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Thermal characterization of compound semiconductor microwave devices for *reliability analysis

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Thermal Characterization of Compound Semiconductor Microwave
Devices for Reliability Analysis
A dissertation submitted in partial fulfillment of the r e q u i r e m e n t s
for the degree of Doctor of Philosophy in Electrical & C o m p u t e r
Engineering at George Mason University
By
Jeffrey A. Mittereder
Master of Science
George Washington University, 1990
Director: Dr. Dimitrios Ioannou, Professor
Department of Electrical and Computer Engineering
Spring Semester 2002
George Mason University
Fairfax, VA
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UMI Number: 3042780
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THERMAL CHARACTERIZATION OF COMPOUND SEMICONDUCTOR
MICROWAVE DEVICES FOR RELIABILITY ANALYSTS
By
Jeffrey A. Mittereder
A Dissertation
Submitted to the
Graduate Faculty
Of
George Mason University
in Partial Fulfillment of
the Requirements for the Degree
of
Doctor o f Philosophy
in Electrical & Computer Engineering
Committee:
wAj.
Dr. Rao Mulpuri, Committee Chair
Dr. Dimitrios loannou, Dissertation Director
lAJ.
Dr. W. Murray Black, SCS
Dr. A lok Berry, ECE Department
Dr. Donald Gantz, Statistics Department
►
<r*m «I. >
Dr. Wallace T. Anderson, Naval Research Lab
Dr. Andres Manitius, ECE Department Chair
Dr. Stephen Nash, Associate Dean, School o f
Information Technology and Engineering
Date:
^
^ .6
O
Spring Semester 2002
George Mason University
Fairfax, VA
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ACKNOWLEDGMENTS
I would like to thank all of my professors for putting up w ith
me, especially those on the committee: Dr. Rao Mulpuri, for b e i n g
the committee chair, his patience, and getting me started;
Dr.
Dimitrious Ioannou for having the courage and humor to be m y
dissertation director; my Section Head, Dr. Wally Anderson, for his
motivation and e n c o u ra g e m e n t throughout the program, e s p e c i a l l y
the c om pre hen sive exams; Dr. Black for his technical expertise a n d
pointed questions; Dr. Berry for his generous presence; and Dr.
Gantz for getting me over a hurdle and for filling in.
I am grateful to the Naval Research Laboratory for s p o n s o r i n g
the Edison Program, and the m anagem ent for their support and u s e
of the facilities. I would especially like to thank my family a n d
friends for their support and encouragem ent, especially Lara a n d
Danny for their sacrifices. Last but not least I would like to t h a n k
the Man and His people upstairs for their guidance and love.
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TABLE OF CONTENTS
Page
List of T ables..............................................................................................................v
List of Figures...........................................................................................................vi
List of A bbreviations/Symbols............................................................................. x
A b str a c t.......................................................................................................................... xi
I. Device Reliability and Thermal Analysis...................................................1
A. Dependence of reliability on thermal behavior
for microwave d e v ic e s .......................................................................... 1
B. Existing measurement techniques....................................................... 15
II.
Thermal Characterization and Simulation...............................................20
A. Semiconductor Microwave Devices...............................................20
1.Gallium Arsenide X-band MMIC.......................................... 20
2. GaAs M M I C ................................................................................ 27
3. Silicon Carbide S-band MMIC............................................. 28
B. Infrared R e sp o n se................................................................................. 30
C. 1st Order M o d e l....................................................................................33
D. Atomic Force Microscopy Technique............................................ 37
E. Finite Element Sim ulation.................................................................51
III.
Measurement and Simulation Results and their significance
in Evaluating Reliability.......................................................................... 53
A. Infrared D ata......................................................................................... 53
1. GaAs Pseudomorphic High Electron Mobility
T ra n sisto r .........................................................................................53
2. GaAs Metal Semiconductor Field Effect
T ra n sisto r.........................................................................................55
3. SiC Metal Semiconductor Field Effect
T ra n sisto r .........................................................................................57
B. Cooke M ethod...................................................................................... 60
C. AFM Measurements........................................................................... 63
1. GaAs P H E M T ............................................................................. 63
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IV
2. GaAs M E S F E T ............................................................................ 71
3. SiC M E S F E T ................................................................................73
D. Accuracy of the Quantitative AFM Thermal
measurement and sources of error...............................................76
E. Finite Element R esults........................................................................82
F. The Effects on Device Reliability Evaluation.......................... 92
IV. Concluding Remarks and Future W ork...............................................94
List
o f R e fe re n c e s .................................................................................................100
Appendix A: Example of 1st Order Thermal Model.............................. 112
Appendix B: Example o f Finite Element Calculation.............................. 114
C irriculum
V ita e ..................................................................................................... 130
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LIST OF TABLES
T able
1.
2.
3.
4.
Page
Summary of
Summary of
and Ist order
Measured and
Summary of
MMIC device infrared thermal measurements....59
MMIC device infrared thermal measurements
thermal modeling results............................................62
simulated temperatures of SiC device..................85
results in degrees Centigrade (°C).............................89
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vi
LIST OF FIGURES
Figure
Page
(I. Device Reliability and Thermal Analysis:)
1.
Schematic of NRL life testing system........................................................ 3
2.
Exposure Time (x-axis) versus Drain Current .................................5
3.
A lognormal plot of the reliability data................................................. 6
4.
Arrhenius plot after RF life testing........................................................... 7
5.
Arrhenius plot with a 1.12 eV slope ..................................................... 9
6.
An SEM image of a failed GaAs power amplifier.............................11
7.
A focus ion beam cross section of a GaAs H E M T ..............................13
8.
An AFM image of a rough Si3N4 passivation................................... 14
9.
Drain Voltage versus pulsed Drain C u rren t...................................16
10. A pair o f topological and thermal AFM images................................. 18
(II.
1 1.
1 2.
13.
14.
15.
16.
17.
18.
19.
20.
2 1.
2 2.
23.
24.
25.
26.
27.
2 8.
Therm al C haracterization and S im u la tio n :)
GaAs PHEMT-based MMIC amplifier (25x).......................................... 21
Close up of one of the GaAs PHEMTs......................................................22
Cross section drawing of the GaAs PHEMT........................................... 23
Drain current and bias vs. gate recess d e p t h .................................24
S-parameters before and after lifetesting........................................ 25
Device fixture with carrier plate and M M IC ....................................... 26
GaAs MESFET-based MMIC amplifier (25x)........................................27
Optical micrograph of SiC MESFET MMIC (25x).............................. 28
Id versus Vd for the SiC MESFET MMIC (Vg=0)................................29
Photograph of the infrared thermal microscope............................ 31
Schematic of infrared thermal microscope technique..................32
Device geometry used in the 1st order thermal model............ 34
Atomic force microscope with acoustic isolation hood............38
The scanning access module accessory............................................... 39
Hand view of SPM head................................................................................. 40
Schematic of SPM head................................................................................41
Schematic of the general tip holder.......................................................42
Drawing of the thermal tip holder.......................................................... 43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vii
29.
30.
3 1.
32.
33.
34.
35.
36.
SEMphotograph o f contact mode tip........................................................ 44
a-b. Close up SEM photos of the tip..........................................................44
Drawing of the thermistor tip......................................................................45
SEM photograph of the bottom of the thermistor tip................ 45
Schematic of the Wheatstone bridge circuit....................................... 46
Instrumentation used in the measurement technique..................49
Tip mounted onto the piezo of the SPM head.................................... 50
3D mesh used in the finite element simulations...............................52
M e asu rem en t a n d S im u la tion Results and their
significance in E v a lu a tin g Reliability:)
3 7 . a. Optical photograph of output stage PHEMTs ............................54
3 7 . b. IR thermal microscope scan of the area in figure 4 6 a..........54
3 8 . a. GaAs MESFET-based MMIC amplifier (25x)................................56
3 8 . b. IR thermal microscope scan of the area in figure 4 7 b ..........56
3 9 . a. Optical micrograph of gate manifold ( I k x ) ................................. 58
3 9 . b. IR thermal image of gate manifold with DC bias...................58
4 0 . 1st order model results for SiC MESFET...........................................61
4 1 . a & b. AFM thermal images at no-bias and pinch-off ................ 64
4 1 . c & d. AFM thermal images at 100 mA and
200 m A ............... 65
4 1 . d & e. AFM thermal images at 300 mA and 400 m A ............... 66
4 2 . a. AFM image o f the gate output stage of the P H E M T ................67
4 2 . b. AFM thermal image with applied DC bias.................................. 67
4 3 . a & b. Close-up AFM thermal image of gate.................................. 68
4 4 . AFM thermal scan voltage versus GaAs temperature..................70
4 5 . AFM thermal scan voltage for the M ESFET ..................................... 72
4 6 . AFM thermal voltage for the SiC MESFET........................................ 74
4 7 . AFM thermal measurements of SiC MMIC with DC bias.............. 75
4 8 . Minimal effect o f different tip resistance....................................... 78
4 9 . Minimal effect o f different days for the same tip....................79
5 0 . Different gain settings for the tip.......................................................80
5 1. Same temperature for different gain se ttings................................ 81
5 2. Thermal results from FEA simulations for SiC.............................. 84
5 3 . GaAs PHEMT with 10 gates....................................................................87
5 4. GaAs MESFET with 14 gates..................................................................88
5 5 . SiC versus GaAs thermal conductivity ............................................ 90
5 6 . SiC versus GaN thermal conductivity ...............................................91
5 7 . Arrhenius plot o f the difference in lifetime prediction............. 93
(III.
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viii
(IV.
5 8.
59.
60.
60.
61.
61.
C onclu din g R em arks and Future Work:)
AFM o f the channel area o f the SiC M E SFET ................................96
An A F M image o f a carbon nanotube............................................ 97
a.GaN on A1203 HEMT at 2 00x ....................................................... 99
b. IR scan of GaN H EM T .....................................................................99
a. GaN on SiC HEMT at ~ 1 0 0 x ........................................................ 100
b. IR o f GaN on SiC H E M T ................................................................100
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IX
LIST OF ABBREVIATIONS / SYMBOLS
Abbreviations
AFM
DUT
FET
FEA
GaAs
IR
MESFET
MMIC
PHEMT
RF
SiC
SThM
atomic force microscopy
Device Under Test
field-effect transistor
Finite Element Analysis
Gallium Arsenide
infrared
metal-semiconductor F E T
monolithic microwave integrated circuit
pseudomorphic high electron mobility transistors
radio frequency
Silicon Carbide
scanning thermal mic roscopy
Sym bols
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A BSTRA CT
THERMAL CHARACTERIZATION OF COMPOUND SEMICONDUCTOR
MICROWAVE DEVICES FOR RELIABILITY ANALYSIS
Jeffrey A. Mittereder, M.S.
George Mason University, 2002
Dissertation Director: Dr. Dimitrios Ioannou
This dissertation
shows
been developed
accurately
normal
that
a new nondestructive
which uses an atomic
determine
operating
the maximum
conditions
corresponding
which
quantitative
to
combined
com pound
have reported
with
the
under
This method
to
to most published
about
temperature
se m iconductor
(AFM) to
of devices
of the device
only qualitative
information
computer
has
is a
tem perature
devices, in that it allows actual n u m b e r s
to the tem perature
thermal
determine
te mperature
to field of microscopic
using an AFM. This is in contrast
results,
microscope
at high resolution.
novel and unique contribution
measurement of electronic
force
technique
of
modeling
microwave
be m e a s u r e d
AFM t h e r m a l
and
indirect
semi-
the sample, and are u n a b l e
the device.
The
is dem onstrated
devices
that
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
technique
for
are
several
used
in
commercial
and
military
applications:
Gallium
Arsenide,
Silicon
Carbide (SiC), and Gallium Nitride (GaN). GaAs devices are c u r r e n t l y
used in the fields of radar
and com m u n ic atio n s
[1]. SiC and GaN
devices, also called wide bandgap devices because of their e l e c t r o n i c
structure,
are
of particular
im portance
in future
applications
in
these fields [2,3].
The channel
temperature
of Gallium Arsenide
was quantitatively measured using the quantitative
microscopy
(SThM) technique,
temperature
of the devices was also characterized
imaging
and
thermal
SThM te m perature
the model,
which
modeling.
scanning t h e r m a l
is a variation
It was
found
of AFM. T h e
by infrared
that
the
values were close to the calculated
and were higher than
These results
(GaAs) d e v i c e s
are useful
those
found
to the reliability
(IR)
m easured
values f r o m
by IR, as p r e d i c t e d .
community
in that
th e y
help to predict a more accurate semiconductor device lifetime.
