.

• “Large signal” means that the test waveform has a large enoughamplitude to switch dipoles in the ferroelectric material.

• As well, the “large signal” measurement captures and integrates allchanges the sample experiences during the test waveform, showing itsentire trajectory.

• The measurement result contains contributions from all components ofthe sample, including the remanent polarization and parasitics.

Page 38: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 38

Small Signal vs Large Signal

• A “large signal” measurement captures every electron that moves intoor out of the capacitor during the stimulus waveform.

Integrate theentire signal

V

t

Page 39: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 39

Small Signal vs Large Signal• The “small signal” measurement is defined as one where the test

amplitude is small compared to that required to switch remanentpolarization in a ferroelectric capacitor.

• Since the response of a non-linear sample changes with the absolutevalue of the voltage applied and the remanent polarization state, the“small signal” measurement must also have a steady state voltagecomponent as well as a remanent polarization pre-set procedure to putthe sample in the appropriate state.

• Therefore, the “small signal” measurement captures and integrates onlythose changes the sample experiences during a small amplitudestimulation of the sample at a specified voltage and polarization state.

By definition, the “small signal” measurement contains no contributionfrom switching dipoles!

Page 40: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 40

Small Signal vs Large Signal

• In “small signal” measurements, many small measurements are taken thatcapture only the small changes associated with small stimuli.

• In a “small signal” measurement, the sequence of DC bias values is the same asthe voltage profile used for hysteresis so the two can be compared directly.

V

t

Integration periods.

Page 41: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 41

Small Signal vs Large Signal• Radiant testers execute both standard “large signal” hysteresis and

“small signal” capacitance measurements.

– “large signal” hysteresis results are normally given in units ofpolarization (µC/cm2) but can be converted to capacitance usingthe CV or Normalized CV plotting functions of the HysteresisTask or the Hysteresis Filter.

– “small signal” measurements are normally given in units ofcapacitance (nF or µF/cm2) but can be converted to equivalentpolarization using the appropriate plotting function of theAdvanced CV measurement task.

Page 42: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 42

Small Signal vs Large Signal• Comparison of the Hysteresis and Polarization of the Small Signal

Capacitance is shown below:

Large and Small Signal Polarization

-60

-40

-20

0

20

40

60

-4 -2 0 2 4

Vdrive

Pola

rizat

ion

(uC

/cm

2)

Hysteresis SSAC

100ux100u900A 20/80Pt/PZT/Pt

Hysteresis = 1KHzSSAC = 4KHz

Page 43: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 43

Small Signal vs Large Signal• Comparison of the Large and and Small Signal Capacitance is shown

below:

Large and Small Signal Capacitance Density

-100

102030405060708090

-4 -3 -2 -1 0 1 2 3 4Vdrive

nC(V

) (uF

/cm

2)

HysteresisSSAC

100ux100u900A 20/80Pt/PZT/Pt

Hysteresis = 1KHzSSAC = 4KHz

Page 44: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.44

Stimulus

time

Switching

Stimulus

time

Non-switching

Hysteresis in Small SignalCapacitance

Page 45: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.45

Stimulus

time

Non-switching

Stimulus

time

Switching

Hysteresis in Small SignalCapacitance

Page 46: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.46

• 1KHz 0.2V test with 182 points

Non-switching CV for the Sampleunder Test

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

Non-switching Small Signal CV[ Radiant Type AB WHITE ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Page 47: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.47

• 1KHz 0.2V test with 182 points

Switching CV for the Sampleunder Test

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

Switching Small Signal CV[ Radiant Type AB WHITE ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Page 48: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.48

• 1KHz 0.2V test with 182 points

Non-switching vs Switching CV

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

1KHz SW vs nSW CV[ Radiant Type AB White, 9V preset ]

uF/c

m^2

Volts

1ms 4V CV nSW: Capacitance (nF) 1ms 4V CV SW: Capacitance (nF)

Page 49: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 49

Q vs V from Small SignalCapacitance

• The small signal capacitance can be multiplied bythe dV to get the dQ per test step.

• The dQs may be integrated to see the polarizationhysteresis contributed by the modulation of smallsignal capacitance by remanent polarization!

Page 50: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 50

Small Signal CapacitancePolarization

• Small signal capacitance forms a hysteresis of its own.

Page 51: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 51

Small Signal CapacitancePolarization

• The contribution of small signal capacitance hysteresis to the overallloop is small in this case.

