The Relationship between
Hysteresis and PUND Responses
Joe T. Evans, Jr.
Radiant Technologies, Inc.
August 1, 2008
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Introduction
• The Hysteresis and pulse polarization tests both
measure polarization.
• In short, a pulse test is a two point hysteresis
test!
• The results of both tests are therefore related
intimately to each other.
• This presentation will relate the geometry of the
hysteresis loop to the results of the pulse
polarization measurement known as the PUND
test.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Samples
• Unless otherwise stated, all data was measured
from a single capacitor on a probe station.
– 1200Å of 4% Niobium doped 20/80 PZT
– Bottom electrode = global layers of 1500Å
Platinum on 400Å titanium
– Top electrode = 1500Å Platinum patterned into
110µ x 110µ squares
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Summary
• What is a hysteresis test?
• What is a PUND test?
• Can the PUND test be executed using
hysteresis loops?
• Correlating the PUND results with the
hysteresis loop.
• Conclusion
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
What is the Hysteresis Test?
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
The Hysteresis Test
Drive Voltage
Time
Preset
Delay
Period
Measurement
A hysteresis test has a preset loop followed after a delay by the
measurement loop. The stimulus Radiant prefers is the triangle wave
because, except for the reversal points, the stimulus has a constant [δV/ δt]
.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
The Hysteresis Test
Drive Voltage
Time
Preset
Delay
Period
Measurement
The charge produced by the sample is measured on a continuous basis
without interruption during the stimulus period from zero volts to zero
volts. Therefore, the measurement gives the total number of electrons that
have left or entered the sample at each time point of the stimulus.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
The Result
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
The change in the number of electrons on the plates of the capacitor
during the voltage stimulation plotted against the stimulus voltage at
which each measurement was made yields the familiar “hysteresis loop”.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
The Preset Loop
Drive Voltage
Time
Preset
Delay
Period
Measurement
The state of the internal polarization of a ferroelectric capacitor is
unknown before the test execution. Therefore, to ensure that we will
measure the entire loop, two loops must be done. The data from the first
loop is ignored while the data from the second loop is used for the plot.
The first loop presets the internal polarization of the sample capacitor to
match the test voltage of the second loop.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
No Preset Loop
S w it c h in g a n d N o n s w itc h in g B ip o la r L o o p s
[ T ype A B W hite ]
P o la riz a t io n (µ C / c m 2 )
10
0
-1 0
-2 0
-3 0
-4 0
-5 0
-6 0
-7 0
-7 .5
-5 .0
-2 .5
0 .0
V o lta g e
2 .5
5 .0
7 .5
If no preset loop is executed, the polarization could start anywhere. In the plot
above of a Type AB capacitor (20/80 PZT), the remanent polarization was already
“Up” when a single positive going-triangle wave was executed without a preset.
Think about the plot. The capacitor is doing exactly what it should.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
There is Always a Preset Loop!
Drive Voltage
Time
Delay
Period
• A single loop measurement like that on the previous
page always has a preset loop. Ferroelectric materials
by definition have memory so the last stimulus you
applied to the sample is its preset loop even it was done
over a year before!
• Only one loop does not have a preset loop: the very
first loop after fabrication!
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
The First Loop
V e ry F irst H y ste re sis L o o p w ith N o P re se t L o o p
[ 1 2 0 0 A 4 /2 0 /8 0 P N Z T w ith P la tin u m e le c tr o d e s ]
P o la r iz a t io n
(µ C /c m 2 )
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lt a g e
1
2
3
4
• Ferroelectric films with symmetrical metal electrodes come
down from the Curie Temperature with zero remanent
polarization.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
The Gap
40
30
20
10
0
-1 0
Gap
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
Many times, the hysteresis loop does not close on itself, stopping at a
different location than it started from after the preset loop.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
The Gap
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
There are several causes for this effect. For a “perfect” capacitor with no
leakage or imprint, the gap still occurs. For the remainder of this
presentation, I will assume we are dealing with a perfect capacitor.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
The Gap
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
The cause of the gap is unknown but it is real. It is directly related to
results measured in the PUND test. It is the bane of FRAM memory
designers who must contend with its presence during read operations.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
Raw vs Centered Data
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
As noted earlier, the polarization state of a device is unknown prior to a
test. The test instrument in use knows not what the starting value should
be. Therefore, the first point of the raw data is always zero!
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
Raw Loops
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
The hysteresis loop in the plot above looks normal but it is offset up
because its first point is at the origin of the graph. This is how the tester
sees the loop.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
P o la r iz a tio n
(µ C /c m 2 )
Centered Loops
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
V o lta g e
1
2
3
4
Vision will center a loop if requested by averaging the +Pmax and –Pmax
values from the raw loop and subtracting that average from every point.
This offset is reported by Vision for all hysteresis loops.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Remanent Hysteresis
Without giving a explanation, I will assert that the offset
value calculated by Vision to center the raw hysteresis loop is
exactly equal to the remanent polarization of the capacitor. I
believe that this assertion can be proven geometrically.
