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b
ab
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1.
I
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RO
D
UCT
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T
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tr
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c
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cr
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s
in
g
l
y
h
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er
[
1
-
3
]
.
E
m
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g
i
n
g
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ee
d
s
in
t
h
is
ar
ea
ar
e
n
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elate
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telec
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m
u
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icatio
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m
ar
k
et,
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u
t
i
n
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th
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f
o
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to
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d
lo
w
p
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w
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co
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s
u
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p
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[
4
]
.
Sin
ce
t
h
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9
0
s
,
a
n
e
w
g
e
n
er
atio
n
o
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s
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m
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d
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p
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as Ga
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b
ased
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f
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c
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m
s
[
6
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.
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to
t
h
ei
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b
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k
d
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w
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ield
[
7
].
T
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p
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m
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f
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MT
,
an
ac
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ate
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en
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n
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er
esti
m
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ted
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ea
r
th
e
t
h
r
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h
o
ld
[
8]
,
[
9
]
.
Ot
h
er
m
o
d
els
o
f
f
er
a
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I
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N:
2088
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8708
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tima
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litt
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[
1
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2
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[
1
3
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e
o
f
GaN
an
d
th
e
co
n
ce
p
ts
o
f
s
p
o
n
ta
n
eo
u
s
a
n
d
p
iezo
elec
tr
ic
p
o
lar
izatio
n
s
,
T
h
e
m
ec
h
a
n
is
m
o
f
t
h
e
f
o
r
m
atio
n
o
f
t
h
e
2
DE
G
at
th
e
A
l
GaN
/
GaN
i
n
ter
f
ac
e
t
h
e
n
s
o
lv
in
g
P
o
is
s
o
n
a
n
d
Sc
h
r
ö
d
in
g
er
eq
u
atio
n
s
to
d
eter
m
in
e
th
e
2
DE
G
d
en
s
it
y
a
n
d
f
i
n
all
y
d
ed
u
ce
t
h
e
c
u
r
r
en
t i
ds
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Sp
o
nta
neo
us
a
nd
P
iezo
elec
t
r
ic
P
o
la
riza
t
io
n
T
h
e
I
I
I
-
V
m
ater
ials
cr
y
s
ta
llo
g
r
ap
h
ic
ar
r
an
g
e
m
e
n
t
s
t
u
d
ied
in
th
is
w
o
r
k
w
il
l
b
e
W
u
r
tzite
,
a
s
s
ee
n
t
h
i
s
cr
y
s
talli
n
e
f
o
r
m
i
s
t
h
e
m
o
s
t
s
tab
le
p
h
ase
an
d
it
p
r
o
v
i
d
es
r
e
m
ar
k
ab
le
p
h
y
s
ica
l
p
r
o
p
er
ties
[
1
4
]
.
T
h
e
co
m
b
i
n
atio
n
o
f
b
o
t
h
g
alli
u
m
a
n
d
n
i
tr
o
g
en
ele
m
e
n
t
s
o
f
d
if
f
er
en
t
elec
tr
o
n
e
g
ati
v
it
ies
ca
u
s
e
s
a
ch
ar
g
e
tr
an
s
f
er
o
f
th
e
ele
m
e
n
t
w
it
h
a
h
i
g
h
elec
tr
o
n
eg
ati
v
it
y
to
th
e
ele
m
e
n
t
h
a
v
in
g
a
lo
w
elec
tr
o
n
e
g
ati
v
it
y
.
T
h
is
p
h
en
o
m
e
n
o
n
i
s
th
e
ca
u
s
e
o
f
th
e
s
p
o
n
ta
n
eo
u
s
p
o
lar
izatio
n
,
w
h
ich
is
t
h
e
f
ir
s
t
ch
ar
ac
ter
is
tic
o
f
th
e
g
alliu
m
n
i
tr
id
e.
T
h
e
s
p
o
n
tan
eo
u
s
p
o
lar
izatio
n
f
ield
o
f
ter
n
ar
y
co
m
p
o
u
n
d
s
ca
n
b
e
ca
lcu
lated
b
y
ap
p
l
y
i
n
g
Ver
g
ar
d
’
s
la
w
[
1
5
]
.
BC
P
AC
P
m
BC
P
C
B
A
P
sp
sp
sp
m
m
sp
1
(
1
)
T
h
e
GaN
is
o
f
ten
d
ev
elo
p
ed
o
n
s
ap
p
h
ir
e,
SiC
o
r
s
ilico
n
.
T
h
e
lattice
m
is
m
atc
h
b
et
w
ee
n
G
aN
an
d
t
h
e
s
u
b
s
tr
ate
i
m
p
o
s
e
s
a
s
tr
ai
n
(
e
x
p
an
s
io
n
o
r
co
m
p
r
ess
io
n
)
i
n
t
h
e
b
ase
p
lan
e
o
f
GaN
la
y
er
s
.
T
h
e
d
ef
o
r
m
atio
n
o
f
th
e
lattice
GaN
en
tr
ai
n
s
a
ch
a
r
g
e
b
ar
y
ce
n
ter
d
is
p
lace
m
e
n
t,
h
en
ce
a
ch
a
n
g
e
i
n
th
e
s
p
o
n
ta
n
eo
u
s
p
o
lar
izatio
n
.
T
h
is
ef
f
ec
t
is
th
e
s
ec
o
n
d
c
h
ar
ac
ter
is
tic
o
f
th
e
g
al
liu
m
n
itrid
e
ca
lled
:
p
iezo
elec
tr
ic
p
o
lar
izatio
n
,
w
h
ic
h
s
tr
en
g
th
e
n
s
o
r
w
ea
k
en
s
th
e
s
p
o
n
tan
eo
u
s
p
o
lar
izatio
n
.
T
h
e
p
i
ez
o
elec
tr
ic
p
o
lar
izatio
n
f
ield
is
g
i
v
en
b
y
[
1
6
]
:
)
(
)
(
)
(
)
(
)
0
(
)
(
)
0
(
2
)
(
33
13
33
31
m
C
m
C
m
e
m
e
a
m
a
a
m
P
p
z
A
lG
a
N
(
2
)
T
ab
le
1
.