Page 52: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 52

Resistive Leakage in a HysteresisLoop

Linear resistance is easy for a triangle wave: ∆P=(Current• ∆time)/Area∴Pi=(Σk

n=0 n • ∆V/R± • ∆t)/Area

∆time=time step per point

∆V=fixed voltage step oftriangle wave

n = point number of digitized triangle wave

Result = “Football” ( R+ ≠ R- )

PLT_F DC Leakage Response

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

-5 -4 -3 -2 -1 0 1 2 3 4 5

Vdrive

PLT_F Leakage

1200Å 4/20/80 PNZT

Page 53: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 53

Resistive Leakage in a HysteresisLoop

The derivative of pure resistive leakage is an “X”.

-2.0

-1.5

-1.0

-0.5

-0.0

0.5

1.0

1.5

2.0

-4 -3 -2 -1 -0 1 2 3 4

Hysteresis of Linear Resistor[ 2.5Mohm 4V 1ms ]

Pola

rizat

ion

Voltage

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

-4 -3 -2 -1 -0 1 2 3 4

nCV of Linear Resistance[ 2.5Mohm 4V 1ms ]

uF/c

m^2

Voltage

Page 54: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 54

IV Test

• The IV, or Current vs Voltage, test is a series of leakage testsexecuted over the voltage profile used for the traditionalhysteresis loop.

V

tThe red line indicatesthe period during whichthe leakage through thesample is measuredafter a soak period.

Page 55: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.55

Hysteresis in Leakage• Leakage in ferroelectric materials does not have to be linear.• Leakage can have its own hysteresis modulated by remanent

polarization.

-1110

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-110

010

-4 -3 -2 -1 0 1 2 3 4

Switched vs Unswitched 1s IV[ Radiant Type AB BLUE ]

Cur

rent

(am

ps)

Volts

4V 1s nSW IV: Current (Amps) 4V 1s SW IV: Current (Amps)

Page 56: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.56

Leakage vs CV vs RemanentPolarization

Hysteresis Parameters

-40

-30

-20

-10

0

10

20

30

40

50

-6 -4 -2 0 2 4 6

Volts

uC/c

m^2

, uA

/cm

^2, u

F/cm

^2

Rhyst

SW CV*10

nSW CV*10

SW IV*2.5

nSW IV*2.5

Page 57: Characterizing Ferroelectric Materials

Radiant Technologies, Inc.57

Leakage vs CV vs RemanentPolarization

nCV Parameters

-5

0

5

10

15

20

25

30

35

40

-6 -4 -2 0 2 4 6Volts

uF/

cm^2

, uA

/cm

^2, u

F/cm

^2

SW CV*10

nSW CV*10

SW IV*2.5

nSW IV*2.5

RnCV/4

Page 58: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 58

Something Left OverIf we measure the remanent polarization, small signal capacitance, andleakage and then subtract them from the full loop, something is left over:(Note the change in Y-axis scales in the graphs below.)

This is the source of the “gap” in the hysteresis loop!

PLT_F Left Overs!

-15

-10

-5

0

5

10

15

-5 -4 -3 -2 -1 0 1 2 3 4 5

Vdrive

Measured - Mode

1200Å 4/20/80 PNZT

PLT_F Components vs Measured Hysteresis

-40

-30

-20

-10

0

10

20

30

40

-5 -4 -3 -2 -1 0 1 2 3 4 5

Vdrive

Model

Full Hysteresis

1200Å 4/20/80 PNZT

Page 59: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 59

Reversed Bias Diodes• A platinum-electrode-based capacitor has two opposing diodes at the

ferroelectric/platinum interface, one of which is always turned off.

• In reverse bias, a diode has a constant current independent of appliedvoltage. See the ideal diode equation below.

Eq(3)

whereVD = the voltage across the diodeVT = the Boltzmann thermal voltageIS = the diode saturation current

When VD is negative, the equation reduces to

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1T

DVV

SD eII

( ) SSD III −=−= 10

Page 60: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 60

Reversed Bias Diodes• The constant current delivers the same amount of charge per unit time

to the test instrument independent of the voltage.

• When tested with a triangle wave where ∆V/ ∆t is constant, thereverse-biased diode thus looks like a capacitor when voltage isincreasing and a negative capacitor when the voltage is decreasing!

1N4002 Diode Conduction

-0.04

0.00

0.04

0.08

0.12

0.16

0.20

0.24

0.28

0.32

0.36

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Anode Voltage

1N4002Reverse Bias Conduction

Forward BiasConduction

C(V) / A

V

Translated toC(V) plot

Page 61: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 61

Reversed Bias Diodes• The hysteresis and nCV of two back-to-back 1N4002 diodes are

plotted below.