Note: This assertion only applies to capacitors with symmetrical loops having no
imprint.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
What is the PUND Test?
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
“PUND”
Drive Voltage
Positive
Switched
Pulse
Positive
Unswitched
Pulse
±Vmax
Time
Preset
Pulse
Delay
Period
Negative
Switched
Pulse
Negative
Unswitched
Pulse
In a PUND test, polarization produced by the nonswitching pulses does not go back to zero! These
values are labeled ±P^r on Radiant Technologies’
testers.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
“PUND” Results
P U N D R e su lts
Drive
Voltage
[ 1 2 0 0 A 4 / 2 0 / 8 0 P N Z T w i t h P l a t i n u m E l e c t ro d es ]
P o la r iz a t io n
(µ C / c m
2 )
50
40
30
20
10
0
Time
-1 0
-2 0
-3 0
-4 0
-5 0
-6 0
0
1
2
3
4
P s e u d o - T im e
5
6
7
8
9
*This data taken from a separate 4/20/80 PNZT capacitor than the remainder of the data.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
“PUND” Results
P U N D R e su lts
[ 1 2 0 0 A 4 / 2 0 / 8 0 P N Z T w i t h P l a t i n u m E l e c t ro d es ]
50
P o la r iz a t io n
(µ C / c m
2 )
Drive Voltage
-dPr
40
-P*
30
-P*r
-P^
-P^r
20
-dP
10
0
Time
+dPr
-1 0
-2 0
+P*
-3 0
+P*r
+P^
+P^r
-4 0
+dP
-5 0
-6 0
0
1
2
3
4
P s e u d o - T im e
5
6
7
8
9
*This data taken from a separate 4/20/80 PNZT capacitor than the remainder of the data.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Can We do the PUND test with
Hysteresis Loops?
Use half loops:
1/2
Period
Switching
Hysteresis Equals PUND
Nonswitching
Radi ant Techn olo gies, Inc.
The Parts of the Hysteresis
Switching and Non-switching half loops:
Switching & Non-switching Loops
70
60
uC/vm^2
50
40
30
20
Switching
Non-switching
10
0
0
Hysteresis Equals PUND
1
2
Volts
3
4
5
Radi ant Techn olo gies, Inc.
“Gap” in the Half Loop
The Non-switching half loop does not go back to
zero!
Non-switching Loop
30
25
Small Signal
Capacitance
uC/vm^2
20
15
Inside?
10
5
The "Gap"
0
0
Hysteresis Equals PUND
1
2
Volts
3
4
5
Radi ant Techn olo gies, Inc.
Remanent Hysteresis
PUND: P*r - P^r = dP = Qswitched
Hysteresis: Switching - Non-switching = Remanence:
Remanent Hysteresis Calculation
70
60
Remanent
Half Loop
uC/vm^2
50
40
30
20
Switching
Difference
10
Non-Switching
0
-10
0
Hysteresis Equals PUND
1
2
3
4
5
Volts
Radi ant Techn olo gies, Inc.
The Full Remanent Loop
R e m a n e n t H y s te r e s is o f P N b Z T C a p a c i t o r
[ 1 2 0 0 A 4 /2 0 / 8 0 P N Z T w i t h P l a t i n u m e l e c t r o d e s ]
U n s w it c h e d - L o g ic 0
S w it c h e d - L o g ic 1
Rem anent
40
30
20
10
0
-1 0
-2 0
-3 0
-4 0
-4
-3
Hysteresis Equals PUND
-2
-1
0
1
2
3
4
Radi ant Techn olo gies, Inc.
Remanent Polarization in the
Hysteresis Loop
P o sitiv e an d N eg ativ e G o in g L o o p s at 1 0 0 m s P erio d
[ 1 2 0 0 A 4 / 2 0 /8 0 P N Z T w i t h P l a t in u m E le c t ro d e s ]
P lo t A ll P o s itiv e L o o p s : P a s s -T h ro u g h F ilte r: 1
P lo t A ll N e g a tiv e L o o p s : P a s s -T h ro u g h F ilte r: 1
40
30
20
10
2 x PR
0
-1 0
-2 0
-3 0
-4 0
-4
-3
-2
-1
0
1
2
3
4
The distance between the gaps is the remanent polarization.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Conclusion
• The gaps in the hysteresis loop are equal to
±P^r.
• 2Pr from the hysteresis loop almost never
equals the remanent polarization.
• deltaP from the PUND test is equal to the value
of 2Pr from the hysteresis loop minus the
magnitudes of the top and bottom gaps.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.
Conclusion
• deltaP is equal to two times remanent
polarization.
• The “offset” value reported for a hysteresis loop
by Vision is equal to the remanent polarization
for a symmetrical loop.
• The PUND test can be executed using halftriangle waves instead of pulses. The results
are the same.
Hysteresis Equals PUND
Radi ant Techn olo gies, Inc.