P
h
y
s
ical
p
ar
a
m
e
ter
s
o
f
I
n
N,
A
lN
a
n
d
GaN
In
N
A
lN
G
a
N
a
0
(
Å
)
3
.
5
8
5
3
.
1
1
0
3
.
1
8
9
e
3
1
(C/
m
2
)
-
0
.
5
7
-
0
.
5
0
-
0
.
3
5
e
3
3
(C/m
2
)
0
.
9
7
1
.
7
9
1
.
2
7
c
1
3
(G
P
a
)
92
108
106
c
3
3
(G
P
a
)
224
373
398
P
s
p
(C/m
2
)
-
0
.
0
4
2
-
0
.
0
9
-
0
.
0
3
4
T
ab
le
1
s
h
o
w
s
th
e
v
al
u
es
f
o
r
r
elev
an
t
p
h
y
s
ical
p
ar
a
m
e
ter
s
o
f
A
lN
a
n
d
GaN
[
1
7
-
19
]
.
T
o
ca
l
cu
late
t
h
e
ef
f
ec
ts
o
f
p
o
lar
izatio
n
in
A
l
m
Ga
1
-
m
N
allo
y
w
e
n
ee
d
th
e
lat
tice
co
n
s
ta
n
t,
p
iezo
elec
tr
ic
co
n
s
ta
n
t
s
an
d
elasti
c
co
n
s
ta
n
ts
o
f
Al
m
Ga
1
-
m
N
w
h
ic
h
ca
n
b
e
ca
lc
u
lated
b
y
a
n
alo
g
o
u
s
l
y
ap
p
l
y
i
n
g
Ver
g
ar
d
’
s
la
w.
T
o
am
o
u
n
t
o
f
t
h
e
p
o
lar
izatio
n
in
d
u
ce
d
ch
ar
g
e
d
en
s
it
y
is
g
i
v
en
b
y
:
s
p
G
a
N
A
lG
a
N
pz
sp
P
P
P
(
3
)
2
.
2
.
Ca
lcula
t
ing
t
he
E
lect
ro
nic D
ens
it
y
a
t
t
he
I
nte
rf
a
ce
W
e
ar
e
p
ar
ticu
lar
l
y
in
ter
ested
b
y
t
h
e
h
eter
o
j
u
n
ctio
n
A
l
GaN
/
GaN
,
b
asic
elem
e
n
t
o
f
th
e
b
ar
r
ier
lay
e
r
an
d
th
e
c
h
a
n
n
el
o
f
t
h
e
tr
an
s
i
s
to
r
s
tu
d
ied
.
T
h
e
p
r
in
cip
le
o
f
th
e
h
eter
o
j
u
n
ctio
n
b
ased
o
n
co
n
tactin
g
o
f
t
w
o
s
e
m
ico
n
d
u
cto
r
m
ater
ial
s
w
it
h
d
if
f
er
e
n
t
b
an
d
g
ap
,
s
u
ch
a
s
o
n
e
h
as
a
lar
g
e
b
a
n
d
g
ap
,
th
e
o
th
er
h
as
a
lo
w
b
an
d
g
ap
.
Dep
en
d
in
g
o
n
t
h
e
m
o
d
el
o
f
An
d
er
s
o
n
w
h
ich
i
s
s
u
p
p
o
r
ted
o
n
th
e
ap
p
r
o
x
i
m
ati
o
n
o
f
Sc
h
o
k
le
y
[
8
]
,
b
r
in
g
i
n
g
in
to
co
n
tact
o
f
t
h
ese
m
ater
ial
s
,
i
n
t
h
e
ca
s
e
o
f
t
h
er
m
o
d
y
n
a
m
ic
eq
u
ilib
r
i
u
m
,
ca
u
s
es
th
e
ali
g
n
m
e
n
t
o
f
th
e
Fer
m
i
le
v
el
a
n
d
t
h
e
tr
a
n
s
f
er
o
f
elec
tr
o
n
s
o
f
t
h
e
w
id
e
b
a
n
d
g
ap
m
ater
ial
to
t
h
e
lo
w
b
a
n
d
g
ap
m
ater
ial.
An
elec
tr
ic
f
ield
is
g
en
er
ated
at
t
h
e
i
n
ter
f
ac
e
a
n
d
a
b
a
n
d
o
f
cu
r
v
atu
r
e
ap
p
ea
r
s
in
it
s
v
ici
n
it
y
.
A
p
o
ten
t
ial
w
e
ll
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il
201
8
:
9
5
4
–
9
6
2
956
cr
ea
ted
at
lo
w
b
an
d
g
ap
s
e
m
ic
o
n
d
u
cto
r
s
id
e;
h
e
n
ce
a
n
ac
c
u
m
u
latio
n
o
f
elec
tr
o
n
s
f
o
r
m
s
a
t
th
e
i
n
ter
f
ac
e.
I
n
a
HE
MT
s
tr
u
ctu
r
e,
th
e
elec
tr
o
n
s
ac
cu
m
u
lated
in
t
h
e
p
o
ten
tial
w
ill
f
o
r
m
a
t
w
o
-
d
i
m
e
n
s
i
o
n
al
elec
tr
o
n
g
as.
Un
d
er
s
ta
n
d
in
g
t
h
e
p
h
y
s
ical
p
h
en
o
m
en
a
g
o
v
er
n
i
n
g
th
e
o
p
er
atio
n
o
f
t
h
e
HE
MT
an
d
t
h
e
f
o
r
m
atio
n
o
f
a
2
DE
G
r
eq
u
ir
es
s
o
l
v
i
n
g
t
h
e
Sc
h
r
ö
d
in
g
er
’
s
eq
u
at
io
n
.
W
it
h
t
h
e
f
ir
s
t
t
w
o
q
u
a
n
t
u
m
s
tates
o
cc
u
p
ie
d
,
th
e
to
tal
2
DE
G
d
en
s
it
y
in
t
h
e
ac
c
u
m
u
latio
n
la
y
er
is
g
i
v
e
n
b
y
[
20
]:
kT
E
E
kT
E
E
kT
m
E
n
F
F
e
F
s
1
0
2
*
e
x
p
1
e
x
p
1
ln
(
4
)
W
h
er
e
E
F
is
th
e
Fer
m
i
lev
el,
E
1
an
d
E
2
ar
e
q
u
an
tu
m
s
tate
o
cc
u
p
ied
.