• The nCV shows the positive/negative capacitance signature of thediodes translated up by the capacitance of the diodes.

Page 62: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 62

Reversed Bias Diode Breakdown• The derivative of a polarization hysteresis loop clearly shows the

contact diode reverse-biased leakage effect and breakdown of thecontact if it is present.

• The leakage of diode reverse-biased breakdown is marked byexponentially increasing current. This produces a “trumpet flare”instead of the “X” of linear leakage.

RN101B at 14V with Vdrive = Top Electrode

0

10

20

30

40

-15 -12 -9 -6 -3 0 3 6 9 12 15

Vdrive

14V RN101B

Beginning of Low CurrentBreakdownDiode Leakage

Page 63: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 63

The Components• Remanent polarization• Linear small signal capacitance (dielectric constant)• Nonlinear small signal capacitance (dielectric constant)• Hysteretic small signal capacitance (remanent polarization

modulation)• Linear resistive leakage• Hysteretic resistive leakage• Electrode diode reverse-biased leakage• Electrode diode reverse-biased exponential breakdown

All of these components are visible in the derivative of thepolarization hysteresis loop!

Page 64: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 64

What is this?

Now let’s analyze some capacitors!

Page 65: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 65

An Excellent Hysteresis Loop

• The nearly “perfect” loop. 20/80 PZT on platinum.

-10

0

10

20

30

40

50

60

70

80

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 66: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 66

An Excellent Hysteresis Loop

• The 20/80 PZT on platinum is so square that the instantaneouscapacitance increases by x250 or more during switching.

0

50

100

150

200

250

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

20/80 PZT on Platinum[ 0.26u thick ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Page 67: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 67

What is this?

• Is this loop as good as the previous loop? Yes! It is 4/20/80PNZT, a different composition from 20/80 PZT. So, it has adifferent shape.

-10

0

10

20

30

40

50

60

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

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 68: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 68

0

5

10

15

20

25

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

4/20/80 PNZT[ 1u thick ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

What is this?

• This loop is good for 4/20/80 PNZT but it is less square than20/80. Note the extra “diode” leakage in the tails that make thesaturated tips of the loop open up. This is the effect of theniobium doping.

Page 69: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 69

What is this?

• A 1nF linear capacitor assigned an arbitrary 10-4 cm2 area.

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 70: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 70

0

1

2

3

4

5

6

7

8

9

10

11

12

-4 -3 -2 -1 -0 1 2 3 4

1nF Linear Capacitor

uF/c

m^2

Voltage

What is this?

• The linear capacitor in nCV format! 1nF with an area of10-4 cm2 yields a capacitance density of 10µF/cm2.

Page 71: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 71

A Harder One

-20

-10

0

10

20

30

40

50

60

-4 -3 -2 -1 -0 1 2 3 4

Pola

rizat

ion

(µC

/cm

2)

Voltage

• Quite a few published papers include loops that look likethis.

Page 72: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 72

A Harder One

• It is only a resistor with a linear capacitor in parallel.

0

5

10

15

20

-4 -3 -2 -1 -0 1 2 3 4

Linear Resistor || Linear CapacitorN

orm

aliz

ed C

apac

itanc

e (µ

F/cm

2)

Voltage

Page 73: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 73

Is this Ferroelectric?

0

250

500

750

1000

1250

1500

1750

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 74: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 74

Is this Ferroelectric?

• Yes, it is! See the ferroelectric switching peaks stickingout of the resistive leakage “X”.

-200

-100

0

100

200

300

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5

Ferroelectric Capacitor || Linear Resistor[ Test Period = 2 seconds ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Page 75: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 75

What Happened Here?

0

10

20

30

40

50

60

70

80

90

100

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

Pola

rizat

ion

(µC

/cm

2)

Voltage

Page 76: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 76

What Happened Here?

• Different electrodes on each interface means a different switchingcharacteristic with direction. No linear leakage but classic back-to-back diodeleakage. Surface diode breakdown occurred at one of theelectrode/ferroelectric interfaces.

-15-10-505

101520253035

-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0

PZT on Nickel Lanthanate - 300ms Period[ EXP09BQ Rev A ]

Nor

mal

ized

Cap

acita

nce

(µF/

cm2)

Voltage

Page 77: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 77

Gotcha!