The
monolithic
thermal
microwave
characteristics
integrated
of
circuits
S-band
m easurem ents
show a much
order
thermal
difference
and accurate
higher thermal
calculations
may be explained
response
and
by an
carbide
(MMICs) have also b e e n
investigated. It was found that high resolution
microscopy
silicon
atomic
force t h e r m a l
finite element
than
that predicted
infrared
increase
spreading on the device due to the improved
sim ulations
by firs t
m easurem ents.
in the
thermal
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
lateral
This
heat
conductivity
of the silicon carbide.
These results
device reliability and packaging.
can
silicon
carbide
a major
effect
To the a uth or’s knowledge,
the first reported work which characterizes
an actual
have
MMIC device,
the thermal
and
it does
resolution.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
on
this is
behavior o f
so
at
high
I.
Device
Reliability
I.A. D e p e n d e n c e
of
m icrow ave
devices
Com pound
extensively
and
reliability
se m iconductor
in commercial
Thermal
on
thermal
microwave
and military
Analysis
b eh a v io r
devices
radar
for
are
used
and c o m m u n i c a t i o n s
markets. The word "compound" in this case refers to materials s u c h
as Gallium Arsenide (GaAs), as opposed to singular materials such a s
silicon (Si). The reliability of these devices in the field depends
many factors,
such as processing
the key factors
d ependence
that
the
operation
in the
reliability
on operational
maximum
and materials.
of the
temperature.
te mperature
of
However,
one o f
devices
is t h e i r
finished
Therefore,
these
on
it is i m p o r t a n t
devices
upon
norm al
be accurately quantified.
One
of
the
te m perature
of
tem perature,
which
most
solid
important
state
is usually
aspects
electronic
the
hottest
of
devices
the
is
location
when it is under bias. This quantity is commonly
m axim um
the
in the
channel
device
used to e x t r a p o l a t e
1
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2
device
lifetimes,
usually
therefore,
that
calculated
to predict
by Arrhenius
this te mperature
derive the Arrhenius
high temperatures
It is i m p o r t a n t ,
measured
and/or
device lifetime. The data used t o
is generated
[5]. A short
[4],
be accurately
an accurate
plots
plots
by reliability
lifetesting
at
review of this testing
procedure
is
given below, which follows generally accepted guidelines [6].
A schematic of the life testing system
this work in shown in figure
each
type
are
tested
used for the devices in
1 [7]. Approximately
at tem peratures
in order
much
to expedite
higher
operating
temperatures
operating
dc bias and RF signals are also applied.
by a com p u ter
forty circuits
than
their failure.
(increases
and
decreases)
in drain current and power. Failure of devices
to
a decrease
predeterm ined
and/or
in device
standard,
or catastrophic.
a
current
However, the device may still be operational.
"Catastrophic"
means
that
non-operational,
has
become
from
in drain
below
values.
device
output
" P a r a m e tr ic "
parameters
such as a 20% decrease
in power
is usually
their initial
the
a IdB decrease
for changes
operating
N o rm al
are
monitored
refers
norm al
The devices
constantly
characterized in two ways: param etric
of
permanently
usually shows obvious visible evidence of the failure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
3
386 PC Controller
with
ADC and DIO
Boards
RF Life Test Rack
Multiplexing
and
Solid State
Relays
Temperature Controllers (4)
DC Power Supplies
4 Gate, 4 Drain
Com puter Controlled RF Life T est System
DC Bias Distribution Box
Eight Channels
Four RF Test Slots
Single RF Test Slot
4 W ay
Power
Divider
Variable
Attenuator
X-Band
DRO
Figure 1. Schematic
Directional
Coupler
Directional
Coupler
Detector
Detector
MMIC
PA
2 0 dB
Attenuator
Detector
of NRL c o m p u te r -c o n tr o lle d
life testing s y s t e m .
[7].
Figure 2 is an example of one type of data monitored
duration
over the
of the test. It is a plot of Exposure Time (x-axis)
versus
Drain Current (y-axis) for a GaAs PHEMT device during reliability life
testing. The device failed after 2892 hours of testing at an e l e v a t e d
temperature of
190°C (top curve) due to a decrease
of greater than
20% from the initial value after periodic
room
te m perature
(bottom
curve).
Another
in drain c u r r e n t
testing a t
plot of exposure
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tim e
4
versus power output revealed that there was more than a 1 dB d r o p
in power across
same testing
the 8 to 12 GHz (X-band)
time. The device could
frequency
band
not be restored
at th e
to its initial
values due to degradation. There was no visible sign of failure in t h e
device.
This
effect
made
it difficult
to
determine
the
physical
mechanism(s) responsible for the failure of these devices in g en e ra l
[ 8 ].
These
decreases
"parametric"
in
performance
failure because
would
be
considered
the device was still operable.
Similar
measurements are made for all of the devices under test at the t h r e e
life
test
temperatures
"powered
down,"
measured.
The
param eter
scalar
interest.
Any
operation
and
power
failure.
their
drain
output
network
1 dB drop
frequency
current
is
and
on
p e r io d ic a lly
power
output
a microwave
s-
at
the
frequency
range
of the power
data
across
sp e cified
of
the
a specified
"infant mortalities,"
sample. These failures
Each device
is measured
analyzer
range
Circuits that fail before
considered
until
device
is
minimum
considered
amount
and are excluded
are usually catastrophic,
the
from
of
failure.
of time a r e
the testing
and due to d e f e c ts
in manufacturing or testing errors.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
500
400
300
Failure by 20% decrease in drain current (as measured
at 30°C) occurred after 2892 hours.
200
T b = 30°C, V Q = -0.484 V, V D = 7.0 V
T b = 190°C, V D = 7.0 V, lD = 450 mA (V G variable)
100
f = 8.0 GHz, Pin = 17.0 dBm
0
1000
2000
3000
4000
Exposure Time (hours)
Figure 2. A plot of Exposure Time (x-axis) versus Drain Current
axis) for a GaAs PHEMT device during reliability life testing [8],
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(y-
6
The time of failure data is tabulated
then plotted on a lognormal
for the 40 devices,
scale (figure 3). The cumulative
and
f a ilu re
percentage for each circuit at a specific testing temperature is f o u n d
from the formula [i/(n + 1)] * 100% . Here "i " is the number of t h e
device
ordered
according
to its failure
devices at the same testing temperature
time
relative
to the o t h e r
(e.g.
I through
10). "n" is
the total number of samples at a specific testing temperature.
10
(0
1_
3
o
a>
3
3
."= 1 0
(0
:
-©
O
Tb = 175°C, t50 = 6980 hours, a = 0.18
— T = 190°C, t
0)
B
E
= 2577 hours, a = 0.25
50
"A— T„B = 205°C, t50 = 1408 hours, c = 0.23
i
10‘
.1
i
5
i
i
20
i
i
50
i
i
80
i
i
i_______ i—
95
99 9 9 .9
Failures (Cum %)
Figure 3. A lognormal plot of the reliability data for the GaAs PHEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This data is further reduced to give an Arrhenius plot as s h o w n
in figure 4.
The data points shown are the average (50%) lif e t im e s
for the three
testing
tem peratures.
The curve
fit of these
three
points is extrapolated to the device lifetime at the normal o p e r a t i n g
temperature.
This
extrapolation
reliability community.
channel
is an
In this case
te m perature
accepted
the military
for GaAs devices
method
standard
in
the
operating
of this type is 140°C. T h is
gave an average device lifetime (t50) of 2.3 x 106 hours, or over 1 0 0
years, which is generally an acceptable value.
O
o
Q.
E
50
II
—I
a t T
C
IT
:< 1 0 6 h r s
2 .3
=
25
102
=
D °C
i
C
(0
O
or
o
© 100
1 .1 J
1 1 1 1nil
103
i i i 11in
104
105
. . . mu
106
i i i i mi l
1 07
1 08
i ■ i 111 ii _-i—< LX11U
1 09
1 0 1C
Median Lifetime (hours)
Figure 4.
An Arrhenius
plot
of device
channel
temperature
median life time after RF life testing for the GaAs PHEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vs.
8
An example
device channel
of the im portance
temperature
can
of determining an
be seen
in figure
accurate
5. This f ig u re
displays Arrhenius plot curves with 1.12 eV slopes equal to the GaAs
PHEMT data
in figure
plotted
for channel
shows
that
this
temperatures
4. The t 50 lines are
te m peratures
difference
the
that differ
in
the
used for the arrhenius
50% failure
by 25°C.
estimation
tem perature)
140°C d e v i c e
minimum
a
device
from
determination
of
temperatures
acceptable
the
life tim e ,
1.3 years (bottom-red line).
Thus, a change of only 25°C can change the predicted
of
channel
curve can result in a d e c r e a s e
from 6 years (average
top-green line) to an unacceptable
The figure
of the
in the extrapolated predicted life time (at the standard
operating
tim es
to
channel
unacceptable.
temperatures from
needs to be very accurate.
lifetim e
Therefore,
the
The determination
the
t e s tin g
m ethod
used should be within plus or minus 5"C. This range can be difficu lt
to obtain for currently used and state of the electronic circuits. T h e
scale
of these
temperature
elements
requires
analysis techniques.
submicron
Fortunately,
resolutions
AFM probes
type resolution, but have yet to be fully utilized.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for
the
have th is
9
1.5 m o.s
1 year
n
y r.s
110
y e a rs
400350O
300-
t
5 0
= 5.6 x 104 hrs (6 years) at T
'
J
'
c h
= 140 °C
:2 5 Ct
5 0
= 1.2 x 104 hrs (1.3 years) at T
v
J
'
c h
= 140 °C
CO 1 5 0
® 100
1 02
1 03
1 04
1 05
1 O6
1 07
1 08
1 09
1 0,c
D evice Life T im e (h o u rs )
Figure 5. Examples of Arrhenius
plot curves
with a 1.12 eV s lo p e
equal to the GaAs PHEMTs in figure 4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
Further
device
evidence
reliability
Some examples
which
show
maximum
gate
is shown
shown
typical
failure
degradation,
in figures
ohmic
device noise, substrate
that
are
on
life te stin g .
devices
related
to
catastrophic
degradation,
current,
after
for different
These include
contact
of te m perature
analysis
6-10
mechanisms
te mperature.
sinking,
effect
in the failure
are
channel
metal
of the dramatic
failu re,
passivation
and contact
the
la y e r
resistance
[9 -14].
Figure 6 is a scanning electron
mic roscope
(SEM) image of a
GaAs power amplifier that catastrophically failed in the channel
due to thermal
overstress
after lifetesting
at high te m perature
area
[9].
The drain is on the left, the gate line is in the middle, and the s o u r c e
is on the right.
together
making
These
the
three
sections
device
of the
inoperable.
device
The
have
small
shorted
balls
are
composed of gold, which have formed from the heat of the gate a n d
ohmic contacts.
An SEM image of the backside of the device f ailu re
area showed another
failure site in the upper
backside area was prepared
part of the gate. T h e
using a sample preparation
technique developed at NRL.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and e t c h i n g
11
#
%
Figure
6.
An
SEM
image
of
a
GaAs
power
amplifier
catastrophically failed in the channel area due to thermal
[9].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that
overstress
12
Figure 7 shows a focus
ion beam
(FIB) cross
section
of the
source, gate, and drain of a GaAs HEMT, which may have failed d u e
to thermally
induced
[10].
examination
Close
degradation
at
the
gate sinking and ohmic
of
source
the
and
image
drain
contact
degradation
reveals
ohmic
interfaces,
a
contact
secondary
thermally induced failure mechanism. A further close-up of the g ate
in figure 9 can show evidence of gate heat sinking on a device. This
type of failure was confirmed
Carlo simulations
for a GaAs PHEMT by running
on the device's cross-sectional
geometry
M o n te in o r d e r
to predict device behavior upon reliability testing. The Id/Vd c u r v e s
from the Monte-Carlo
simulations
of the PHEMT show that thermally
and experimental
induced
m easurem ents
gate sinking of only 6
nanometers (60 angstroms) can cause device failure. This p a r t i c u l a r
effect
can
be
difficult
transmission electron
preparation
when
characterize
microscopy
for TEM can
accomplished,
to
the
establish,
(TEM) is usually required.
be accomplished
small
and
using careful
dimensions
desired
u n a t ta i n a b le .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
S am p le
FIB. Even
may
be
13
Figure 7. A focus ion beam cross-section
of the source,
drain of a GaAs HEMT [10].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
gate, a n d
14
Another
surface
rough
possible
passivation
breakdown.