W
e
estab
lis
h
a
f
ir
s
t
eq
u
atio
n
o
f
2
DE
G
d
en
s
it
y
n
o
ted
n
s
(E
F
)
th
at
b
i
n
d
s
t
h
e
elec
tr
o
n
s
d
e
n
s
it
y
a
t
t
h
e
i
n
ter
f
ac
e
A
lGaN
/GaN,
to
th
e
Fer
m
i
lev
e
l.
A
s
ec
o
n
d
r
elatio
n
o
f
t
h
e
t
y
p
e
n
s
(V
gs
, E
F
)
ca
n
b
e
estab
li
s
h
ed
b
y
in
te
g
r
atin
g
t
h
e
P
o
is
s
o
n
eq
u
ati
o
n
.
W
e
o
b
tain
th
F
gs
F
gs
s
V
q
E
V
qd
E
V
n
)
,
(
(
5
)
W
ith
ε
is
GaN
d
ielec
tr
ic
co
n
s
t
an
t
.
Hen
ce
t
h
e
eq
u
atio
n
g
o
v
er
n
in
g
t
h
e
ev
o
l
u
tio
n
o
f
th
e
t
h
r
es
h
o
ld
v
o
ltag
e
d
d
qN
q
E
q
V
D
c
b
th
2
2
(
6
)
W
h
er
e
φ
b
i
s
t
h
e
Sc
h
o
tt
k
y
b
ar
r
ier
h
ei
g
h
t,
Δ
E
c
is
th
e
co
n
d
u
ct
i
o
n
b
an
d
d
is
co
n
ti
n
u
i
t
y
b
et
w
ee
n
A
l
GaN
a
n
d
GaN
,
N
D
A
lGaN
la
y
er
d
o
p
in
g
a
n
d
d
is
A
lGaN
la
y
er
t
h
ick
n
es
s
.
So
lv
i
n
g
t
h
e
s
y
s
te
m
o
f
E
q
u
atio
n
s
(
4
)
an
d
(
5
)
allo
ws
th
e
e
v
o
lu
tio
n
o
f
ca
r
r
ier
co
n
ce
n
tr
atio
n
n
s
in
th
e
w
ell
a
s
a
f
u
n
ctio
n
o
f
V
gs
.
W
e
ca
n
o
b
tai
n
ap
p
r
o
x
i
m
ate
s
o
l
u
tio
n
s
in
th
r
ee
s
p
ec
i
f
ic
b
ias r
a
n
g
e
s
:
w
ea
k
in
v
er
s
io
n
,
m
o
d
er
ate
in
v
e
r
s
io
n
an
d
s
tr
o
n
g
i
n
v
er
s
io
n
.
2
.
3
.
Wea
k
I
nv
er
s
io
n
Fo
r
lo
w
elec
tr
o
n
s
d
e
n
s
itie
s
at
th
e
in
ter
f
ac
e:
t
h
e
Fer
m
i
lev
e
l
is
lo
ca
ted
b
ey
o
n
d
th
e
f
ir
s
t
e
n
er
g
y
s
u
b
-
b
an
d
.
E
x
h
ib
ito
r
s
ap
p
ea
r
i
n
g
i
n
E
q
u
atio
n
(
4
)
ar
e
n
eg
ati
v
e
an
d
li
m
ited
d
ev
elo
p
m
e
n
t
t
y
p
e
l
n
(
1
+
ε)
=
ε
o
f
th
is
eq
u
atio
n
allo
w
s
g
i
v
i
n
g
:
kT
E
kT
E
kT
E
kT
m
n
F
e
s
1
0
2
*
e
x
p
e
x
p
e
x
p
(
7
)
Fo
r
th
is
elec
tr
ic
p
o
lar
izatio
n
r
eg
i
m
e,
E
0
an
d
E
1
ar
e
less
th
a
n
KT
s
o
th
at
kT
E
kT
m
n
F
e
s
e
x
p
2
2
*
(
8
)
As
w
ell
t
h
e
Fer
m
i e
n
er
g
y
E
F
i
s
b
o
n
d
ed
to
th
e
elec
tr
o
n
d
en
s
it
y
b
y
t
h
e
r
elatio
n
kT
m
n
kT
E
e
s
F
*
2
2
ln
(
9
)
B
y
p
o
s
tp
o
n
in
g
th
is
e
x
p
r
ess
io
n
i
n
t
h
e
E
q
u
atio
n
(
4
)
an
d
s
u
p
p
o
s
in
g
t
h
at
t
h
e
d
e
n
s
it
y
is
w
e
ak
co
m
p
ar
ed
to
t
h
e
d
en
s
it
y
o
f
s
ta
tes as
s
o
ciate
d
w
i
th
th
e
b
o
th
f
ir
s
t su
b
-
b
an
d
s
,
w
e
g
et:
kT
m
V
V
q
kT
m
n
th
gs
e
s
)
(
e
x
p
2
2
*
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
n
a
lytic
E
s
tima
tio
n
o
f Tw
o
-
Dimen
s
io
n
a
l E
lectro
n
Ga
s
Den
s
ity
a
n
d
…. (
B
a
b
a
ya
A
s
ma
e
)
957
No
te
th
at
i
n
w
ea
k
i
n
v
er
s
io
n
r
eg
i
m
e,
t
h
e
p
o
ten
tial
w
ell
is
q
u
ite
lar
g
e
a
n
d
n
o
t
to
o
d
ee
p
,
it
r
esu
lt
s
th
a
t
th
e
q
u
an
tizat
io
n
o
f
elec
tr
o
n
ic
s
ta
tes
is
lo
w
a
n
d
th
a
t
th
e
s
tr
u
ct
u
r
e
h
as
a
n
o
f
f
s
et
r
elati
v
e
to
a
t
w
o
-
d
i
m
e
n
s
io
n
al
elec
tr
o
n
g
as.
2.
4.