• What is this??? Is it some kind of breakdown???

0

250

500

750

1000

1250

-5 -4 -3 -2 -1 0 1 2 3 4 5

uF/c

m^2

Voltage

Hyst 100ms: Polarization (µC/cm2): 2

Page 78: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 78

Partial Switching!

• It is a sub-saturated loop which can sometimes look like breakdown.

0

250

500

750

1000

1250

-5 -4 -3 -2 -1 0 1 2 3 4 5

Nested Loops[ LSCO/PNAT/LSCO ]

uF/c

m^2

Voltage

Hyst 100ms: Polarization (µC/cm2): 2 Hyst 100ms: Polarization (µC/cm2): 4

Page 79: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 79

Partial Switching!

• Here are the hysteresis loops.

-1500

-1000

-500

0

500

1000

1500

-5 -4 -3 -2 -1 0 1 2 3 4 5

Nested Loops[ LSCO/PNZT/LSCO ]

Pola

rizat

ion

Voltage

Hyst 100ms: Polarization (µC/cm2): 2 Hyst 100ms: Polarization (µC/cm2): 4

Page 80: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 80

Triangle Wave• All of the modeling described above is dependent upon

using a triangle wave to stimulate the sample.

• ∆V/ ∆t is constant.

nCV = ∆Q/ ∆V

I = ∆Q/ ∆t ≈ ∆Q /k ∆V = k x nCV

• This is the reason that Vision on Radiant testers alwaysdefaults to the triangular test profile!

Page 81: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 81

Conclusion of Components• Geometry is everything, well almost.

• The ferroelectric hysteresis loop may be broken down intoindependent components.

• The mathematical derivative of the PE loop is a tool thatallows identification by inspection of the componentscontributing to the response of the sample.

• Practice makes perfect.

Page 82: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 82

Instrumentation

• The capacitor under test is never alone.

• It is part of a larger circuit that includes the tester stimulusand measurement circuitry.

• The measurement results include contributions by thestimulus circuit, the measurement circuit, the fixture, or allthree.

• The next section discloses how to recognize the tester’scontribution.

Page 83: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 83

The DUT Model of FeCaps• The non-linear capacitor under test generates a new charge

state for every new voltage state.

• The device may be modeled as a voltage controlled chargesource.

• Infinite impedance may be considered to exist between thevoltage input and charge output of the Device Under Test.

StimulusVoltage

Q(v)

Capacitor

Page 84: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 84

The DUT Model of FeCaps• Any electrical device may be modeled in this manner but

its output must be mapped into polarization space asdescribed earlier in the modeling section of this tutorial.

• NOTE: Since an infinite impedance exists between theinput of this DUT model and its output, the input has noknowledge of the output! It could be 2 volts or 1500 voltsor a magnetic field. The input only sees changes in thecharge state.

StimulusVoltage

Q(v)

Capacitor

Page 85: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 85

The DUT Model of FeCaps• To test this device, a test instrument must have

An arbitrary waveform generator to stimulate the DUT.

A charge measurement circuit to capture the chargestate.

• That architecture is shown on the next page.

StimulusVoltage

Q(v)

Capacitor

Page 86: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 86

Test System Diagram

Digital toAnalog

Converter

Analog toDigital

Converter

HostComputer

Power Supply(±15V, 5V, 3.3V)

AWFG

Electrometeror

Ammeter

Page 87: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 87

The Subsystems

• Host computer• Communications channel• DAC (bits, speed)• Output circuit (current limit and frequency)• Cable• Fixture• Cable (virtual ground)• Input circuit (current limit and frequency)• ADC ( bits, speed)• Memory (width, depth, bits, location)

Page 88: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 88

The Test Circuit•To the left is oneexample of a testpath for aferroelectrictester.

•This is thecircuit for theRadiant EDU, avery simpletester.

•The EDU usesan integratorcircuit to collectcharge.

+-

R1

R2

R3

DAC

+

-ADCY Channel

SenseCapacitor

DischargeSwitch

CurrentAmplifier

ADCX Channel

Input

Page 89: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 89

Another Test Circuit•This circuit uses atransimpedanceamplifier to createthe virtual ground.

•On both thiscircuit and theEDU circuit theinput amplifierforces the input toremain at ground.

ADCY Channel

+-

R1

R2

R3

DAC

+

-

SenseResistor

ADCX Channel

Input

Page 90: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 90

Virtual Ground Circuit

• The charge amplifier in the figure above generates an output voltageproportional to the amount of charge that has flowed into or out of itsinput node.