Si3N4 passivation
tem perature
AFM image
thermally
layer
failure
mechanism
is
Figure 8 shows an AFM image of a
of a tested
and DC bias (surface
of the
induced
roughness
Si3N4 passivation
GaAs PHEMT at
1.99
layer of an
nm).
A sm ooth
un-tested
PHEMT has a surface roughness of 1.01 nm [11].
nM
Figure 8. An AFM image of a rough Si3N4 passivation layer of a
tested GaAs PHEMT at high temperature and DC bias [11].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
high
GaAs
15
I.B .
E x istin g
There are
m e a su r e m e n t
a number
temperature
dependent
of methods
including
current/voltage
references
(y-axis)
junction
for
temperature
The
best
temperature
crystals,
methods).
measurement
versus
pulsed
the c h a n n e l
tem perature
atomic force m i c r o s c o p y
and the finite
An informative
techniques
Figure 9 shows one example,
Drain Voltage (x-axis)
Current
liquid
(such as the Cooke Model,
thermal
[16-24],
to determine
characteristics,
and finite difference
these and other
used
IR imaging,
(AFM), and calculations
element
tech n iqu es
(solid)
a GaN HEMT is used
and
review o f
is found
where
a plot o f
un-pulsed
in order
in t h e
D r a in
to d e t e r m i n e
[15].
quantitative
m e asu rem e n t
spatial
resolution
methods,
about
obtained
I m icrom eter,
of
all
has u s e d
liquid crystals. However, liquid crystals are limited to the t r a n s i t i o n
temperature
that
rarely
Also, the technique
device
surface.
currently
the
resolution
and
is destructive
O f all
most
corresponds
the
popular
nondestructive
to the channel
tem perature.
in that a liquid is placed on t h e
other
techniques
due
to its spatial
employed,
and
nature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AFM is
tem perature
16
200
26 C
180
160
100 C -
140
<120
150 C 200 C
•s
c 100
26 C, DC -
80
60
40
All curves with UV w/pyrex
20
5
0
15
10
Drain Voltage (V)
20
Figure 9. A plot o f Drain Voltage (x-axis) versus pulsed (solid)
un-pulsed
Drain
determine junc tion
Current
(y-axis)
temperature
for
a GaN HEMT in order
[15].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
to
17
Some
fairly
complete
reviews
thermal A F M techniques [23-25].
variations:
31],
thermally
scanning
Several
results
e.g. tem perature
temperature
or
(right)
not
above
or
thermal
include
being
properties
topology
in figure
(left)
and
of a piece of copper
afm
the
an
than
[ 3 6 -5 5 ] .
but only
tem perature,
unknown
reference
but insufficient in t h e
of a circuit.
10 a pair
the
(dark
of AFM images
c o rre sp o n d in g
area)
show
thermal
encased
between
image (right)
the copper
shows
( d ark -c o o ler)
This is the kind of inform ation
issue is that
makes them
the complexity
less than
a distinctive
and
in epoxy
( w h i te
contrast
while
difference
the epoxy ( w h i t e - w a r m e r ) .
published
o f some
the
response
area). The surface topology image (left) shows little contrast,
the thermal
[35].
quantitative
measured,
other
below
wire [28-
therm ocouples
To- This is information is helpful
For example,
surface
do
o r devices
overall thermal characterization
scanning
Wollaston
and
investigated
thermal
ranges
[26-27],
[32-34],
presented
of the samples
contrasts
probes
have
summ arized
Several studies have used AFM tip
expansion
references
the
te m peratures
thermal
joule
other
However,
resistive
have
in the literature.
of the
available
straightforward.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A nother
techniques
1 8
T
i I mI B
IS K
Figure
u
IJ
10. A pair of AFM images
(left) and the corresponding
that show
thermal
response
the
surface
to p o lo g y
(right) of a piece o f
copper (dark area) encased in epoxy (white area).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
19
As a result of these deficiencies, the objective of this study was
to
develop
a
simple
technique
temperature
of electronic
commercial
AFM
to
devices
employing
a
quantitatively
using an AFM. To this
linear
resistive
(thermistor) was used to measure the absolute
of
microwave
semiconductor
theoretically calculated
is commercially
measure
devices,
end,
thermal
a
tip
channel t e m p e r a t u r e
and
compare
values. The fact that the instrument
available is an advantage
th e
to other
it
to
u tilized
professionals
in
the interested community who may desire to duplicate the method.
Another advantage of the AFM used is that the thermal
employs does not negatively affect the measurement.
mostly
of silicon
nitride
( S i3N 4), an insulator.
It is c o m p o s e d
Therefore,
therm al
loss from the sample surface to the tip is kept to a minimum.
the technique
is non-destructive
an expanded
range
measured;
and
the
over
which
calibration
to the sample
sub-micron
of the
surface.
sample
Also,
It p r o v id e s
temperature
tip and
tip it
can
be
produces
quantitative information. To the author’s knowledge,
this is the first
accurate,
temperature
quantitative
measurement
of the channel
compound semiconductor devices using AFM.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of
II. THERMAL CHARACTERIZATION AND SIMULATION
II.
A.
I I .A .l.
S em ico n d u cto r
G allium
M icrow ave
Arsenide
X-band
D evices
M M IC
The GaAs devices measured were Pseudomorphic High E lec tron
Mobility Transistors (PHEMTs) and M e ta l-S em ico n d u cto r
Transistors
(MESFETs) in Monolithic
Microwave
Field Effect
Integrated
C irc u its
(MMICs) [56]. The PHEMT MMIC is shown in figure 11. The total c h i p
size is 3 x 5 millimeters
(mm),
and contains
4 small input PHEMTs
(on the left), and 4 larger output
PHEMTs (on the right).
length
0.25
for
all
magnification
the
PHEMTs
photograph
is
microns
is shown in figure
(um).
The g a t e
A
12, in which
higher
the k ey
elements of the device are labeled. Most of the gate width is c o v e r e d
by the source
air
bridge;
however,
exposed to allow sufficiently accurate
temperature
structure
to
be
to reduce
made.
Also,
the
enough
of the
m easurem ents
gate
the gate resistance,
fingers
gate
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is
of the c h a n n e l
have
with the top
being 0.5 um long.
area
a T -g a te
of the g a t e
Figure 11. GaAs PHEMT-based MMIC amplifier (25x).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
22
tircen
Figure 12. Close up of one of the GaAs PHEMTs.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23
A cross sectional drawing of a single device is shown in f ig u r e
13. The MMIC normally operates at a drain current of 450 m illia m p s
(mA),
with
calculated
each
and
characteristics
output
measured
stage
I-V curves
of a typical
devices are mounted
PHEMT drawing
device
on carrier
are
are
plates
72
shown
shown
mA.
Some
in figure
in figure
and placed
14.
15.
RF
The
into fixtures
shown in figure 16.
Source
Drain
Gate
y
N+ GaAs
AIGaAs
N+ GaAs
gate sinking
InGaAs
AIGaAs
degradation of AIGaAs surface / Si3N4
passivation layer interface
GaAs Superlattice Buffer
GaAs Semi Insulating Substrate
Figure 13. Cross-section drawing of the GaAs PHEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
as
24
500
i
E
<
g
9 6.0 n m
gs
■
400
97.S n m
300
1
i i f c 11 n i * 11
1
3
« 9 9 .d n m
g 200
Q
100.5 n m
100
m 102.0 n m
0
2
Figure 14. Calculated drain
4
D rain b i a s , V
current
vs. drain
6
8
bias as a function
gate recess depth for the PHEM T geometry in figure 13.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of
25
'2 1
20.0
15.0
r= -0.139 V, V D =
10.0
TX)
V, T b = 175°C''
D = 450 mA (before), lD = 382 mA (after)
‘*\
5.0
Before life testing
After gradual failure at 6796 hoj
0.0
-5.0
-
10.0
-15.0
-
J
20.0
2.0
4.0
6.0
8.0
L-
10.0
-»
12.0
14.0
■
1—
16.0
18.0
20.0
Frequency (GHz)
Figure 15. Typical S-parameters
before
and after lifetesting
GaAs PHEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for t h e
26
Figure 16. Device fixture with carrier plate and MMIC.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
27
II.A.2. GaAs MMIC
The GaAs MESFET studied is shown in figure 17. It consists of o n e
input FET (left) and two output
FETs (right).
Its gate length is 0 . 5
um, and it operates at a drain voltage of 7 volts and drain current
650 mA, with each of the output
of
FETs drawing 228 mA. It is also a n
X-band MMIC, similar to the PHEMT.
1.0 mm
3; . Ih-rPii
Figure 17. GaAs MESFET-based MMIC amplifier (25x).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
II.A.3.
Silicon C arb id e S-band
The SiC device
used for thermal
MMIC. An optical photograph
shown
in figure
MMIC
analysis
is a MESFET b a s e d
of the device at 25x magnification
18. The chip size is approxim ately
3.25
mm
is
per
side. The total gate width is 300 mm with 6 gate fingers, or 500 u m
per finger. It is designed to operate at S-band frequencies (2-4 G H z),
at a drain
voltage
of 10 V and a drain
current
of 650
mA. T h e
current-voltage (I-V) characteristics at zero gate voltage in figure 1 9
show that the device begins to saturate
to 650 mA at 10 Vd. T h e
devices pinch-off at a gate voltage of -5 V [57],
Drain
Figure 18. Optical micrograph of SiC MESFET MMIC (25x).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29
0
Idss (amps)
0.8
0.6
0.4
0.2
0
0
2
4
6
Vd (volts)
8
1 0
Figure 19. Id versus Vd for the SiC MESFET MMIC (Vg=0).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
30
II. B.
Infrared
R esponse
A Barnes
Com putherm
used to measure
HI infrared
the relative
temperature
biasing, and to locate the hottest
of an IR microscope
were
instrument,
te m perature
at
the
and
rise of the device
is shown in figure 20, and a schematic
and magnification
made
microscope
show
lenses
maximum
below this temperature
upon
lOx. The
resolution
(12
increase
calibrations
to calculate
of t h e
has a liquid nitrogen
up to
a tem perature
of 100(>C. Radiance
was
area of the devices. A p h o t o g r a p h
technique in figure 21. The microscope
detector,
thermal
m easurem ents
microns)
above
are made
an emissivity.
along with a device under test (DUT) calibration
cooled
of
th e
a baseplate
above
and
This c a l c u l a t i o n
is used to form t h e
temperature image [58], It is usually difficult to discern the d i f f e r e n t
circuit elements
photograph.
This low resolution
rise in channel
disadvantage
of an area as com pared
temperature
to a corresponding
is reflected
in a low t e m p e r a t u r e
above the baseplate,
of the technique
and
o p tic a l
instrument
which reveals
in averaging
large areas.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
over
31
Figure
20.
a s so c ia te d
Photograph
of the
infrared
thermal
microscope
com p uter.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
32
EYEPECE
RETICLE
VISUAL
OBJECTIVE
OBJECT
Figure 21. Schematic of infrared thermal microscope technique [5 8].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
II. C. 1st Order Model
The Cooke thermal model was used to predict the t e m p e r a t u r e
of the GaAs in the area of the AFM measurement
a precise
technique
for finding the temperature
uses a simple closed-form
equation
derived
that the gate segments of the transistor
is usually
the case. The equations
presented
in the
references
of
[59], The model is
of a transistor.
under
the a s s u m p t i o n
are the heat sources,
used
w hich
for the Cooke model
[59,60].
Some
It
of the
are
r e s u lt in g
equations will be presented here.
The final equation for thermal resistance, 0 , is in a form w hich
is normalized to the total FET width, Z, and the thermal
c o n d u c tiv i ty ,
Kth:
GZKth = n /n [2(n-1)/ln M
- (n-2)/ln P]
where
M= {2{[cosh7t(S+L)/4F][cosh7t(S-L/4F)]}1/2 + 1}/
{[cosh7t(S+L)/4F][cosh7t(S-L/4F)]}1/2 - 1}
and
P = 2{{[l+sech(7tL/4F)]/ [ l-sech(7rL/4F)J} 1/2 }.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
“n” is the number of gate fingers, “S” is the gate-to-gate
pitch,
“L” is the gate length,
and
“F ’ is the
substrate
spacing o r
thickness.
These are shown in figure 22.
Z/n
Figure 22. Device geometry
used
in the
1st order
[59],
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
thermal
model
35
Because
increasing
the
thermal
tem p eratu re,
conductivity
the Cooke model
often
decreases
w ith
uses a simple a l g o r i t h m
for Kth. For example, the thermal conductivity of GaAs is
represented
as:
K th = 1.08T0 26 Watts/cm "C
Thus, at 25°C, K th = 0.47
quoted
in the
substrate
literature.
materials.