M
o
dera
t
e
I
nv
er
s
io
n
I
n
th
is
r
eg
i
m
e,
th
e
Fer
m
i
le
v
el
i
s
at
t
h
e
b
o
tto
m
o
f
th
e
p
o
ten
tial
w
ell,
j
u
s
t
a
f
e
w
k
T
ab
o
v
e
th
e
co
n
d
u
ctio
n
b
an
d
.
T
h
e
s
tr
u
ct
u
r
e
th
en
o
p
er
ates n
ea
r
to
th
e
t
h
r
e
s
h
o
ld
.
As
w
ell
w
e
ca
n
r
e
w
r
i
te
th
e
eq
u
atio
n
:
kT
E
n
kT
E
n
n
F
s
F
s
s
1
0
0
(
1
1
)
B
y
co
m
b
i
n
i
n
g
th
e
t
w
o
eq
u
at
io
n
s
E
q
u
atio
n
(
4
)
an
d
E
q
u
atio
n
(
1
1
)
,
w
e
f
i
n
d
th
a
t:
kT
m
dn
q
m
qdn
m
V
V
kT
m
q
E
s
s
th
gs
F
)
(
)
(
)
(
)
(
0
2
0
(
1
2
)
Fin
all
y
,
w
e
g
e
t th
e
r
elatio
n
lin
k
in
g
n
s
to
V
gs
in
m
o
d
er
ate
in
v
er
s
io
n
r
eg
i
m
e:
kT
m
dn
q
m
qdn
m
V
V
kT
m
q
n
n
s
s
th
gs
s
s
)
(
)
(
)
(
)
(
e
x
p
0
2
0
0
(
1
3
)
W
ith
n
s0
a
s
th
e
eq
u
ilib
r
iu
m
s
h
ee
t c
ar
r
ier
d
en
s
it
y
at
E
F
=0
.
2
.
5
.
Str
o
ng
I
nv
er
s
io
n
T
h
e
elec
tr
o
n
d
en
s
it
y
i
n
th
e
c
h
an
n
el
b
ec
o
m
e
s
s
u
f
f
icie
n
tl
y
i
m
p
o
r
tan
t
,
th
at
th
e
Fer
m
i
le
v
el
g
o
es
ab
o
v
e
th
e
b
o
tto
m
o
f
th
e
s
ec
o
n
d
s
u
b
-
b
an
d
E
1
.
T
h
e
ex
p
o
n
en
tial
s
ter
m
s
i
n
E
q
u
at
io
n
(
4
)
th
e
n
b
ec
o
m
e
m
u
c
h
h
ig
h
er
t
h
an
1
an
d
w
e
ca
n
w
r
ite
ap
p
r
o
x
i
m
a
ted
as:
1
0
2
*
2
E
E
E
m
n
F
e
s
(
1
4
)
Hen
ce
th
e
e
x
p
r
ess
io
n
o
f
E
F
ca
n
b
e
d
ed
u
ce
d
s
e
F
n
m
E
E
E
*
2
1
0
2
(
1
5
)
E
x
p
licit t
h
e
ter
m
s
o
f
E
0
an
d
E
1
is
o
b
tain
ed
s
e
s
F
n
m
n
E
*
2
3
2
1
0
2
(
1
6
)
B
y
p
o
s
tp
o
n
i
n
g
th
i
s
ex
p
r
es
s
io
n
in
th
e
E
q
u
a
tio
n
(
5
)
,
w
e
g
e
t
th
gs
s
e
s
V
V
d
m
n
d
q
m
dm
q
m
n
2
)
(
2
)
(
2
)
(
1
3
2
2
1
0
*
2
2
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il
201
8
:
9
5
4
–
9
6
2
958
I
n
s
tr
o
n
g
in
v
er
s
io
n
r
eg
i
m
e,
th
e
li
n
ea
r
ter
m
i
s
d
o
m
in
a
n
t
in
n
s
,
s
o
t
h
at
t
h
e
e
lectr
o
n
d
en
s
it
y
f
o
llo
w
s
a
n
ap
p
r
o
x
im
a
tel
y
l
in
ea
r
la
w
,
t
h
er
ef
o
r
e
is
g
i
v
e
n
b
y
th
gs
e
e
s
V
V
m
m
dq
m
m
q
n
2
*
2
*
)
(
2
)
(
2
(
1
8
)
T
h
e
HE
MT
A
lGaN/Ga
N
m
ai
n
l
y
o
p
er
ate
i
n
th
e
s
tr
o
n
g
in
v
er
s
io
n
r
eg
io
n
,
th
e
c
u
r
r
en
t
i
n
t
h
is
r
e
g
io
n
ac
t
u
all
y
d
eter
m
in
e
s
th
e
p
er
f
o
r
m
an
ce
o
f
A
lGa
N
/ G
aN
HE
MT
f
o
r
h
ig
h
p
o
w
er
ap
p
licatio
n
s
.
2
.
6
.
C
urre
nt
-
v
o
lt
a
g
e
C
ha
ra
c
t
er
is
t
ic
T
h
e
d
r
ain
-
s
o
u
r
ce
c
u
r
r
en
t
i
ds
c
an
b
e
o
b
tain
ed
f
r
o
m
t
h
e
r
elati
o
n
b
et
w
ee
n
t
h
e
cu
r
r
en
t
in
te
n
s
it
y
a
n
d
th
e
elec
tr
ic
ch
ar
g
e
ac
c
u
m
u
lated
i
n
th
e
elec
tr
o
n
g
a
s
[
1
9
]
:
)
(
x
v
w
q
n
i
s
ds
(
1
9
)
W
h
er
e
w
is
t
h
e
g
ate
w
id
t
h
,
v
(
x
)
is
th
e
v
elo
cit
y
o
f
t
h
e
elec
tr
o
n
s
in
t
h
e
ch
a
n
n
e
l
at
th
e
ab
s
ci
s
s
a
x
.
