Joe T. Evans, Jr. Radiant Technologies, Inc. · 2012-12-17 · Joe T. Evans, Jr. Radiant Technologies, Inc. August 1, 2008 . Radiant Technologies, Inc. Hysteresis Equals PUND Introduction

Radi ant Technologies, Inc.Hysteresis Equals PUND

The Relationship between

Hysteresis and PUND Responses

Joe T. Evans, Jr.

Radiant Technologies, Inc.

August 1, 2008


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.


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


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


What is the Hysteresis Test?


The Hysteresis Test

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]

.

Drive Voltage

Time

Delay

Period

Preset Measurement


The Hysteresis Test

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.

Drive Voltage

Time

Delay

Period

Preset Measurement


The Result

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”.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e


The Preset Loop

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.

Drive Voltage

Time

Delay

Period

Preset Measurement


No Preset Loop

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.

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

1 0

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

S w i t c h in g a n d N o n s w i tc h in g B ip o la r L o o p s[ T ype A B W hi te ]

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o l ta g e


There is Always a Preset Loop!

• 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!

Drive Voltage

Time

Delay

Period


The First Loop

• Ferroelectric films with symmetrical metal electrodes come

down from the Curie Temperature with zero remanent

polarization.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

V e r y F i r s t H y s t e r e s i s L o o p w i t h N o P r e s e t L o o p[ 1 2 0 0 A 4 /2 0 /8 0 P N Z T w i th P l a t i n u m e l e c t r o d e s ]

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o l t a g e


The Gap

Many times, the hysteresis loop does not close on itself, stopping at a

different location than it started from after the preset loop.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e

Gap


The Gap

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.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e


The Gap

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.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e


Raw vs Centered Data

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!

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e


Raw Loops

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.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e


Centered Loops

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.

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

Po

lar

iza

tio

n

(µ

C/

cm

2)

V o lta g e


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.


What is the PUND Test?


“PUND”

In a PUND test, polarization produced by the non-

switching pulses does not go back to zero! These

values are labeled ±P^r on Radiant Technologies’

testers.

Drive Voltage

Time

Preset

Pulse Delay

Period

±Vmax

Positive

Switched

Pulse

Positive

Unswitched

Pulse

Negative

Switched

Pulse

Negative

Unswitched

Pulse


“PUND” Results

*This data taken from a separate 4/20/80 PNZT capacitor than the remainder of the data.

- 6 0

- 5 0

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

4 0

5 0

0 1 2 3 4 5 6 7 8 9

P U N D R e s u l t s[ 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 ]

Po

lar

iza

tio

n

(µ

C/

cm

2)

P s e u d o - T i m e

Drive

Voltage

Time


“PUND” Results

*This data taken from a separate 4/20/80 PNZT capacitor than the remainder of the data.

- 6 0

- 5 0

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

4 0

5 0

0 1 2 3 4 5 6 7 8 9

P U N D R e s u l t s[ 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 ]

Po

lar

iza

tio

n

(µ

C/

cm

2)

P s e u d o - T i m e

Drive Voltage

Time

+P* +P*r +P^ +P^r

-P* -P*r -P^ -P^r

+dP

+dPr

-dP

-dPr


Can We do the PUND test with

Hysteresis Loops?

Use half loops:

Switching Non-

switching

1/2

Period


The Parts of the Hysteresis

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

/vm

^2

Switching

Non-switching


“Gap” in the Half Loop

The Non-switching half loop does not go back to

zero!

Non-switching Loop

0

5

10

15

20

25

30

0 1 2 3 4 5Volts

uC

/vm

^2

The "Gap"

Small Signal

Capacitance

Inside?


Remanent Hysteresis

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 5

Volts

uC

/vm

^2

Switching

Difference

Non-Switching

Remanent

Half Loop


-4 0

-3 0

-2 0

-1 0

0

1 0

2 0

3 0

4 0

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

R e m a n e n t H y s t e r e s i s 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 R e m a n e n t

The Full Remanent Loop


The distance between the gaps is the remanent polarization.

Remanent Polarization in the

Hysteresis Loop

- 4 0

- 3 0

- 2 0

- 1 0

0

1 0

2 0

3 0

4 0

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

P o s i t i v e a n d N e g a t i v e G o i n g L o o p s a t 1 0 0 m s P e r i o d[ 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 e s ]

P lo t A l l P o s i ti v e L o o p s : P a s s - T h r o u g h F i l te r : 1

P lo t A l l N e g a ti v e L o o p s : P a s s - T h r o u g h F i l te r : 1

2 x PR


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.


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 half-

triangle waves instead of pulses. The results

are the same.

Documents

Joe T. Evans, Jr. Radiant Technologies, Inc. · 2012-12-17 · Joe T. Evans, Jr. Radiant Technologies, Inc. August 1, 2008 . Radiant Technologies, Inc. Hysteresis Equals PUND Introduction