Joyce’s equation
temperature,
W/cm
Similar methods
The equation
[60],
°C, which
to provide
for
is the
are
value
used
K th is then
an expression
norm ally
for the
other
combined
w ith
for the
channel
Tt :
T t = [0.74 (AT)^,-"-26 + To+0-74]'-35 ’C
where:
T 0 = the heat sink (or baseplate) temperature in °C, and
AT = the temperature rise calculated by Q Z K th,
= 0
x
the power dissipated by the FET
These equations can be solved on a small personal computer.
For an example, if we look at the GaAs PHEMT, the dc p o w e r
can be represented as:
Pdc = Voltage x Current = 10V x (450 mA x le-3 A/mA) = 4.5 Watts
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
Then, since the device has 8 FETs:
4.5 Watts/8 devices = 0.5625 Watts/device
assuming that each FET receives the same amount of power. This is
not always the case,
been
found
to
but the differences
have
a
negligible
generated
effect
on
in power
the
have
calculated
temperatures. This value would be substituted into the Cooke m o d e l
for the power applied to the device.
Some of the other inputs needed (listed in parentheses
GaAs PHEMT) are the gate-to-gate
for t h e
spacing (S = 40 um), gate length
(L = 0.25 um), total gate width (Z = 0.85 mm), number of gates (n =
10), substrate/die
thickness
(F = 100 um),
(T„ = 100°C which corresponds
thermal
conductivity.
te m perature
Macintosh
The output
baseplate
to the IR measurem ent),
of the simulation
of the device upon biasing. The program
PowerPC
using
tem perature
Mathematica
software.
solution is shown in Appendix A.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and t h e
is the c h a n n e l
was run on a
An
exam ple
37
II.
D.
A tom ic
F orce
A Digital
thermal
probe
M icroscopy
Instruments
Dimension
tip was used
device on the submicron
Technique
III AFM with
to measure
the
scale. Photographs
a r e s is t i v e
temperature
of t h e
of the instrument
are
shown in figures 23-26. Figure 23 shows the AFM with the a c o u s t i c
isolation
the
hood. When closed,
measurement
which it resides,
the hood
environment;
and
minimizes
with
the
vibrations
isolation
from
table
on
helps to increase the resolution of the i n s t r u m e n t .
The mainframe electronics sit on top of the table, and the c o m p u t e r
control system is shown.
The scanning access module
accessory
is displayed
in f ig u r e
24. This component is connected between the tip and the c o m p u t e r ,
and allows signals
essential
to be measured
to and from the tip. This w as
in enabling the reading of the thermal
voltages
thermistor tip for the quantitative portion of the thermal
Deciphering
connectors
the
from
developm ent
this
of
com munications
experiments
voltage
with
signals
module
the
the
that
were
was one
quantitative
m anufacturer,
output
of the
the
challenges
several
bnc
in t h e
Frequent
repetitive
were necessary to ensure accurate interpretation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
technique.
from
technique.
and
from
38
Figure 23. Photograph
of Atomic
force
microscope
isolation hood [61].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with
acoustic
Figure 24. The scanning access module accessory.
One of the
contains
the
most
laser,
tip
important
holder,
parts
and
of the instrument,
tip,
is the
w h ic h
Scanning
P ro b e
Microscopy (SPM) head. A hand-held view of the SPM head is s h o w n
in figure
25,
and
a cross
sectional
operation
of the head involves a laser, which focuses on the top o f
the tip. The signal is then reflected
then
fed into the computer.
critical,
as well as the
detector.
This must
schematic
in figure
into a photodiode
26.
detector,
The
and
Alignment of the laser onto the tip is
maximizing
be maintained
the
reflected
th roughout
the
signal
into
the
m easurem ent,
and any drift needs to be compensated.
The deflection of the laser signal upon scanning of a sample is
related to the topography
of the sample's
is relayed
computer
back
to
the
and
surface. This i n f o r m a t i o n
converted
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
into
surface
40
topography
monitor
information
which
is
[61]. Control of the head, tip holder,
the sample surface can be automatic
with a trackball
manual
displayed
on
the
com puter
and tip to and f r o m
using the com puter
device. For some high temperature
operation was necessary.
Figure 25. Hand-held view of SPM head.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
or m a n u a l
m easurem ents,
41
Laser Spot Detector Screen (dark red)
Laser aim adjustments
Position Sensitive Detector
(special photodiode)
Laser diode
Beamsplitter
(behind screen J1
Detector
Mirror
positioners
Focusing lens
a
L a s e rL ig h ts
Beam path
dd
Tracking Lens
(conBctive)
Adjustable(detector)
m inor
Fixed mi rror
Probe Tip Holder
C antilever
Figure 26. Schematic o f SPM head.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
Drawings
tip holders
and
tips
are
(figure
maintains
the
tip's position by a spring-loaded clamp. The holder also contains
the
shown
and
in figures
piezoelectric
topography.
photographs
27-32.
element,
of the
The tip holder
which
This information
senses
is relayed
changes
27)
in
sample
surface
back to the electronics
by
changes in the laser signal in the SPM head. The actual
thermal
tip
holder (figure 28) is slightly different from the standard
holder,
but
the operating
same.
The
modification
principle
for height
to this holder
and deactivates
measurement
is the
is a lever on one side,
the sensitive therm istor
which a c t i v a t e s
based upon the position
the lever.
SIDE VIEW
tip is installed
Cantilever Probe Tip
( tip faces down )
Spring Loaded Probe Clip
Electrical Mounting Sockets ( 4 pics)
Cantilever
Mounting
Groove
(n o tip
installed)
& T l=
BOTTOM VIEW
( TIP SIDE )
no tip installed
Figure 27. Schematic of the general tip holder.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of
43
Figure 28. Drawing of the thermal tip holder [62],
The standard
contact
30. This tip is composed
tip
(figures
31
and
32)
mode cantilever
of silicon nitride
consists
of
is shown in figures 2 9 (Si3N4). The t h e r m i s t o r
a modified
contact
mode
cantilever with a thermistor integrated into the tip structure. The tip
has a square pyramid shape, and a nominal
radius of curvature
of ~
100 nanometer (nm). The spatial resolution is specified at - 200 n m
depending on the sample, and ~ 0.5 ° C temperature
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
resolution
[62].
44
Figure 29. SEM photograph of contact mode tip.
Figure 30a-b. Close up SEM photos of the tip.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
Thermistor
Figure 31. Drawing of the thermistor tip [63]
Figure
32.
SEM of
the
bottom
of
the
thermistor
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tip
[62]
46
The
operates
thermistor
on the
coating
Wheatstone
is
a
platinum /iridium
bridge
principle
alloy,
(figure
33).
and
As t h e
sample surface heats up or cools down, Rtip heats up or cools d o w n ,
and Vtip = V Qff yields a voltage
amplifier
proportional
at the output
to the te m perature
of the d i f f e r e n t i a l
at the therm isto r
[63].
This voltage is then measured with a digital meter, and correlated
the tem perature
for
the
reading of a the rm oc ouple
calibration
quantitative
calibration
portion
of
the
and operating
attached
to the s a m p l e
m easurem ents.
temperature
to
For
the
m easurem ents,
the AFM probe is held at a scan speed of zero.
(Tip)
Gain
bridge ~=~
Figure 33. Schematic of the Wheatstone bridge circuit o f the t h e r m a l
mode of the scanning probe microscope [63].
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
47
Since
the
therm istor
nitride
MMICs are
tip accurately
passivation
temperature
passivated
measures
with
silicon
the temperature
with which it is in contact.
just below the gate should
nitride,
the
of the silico n
The actual
be somewhat
channel
higher
[64].
Since the tip is composed mainly of Si3N4, which is an insulator,
transfer
thermal
of heat
from
the
measurement
surface
techniques
to the tip is negligible.
such
as
to be considered.
The tip is also not changed
O ther
th erm ocouples
Walloston wires use thick metal, so that the transfer
the
and
of heat n e e d s
physically
after
the
m easurem ent.
A technique
temperature
was finalized
of a surface
for
quantitatively
for an electronic
using a setup represented in the schematics
measuring
the
device with the D 3 I 0 0 ,
in figures 34 and 35.
A
step-by-step list of the procedure is outlined below:
1. Attach
a heater
to the
sample,
and
a thermocouple
near
the
surface to be measured.
2.
Set the gain of the thermal
scope
mode,
or a digital
head to some value, as read from t h e
multimeter
connected
to Aux D of t h e
Signal Access Module.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
3. Set the thermal
voltage to zero using the coarse and fine o f f s e t
knobs. Set the laser d etector
signal to 0,0. Set the scan size to z e r o
to engage at only one spot.
4. Engage and measure the thermal voltage, as in step 2.
5. Heat the sample up 5 degrees, and let it stabilize.
6. Re-set the thermal
voltage to 0, and the laser detector
signal t o
0 ,0.
7. Engage and measure the thermal voltage.
8. Repeat steps
5 -7
until
the
laser
sum
signal
begins
to d r o p ,
around 55°C.
9. Turn off the heater (or repeat the measurement
to room temperature;
10.
Plot the
results:
its
going back d o w n
reproducible).
thermal
voltage
versus
tem perature
(see
attached).
11. Apply dc bias as required.
and
Let the device
stabilize
e l e c t r ic a l ly
thermally.
12. Re-set the thermal
voltage to 0, and the laser detector
0 ,0 .
13. Engage and measure the thermal voltage.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
signal t o
49
14.
the
Extrapolate the thermal voltage measured to the curve fit line o f
calibration
corresponding
part
of
temperature.
the
measurement,
and
read
The value should be accurate
off
the
to w ith in
+,- 5 degrees Centigrade [65].
This m ethod
was verified
with the application
scientists
and
engineers o f the instrument manufacturer - Digital Instruments.
Microscope
and AFM
thermal tip
Visual
Displays
Tip
Controls
Digital Instruments
Model 3100
Signal
Breakout
Box
Voltage
meter
Output
Data: AFM linear tip voltage
a function of temperature
versus DC bias
Figure
34.
m e a su r e m e n t
A
schematic
of
the
instrumentation
te chnique.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
used
in
the
50
Extended
Retracted
Z Piezo
( D i s t a n c e fix e d
b y h e a d h e i g h t .)
-220 V
+220 V
Sample
_Travel distance defined by
Z scan size parameter.
Figure 35. Tip mounted onto the piezo of the SPM head, and the two
positions of the head and tip [61].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
II.E .
F inite
The
Elem ent
finite
commercially
software,
S im u lation
element
available
simulations
Silvaco
were
International
done
device
and run on HP and Sun workstations.
using
the
s im u la t io n
The T h e r m a l 3 D
module in the Atlas portion of the software is used to solve Poisson’s
steady-state heat equation for 3D mesh structures:
V[k(T) VT] = q
w here:
T = steady state temperature,
k = temperature-dependent
thermal
q = the power
per
sources)
generation
volume
in the medium
(heat
[67].
The user defines heat sources
power.
unit
conductivity, and
The results
are plotted
and sinks, thermal
conductivity,
in the TonypIot3D
module
and
of t h e
software. An example o f the meshes used in shown in figure 36. T h e
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52
number
of
capabilities,
points
and
solvable
was
always
is
determ ined
maximized.
by
An
the
c o m p u t e r ’s
example
simulation generated is shown in Appendix B.
/
Figure 36. Example of the 3D mesh used in the finite element
sim ulations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of
the
III.
MEASUREMENT AND SIMULATION RESULTS AND THEIR
SIGNIFICANCE IN EVALUATING RELIABILITY
III.A .
In frared
II I .A .l.
G aA s
T ransistor
A Barnes
used to measure
D ata
P seu d o m o r p h ic
C om putherm
the relative
High
III infrared
E lectro n
thermal
temperature
Mobility
microscope
was
rise of the device
upon
biasing, and to locate the hottest area of the PHEMT. An IR t h e r m a l
microscope scan of the area of interest
measurement was made at the maximum
the IR
is shown in figure 37b. This
resolution
instrument, and shows a te m perature
figure
of the
as compared
the
technique
in
and
averaging over large areas [68].
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
in
w hich
of
reflected
photograph
temperature rise in channel temperature above the baseplate,
disadvantage
is
the optical
20°C
the
low resolution
to
the different c i r c u it
low
reveals
37a. The
area
of
increase of 2 0 ° C a b o v e
the baseplate. Note that it is difficult to discern
elements
(12 microns)
instrument
in
54
Figure 37a. A top view optical photograph close-up of one of output
stage PHEMTs (71 Ox) [68].
Figure 37b. IR thermal microscope scan of the area in figure a.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
III.A .2 .