T
h
e
g
ate
v
o
ltag
e
r
ep
lace
d
b
y
t
h
e
ef
f
ec
tiv
e
g
ate
v
o
lta
g
e
(
V
gs
-
V(
x
)
)
a
t
th
e
p
o
s
itio
n
x
,
t
h
e
elec
tr
o
n
g
as
d
en
s
it
y
i
n
th
e
ch
an
n
el
ca
n
b
e
ex
p
r
ess
ed
as:
th
gs
e
e
s
V
x
V
V
m
m
dq
m
m
q
n
)
(
)
(
2
)
(
2
2
*
2
*
(
2
0
)
W
ith
c
s
a
t
c
E
x
E
v
E
x
E
E
x
E
x
E
x
v
)
(
,
)
(
,
)
(
1
)
(
1
0
(
2
1
)
an
d
dx
x
dV
x
E
)
(
)
(
(
2
2
)
Usi
n
g
t
h
e
E
q
u
atio
n
s
(
1
9
)
,
(
2
0
)
,
(
2
1
)
an
d
(
2
2
)
,
w
e
o
b
tain
dx
x
dV
V
x
V
V
m
m
dq
m
m
q
wq
dx
x
dV
E
i
th
gs
e
e
ds
)
(
)
(
)
(
2
)
(
2
)
(
1
1
2
*
2
*
1
(
2
3
)
T
h
e
in
teg
r
atio
n
o
f
eq
u
a
tio
n
al
o
n
g
t
h
e
ch
a
n
n
el
le
n
g
th
w
i
th
t
h
e
f
o
llo
w
i
n
g
b
o
u
n
d
ar
y
co
n
d
it
io
n
s
V(
x
)
x
=
0
=I
ds
R
s
an
d
V(
x
)
x=
Lg
=V
ds
-
i
ds
(R
s
+R
d
)
al
lo
w
s
r
ea
c
h
in
g
t
h
e
r
elatio
n
i
ds
(V
ds
)
1
3
1
2
2
2
2
4
ds
i
(
2
4
)
W
h
er
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
n
a
lytic
E
s
tima
tio
n
o
f Tw
o
-
Dimen
s
io
n
a
l E
lectro
n
Ga
s
Den
s
ity
a
n
d
…. (
B
a
b
a
ya
A
s
ma
e
)
959
))
(
2
(
)
(
2
)
(
4q
))
(
)
2
)(
((
)
(
2
)
(
4q
E
2R
-
)
R
2R
(R
)
(
2
)
(
2q
=
2
2
*
2
*
0
2
3
2
*
2
*
0
2
1
2
1
s
d
s
2
d
2
*
2
*
0
2
1
Th
gs
ds
ds
e
e
d
s
ds
d
s
Th
gs
e
e
ds
g
d
e
e
V
V
V
V
x
m
dq
m
x
w
R
R
V
R
R
V
V
x
m
dq
m
x
w
E
V
L
R
x
m
dq
m
x
w
(
2
5
)
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
W
e
ca
lcu
late
th
e
ch
ar
ac
ter
is
tic
s
o
f
A
l
GaN
/GaN
HE
MT
f
o
r
L
g
=
2
0
0
n
m
a
n
d
W
g
=
1
µ
m
,
th
e
v
alu
e
o
f
th
e
a
l
u
m
in
u
m
m
o
lar
f
r
ac
tio
n
is
ch
o
s
e
n
i
n
t
h
e
r
an
g
e
o
f
[
0
.
2
;
0
.
3
]
,
w
h
ic
h
allo
w
s
to
h
av
e
a
p
iezo
elec
tr
ic
p
o
lar
izatio
n
b
en
ef
icia
l
f
o
r
th
e
ac
cu
m
u
lat
io
n
o
f
t
h
e
t
w
o
-
d
i
m
en
s
o
n
al
e
lectr
o
n
g
a
s
i
n
th
e
q
u
an
t
u
m
w
ell.
T
h
e
th
eo
r
y
m
en
t
io
n
ed
ab
o
v
e
s
h
o
ws
th
at
t
h
e
d
en
s
it
y
o
f
elec
tr
o
n
s
tr
an
s
f
er
r
ed
to
th
e
p
o
ten
tial
w
ell
d
ep
en
d
s
o
n
th
e
A
l
u
m
i
n
u
m
m
o
lar
f
r
ac
tio
n
co
n
ten
t,
th
e
AlGaN
la
y
er
th
i
k
n
ess
an
d
A
l
GaN
la
y
er
d
o
p
in
g
.
Fig
u
r
e
1
s
h
o
w
s
th
e
v
ar
iatio
n
s
o
f
th
e
2
DE
G
d
en
s
i
t
y
as
a
f
u
n
ctio
n
o
f
th
e
g
ate
v
o
ltag
e
f
o
r
d
if
f
er
en
t
v
alu
e
s
o
f
alu
m
i
n
u
m
m
o
lar
f
r
ac
tio
n
.
T
h
e
2
DE
G
d
en
s
i
t
y
i
n
cr
e
ases
w
it
h
t
h
e
al
u
m
i
n
u
m
c
o
n
ten
t.
T
h
i
s
r
es
u
lt
ca
n
b
e
ex
p
l
ain
ed
b
y
th
e
t
h
eo
r
y
d
is
cu
s
s
ed
ab
o
v
e.
T
h
u
s
in
cr
ea
s
in
g
th
e
co
n
d
u
ctio
n
b
a
n
d
d
is
co
n
ti
n
u
i
t
y
o
f
A
lGaN
/ G
aN
h
eter
o
j
u
n
ctio
n
,
m
a
k
es i
t
p
o
s
s
ib
le
to
im
p
r
o
v
e
th
e
co
n
f
i
n
e
m
e
n
t
o
f
2
DE
G
in
t
h
e
q
u
an
t
u
m
w
ell
as
w
ell
as
t
h
e
p
r
esen
ce
o
f
s
tr
o
n
g
p
iezo
elec
tr
ic
an
d
s
p
o
n
ta
n
eo
u
s
p
o
lar
izatio
n
s
at
th
e
i
n
ter
f
ac
e,
W
h
ich
ar
e
d
ir
ec
tl
y
d
ep
en
d
en
t
o
n
t
h
e
al
u
m
i
n
u
m
m
o
lar
f
r
ac
tio
n
.
O
n
t
h
e
o
th
er
h
an
d
th
e
t
h
r
es
h
o
ld
v
o
ltag
e
i
n
cr
ea
s
es
i
n
ab
s
o
lu
te
v
al
u
e
w
it
h
t
h
e
alu
m
i
n
u
m
m
o
lar
f
r
ac
tio
n
.
