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Radiant Technologies, Inc.
Component Model ofFerroelectric Capacitors
Joe T. Evans,Radiant Technologies, Inc.
January 16, 2011www.ferrodevices.com
Radiant Technologies, Inc.2
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.3
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.4
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.5
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.6
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.7
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.8
• 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.9
• 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.10
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.11
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.12
Integration
• Some measurements determine capacitance.– Small signal capacitance vs. Voltage
• Mathematical integration will convert the capacitance to itsequivalent polarization contribution at each voltage.
Radiant Technologies, Inc.13
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.14
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.15
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.16
Non-linear Capacitance
• When the electric field begins to move atoms in the lattice,the lattice stretches, changing its spring constant.Capacitance goes down.
-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.17
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.18
Linear vs. Non-linear Capacitance
This device has both linear and non-linear capacitance. The linearcapacitance is the vertical offset of the nCV plot. The tips do nottouch zero.
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.19
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 polarization.
Drive Voltage
Time
PresetPulse
DelayPeriod
±Vmax
PositiveSwitched
Pulse
PositiveUnswitched
Pulse
NegativeSwitched
Pulse
NegativeUnswitched
Pulse
Radiant Technologies, Inc.20
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.
Switching Non-switching
1/2Period
Radiant Technologies, Inc.21
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.22
• PUND: P*r - P^r = dP = Qswitched• Hysteresis: Switching - Non-switching = Remanence:
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.23
• 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
Radiant Technologies, Inc.24
• The first stage of the experiment consisted of measuring two 4Vhysteresis loops going in opposite directions (including their gaps) and a4V remanent polarization loop.
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 full loops inopposite directionsoverlay exactly.
• The Vc of theremanent loop liesoutside that of thenormal loops. Why?(Hint: the reason ispurely mathematical.)
• The Vc of theremanent loop is thetrue Vc.
Radiant Technologies, Inc.25
The Derivative
• The nCV of the remanent polarization loop rests on the X-axis because it has no capacitance on the 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.26
The Perfect Capacitor• A perfect capacitor combines non-linear capacitance with
remanent polarization.
-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.27
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. 28
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. 29
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. 30
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. 31
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. 32
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. 33
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. 34
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.35
Stimulus
time
Switching
Stimulus
time
Non-switching
Hysteresis in Small SignalCapacitance
Radiant Technologies, Inc.36
Stimulus
time
Non-switching
Stimulus
time
Switching
Hysteresis in Small SignalCapacitance
Radiant Technologies, Inc.37
• 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.38
• 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.39
• 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. 40
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. 41
Small Signal CapacitancePolarization
• Small signal capacitance forms a hysteresis of its own.
Radiant Technologies, Inc. 42
Small Signal CapacitancePolarization
• The contribution of small signal capacitance hysteresis to the overallloop is small in this case.
Radiant Technologies, Inc. 43
Resistive Leakage in a HysteresisLoop
A common problem in ferroelectric ceramics is alinear resistance function. Usually, it appears due toleakage along grain boundaries although it can occurfrom dopants or defects in the grains themselves.
Radiant Technologies, Inc. 44
Resistive Leakage in a HysteresisLoop
Linear resistance is easy for a triangle wave: ∆P=(Current• ∆time)/Area∴P=(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”
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. 45
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. 46
IV Test
• The IV, or Current vs Voltage, test is a series of leakage testsexecuted over the voltage profile used for the traditionalhysteresis loop.
• It is necessary because resistive leakage is not always linear!
V
tThe red line indicatesthe period during whichthe leakage through thesample is measuredafter a soak period.
Radiant Technologies, Inc.47
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.48
Leakage vs CV vs RemanentPolarization
Hysteresis Parameters
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-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
• Are the remanent polarization, IV, and CV related? YES!
Radiant Technologies, Inc.49
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
• The derivative of the remanent polarization makes therelationships clear.
Radiant Technologies, Inc.50
• If remanent polarization saturates nicely, why is the fullloop (both switching and non-switching) open at the end?
Remanent Hysteresis Calculation
-10
0
10
20
30
40
50
60
70
0 1 2 3 4 5Volts
uC/v
m̂2
SwitchingDifferenceNon-Switching
Saturated
The Gap
Not saturated
Radiant Technologies, Inc. 51
Something Left OverIf we measure the remanent polarization, small signalcapacitance, and leakage and then subtract them from the fullloop, something is left over:
This is 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. 52
Reversed Bias Diodes• A platinum electrode based capacitor has two opposing
diodes at the ferroelectric/platinum interface, one of whichis always turned off.
• In reverse bias, a diode has a constant current independent of voltage.This makes a “bow tie” on the nCV plot.
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. 53
Reversed Bias Diodes• A pair of back to back diodes have a unique signature on a
virtual ground test system which uses a triangular drivevoltage.
Radiant Technologies, Inc. 54
Reversed Bias Diode Breakdown• The derivative of a polarization hysteresis loop clearly
shows the diode reverse-biased leakage 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. 55
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. 56
What is this?
Let’s analyze some capacitors!
Radiant Technologies, Inc. 57
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. 58
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. 59
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. 60
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. Note the extra “diode”leakage in the tails that make the saturated tips of the loop openup.
Radiant Technologies, Inc. 61
What is this?
• A linear capacitor.
-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. 62
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?
• A linear capacitor. In this measurement, it has acapacitance density of 10µF/cm2.
Radiant Technologies, Inc. 63
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. 64
A Harder One
• It is only a resistor and 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. 65
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. 66
Is this Ferroelectric?
• Yes, it is! See the ferroelectric switching peaks stickingout of the resistor “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. 67
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. 68
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 at one of the electrode/ferroelectricinterfaces.
-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. 69
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. 70
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. 71
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. 72
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
Radiant Technologies, Inc. 73
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.