• The output of the amplifier always acts to force the “-” node to equalthe “+” node, or ground. Hence, the name “virtual ground”.

IntegratingCapacitor (Ci)

Vout =-∆QCi Ci

Device Under Test +

-Op Amp

Input node

Rule: V+ ≡ V-

Page 91: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 91

Virtual Ground Circuit

• The transimpedance amplifier in the figure above generates an outputvoltage proportional to the current flowing into or out of its input node.

• This circuit also maintains a “virtual ground” on its input node.

Feedback Resistor

Vout =-Iin x R Capacitor under test +

-Op Amp

Input node

Rule: V+ ≡ V-

Page 92: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 92

The Virtual Ground• Electrons in the wire connected to the virtual ground input

move freely into or out of that node in response to outsideforces.

• The virtual ground input has no blocking force to thatmovement, i.e. it has zero impedance.

• The transimpedance amplifier measures the flow ofelectrons into or out of its input node.

• The integrator, or charge amp, counts electrons movinginto or out of its input node.

Page 93: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 93

Mathematics• Transimpedance amplifier:

- Measures “I”

- Integrate “I” to get charge: P = ∫ I δt / Area

• Integrator:- Measures “Q”- Divide by area to get “P”

- Derivative yields current density “J”: J = [ δQ/ δt ] / Area

Page 94: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 94

Cables• Ferroelectric testers usually have BNC connectors for

attaching coaxial cables.

• Coaxial cables consist of a center wire conductorsurrounded by plastic which itself is covered with a wirebraid.

• The center conductor carries the signal.

• The outside braid is usually connected to the tester ground.

Page 95: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 95

Cables

• Op amps amplify the difference between their input nodes.

• If the coax braid is connected to the ground node, then thetest circuit ground extends to the sample!

IntegratingCapacitor (Ci)

Capacitor under test +

-Op Amp

Page 96: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 96

Cables

• Any ambient electrical noise picked up by the cable braidbecomes part of the ground reference of the op amp.

• If the same noise is picked up by the signal wire, it issubtracted out!

IntegratingCapacitor (Ci)

Coaxial Cable

+

-Op Amp

Page 97: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 97

Cables

• Where the center signal wire extends beyond the cablebraid, it can pick up noise the braid does not see.

• This noise is not common mode and is not subtracted out.

IntegratingCapacitor (Ci)

+

-Op Amp

Exposed signal wire

Coaxial Cable

Page 98: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 98

Cables

• Use coaxial cable as much as possible.

• Leave as little exposed signal wire a possible.

Page 99: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 99

Test Fixtures

• The test fixture is an intimate part of the test circuitincluding the ferroelectric capacitor.

• It can affect the results of your tests.

• The temperature and lighting of the test fixture are twosources of variance.

• Two little known issues: current injection and noise.

Page 100: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 100

Current Injection

• A tester counts electrons or meters current flow.• Any low impedance connection to the virtual ground input

can add electrons to that cable.

• The sample must be insulated from the test fixture.

IntegratingCapacitor (Ci)

Coaxial Cable

+

-Op Amp

Σ

Metal

Page 101: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 101

Noise Injection

• Any metal in a test fixture is an antenna.• Any EMF signals near the test fixture will oscillate the free

electrons in that metal. The electrons in turn re-radiate thesignal towards the sample.

• The sample will pick up the electric field, injecting thatEMF signal into the measurement.

• Solution: Make the noise signal common mode.

Connect all of the metal parts of a test fixture to theground connection of the tester.

Page 102: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 102

• The tester with no external cables or test fixture attached.

No Noise Injection – 1 Hz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

No Noise Injection - 1 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 1000ms: Polarization (µC/cm2)

Page 103: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 103

• The tester with no external cables or test fixture attached.

No Noise Injection – 10 Hz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

No Noise Injection - 10 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 100ms: Polarization (µC/cm2)

Page 104: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 104

• The tester with no external cables or test fixture attached.

No Noise Injection – 100 Hz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

No Noise Injection - 100 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 10ms: Polarization (µC/cm2)

Page 105: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 105

• With no external connections, the measurement is clean, indicating that thetester itself is injecting no 60Hz noise.

No Noise Injection – 1 kHz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

No Noise Injection - 1 kHz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 1ms: Polarization (µC/cm2)

Page 106: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 106

• 1 second test period = 60 noise cycles!