F
ig
u
r
e
1
.
V
ar
iatio
n
s
o
f
t
h
e
2
-
DE
G
d
en
s
it
y
as
f
u
n
ctio
n
o
f
t
h
e
g
ate
v
o
lta
g
e
f
o
r
d
if
f
er
en
t
v
al
u
es o
f
al
u
m
i
n
u
m
m
o
lar
f
r
ac
tio
n
Fig
u
r
e
2
an
d
Fi
g
u
r
e
3
s
h
o
w
th
e
i
n
f
l
u
e
n
ce
o
f
t
h
e
A
lGaN
l
a
y
er
th
ic
k
n
ess
o
n
th
e
ca
lcu
la
ted
2
DE
G
d
en
s
it
y
as
a
f
u
n
ctio
n
o
f
t
h
e
v
o
ltag
e
ap
p
lied
to
th
e
g
ate,
f
o
r
tw
o
s
tr
u
ct
u
r
es
A
l
0.
2
Ga
0.
8
N/
Ga
N
an
d
A
l
0.
26
Ga
0.
74
N/
GaN
.
T
h
e
v
ar
iatio
n
o
f
t
h
e
A
l
GaN
la
y
er
t
h
ick
n
es
s
f
r
o
m
2
0
n
m
to
2
6
n
m
i
s
a
s
s
o
ciate
d
w
it
h
an
i
n
cr
ea
s
e
i
n
t
h
e
2
DE
G
d
en
s
it
y
f
o
r
th
e
b
o
th
s
tr
u
ctu
r
e.
An
i
n
cr
ea
s
e
i
n
t
h
e
ab
s
o
lu
te
v
a
lu
e
o
f
t
h
e
th
r
e
s
h
o
ld
v
o
ltag
e
o
f
t
h
e
HE
MT
tr
an
s
i
s
to
r
is
also
o
b
s
er
v
ed
.
T
h
at
s
h
o
w
s
m
o
r
e
th
e
A
l
GaN
la
y
er
th
ick
n
es
s
is
h
i
g
h
,
h
ig
h
er
th
e
th
r
esh
o
ld
v
o
lta
g
e
to
b
e
ap
p
lied
to
d
e
p
lete
th
e
2
DE
G
m
u
s
t
b
e
r
aised
in
r
e
v
er
s
e
p
o
lar
izatio
n
.
T
h
e
v
alu
e
s
o
f
t
h
e
2
DE
G
d
en
s
it
y
ar
e
attr
ib
u
ted
to
th
e
p
r
esen
ce
o
f
t
h
e
ch
ar
g
es
in
d
u
ce
d
b
y
th
e
to
tal
p
o
lar
izatio
n
at
th
e
i
n
ter
f
ac
e
o
f
th
e
A
lGaN
/
GaN
h
eter
o
j
u
n
ctio
n
,
as
t
h
e
th
eo
r
y
in
d
iq
u
e
.
T
h
e
s
lo
p
e
o
f
th
e
p
lo
t
n
s
(
Vg
s
)
allo
w
s
u
s
to
f
i
n
d
th
e
g
ate
ca
p
ac
itan
ce
v
alu
e
o
f
t
h
e
s
tr
u
ct
u
r
e,
w
h
ic
h
is
r
elate
d
to
t
h
e
t
h
ic
k
n
e
s
s
o
f
t
h
e
AlGaN
la
y
er
;
t
h
e
latter
is
g
r
o
w
i
n
g
m
o
r
e
ca
p
ac
ities
d
ec
r
ea
s
es,
th
is
i
s
d
em
o
n
s
tr
ated
f
o
r
d
=2
0
n
m
t
h
e
s
l
o
p
e
is
2
.
6
*
1
0
12
cm
-
2
V
-
1
,
w
h
i
le
th
at
f
o
r
d
=2
6
n
m
t
h
e
s
lo
p
e
is
1
.
9
9
*
1
0
12
cm
-
2
V
-
1
f
o
r
th
e
f
ir
t
s
tr
u
ct
u
r
e;
t
h
e
s
a
m
e
i
s
o
b
s
er
v
ed
f
o
r
th
e
s
ec
o
n
d
s
t
r
u
ctu
r
e,
w
e
o
b
tain
2
.
5
9
*
1
0
12
cm
-
2
V
-
1
a
n
d
1
.
9
8
*
1
0
12
cm
-
2
V
-
1
f
o
r
2
0
n
m
an
d
2
6
n
m
r
esp
ec
tiv
e
l
y
.
I
t
is
al
s
o
o
b
s
er
v
ed
th
at
th
e
g
ate
ca
p
ac
itan
ce
i
s
m
o
r
e
s
e
n
s
iti
v
e
to
th
e
v
ar
iat
io
n
i
n
th
e
A
lG
aN
la
y
er
th
ic
k
n
es
s
t
h
an
to
t
h
e
v
ar
iatio
n
in
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
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lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il
201
8
:
9
5
4
–
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6
2
960
alu
m
in
u
m
m
o
lar
f
r
ac
tio
n
.
T
h
is
s
h
o
w
s
th
a
t
h
ig
h
v
al
u
es
o
f
A
l
GaN
la
y
er
t
h
ic
k
n
e
s
s
ar
e
f
a
v
o
r
ab
le
to
ac
h
ie
v
e
s
ig
n
i
f
ica
n
t 2
DE
G
d
en
s
it
y
a
n
d
to
o
b
tain
lo
w
g
ate
ca
p
ac
ita
n
ce
v
al
u
e
s
.
Fig
u
r
e
2
.
Var
iatio
n
s
o
f
t
h
e
2
D
E
G
d
en
s
it
y
f
o
r
d
if
f
er
e
n
t v
a
lu
e
s
o
f
t
h
e
A
lGaN
la
y
er
th
i
k
n
es
s
an
d
f
o
r
m
=0
.
2
Fig
u
r
e
3
.