G aAs
M etal
Sem icon du ctor
F ield
E ffect
To confirm the results of the PHEMT thermal
GaAs MMIC MESFET was also ch aracterized.
second
a
of t h e
of one input
FET
FETs (right). A close up view of the gate a r e a
looks
analogous
upon
biasing is shown
corresponding
measurements,
A photograph
device is shown in figure 38a. It consists
(left) and two output
T ransistor
to the PHEMT in figure
in figure
to the three
38b.
12. An IR thermal
Note
the
three
white
im age
spots
MESFETs on the circuit.
The m e a s u r e d
temperature of each of these FETs was approxim ately
the same. T h e
highest temperature
found using this technique
was 35 °C above t h e
baseplate in the same gate areas as the PHEMT in figure 37b [68].
Even though the scan size is larger for the images shown l a r g e r
compared to the previous PHEMT images, the results were c o n f i r m e d
by using the maximum resolution
of devices,
analyzed.
thermal
of the microscope.
an average of thirty to forty
This gave a more
response.
devices
representative
The higher value measured
MMIC is due to the increased
current
For both t y p e s
of each type w as
characterization
of t h e
for the MESFET-based
flow through the device. Also,
the architecture of this circuit is more com pact,
with the FETs b e i n g
consolidated rather than widely distributed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
Figure 38a. GaAs MESFET-based MMIC amplifier (25x) [68]
Figure 38b. IR thermal microscope scan of the area in figure 46a.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
III.A .3 .
SiC
M etal
S em icon d u ctor
F ield
E ffect
T ra n sistor
A close-up of one of the gate manifolds of the SiC MESFET at 1
kx magnification
is shown
in figure
39a.
This
same
area
was
analyzed by an infrared (IR) thermal microscope upon DC biasing o f
10 Vd and 650 mA.
highest
resolution
te m perature
substrate
The results
of
measured
the
are shown in figure 39b using t h e
instrument
in the channel
(12
is held at 100°C, this is equivalent
this m easurem ent
makes the measured
channel
tends
m axim um
to a rise in c h a n n e l
of 39°C. It should be n o t e d
to average
tem peratures
The
region was 139°C. Since t h e
temperature above that of the substrate
that
um).
over a large area,
lower than the actual
m axim um
temperature of the device.
A summary
of the IR results for all of the devices
is shown in
Table 1. Also included in the table are recently measured
some
w h ic h
GaN HEMTs for
increase
from
the
comparison.
IR measurem ent
sapphire
substrate
(A1203)
substrate,
even though
is
Note
for
higher
that
the
tem p eratu re
GaN HEMT with
than
the dc power is greater
This shows the importance
the
results f o r
that
with
the
the
SiC
for the SiC d e v i c e .
of using thermally conductive
for power devices.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
substrates
58
Drain
Figure 39a.
Optical micrograph o f gate manifold (Ikx).
Figure 39b. IR thermal image of gate manifold with DC bias.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
Table
1. Summary of MMIC device infrared thermal measurements.
D e v ic e
Therm al
C o n d u c tiv ity
[W/cmK]
DC p o w er
(W atts)
T e m p e r a tu r e
In c re a s e from IR
M e a s u re m e n t (°C)
G aA s
PHEMT
0.45
3.15
19
G aA s
MESFET
0.45
4.55
30
SiC
MESFET
3.3
6.5
39
G aN /A I203
HEMT
1.3/0.45
0.55
68
GaN/SiC
HEMT
1.3/3.3
1.5
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
III.B .
C ooke
M ethod
The Cooke thermal model was used to predict the t e m p e r a t u r e
of the GaAs in the area
PHEMT and
the
of the AFM m e a s u r e m e n t . With both
MESFET, the
Cooke
model
temperature lower than the actual value.
unlike
the
methods,
more
precise
which calculate
predicts
a
This is expected
finite difference
and
channel
because,
finite
using very small volumes
the
elem ent
of the d e v i c e ,
the Cooke model cannot calculate the very highest tem perature
just
under the gate of the device.
The results
of the calculations
for the SiC MESFET at v a r io u s
baseplate temperatures are shown in figure 40 [69]. From this plot it
is seen that the maximum
above
the baseplate
channel
te mperature
close to that of 3 9 ° C found
comparison
resolution
shows that
the
measurements can
order
thermal
temperature
importantly
these m easurem ents
insufficient
in
predicting
the IR measurement.
predict channel
lower than the actual channel
the
rise of the d e v i c e
of 100°C is 35°C. This value
from
first
temperature
This c l o s e
models
tem p eratu res
of the device.
and calculations
and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
low-
that a r e
But m o r e
are found
channel te m perature
is
to b e
device
61
heating for this type of device as shown below by the more a c c u r a t e
AFM measurements
calculations
and
and
low
FEA calculations.
resolution
Therefore,
DR. measurements
can
first
order
negatively
effect reliability predictions and packaging designs.
400
350
300
O
250
0)
c
(0
£
200
O
*“
150
100
- * - V d = 1 0 V, l d = 6 5 0 mA
:
No Bias
50
50
100
150
250
30 0
350
B a se D la te
Figure 40. Temperature
predictions
from
1st order
MESFET [69].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
model
for SiC
62
Table 2 shows the results of the IR and Cooke thermal
model
calculations for all of the devices. It is interesting to note that t h e r e
is a greater
difference
between
values for the GaAs devices
the
measured
and opposed
versus
to the SiC. This can
explained by the difference in thermal conductivity
materials. The increased
more
lateral
thermal
heat spreading
conductivity
across
between the t w o
resulting
in c l o s e r
temperature.
Table 2. Summary of MMIC device infrared thermal measurements
and 1st order thermal
modeling results.
(W atts)
Temperature
Increase from
IR
Measurement
(°C)
1st Order
Thermal Model
(Cooke)
(°C)
Difference
(°C)
DC
power
be
of the SiC allows f o r
the device,
measured and calculated values of channel
calculated
Device
Thermal
Conductivity
[W/cmK]
GaAs
P H EM T
0.45
3 .1 5
19
44
25
GaAs
M E S FE T
0.45
4 .5 5
30
90
60
SiC
M E S FE T
3.3
6 .5
39
37
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
III.C .
AFM
M easu rem en ts
III.C .l. GaAs PHEM T
Refer again to the IR thermal
interest
microscope
scan of the area o f
upon biasing shown in figure 37(b). This shows a low 2 0 ° C
rise in channel
measured
tem perature
under
the
same
above
biasing
the
baseplate.
conditions
mode of the AFM is shown in figures 41(a-e),
The same
using
the
42(a-b),
area
therm al
and 4 3 ( a - b ) .
Note that it is easier to discern the different circuit elements in t h e
area of interest, and the hot spot of the device where the gate e n t e r s
the channel is revealed.
The tip was calibrated
to the sample of interest as is shown in
figure 42 for the PHEMT. The area chosen
GaAs adjacent
figure 42b).
to where
the gate enters
The IR scan
the
tip
baseplate
positioned
only
was
digitally
tem perature,
the channel
and AFM thermal
region to be relatively uniform
of
for calibration
in temperature.
recorded
which
image
was
as
a
be conducted
to a baseplate
(specified
both
reveal
The thermal
function
measured
as near to the device as possible.
was t h e
of
in
th i s
v o lta g e
in c r e a s i n g
by a t h e r m o c o u p l e
The calibration
temperature
could
of 5 5 °C , due
radiant heating of the cantilever from the large block.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to
64
G a te
feed
of
stressed
G aA s
PHEMT:
No
Bias
G ate
feed
of
stressed
GaAs
PHEMT:
P i n c h —o ff
Figure 41 (a & b). AFM thermal images o f the PHEMT gate area at no­
bias (a) and pinch-off (b).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
Ga+e feed of stressed GaAs
PHEMT: Id =
100 mA
-------------------------------------------T-------- ----------------------------------- l-o
0
10. 0
20.0
UM
Gate
fe e d
of stressed GaAs
PHEMT: Id =
200
mA
Figure 41 (c & d). AFM thermal images of the PHEMT gate area at
100 mA (c) and 200 mA (d). Note the increased heating in the
channel
area.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Got© feed of stressed GaAs PHEMT: Id =
300
20. 0
mA
-0.5 V
0 .3
ID. D
fe e d
of
s tresse d
I
■ o.a v
20. 0
10. 0
G a te
U
GaAs
PHEMT: Id =
400
mA
Figure 41 (d & e). AFM thermal images of the PHEMT gate area
300 mA (d) and 400 mA (e).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
Figure 42(a). AFM image of the gate output stage of the PHEMT.
Figure 42(b). AFM thermal image with applied DC bias (Id = 450 mA
for the MMIC, and 72 mA for each output stage PHEMT).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
1.00
2.00
3.00
JIM
Figure 43 (a & b). Close-up AFM image (a-top) and AFM thermal
image (b-bottom) of PHEMT gate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
After
the
temperature
calibration,
and the thermal
This value was extrapolate d
channel
the
temperature
temperature).
of
voltage
was
biased
at
of the GaAs area
room
m easured.
to the plot in figure 44 to determine
83.4
This measured
result measured
PHEMT
°C
( 6 0 .4 ° C
tem perature
above
the
a
baseplate
value is greater than t h e
by the I R ( 1 9 0C above baseplate),
and predicted
by
the Cooke thermal model (44°C above baseplate) (see Table 2).
These
resolution
differences
between
measurement's
can
the
ultimate
be
explained
techniques
resolution
by
and
the
changes
calculations.
is specified as 12 um.
in
The
IR
Also t h e
instrument tends to average the analysis over large areas. The C o o k e
model is not as refined as other calculation
methods,
element analysis. Intrinsically it is assumed
reliability community
and well accepted
that these two methods
but provide a good "first cut" at the thermal
Other
physical
measurem ent
have the shown the channel
methods
confidence
analysis of the d e v i c e .
as well as FEA s i m u l a t i o n s
temperatures
in the results
in t h e
are of low a c c u r a c y ,
for devices in general
be higher than those found in the aforem entioned
lends more
such as fin ite
techniques.
of the AFM probe,
known to have a smaller size and resolution.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to
T h is
which
is
70
>
2.5
<D
U)
CO
o
>
CO
E
<D
Calibration curve
LL
<
- - □ - - ld=450mA
0.5
20
40
60
80
100
120
G a A s T e m p e r a t u r e (°C )
Figure 44. Plot of AFM thermal scan voltage versus GaAs t e m p e r a t u r e
for the PHEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
III.C.2. GaAs MESFET
An AFM thermal
m easurem ent
was conducted
on the
GaAs
MESFET similar to that
done for the PHEMT, and the area chosen
the
analogous to that for the PHEMT in figure 42.
measurement
was
The results are shown in figure 45, and show a channel
of 130°C at 650mA (a 107°C rise above the baseplate
The Cooke model
predicted
a channel
te m perature
MESFET operating at 1.596 W at a baseplate
9 0 ° C rise in channel
for
tem perature
tem perature).
of 113°C for a
tem perature
of 2 3 ° C ( a
tem perature). The IR measurement
for this
device averaged around 3 0 °C .
Once
again,
significantly
average
the
measured
higher
than
value measured
temperature
the
of the
lower resolution
for these
AFM technique
methods.
MESFET devices
is
Also, the
was higher
that of the PHEMTs. This was due to the larger drain current
th a n
drawn
by the MESFET versus the PHEMT (650 mA versus 450 mA). A n o t h e r
factor
to consider
heat around
output),
Therefore,
and
was that
the MESFETs layout
had centered
three FETs. The PHEMT had eight devices
the
four
output
devices
drew
the heat was more distributed
the main point is the increased
tem perature
more
(4 input,
the
4
drain
current.
for this circuit.
However
measured
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by the AEM.
72
AFM Thermal Voltage (V)
4
3
2
■e— Calibration curve
1
-
- ld=650mA
0
20
40
60
80
100
120
140
G a A s T e m p e r a t u r e (°C )
Figure 45. Plot of AFM thermal scan voltage versus GaAs temperature
for the MESFET.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
III.C.3. SiC MESFET
To confirm
AFM thermal
under
these findings for wide band gap devices,
m e asurem ents
bias. The results
areas
near
contact
baseplate
the gate
are shown
manifold.
tem peratu re
that
channel
area
the
of the
itself
unattainable
space involved.
The results
46 and 47 for t h r e e
the
probe
with a therm ocouple
a
of
the
was 4 3 °C .
172°C
was
near
A m easurem ent
higher
from
tip was in
on top of the SiC. T he
as expected.
yield
due to probing
in figures
tem p erature
device
would
of the SiC MESFET device
passivation
measured
maximum
made
In all cases,
with the silicon nitride
is seen
channel
were
s im ila r
te m p erature,
top
surface
are very similar
to those
the
in t h e
but
and
It
was
the
small
found
for a
finite element method discussed below, which corroborate this d a t a .