Low Noise Injection – 1 Hz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Low Noise Injection - 1 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 1000ms: Polarization (µC/cm2)

Page 107: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 107

• The tester with virtual ground shield connected to probe station table.

Low Noise Injection – 10 Hz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Low Noise Injection - 10 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 100ms: Polarization (µC/cm2)

Page 108: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 108

• The 60Hz injected noise makes this loop look like a lossy capacitor.

Low Noise Injection – 100 Hz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Low Noise Injection - 100 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 10ms: Polarization (µC/cm2)

Page 109: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 109

• With low amplitude noise, there is little apparent effect at speeds much higherthan the period of the noise.

Low Noise Injection – 1 kHz

-40

-30

-20

-10

0

10

20

30

40

-4 -3 -2 -1 -0 1 2 3 4

Low Noise Injection - 1 kHz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 1ms: Polarization (µC/cm2)

Page 110: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 110

• The tester with virtual ground signal connected to probe station table.

High Noise Injection – 1 Hz

-75

-50

-25

0

25

50

75

-4 -3 -2 -1 -0 1 2 3 4

High Noise Injection - 1 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 1000ms: Polarization (µC/cm2)

Page 111: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 111

• Six noise cycles in 100ms ≈ 16.7ms period (60Hz)

High Noise Injection – 10 Hz

-75

-50

-25

0

25

50

75

-4 -3 -2 -1 -0 1 2 3 4

High Noise Injection - 10 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 100ms: Polarization (µC/cm2)

Page 112: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 112

• The test period (10ms) is just over half of the noise period (16.7ms).

High Noise Injection – 100 Hz

-75

-50

-25

0

25

50

75

-4 -3 -2 -1 -0 1 2 3 4

High Noise Injection - 100 Hz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 10ms: Polarization (µC/cm2)

Page 113: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 113

• This type of result at a fraction of the period of the injected noise is a classicindication of external noise injection.

High Noise Injection – 1 kHz

-75

-50

-25

0

25

50

75

-4 -3 -2 -1 -0 1 2 3 4

High Noise Injection - 1 kHz[ 1nf Reference Capacitor ]

Pola

rizat

ion

Voltage

Hyst 1ms: Polarization (µC/cm2)

Page 114: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 114

Noise Injection• Recognize the signature of external noise injection.• Ground the probe station to the tester frame.• Use coaxial cable as much as possible.

• The metal table above was the “antenna” I used to inject 60Hz.

Page 115: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 115

Output circuits

• A digital-to-analog converter (DAC) accepts digital wordsfrom the computer and converts them into voltages.

• The DAC is cycled by a master clock, also set by the hostcomputer.

• No test cannot run any faster than one output voltage stepper clock tick.

Page 116: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 116

Output StimulusThe stimulus waveform

consists of a series of discrete steps

where each step is one tick of the clock.

time

OutputVoltage Point A

time

StimulusVoltage

IntegratorVoltage

One Point

Measurement

Page 117: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 117

Current Limit• The output amplifier can only generate a specified current

while maintaining the assigned voltage.

• The sample area determines how much current is neededduring the test.

I = ( ∆P x Area ) / ∆t

• Examine the measured stimulus waveform for distortion.Any variance from the triangle wave shape indicatescurrent starvation.

Page 118: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 118

Current Limit• To see if the

current limit isexceeded, lookat the outputwaveform:

0

50

100

150

-1000

0

1000

0 100 200 300 400 500 600 700 800 900 1000

One Second Test[ Bulk Ceramic Sample ]

Pola

riza

tion

(µC

/cm

2)D

rive

Volts

Time in Milliseconds

Drive Volts

Page 119: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 119

Current Limit• The same sample

tested with ashorter period.

• The currentdemand on theoutput amplifier istoo high!

0

25

50

75

-20

-10

0

10

0 10 20 30 40 50 60 70 80 90 100

100 Millisecond Test[ Bulk Ceramic Sample ]

Pola

riza

tion

(µC

/cm

2)D

rive

Volts

Time (ms)

Hysteresis Data Drive Volts

Page 120: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 120

Input circuits

• An analog-to-digital converter (ADC) converts an inputanalog voltage to a digital word on each clock pulse.

• The ADC is also cycled by a master clock, usually thesame one clocking the DAC.

• No test cannot run any faster than one input voltagemeasurement per clock tick.

The clock cannot run any faster than the maximum speed ofthe ADC or the DAC, whichever is slower!