Var
iatio
n
s
o
f
t
h
e
2
D
E
G
d
en
s
it
y
f
o
r
d
if
f
er
en
t
v
alu
e
s
o
f
t
h
e
A
lGaN
la
y
er
th
i
k
n
e
s
s
a
n
d
f
o
r
m
=0
.
2
6
T
h
e
d
ep
en
d
en
c
y
o
f
t
w
o
-
d
i
m
e
n
s
io
n
al
elec
tr
o
n
g
az
to
A
lGa
N
la
y
er
d
o
p
in
g
f
o
r
m
=0
.
2
6
is
g
i
v
i
n
g
b
y
F
ig
u
r
e
4
.
As
t
h
e
t
h
ic
k
n
e
s
s
a
n
d
d
o
p
in
g
o
f
A
lGaN
la
y
er
i
n
cr
ea
s
e,
t
h
e
2
DE
G
d
en
s
it
y
also
in
cr
ea
s
e
s
.
T
h
e
s
en
s
iti
v
it
y
o
f
2
DE
G
to
th
e
t
h
ic
k
n
e
s
s
o
f
t
h
e
A
l
GaN
la
y
er
i
s
g
r
ea
ter
w
it
h
a
h
i
g
h
d
o
p
in
g
co
n
c
en
tr
atio
n
.
A
l
s
o
,
th
e
A
l
GaN
la
y
er
d
o
p
in
g
h
as
a
lar
g
er
i
m
p
ac
t
o
n
t
h
e
2
DE
G
d
en
s
it
y
at
lar
g
e
v
al
u
e
s
o
f
la
y
er
t
h
ik
n
e
s
;
Fo
r
AlGaN
la
y
er
t
h
ic
k
n
e
s
s
v
ar
ie
f
r
o
m
1
0
n
m
to
2
0
n
m
,
w
e
n
o
tice
th
a
t
2
DE
G
s
li
tg
h
l
y
i
n
cr
ea
s
e
w
it
h
AlGaN
la
y
er
d
o
p
in
g
,
th
u
s
w
e
o
b
s
er
v
e
t
h
a
t
2
DE
G
b
ec
a
m
e
m
o
r
e
i
n
f
l
u
e
n
ce
d
b
y
d
o
p
in
g
w
h
e
n
A
lGaN
la
y
er
th
ic
k
n
es
s
ar
e
o
v
er
th
an
2
0
n
m
.
T
h
is
r
esu
l
t
ca
n
b
e
ex
p
lain
t
h
at
t
h
e
A
lGaN
la
y
e
r
d
o
p
in
g
w
id
e
n
s
t
h
e
b
an
d
g
ap
o
f
th
e
AlGaN
s
e
m
ico
n
d
u
cto
r
,
w
h
ic
h
i
n
f
l
u
e
n
ce
s
th
e
co
n
d
u
c
tio
n
b
an
d
d
is
c
o
n
tin
u
it
y
o
f
A
lGa
N
/
GaN
h
eter
o
j
u
n
ctio
n
,
th
at
i
m
p
lies
an
in
cr
ea
s
e
i
n
t
h
e
2
DE
G
co
n
f
in
e
m
e
n
t i
n
th
e
q
u
an
tu
m
w
e
ll.
T
h
er
ef
o
r
e,
it i
s
e
v
id
en
t
t
h
at
o
b
tain
in
g
h
i
g
h
d
en
s
itie
s
o
f
2
DE
G
r
eq
u
ir
es e
it
h
er
a
h
i
g
h
d
o
p
in
g
o
r
a
h
ig
h
er
A
l
GaN
la
y
er
t
h
ic
k
n
e
s
s
.
Fig
u
r
e
4
.
V
ar
iatio
n
s
o
f
t
h
e
2
D
E
G
d
en
s
it
y
f
o
r
d
if
f
er
en
t
v
al
u
e
s
o
f
th
e
AlGaN
la
y
er
d
o
p
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
A
n
a
lytic
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s
tima
tio
n
o
f Tw
o
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Dimen
s
io
n
a
l E
lectro
n
Ga
s
Den
s
ity
a
n
d
…. (
B
a
b
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s
ma
e
)
961
T
h
e
co
r
r
ec
tn
ess
o
f
th
e
c
u
r
r
en
t
-
v
o
ltag
e
m
o
d
el
d
ep
en
d
s
o
n
t
h
e
ac
c
u
r
ac
y
o
f
t
h
e
m
o
d
el
f
o
r
th
e
2
DE
G
co
n
ce
n
tr
atio
n
as
a
f
u
n
ctio
n
o
f
g
a
te
v
o
lta
g
e,
s
i
n
ce
it
d
ir
ec
t
l
y
a
f
f
ec
t
s
t
h
e
elec
tr
ic
f
ield
i
n
th
e
A
lGa
N
la
y
er
.
Fig
u
r
e
5
s
h
o
w
s
t
h
e
cu
r
r
en
t
-
v
o
ltag
e
ch
ar
ac
ter
i
s
tic
as
a
f
u
n
cti
o
n
o
f
th
e
d
r
ain
-
s
o
u
r
ce
v
o
ltag
e
f
o
r
d
if
f
er
en
t
g
ate
-
s
o
u
r
ce
v
o
ltag
e
v
alu
e
s
r
an
g
i
n
g
f
r
o
m
-
8
V
to
0
V.
T
h
ese
ch
ar
ac
ter
is
tics
co
r
r
esp
o
n
d
to
an
id
e
al
HE
MT
s
tr
u
ctu
r
e.
Hig
h
c
u
r
r
en
ts
ar
e
attr
ib
u
ted
t
o
v
er
y
h
i
g
h
2
DE
G
d
en
s
it
y
,
r
e
s
u
lt
in
g
f
r
o
m
lar
g
e
co
n
d
u
ctio
n
b
an
d
d
is
co
n
t
in
u
it
y
an
d
s
tr
o
n
g
p
o
lar
izatio
n
ef
f
ec
ts
.
T
h
e
s
atu
r
atio
n
cu
r
r
en
t in
cr
ea
s
es
w
it
h
t
h
e
g
ate
v
o
ltag
e.
Fig
u
r
e
5
.