Clearly the higher resolution
AFM m easurem en t
technique
is m o r e
accurate than the infrared thermal microscope for this device [70].
The number
m e asurem e nt
of calibration
data points
was decreased
for th e
of this device as well as for the GaAs MESFET. This is
due to the familiarity
the extrapolation
with the technique,
and the confidence
was valid to within the desired
m easurem ent.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
accuracy
that
of t h e
74
8
DC b i a s m e a s u r e m e n t s
7
6
O)
5
4
3
u. 2
1
C a l ib r a ti o n m e a s u r e m e n t s
0
0
5 0
150
1 00
T e m p e r a t u r e (°C )
200
Figure 46. AFM thermal voltage versus device temperature for the
SiC MESFET.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
Gold
Drain
ourte
Figure 47. AFM thermal measurements of SiC MMIC with DC bias.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
III.D.
A ccu racy
m easu rem en t a n d
There
are
m easurem ent
measured
of
the Q u a n tita tiv e
sources o f error.
some
quantitative,
temperatures.
experience
concerns
of
the
in making
and
the
These
author,
AFM
accuracy
concerns
but
the
the
AFM
of
were
majority
T herm al
therm al
the
resulting
based
were
on
the
from
the
manufacturer of the instrument, but were quickly justified.
these
are - the linear extrapolation
respect
to temperature,
the
of AFM thermal
changes
in resistivity
measurements
made on different
days and/or
using different
gain settings
the
These
phenom ena
possible
throughout
for
Some o f
voltage
between
different
times,
with
tips,
and
tips during the m e a s u r e m e n t .
were investigated
the measurement
and
tested as thoroughly
of the devices.
as
Some of t h e
results are shown below.
It has been proven experimentally
changes
with temperature
[71].
that a material's
For metals,
this resistance
resistiv ity
usually
increases with temperature; while for semiconductors and i n s u l a t o r s
it often decreases. Over specific ranges of temperature the follo w ing
equation is valid:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
p = p ref(l + a A T )
where:
p = the resistivity at temperature T,
Pref = the resistivity at some reference temperature, T ref, usually
room
te m p e r a tu r e ,
AT = T - Tref, and
a = temperature coefficient of resistivity, which is an e x p e r i m e n t a l l y
d e te r m in e d
co nstant.
Typical values for a can be found in various handbooks,
CRC [72]. It is this linear relationship
such as th e
of the m aterial’s resistivity t o
temperature that allows the extrapolation of a linear curve fit to t h e
calibrated data in the AFM thermal
the extrapolation
measurement,
thereby
valid.
Figure 48 shows the results during the calibration
an AFM m e a su re m e n t
different
rendering
resistivity.
of a GaAs PHEMT for
Normally
there
is not
two
this
portion
tips with
much
of
vastly
resistance
variation between tips; however this case was an exception. It is se en
that
there
is
negligible
difference
between
the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
calibrated
data
78
between
the two tips. From this result it was concluded
then
that
this phenomena had little effect on the measurement.
50
a>
o>
cs
**
40
■e— G = 2 ,1 -29-99, 1 kohm tip
30
s — G=2, 5-6-99, 2 kohm tip
o
>
75
20
a>
10
o_
CO
0
E
>_
-10
20
25
30
35
40
45
50
55
Therm ocouple tem perature (°C )
60
Therm ocouple tem perature (x axis, °C) versus m easured and predicted
normalized SPM thermal voltage (y-axis, volts) for a GaAs wafer a s a
function of SPM gain setting (G) using a linear curve fit.
Figure
48.
resistance
An example
on
temperature
Another concern
of the
effect
of different
tip
measurement.
was the effect of making the m e a s u r e m e n t s
with the same tip on different
consistency
minimal
in the measurement.
days or times,
The results
in order
to test
the
in figures
49 and
50
show that this effect was also minimal. Different
gain settings
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w ere
79
used
to verify
measured.
The
assumption.
that
plots
the
same
in
maximum
figures
50
Based on the information
found that the AFM quantitative
temperature
and
51
would
substantiate
be
th is
from the above tests, it w as
thermal
measurement
was a c c u r a t e
to +/- 0.5°C. Overall, this appears to be the accuracy of AFM.
Vphase/T.data.Si3N 4.G aA s.8-3-99
5
o
4
o>
<(0
->
o
>
1
r
“l
1
r
-e— G=2, 8-3-99, 2 kohm tip
-b— G=2, 8-4-99, 2 kohm tip
y = -1.05 + 0.045357X R= 0.9869
3
y = -0.93571 + 0 .0 4 4 2 8 6 x R = 0.9 7 6 8 9
£u .
<D
.C
Is
Q.
CO
t
60
i
80
l
l
100
!
---- 1_______L.
120
T(C)
Figure 49. A comparison showing the minimal effect of different
days of temperature measurement for the same tip.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
III!
“i—i i |—i—i—i—i—|—n —i—i—|—i—i—i—i—j—i—i—m —j—i—i
— ©— G =2
— b — G =4
- - o - - G =6
— x- G =8
o
O)
<0
i r~|—n —r~r~
(measured)
(measured)
(predicted)
(predicted)
o
>
E
0)
Q_
<0
20
25
30
35
40
45
50
55
60
T herm ocouple te m p e ra tu re (°C )
Thermocouple temperature (x axis, °C) versus measured and predicted
normalized SPM thermal voltage (y-axis, volts) for a GaAs wafer as a
function of SPM gain setting (G) using a linear curve fit.
Figure 50. Measured and predicted values of AFM temperature
measurement using different gain settings for the tip during the
calibration
measurement.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
6
5
©
O)
«
o
>
4
— ©
Calibration curve. Gain = 2
— □ - - ld=450mA
— O—
3
E
—
A
-
Calibration curve, G ain = 4
-
Id = 450 mA
0>
2
\.n .
1
0
20
40
60
80
100
120
GaAs T em perature (°C )
Figure 51. A plot confirming that the same final DC bias temperature
is measured for different gain settings.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
III.E. Finite Elem ent Results
An associated
response
and more
of the device upon
accurate
biasing is obtained
analysis (FEA). These methods
resolution
calculation
offer increased
by solving for device geometries
and have been used extensively
the GaAs devices
program.
of the t h e r m a l
by finite e l e m e n t
accuracy
and h ig h e r
on a much
finer scale,
[73-77], Calculations were made f o r
and the SiC MESFET in the MMICs using
The dimensions
used matched
those of the actual
such
a
MESFET
and substrate. For the SiC MESFET, these values were: 6 gate fingers,
gate to gate spacing (pitch)
substrate
possible
thickness
= 400
= 40 um, gate length
um.
The mesh
value for the calculation,
and
= 500 um,
was set
to the
the baseplate
and
h ig h e s t
tem perature
was the same as the AFM measurement, 4 3 ° C .
Three areas on the SiC device were monitored
the te m peratures
measured
for the same
to compare with
locations by the AFM. A
power value of 1.23 watts per gate finger was used
to match
th e
simulated temperature at location T1 ( 1 7 2 ° C ) . This closely m a t c h e d
the value
obtained
from the I-V characteristics in figure
subsequent
thermal
response
19. The
for this simulation is shown in figure
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83
52, and the results
values compared
listed in table 3. It is seen that
well with the AFM measured
TS. The maximum
temperature
the s i m u l a t e d
values for areas T I ­
(T4) rise calculated
was
temperature
rise
above the baseplate
middle (250
um)
of the 4th and 5th gate fingers. This t e m p e r a t u r e
can be assumed
device.
order
the
This value is much
thermal
finite
between
calculation
element
the
importance
have
to be the maximum
low
channel
higher than
of 143°C ) in t h e
te m perature
the results
from
as a result of the increased
analysis
method.
The
and high resolution
o f using high resolution
high thermal
temperature
186°C ( a
conductivity
difference
of t h e
the
f irs t
accuracy
in
of
results
techniques dem onstrates
methods
and large
the
for SiC devices, w h ic h
heat
spreading
effects
compared to Si or GaAs devices.
One point to note
devices,
available
meaning
that
commercially.
is that
the SiC MMICs are r e s e a r c h - g r a d e
they haven't
Therefore,
actual SiC chip is probably
been
the
developed
physical
not as mature,
refined,
enough
packaging
to be
of t h e
and efficient as
for the GaAs devices. This can have an effect on the die attach of t h e
substrate
to
the
carrier
plate.
maintaining adequate thermal
This
interface
heat transfer.
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is
critical
for
84
T4
T2
I
-T 1
\
i
T3
i
Figure 52. Thermal results from FEA simulations for the SiC MESFET.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Table
3. Measured
and
simulated
temperatures
of SiC device
Figure 60.
L o c a tio n
M easured
S im u la te d
(AFM)
(FEA)
T1
17 2 ° C
172°C
T2
16 3 ° C
163°C
T3
15 8 ° C
147°C
T4
->
186°C
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
Similar
calculations
were
made
for
the
GaAs
PHEMT a n d
MESFET. The results are shown in figures 53 and 54. Once again t h e
AFM measurements, which were as close to the channel
as p o s s i b le ,
were used to augment the calculations for both types of devices. T h e
GaAs PHEMT showed
a maximum
temperature
of 128°C, or a 40°C
increase,
in the middle part of the device. The MESFET showed
increase
of
36°C from
the
AFM measurement
location,
an
for
a
maximum temperature of 166°C. This was also located in the m i d d l e
part of the device, in the center of the gate line.
A comparison of the thermal characterization data of the GaAs
and SiC devices is shown in Table 4. Note that because o f the g r e a t e r
heat spreading effect of the SiC substrate,
value is much closer to the actual
which
thermal
is usually
not
conductivity
temperature
comparison
are
available
a measured
maximum
in
for SiC versus GaAs and GaN as a function
of
shown
in
probing.
figures
of the large heat spreading
The
tem perature,
differences
clearly
for
channel
tem p eratu re
55
effects
and
56.
A nother
com pared
to GaAs
devices is that the temperature decrease from the heat source
under
the gate to the drain of a SiC MESFET has been found to be less t h a n
1°C, compared to 12°C for a GaAs device of similar geometry [78].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
S im ulated T m ax . = 128 °C
A FM m eas u rem en t = 84 °C
i
i
Figure 53. GaAs PHEMT with 10 gates.
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88
S im ulated T m ax . = 166 °C
AFM m easu rem en t = 130 °C
Figure 54. GaAs MESFET with 14 gates.
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89
Table 4. Summary of results in degrees Centigrade (°C).
D ev ic e
GaAs
M easured
(AFM)
(°C)
S im u la te d
(FEA)
(°C)
Increase
from
m easured
location
(°C)
T h erm al
Conductivity
[W/cmK]
84
128
44
0 .4 5
130
16 6
36
0 .4 5
172
1 86
14
3.3
PHEMT
GaAs
MESFET
SiC
MESFET
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90
SiC/GaAs thermal conductivity
3.5
(W/cm
2.5
2.0
Kth
°C)
3. 0
1 .0
*—
■e—
■—
s—
1 .5
Kth
Kth
Kth
Kth
SiC (exp.)
SiC (calc.)
GaAs (exp.)
GaAs (calc.)
0.50
0.0
0
50
100
150
200
250
300
350
T (°C)
Figure 55. Plot of SiC versus GaAs thermal
of
conductivity
te m perature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
as a f u n c tio n
91
3.5
a?
■a
*
E
G a N (GaAs T dependence)
3 .0
4 H -S iC (G aA s T dependence)
o
g
2 .5
£
2.0
o
3
T3
C
O
o
1 .5
75
E
1.0
0 .5
0
50
100
150
200
250
300
350
T e m p e r a t u r e (°C)
Figure 56. Plot of SiC versus GaN thermal
of
conductivity
tem perature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
as a f u n c tio n
92
III.F.
The
Effects
on
Device
R eliability
Evaluation
An example of the effect of using low resolution
resolution
techniques
and reliability
device
for determining
is shown
extrapolations
in figure 57.
that are
device
versus high-
channel
tem p eratu re
The two curve
based
on
lines are
the combined
the
channel
temperatures found by the IR and Cooke methods (red -lower c u r v e )
versus
the AFM and
FEA methods
(green-upper
curve).
The s l o p e
used for the arrhenius plot curves is the same 1.12 eV found for t h e
GaAs PHEMT device reliability test results (figure 4, page 7).