Page 121: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 121

Amplifier Circuits• There will be one amplifier chain and DAC to generate the

output stimulus from the tester.

• There will be multiple amplifier chains and ADCS for thesignals to be measured:- The output stimulus- The virtual ground input- The output of an external high voltage amplifier- Independent external voltage signals

Displacement sensorThermocoupleForce sensor

Page 122: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 122

Amplifiers!• The amplifier stages are the most difficult part of the

design of a non-linear materials tester.

• To use a tester properly and to have confidence in theresults, you must understand how amplifiers affect yourresults.

Page 123: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 123

Amplifier Characteristics

• All amplifiers delay the signal from the input to the output.

• All amplifiers reduce the amplitude of the signal from theinput to the output.

• Distortion is the difference between 1) the true shape ofthe property being measured and 2) the measured shape ofthat property.

• Right now, it is impossible to prove after the measurementof a non-linear material that the result of the measurementis the true shape.

Page 124: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 124

Amplifier Characteristics

• The delay and amplitude reduction introduced by theamplifier is a continuous function of- the instantaneous frequency content of the signal,

- the output voltage amplitude of the amplifier, and

- the current demand on the amplifier output.

• You control these factors when you select the area of thesample and set the period of the hysteresis loop.- These two factors establish the current demand during the test.

Page 125: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 125

Amplifier Characteristics• The simplest model for amplifier effects is the

Resistor/Capacitor low pass filter.

• Voltage out = Vin ( 1 – e-t/RC)- RC can be considered the unity gain frequency of the amplifier.- 99.9% = 6.9 RC time constants- To have near perfect stimulus and response, each output clock tick

should be longer than 7 RC time constants.- A 1000 point test thus should run 7000 times slower than the unity

gain bandwidth of the amplifier!

Page 126: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 126

Amplifier Characteristics

• In short, run your tests as slow as you can tolerate.

• The slower you go, the “sharper” and “squarer” the loopwill appear.- Some of the change will be due to the tester.

- Some of the change will be due to the sample changing itsresponse with frequency.

- It is difficult to separate the two effects out accurately.

Page 127: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 127

Instrumentation Conclusion

• Know the limits of your test equipment.

• Minimize noise pick-up from the cables and test fixture.

• Choose the properly sized sample for the test that you wantto run:- Larger samples give better signal-to-noise.

- Smaller samples lower the current demand on the testequipment, lowering distortion.

Page 128: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 128

Test Definitions• Hysteresis – the polarization curve due to a continuous

stimulus signal. The signal can have any shape.

• Pulse – the polarization change resulting from a single stepup and step down in voltage. Essentially a 2-pointhysteresis loop.

• Leakage – the current continuing to pass from or throughthe sample after the polarization has quit switching.

• IV – Individual leakage tests conducted over a voltageprofile.

Page 129: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 129

Tests• Small Signal Capacitance – The polarization response of

the sample when stimulated by a voltage change smallerthan that required to move remanent polarization.

• CV – small signal capacitance measured over a voltageprofile.

• Piezoelectric Displacement – the change in dimensions ofthe capacitor during voltage actuation. Each test listedabove has its counterpart measurement of piezoelectricdisplacement.

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Reliability• Fatigue – The loss of a property of the capacitor with

repeated cycling of the capacitor around its polarizationloop. Non-switching signals may not fatigue the capacitor.

• Imprint– Changes in the hysteresis loop with time in state.It starts the instant after the first voltage is applied andnever stops.

• The changing property can be any property of the capacitor,not just polarization.

• Our model at Radiant is that memory imprint in FeRAMsand traditional capacitor ageing are the same mechanism.

Page 131: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 131

Fatigue

Fatigue causes a loss of polarization from repeated cycling of thecapacitor around its loop. Experience indicates that polarization mustswitch direction for fatigue to occur.

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Hysteresis BEFORE and AFTER Fatigue[ Radiant Type AB WHITE ]

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Voltage

Hyst AFTER Fatigue: Polarization (µC/cm2)

Hyst BEFORE Fatigue: Polarization (µC/cm2)

Page 132: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 132

Fatigue

It appears that the switching peak evaporates as fatigue progresses. Thelinear capacitance and leakage, already small before the test began,change little.

