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Radiant Technologies, Inc.
Characterizing FerroelectricMaterials
Joe T. Evans,Radiant Technologies, Inc.
March 7, 2011www.ferrodevices.com
Based on the tutorial at ISAF-ECAPD ‘10
Radiant Technologies, Inc.2
Tutorial Outline
• Introduction
• A device model for non-linear capacitors
• Instrumentation theory
• Definitions of tests
• Fatigue and Imprint
• Conclusion
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.
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.
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
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
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
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.
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
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
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
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
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
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.
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.
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
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.
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
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
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
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.
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
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
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
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
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
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
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-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
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.
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
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
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
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
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
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
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.
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.
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.
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
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!
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.
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.
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
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
Radiant Technologies, Inc.44
Stimulus
time
Switching
Stimulus
time
Non-switching
Hysteresis in Small SignalCapacitance
Radiant Technologies, Inc.45
Stimulus
time
Non-switching
Stimulus
time
Switching
Hysteresis in Small SignalCapacitance
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
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
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)
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!
Radiant Technologies, Inc. 50
Small Signal CapacitancePolarization
• Small signal capacitance forms a hysteresis of its own.
Radiant Technologies, Inc. 51
Small Signal CapacitancePolarization
• The contribution of small signal capacitance hysteresis to the overallloop is small in this case.
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
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
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.
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)
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
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
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
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
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
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.
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
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!
Radiant Technologies, Inc. 64
What is this?
Now let’s analyze some capacitors!
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
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
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
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.
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
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.
Radiant Technologies, Inc. 71
A Harder One
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-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.
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
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
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
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
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
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
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
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
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!
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.
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.
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
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
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
Radiant Technologies, Inc. 86
Test System Diagram
Digital toAnalog
Converter
Analog toDigital
Converter
HostComputer
Power Supply(±15V, 5V, 3.3V)
AWFG
Electrometeror
Ammeter
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)
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
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
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-
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-
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.
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
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.
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
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
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
Radiant Technologies, Inc. 98
Cables
• Use coaxial cable as much as possible.
• Leave as little exposed signal wire a possible.
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.
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
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.
Radiant Technologies, Inc. 102
• The tester with no external cables or test fixture attached.
No Noise Injection – 1 Hz
-40
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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)
Radiant Technologies, Inc. 103
• The tester with no external cables or test fixture attached.
No Noise Injection – 10 Hz
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-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)
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)
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)
Radiant Technologies, Inc. 106
• 1 second test period = 60 noise cycles!
Low Noise Injection – 1 Hz
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-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)
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)
Radiant Technologies, Inc. 108
• The 60Hz injected noise makes this loop look like a lossy capacitor.
Low Noise Injection – 100 Hz
-40
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-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)
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)
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)
Radiant Technologies, Inc. 111
• Six noise cycles in 100ms ≈ 16.7ms period (60Hz)
High Noise Injection – 10 Hz
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-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)
Radiant Technologies, Inc. 112
• The test period (10ms) is just over half of the noise period (16.7ms).
High Noise Injection – 100 Hz
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-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)
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
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-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)
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.
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.
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
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.
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
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
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!
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
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.
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.
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.
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!
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.
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.
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.
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.
Radiant Technologies, Inc. 130
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.
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.
-40
-30
-20
-10
0
10
20
30
40
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Hysteresis BEFORE and AFTER Fatigue[ Radiant Type AB WHITE ]
Pol
ariz
atio
n
Voltage
Hyst AFTER Fatigue: Polarization (µC/cm2)
Hyst BEFORE Fatigue: Polarization (µC/cm2)
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.
0
50
100
150
200
250
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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
2.5
5.0
7.5
10.0
12.5
15.0
-5.0 -2.5 0.0 2.5 5.0
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)
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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-20
-10
0
10
20
30
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Rhyst BEFORE and AFTER Fatigue[ Radiant Type AB WHITE ]
Pol
ariz
atio
n
Voltage
Rhyst AFTER Fatigue: Polarization (µC/cm2)
Rhyst BEFORE Fatigue: Polarization (µC/cm2)
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.
-100
-75
-50
-25
0
25
50
75
100
100 101 102 103 104 105 106 107 108 109 1010 1011
3kHz Triangle Fatigue @ 6V[ Radiant Type AB WHITE ]
Pol
ariz
atio
n
Cumulative Cycles
P* (µC/cm2) P^ (µC/cm2) -P* (µC/cm2) -P^ (µC/cm2)
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.
-100
-75
-50
-25
0
25
50
75
100
100 101 102 103 104 105 106 107 108 109 1010 1011
3kHz Triangle Fatigue @ 6V[ Radiant Type AB WHITE ]
Pol
ariz
atio
n
Cumulative Cycles
dP (µC/cm2) dPr (µC/cm2) -dP (µC/cm2) -dPr (µC/cm2)
Radiant Technologies, Inc. 136
Fatigue-Free
Radiant PZT with LSCO electrodes does not fatigue!
-50
-40
-30
-20
-10
0
10
20
30
40
50
100 101 102 103 104 105 106 107 108 109 1010 1011
2nd Fatigue 3kHz BLUE[ LSCO-1001 BLUE TO-18 ]
Pola
riza
tion
Cumulative Cycles
dP (µC/cm2) -dP (µC/cm2)
Radiant Technologies, Inc. 137
Low Fatigue
Radiant PZT on LNO electrodes fatigues slowly.
-75
-50
-25
0
25
50
75
100 101 102 103 104 105 106 107 108 109 1010 1011
3kHz 9V Fatigue ORANGE [ LNO-1001 TO-18 ]
Pola
riza
tion
Cumulative Cycles
dP (µC/cm2) -dP (µC/cm2)
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.
-40
-30
-20
-10
0
10
20
30
40
-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
Hysteresis Before and After 155C Imprint[ Type AB WHITE Unpackaged Die ]
Pol
ariz
atio
n
Voltage
Hystersis AFTER: Polarization (µC/cm2)
Hysteresis BEFORE: Polarization (µC/cm2)
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.
-5.0
-2.5
0.0
2.5
5.0
100 101 102 103 104 105 106 107 108
Coercive Voltage Shift due to 155C Imprint[ Type AB WHITE Unpackaged Die ]
Vc
Cumulative Time (s)
Vc -Vc
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.
-30
-20
-10
0
10
20
30
-7.5 -5.0 -2.5 0.0 2.5 5.0 7.5
Polarization vs Time at 85C[ LSCO-1001 ORANGE ]
Pola
rizat
ion
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
Radiant Technologies, Inc. 141
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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