It is seen that if the low-resolution
to have a less than
techniques
are
used,
device
is predicted
hours,
or less than a year. This lifetime would be unacceptable
almost any application.
more accurate,
than
lifetime
100 years. This perform ance
any application,
the importance
adequate lifetime of 4 x 103
The higher resolution
acceptable
especially
techniques
for
predict
a
of 6.5 x 10 6 hours,
or g r e a t e r
would be acceptable
for a l m o s t
military and space
of using the most accurate
channel te m peratures
the
in device reliability.
systems.
method
This s h o w s
for d e t e r m i n i n g
It also dem onstrates
need for the quantitative AFM technique and its small probe size.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
93
400
3 5 0;
O
3 00
A F M /F E A => device life tim e of
©
200
6 . 5 x 1 0 s hours ( > 100 years)
IR /C oo ke => lifetim e of
4x10
hours (< 1 year)
D evice Life Time ( h o u rs )
Figure 57. An example Arrhenius
in
device
thermal
lifetime
prediction
characte rization
plot demonstrating
from
low
versus
techniques.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the d i f f e r e n c e
h ig h - r e s o l u t i o n
IV. CONCLUDING REMARKS AND FUTURE WORK
It
is concluded
thermistor
probe
the channel
that
by
tip, a quantitative
tem perature
channel
calibration
te mperature
tem perature
advances
the state
measurem ent
calculation,
can be substantiated
such
as
an
AFM
m e asu rem e n t
the
of the art
field by being
reported quantitative AFM thermal measurement.
measurements
of
the
element
f irs t
The results o f t h e
by applying a suitable
finite
in t h e
analysis.
therm al
Secondary
measurement and calculation techniques, such as IR microscopy
the
Cooke
model,
information
about
published
results
determine
the
described
can
also
the thermal
using
channel
are applicable
which the channel
of
of the GaAs PHEMTs and SiC MESFETs c a n
be made. This new technique
device
careful
be
useful
response
to other
(or junction)
providing
of the device.
AFM techniques
temperature
in
have
been
quantitatively.
types
of electronic
temperature
and
further
P re v io u s ly
unable
to
The m e t h o d s
devices
can be probed
for
from
the top surface of the device.
The
temperature
first
reported
and thermal
characterizations
response
of an actual
of
the
channel
SiC MESFET MMIC
were made.
Infrared microscopy and first order thermal c a l c u l a t i o n s
predicted a
low maximum temperature increase above
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the b a s e p l a t e
95
of 3 5 - 3 9 ° C upon DC bias. Atomic force thermal
finite
element
simulations
predicted
a
m easurem ents
more accurate
and
value
of
143°C. The entire area of source, gate, and drain is much higher in
temperature compared to devices
fabricated
in other materials (e.g.
GaAs) due to the lateral heat spreading on the device as a result o f
the improved
temperature
device
thermal
conductivity
measurem ent
operational
of the SiC. This difference
will affect
lifetime,
and
the reliability
can
also
in
prediction
be expected
of
to a f f e c t
design and packaging considerations. As electronic devices using SiC
become
correct
predict
more
temperature
the
temperatures
Future
include
common,
important
work
being
is
resolution
of
in choosing
and thermal
these devices,
the
model
and
to
the
locations.
probing
the
in several
of the device
probe
tip,
areas.
These
channel
area,
analysis
of
GaN
mapping of device areas, and c o m p l e t e
of the quantitative
of the potential
of
undertaken
AFM thermal
microwave devices, thermal
automation
technique
tem perature
at other
the
should be used
m e asurem e nt
channel
in-depth
increasing
caution
AFM thermal
thermal
AFM technique.
measurem ent
An e x a m p l e
in the device
channel
area is shown in figure 58 for the SiC MESFET. One of the c h a l le n g e s
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
in this particular
shorting
situation
to ground
is to prevent
in this
confined
the
area.
thermistor
However,
tip f r o m
experience
gained from the past measurements in this study has shown that th is
may not be as strong a consideration
m anufacturer.
upon
The thermistor
contact
with
metal
as stated
tip seems
surfaces
than
by the i n s t r u m e n t
to be more
previously
operational
assumed.
should increase the feasibility of the measurement.
5
10
Mm
X
Z
SIC MMIC w a f e r ;
5.000 yu/div
1 5 0 0 . 0 0 0 m t /d iu
1st c h a n n e l In FET ( 0 o ) , S —left
Figure 58. AFM of the channel area of the SiC MESFET.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This
97
To enhance
the
in-channel
measurement
and
to increase
resolution of the probe, it has been proposed
to add a nanotube
the end of the tip. The dimensions
nanotubes
of these
shown to be on the order of single wall (30 angstroms)
(300 Angstroms).
This is at least a factor of three
the ultimate resolution of the measurement.
wall carbon
nanotube
going project
th e
on
have b e e n
to m ulti-w all
improvement
in
An example of a m u l t i ­
is shown in figure 59, which is from an o n ­
with NASA. Some obstacles
to be overcome
are th e
attachment of the nanotube to the tip, the influence of the n a n o t u b e
thermal
conductivity
on the measured
value of the voltage
should be minimal), and the determination
(w h ic h
of the actual d i m e n s i o n s
of the nanotube.
0
D a ta t y p e
Z ran g e
1 . 7 0 um
H e ig h t
1 5 0 .0 nn
0
D a ta t y p e
Z ran g e
1 . 7 0 UN
H e ig h t
1 5 0 . 0 nM
0
D a ta ty p e
Z ran g e
Figure 59. AFM images of carbon nanotubes.
R e p ro du ced with permission o f the copyright owner. Further reproduction prohibited without permission.
1 . 7 0 dm
ftM p l i tu d e
1 .0 0 0 0 U
98
Preliminary
IR results
have also
been
obtained
for GaN o n
sapphire ( A U 0 3) and GaN on SiC HEMTs, as shown in figures 6 0 - 6 1 .
The change in material
SiC) represents
AFM thermal
thermal
measured
will dictate
the
and
tem peratures
(A1203 a n d
significant challenges in the interpretation
conductivity
sapphire
from device (GaN) to substrate
and calculated
between
their
due
substrates
maximum
substrates
will
to their
results.
poor
GaAs. The GaN and SiC materials
The differences
for the different
te m peratures
most
of f u t u r e
likely
thermal
upon
the device, and may reveal lower maximum
devices
biasing.
show
the
conductivity,
have better
in
The
highest
similar
to
heat flow away f r o m
te m p eratu res
depending
on their bias conditions.
To
obtain
technique
will
program m ing
thermal
maps of device
require c o m p u te r-a id e d
analog
to
digital boards
to
areas
using
such
as
synchronize
with
the
scans. These are feasible, and the author
experience
and
required
for
complete
in this
area.
automation
has e x t e n s i v e
Similar
e q u ip m e n t
of
quantitative
the
AFM
electronics,
instrument
ideas
the
would
be
therm al
measurement of the AFM, including the heating of the sample. T h e s e
ideas are being refined and will be implemented in future research.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
Figure 60 a. GaN on A1203 HEMT at 200x.
Figure 60 b. IR scan of GaN HEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 61 b. IR of GaN on SiC HEMT.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
REFERENCES
101
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
REFERENCES
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TI THERMAL CHARACTERIZATION AND SIMULATION
fTT A. Semi conductor Microwave Devices^
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APPENDIX A
Example o f 1st Order Thermal Model:
(* Thermal calculation for SiC MESFETs based on Cooke Method *)
(*
(*
(*
(*
(*
(*
(*
(*
(*
JM revised 4-10-97; K. Christianson 9/30/93 *)
enter values: *)
s = gate-to-gate spacing (microns) *)
1 = gate length (microns) *)
z = total gate width (mm) *)
n = number of gate fingers *)
f = substrate thickness (microns) *)
tb = baseplate temperature (oC) *)
pwr = power input (watts) *)
s= 4 0 ;
1=0.7;
z=3;
n= 6;
f= 400 ;
tb = 2 5 ;
p w r = 6 .5 ;
p = 2 * S q r t[ ( t + S e c h [ ( 3 . 14 159* 1 )/(4 f ) ] ) / ( I - S e c h [ ( 3 . 14 1 5 9 * l ) / ( 4 f ) ] )];
m = ( 2 ( C o s h [ 3 . 1415 9 * ( s + l ) /( 4 f ) ] / C o s h [ 3 . 14 1 59*(sl ) / ( 4 f ) ] ) A0 . 5 + l ) / ( ( C o s h [
3 . l 4 1 5 9 * ( s + l ) / ( 4 f ) ] / C o s h [ 3 . l 4 l 5 9 * ( s - l ) / ( 4 f ) ] ) A0 . 5 - l ) ;
t z k = n / ( 3 . 1 4 1 5 9 * ( ( 2 ( n - l ) / L o g [ m ] ) - ( n - 2 ) / L o g [ p ] ));
k th = 7 . 7 4 7 9 t b A- 0 . 2 5 2 3 2 ;
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(* program outputs: *)
(* theta = thermal resistance (oC/W) *)
(* dt = channel temperature rise (oC) *)
(* tch = channel temperature (oC) *)
(* tt = channel temperature (oC), corrected for kth=f(T)
th eta= tzk/((z/10)*kth)
3 .8 9 2 2 6
dt = pwr theta
25.2997
tch = dt + tb
50.2997
0.74 dt
tt = (---------+ tb
0.26
tb
0.74
1.35
)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX B
Example of Finite Element Calculation:
executing
/u s r 2 /s i l vaco/1 ib/a tl a s /5 .2 .0 .R / h p 7 0 0 - h pux901 /at las. exe
ATLAS
Version:
atlas 5.2.0.R (Thu Mar 2 16:47:55 PST 2000)
Copyright 1989 - 1998 SILVACO International
All rights reserved
We acknowledge the contribution of the following collaborative
partners:
Stanford University
University of Texas at Austin
University of Florida
Harris Semiconductor
Dynamics Research Corporation
Vanderbilt University
ATLAS
: enabled
C Interpreter
: enabled
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
ESD Model
: not licensed
S-PISCES
: enabled
BLAZE
: enabled
GIGA
: enabled
LUMINOUS
TFT
MIXEDMODE
: enabled
: enabled
: enabled
LASER
: not licensed
FERRO
: not licensed
QUANTUM
SiC
DEVICE3D
THERMAL3D
INTERCONNECT3D
: not licensed
: not licensed
: enabled
: enabled
: not licensed
GIGA3D
: not licensed
BLAZE3D
: not licensed
MIXEDMODE3D
TFT3D
QUANTUM3D
: not licensed
: not licensed
: not licensed
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
Thu Dec 6 15:04:34 2001
Executing on host: sinh
ATLAS>
ATLAS> # SiC-5-17-01 -c: more planes
ATLAS>
ATLAS> mesh inf=SiC-5-17-0 l-c2.str three.d
Reading MASTER format file SiC-5-17-01-c2.str from DEVEDIT3D.
Read 5688 sem & ins nodes and 0 metal nodes.
Read 9 z planes.
Read 9248 sem & ins prizms and 0 metal prizms.
Read 10 regions.
Read 0 electrodes.
698273 net bytes allocated during read.