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nCV BEFORE and AFTER Fatigue[ Radiant Type AB WHITE ]

uF/c

m^2

Voltage

Hyst AFTER Fatigue: Polarization (µC/cm2)

Hyst BEFORE Fatigue: Polarization (µC/cm2)

0.0

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nCV BEFORE and AFTER Fatigue[ Radiant Type AB WHITE ]

uF/c

m^2

Voltage

Hyst AFTER Fatigue: Polarization (µC/cm2)

Hyst BEFORE Fatigue: Polarization (µC/cm2)

Page 133: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 133

Fatigue

The remanent hysteresis before and after fatigue indicates that remanentpolarization decreases substantially but some still exists after fatigue.

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Rhyst BEFORE and AFTER Fatigue[ Radiant Type AB WHITE ]

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Rhyst AFTER Fatigue: Polarization (µC/cm2)

Rhyst BEFORE Fatigue: Polarization (µC/cm2)

Page 134: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 134

Fatigue

The classic fatigue test monitors the PUND values as a function of cycles.This capacitor was cycled with a 3kHz triangle wave at 6V to produce thefatigue effect. Switched and non-switched polarization (P* & P^) areplotted above.

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3kHz Triangle Fatigue @ 6V[ Radiant Type AB WHITE ]

Pol

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Cumulative Cycles

P* (µC/cm2) P^ (µC/cm2) -P* (µC/cm2) -P^ (µC/cm2)

Page 135: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 135

Fatigue

It is the remanent polarization (P*-P^) that fatigues. The capacitor in thistest has PZT on platinum electrodes which is known to fatigue strongly.

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3kHz Triangle Fatigue @ 6V[ Radiant Type AB WHITE ]

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Cumulative Cycles

dP (µC/cm2) dPr (µC/cm2) -dP (µC/cm2) -dPr (µC/cm2)

Page 136: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 136

Fatigue-Free

Radiant PZT with LSCO electrodes does not fatigue!

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2nd Fatigue 3kHz BLUE[ LSCO-1001 BLUE TO-18 ]

Pola

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Cumulative Cycles

dP (µC/cm2) -dP (µC/cm2)

Page 137: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 137

Low Fatigue

Radiant PZT on LNO electrodes fatigues slowly.

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3kHz 9V Fatigue ORANGE [ LNO-1001 TO-18 ]

Pola

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Cumulative Cycles

dP (µC/cm2) -dP (µC/cm2)

Page 138: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 138

Imprint

The primary mechanism is the gradual growth of an internal DC bias overtime that shifts the hysteresis loop horizontally on the voltage axis. It isaccelerated by temperature. The capacitor above saw 2300 seconds at155°C between the blue loop and the red loop.

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Hysteresis Before and After 155C Imprint[ Type AB WHITE Unpackaged Die ]

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Hystersis AFTER: Polarization (µC/cm2)

Hysteresis BEFORE: Polarization (µC/cm2)

Page 139: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 139

Imprint

1x109 seconds is equal to 30 years. The imprint drift occurs constantly aslong as the capacitor remains in the same remanent polarization state.This data is of PZT on platinum electrodes, known to imprint strongly.

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Coercive Voltage Shift due to 155C Imprint[ Type AB WHITE Unpackaged Die ]

Vc

Cumulative Time (s)

Vc -Vc

Page 140: Characterizing Ferroelectric Materials

Radiant Technologies, Inc. 140

Imprint on LSCO

The addition of LSCO electrodes to Radiant’s PNZT results in a very lowimprint rate below 85°C. The plot above shows eight loops measuredover 10,000 seconds at 85°C.

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Polarization vs Time at 85C[ LSCO-1001 ORANGE ]

Pola

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Voltage

Hysteresis 9V 1ms: Polarization (µC/cm2): 1 Hysteresis 9V 1ms: Polarization (µC/cm2): 2 Hysteresis 9V 1ms: Polarization (µC/cm2): 3 Hysteresis 9V 1ms: Polarization (µC/cm2): 4

Hysteresis 9V 1ms: Polarization (µC/cm2): 5 Hysteresis 9V 1ms: Polarization (µC/cm2): 6 Hysteresis 9V 1ms: Polarization (µC/cm2): 7 Hysteresis 9V 1ms: Polarization (µC/cm2): 8

Page 141: Characterizing Ferroelectric Materials

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Conclusion• This presentation has only touched the surface of the test

environment.

• Tests may be run as a function of time, temperature,pressure, history, frequency, voltage, rise time, and presetvalues. Other stimuli such as temperature or magneticfield may be used. Many properties have not beenadequately examined to date.

• Each and every test must be executed within the limits ofthe test equipment to prevent distortion.

• Visit Radiant’s web site periodically to see applicationnotes on test procedures or test results.


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