ATLAS>
ATLAS> electrode num = l
y .m ax=400.0
x.min=0.0 x.max=280.0 y.min=400.0
Electrode # 1
Name: #1
Number of boundary nodes:
Dimensions in microns:
min
max
x 0.000e+00
2.800e+02
y 4.000e+02
4.000e+02
z 0.000e+00
7.000e+02
ATLAS>
ATLAS> material region=l
135
tc.const=3.3
Mesh statistics:
Total number of grid points
=
Number of grid points in plane =
Number of triangles in plane
=
5688
632
1156
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
Obtuse triangles in plane
=
0 ( 0.0)
Total number of z planes
=
9
Total number of prisms
=
9248
power= 1.23
region=2
tc.const=3.3
ATLAS> material
ATLAS> material region=3 tc.const=3.3 power= 1.23
ATLAS> material region=4 tc.const=3.3 power= 1.23
ATLAS> material region=5 tc.const=3.3 power= 1.23
ATLAS> material region=6 tc.const=3.3 power=1.23
ATLAS> material region=7 tc.const=3.3 power=1.23
ATLAS> material region=8 tc.const=3.3
ATLAS> material region=9 tc.const=3.3
ATLAS> material region=10 tc.const=3.3
ATLAS>
ATLAS>
ATLAS> models I:hermal print
ATLAS>
ATLAS> method newton
Block-iterative
carriers = 2
CONSTANTS:
Boltzmann's constant
= 1.38066e-23 J/K
Elementary charge
= 1.6023e-l9 C
Permitivity in vacuum = 8 .85 418e-14 F/cm
Temperature
= 300 K
Thermal voltage
= 0.0258502 V
REGIONAL MATERIAL PARAMETERS:
Region
:
1
2
3
4
5
6
7
8
9
10
11
Material
:
Silicon Silicon Silicon Silicon Silicon Silicon
Silicon
Silicon
Silicon
Silicon Conductor
Type
:
semicond. semicond. semicond. semicond. semicond.
semicond. semicond. semicond. semicond. semicond.
metal
Epsilon
:
11.8
11.8
11.8
11.8
11.8
11.8
11.8
11.8
11.8
11.8
Band Parameters
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
1.08
1.08
1.08
1.08
Eg (eV)
:
1.08
1.08
1.08
1.08
1.08
1.08
4.17
4.17
4.17
4.17
4.17
Chi (eV)
:
4.17
4.17
4.17
4.17
4.17
2.8e+19
2.8e+l9
2.8e+19
2.8e+19
2.8e+l9
Nc (per cc) :
2.8e+19
2.8e+19
2.8e+19
2.8e+l9
2.8e+19
Nv (per cc) : 1.04e+19 1.04e+19 1.04e+19 1.04e+19 1.04e+19
1.04e+19 1.04e+19
1.04e+19
1.04e+19
l.04e+19
ni (per cc) : 1.45e+10 1.45e+10 1.45e+10 1.45e+10 1.45e+10
1.45e+10
I.45e+10
1.45e+10
1.45e+10
1.45e+l0
2
2
2
2
2
Gc
:
2
2
2
2
2
4
4
4
4
4
Gv
:
4
4
4
4
4
0.044
0.044
0.044
0.044
Ed (eV)
:
0.044
0.044
0.044
0.044
0.044
0.044
0.045
0.045
0.045
0.045
Ea (eV)
:
0.045
0.045
0.045
0.045
0.045
0.045
Recombination Parameters
le-07
le-07
le-07
le-07
Lifetime (el):
le-07
le-07
le-07
le-07
le-07
le-07
le-07
le-07
le-07
le-07
Lifetime (ho):
le-07
le-07
le-07
le-07
le-07
le-07
2.8e-31 2.8e2.8e-31 2.8e-31
Auger cn
: 2.8e-31
2.8e-31
2.8e-31
31
2.8e-31
2.8e-31
2.8e-31
9.9e-32
9.9e9.9e-32
9.9e-32
Auger cp
: 9.9e-32
9.9e-32
9.9e-32
32
9.9e-32
9.9e-32
9.9e-32
0
0
0
0
0
Auger kn
:
0
0
0
0
0
0
0
0
0
0
Auger kp
:
0
0
0
0
0
0
0
0
0
0
Copt
:
0
0
0
0
0
110
110
110
110
An**
:
110
110
110
110
110
110
30
30
30
30
30
Ap**
:
30
30
30
30
30
Impact Ionization Model Parameters
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
betan
1
1
betap
1
1
1
1
1
1
1
1
4e+05
4e+05
4e+05
egran
:
4e+05
4e+05
4e+05
4e+05
4e+05
4e+05
4e+05
:
7.03e+05 7.03e+05 7.03e+05 7.03e+05 7.03e+05
an I
7.03e+05 7.03e+05
7.03e+05 7.03e+05
7.03e+05
:
l.23e+06 l.23e+06 l.23e+06 l.23e+06 l.23e+06
bnl
1.23e+06 1.23e+06
1.23e+06 1.23e+06
1.23e+06
:
7.03e+05 7.03e+05 7.03e+05 7.03e+05 7.03e+05
an 2
7.03e+05
7.03e+05
7.03e+05 7.03e+05
7.03e+05
:
1.23e+06 1.23e+06 1.23e+06 1.23e+06 1.23e+06
an2
1.23e+06 1.23e+06
I.23e+06 I.23e+06
1.23e+06
:
6.7 le+05 6.71e+05 6.71e+05 6.71e+05 6.71e+05
apl
6.7
le+05
6.7 le+05
6.7 le+05 6.7 le+05
6.7 le+05
:
l.69e+06 1.69e+06 1.69e+06 l.69e+06 1.69e+06
bp I
I.69e+06 I.69e+06
I.69e+06 1.69e+06
l.69e+06
:
l.58e+06 1.58e+06 l.58e+06 1.58e+06 1.58e+06
ap2
1.58e+06 1.58e+06
1.58e+06 1.58e+06
1.58e+06
:
2.04e+06 2.04e+06 2.04e+06 2.04e+06 2.04e+06
bp2
2.04e+06 2.04e+06
2.04e+06 2.04e+06
2.04e+06
Saturation Velocities
Vsatn (cm/s) :
I.03e+07 1.03e+07 1.03e+07
1.03e+07
1.03e+07
1.03e+07
1.03e+07
1.03e+07 1.03e+07
Vsatp (cm/s) :
1.03e+07 1.03e+07 1.03e+07
1.03e+07
1.03e+07
1.03e+07
1.03e+07
1.03e+07 1.03e+07
REGIONAL MODEL FLAGS:
7
8 9
Region:
1 2
3 4
5
6
SRH
F F F F F F F F F F
consrh
F F F F F F F F F F
klasrh
F F F F F F F F F F
Auger
F F F F F F F F F F
klaaug
F F F F F F F F F F
optr
F F F F F F F F F F
bgn
F F F F F F F F F F
incomplete
F F F F F F F F F F
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.03e+07
l.03e+07
120
bbt
F F F F F F F F F F
bbtauto
F F F F F F F F F F
Boltzmann
T T T T T T T T T T
Fermi-Dirac
F F F F F F F F F F
Laser gain model
gain model
0 0 0 0 0 0 0 0 0 0 0
REGIONAL MOBILITY MODEL SUMMARY:
Region #1:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #2:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Reproduced with permission of the copyright owner. Further reproduction prohibited w i t h Z ^ S T
121
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #3:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #4:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #5:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #6:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #7:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #8:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #9:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
Region #10:
Model for Electrons:
Concentration Independent Mobility
(CONMOB=F)
mu = 1000
tmu = 1.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
Model for Holes:
Concentration Independent Mobility
(CONMOB=F)
mu = 500
tmu = 1.5
#1
I
.000
.000E+00
.000E+00
.000E+00
ATLAS>
ATLAS> solve 11=316
DECKBUILD WARNING: No prompt detected. Auto-inserting newline...
Region #1
W /cm **3
Region #2
W /cm **3
Region #3
W /cm **3
Region #4
W /cm **3
Region #5
W /cm **3
Region #6
W /c m * * 3
Region #7
W /cm**3
Region #8
W /cm **3
Region #9
W /c m * * 3
Region #10
0 .000 0e+ 00
volume = 7.8399e-05 cm**3 power density — 0.0000e+00
volume = 1.0000e-l0 cm**3 power density
1.2300e+10
volume = I.0000e-I0 cm**3 power density = i.2300e+10
volume = 1.0000e-10 cm**3 power density IS 1.2300e+l0
volume = 1.0000e-10 cm**3 power density
1.2300e+10
volume = 1.0000e-10 cm**3 power density = 1.2300e+l0
volume = 1.0000e-10 cm**3 power density
1.2300e+10
volume = 5.0000e-14 cm**3 power density ST 0.0000e+00
volume = 5.0 000e-14 cm**3 power density = 0.0000e+00
volume = 5.0000e-14 cm**3 power density =
W/cm**3
Temperature on thermal electrode #1 316K
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126
Heat flow equation solution started
Nonlinear iteration #1
Temperature Correction:
122.344
Nonlinear iteration #2
Temperature Correction:
45.339
Nonlinear iteration #3
Temperature Correction:
18.2613
Nonlinear iteration #4
Temperature Correction:
6.39042
Nonlinear iteration #5
Temperature Correction:
3.52788
Nonlinear iteration #6
Temperature Correction:
1.43726
Nonlinear iteration #7
Temperature Correction:
0.393511
Nonlinear iteration #8
Temperature Correction:
0.211255
Nonlinear iteration #9
Temperature Correction:
0.103553
Nonlinear iteration #10
Temperature Correction:
0.0385494
Nonlinear iteration #11
Temperature Correction:
0.0156363
Nonlinear iteration #12
Temperature Correction:
0.00766671
Nonlinear iteration #13
Temperature Correction:
0.00336641
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
127
Nonlinear iteration #14
Temperature Correction:
0.00110587
Nonlinear iteration #15
T em perature Correction:
0.000559527
Nonlinear iteration #16
T em perature Correction:
0.000260175
Nonlinear iteration #17
T emperature Correction:
7.6493e-05
Nonlinear iteration #18
T emperature Correction:
3.99129e-05
Nonlinear iteration #19
T em perature Correction:
0.000449218
Nonlinear iteration #20
T emperature Correction:
0.260093
Nonlinear iteration #21
Temperature Correction:
0.345943
Nonlinear iteration #22
Temperature Correction:
0.118342
Nonlinear iteration #23
T emperature Correction:
0.0322821
Nonlinear iteration #24
T emperature Correction:
0.00568298
Nonlinear iteration #25
T em perature Correction:
0.000685581
Heat flow equation solution completed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
128
1.60e+02um Y
1.67e-02um Z
Region #1 MaxTemp 4.59e+02K X
= 9.75e+01um
3.67e+02um Z
MinTemp 3.16e+02K X = 1.33e+01um Y
= 5.00e-02um
4.04e+01um Y
1.67e-02um z
Region #2 MaxTemp 4.52e+02K X
=
= 3.50e+02um
1,83e-0lum z
4.01e+01 um Y
MinTemp 4.48e+02K X
=
= 3.50e+02um
8.04e+0lum Y = 1,67e-02um z
Region #3 MaxTemp 4.57e+02K X
= 3.50e+02um
8.01e+01um Y — 1,83e-01um z
MinTemp 4.53e+02K X
=
= 3.50e+02um
1.20e+02um Y
1,67e-02um z
Region #4 MaxTemp 4.59e+02K X
=
=
= 3.50e+02um
1.83e-0lum z
1.20e+02um Y
MinTemp 4.54e+02K X
= 3.50e+02um
1.67e-02um z
1.60e+02um Y
Region #5 MaxTemp 4.59e+02K X
=
= 3.50e+02um
1.83e-01um z
1.6le+02um Y
MinTemp 4.54e+02K X
= 3.50e+02um
2.00e+02um Y — 1.67e-02um z
Region #6 MaxTemp 4.57e+02K X
= 3.50e+02um
1.83e-01um z
MinTemp 4.53e+02K X = 2.01e+02um Y
=
= 3.50e+02um
8.33e-03um z
2.40e+02um Y
Region #7 MaxTemp 4.53e+02K X
=
= 3.50e+02um
2.4le+02um Y = 1.92e-01um z
MinTemp 4.49e+02K X
= 3.50e+02um
Region #8 MaxTemp 4.44e+02K X = 2.20e+02um Y = 1,67e-02um z
= 9 .5 0 e + 0 lu m
2.24e+02um Y = 9 . 17e-02um z
MinTemp 4.44e+02K X
= 9.50e+01um
2.60e+02um Y ZT 1,67e-02um z
Region #9 MaxTemp 4.36e+02K X
= 9.01e+01um
MinTemp 4.36e+02K X — 2.64e+02um Y = 9 . 17e-02um z
= 9.01e+01um
Region #10
MaxTemp 4.20e+02K X = 2.40e+02um Y = 1.67e02um Z = 5.00e-02um
MinTemp 4.20e+02K X = 2.44e+02um Y = 9.17e-02um Z
= 5.00e-02um
—
—
—
—
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
129
ATLAS> ATLAS>
ATLAS> #outfile=SiC -5-17-0 l-c-T.str
ATLAS>
ATLAS> quit
ATLAS version 5.2.0.R finished at Thu Dec
real
user
sys
6 15:15:54 2001
11:20.4
10:55.7
1.7
END
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
130
CIRRICULUM VITAE
Jeffrey A. Mittereder was born on November 30, 1961 in N a t r o n a
Heights, Pennsylvania, and is an American citizen. He g r a d u a t e d
from Burrell High School, Lower Burrell, Pennsylvania, in 1980, a n d
received the Bachelor of Science in Metallurgical Engineering &
Materials Science with Electronic Materials Option from C a rn e g ieMellon Unversity, Pittsburgh, Pennsylvania in 1984. He received t h e
Master of Science in Materials Engineering and Solid Mechanics f r o m
George Washington University in Washington, DC in 1990. He is wi t h
the Reliability Science Section, Microwave Technology Branch, of t h e
Electronics Science and Technology Division at the Naval R e s e a r c h
Laboratory, Washington, D.C., where he works on the relia bility
testing and failure analysis of compound semiconductor devices.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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