C
u
r
r
en
t
-
v
o
ltag
e
c
h
ar
ac
ter
is
tic
I
d
s
-
Vd
s
f
or
A
lGaN/
GaN
HE
MT
f
o
r
d
if
f
er
en
t
v
alu
e
s
o
f
G
ate
v
o
lta
g
e
4.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
w
e
h
av
e
an
a
l
y
t
icall
y
esti
m
ated
th
e
2
DE
G
d
en
s
it
y
in
A
lGa
N/GaN
HE
MT
,
th
e
m
o
s
t
i
m
p
o
r
tan
t
p
ar
a
m
eter
i
n
ch
ar
a
cter
izin
g
an
d
ev
al
u
ati
n
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
AlGaN
/GaN
HE
MT
.
First,
th
e
p
h
en
o
m
e
n
a
r
e
s
p
o
n
s
ib
le
f
o
r
f
o
r
m
al
izin
g
th
e
t
w
o
-
d
i
m
e
n
s
io
n
al
elec
tr
o
n
g
as
h
a
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ted
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l
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s
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h
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N
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N
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er
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d
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a
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as
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en
s
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y
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RE
F
E
R
E
NC
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S
[1
]
W
.
Ch
u
n
g
,
e
t
a
l,
"
A
l
G
a
N/
G
a
N
H
EM
s
w
it
h
3
0
0
G
Hz
F
M
A
X
,
"
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El
e
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tro
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ic
De
v
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L
e
tt
e
rs
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v
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l.
3
1
,
p
p
.
1
9
5
-
1
9
7
,
A
p
ril
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0
1
0
.
[2
]
Y.Na
k
a
sh
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,
e
t
a
l,
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5
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r
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il
li
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ter
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ra
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ive
rs
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o
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n
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ico
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it
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y
m
p
o
siu
m
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p
.
1
-
4
,
2
0
1
0
.
[3
]
S
.
T
irelli
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e
t
a
l,
"
1
0
7
-
G
Hz
(
A
l,
Ga
)N/Ga
N
HEM
Ts
o
n
S
il
ico
n
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it
h
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p
ro
v
e
d
M
a
x
i
m
u
m
Os
c
il
latio
n
F
re
q
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e
n
c
ies
,
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E
El
e
c
tro
n
De
v
ice
L
e
tt
e
rs
,
v
o
l.
3
1
,
A
p
r
il
2
0
1
0
.
[4
]
H
.
K
.
Ju
n
g
,
“
P
ro
jec
ted
Ra
n
g
e
De
p
e
n
d
e
n
t
T
u
n
n
e
li
n
g
C
u
rre
n
t
o
f
A
s
y
m
m
e
tri
c
Do
u
b
le
G
a
te
M
OSF
ET
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
t
e
r E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
V
o
l
.
6
,
No
.
1
,
F
e
b
r
u
a
ry
2
0
1
6
,
p
p
.
1
1
3
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1
1
9
[5
]
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.
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Ra
a
b
,
e
t
a
l
,
"
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o
w
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r
Am
p
li
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n
d
T
ra
n
s
m
it
ters
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r
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a
n
d
M
icro
w
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v
e
,
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E
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ra
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ti
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n
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p
p
.
1
9
5
-
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9
7
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M
a
rc
h
2
0
0
2
.
[6
]
R.
K.
Ya
d
a
v
,
e
t
a
l,
"
T
CAD
S
im
u
latio
n
s
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n
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m
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ll
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ig
n
a
l
M
o
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li
n
g
o
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l
Ga
N/
G
a
N
HFE
T
,
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ter
n
a
ti
o
n
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l
J
o
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rn
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l
o
f
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e
c
trica
l
a
n
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t
e
r E
n
g
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n
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rin
g
(
IJ
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)
,
V
o
l
.
7
,
No
.
4
,
p
p
.
1
8
3
9
-
1
8
4
9
,
2
0
1
7
.
[7
]
S
.
Kh
a
n
d
e
lw
a
l
a
n
d
T
.
A
.
F
jeld
ly
,
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p
h
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s
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se
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m
p
a
c
t
m
o
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o
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n
d
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–
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c
h
a
ra
c
teristics
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n
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l
G
a
N/
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N
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T
d
e
v
ice
s,
"
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o
li
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te E
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ics
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o
l
.
7
6
,
p
p
.
6
0
–
6
6
,
Ju
ly
2
0
1
2
.
[8
]
D.
De
lag
e
b
e
a
u
d
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u
f
a
n
d
N.T
.
L
in
h
,
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e
tal
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(n
)
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IGa
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s
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a
As
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o
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m
e
n
sio
n
a
l
El
e
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tro
n
G
a
s
F
ET
,
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E
T
ra
n
sa
c
ti
o
n
s
o
n
El
e
c
tro
n
De
v
ice
s
,
Vo
l.
2
9
,
p
p
.
9
5
5
-
6
0
,
J
u
n
e
1
9
8
2
.
[9
]
Ra
sh
m
i,
e
t
a
l
"
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n
a
l
y
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a
l
m
o
d
e
l
f
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r
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h
a
ra
c
teristic
s
a
n
d
sm
a
l
l
sig
n
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l
p
a
ra
m
e
ters
o
f
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l
Ga
N/
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N
m
o
d
u
lati
o
n
d
o
p
e
d
f
ield
-
e
ff
e
c
t
tran
sisto
rs
f
o
r
m
icro
w
a
v
e
c
ircu
it
a
p
p
li
c
a
ti
o
n
s,"
M
icr
o
wa
v
e
Op
ti
c
a
l
T
e
c
h
n
o
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o
g
y
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e
tt
e
rs
;
v
o
l.
2
7
,
p
p
.
4
1
3
–
9
,
2
0
0
0
.
[1
0
]
H.A
h
n
a
n
d
M
.
E.
N
o
k
a
li
,
"
A
n
a
n
a
l
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ti
c
a
l
m
o
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l
f
o
r
h
ig
h
e
lec
tr
o
n
m
o
b
il
it
y
tran
sisto
rs,"
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E
T
ra
n
sc
a
ti
o
n
o
n
El
e
c
tro
n
De
v
ice
s
,
v
o
l.
4
1
,
p
p
.
8
7
4
–
8
,
1
9
9
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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p
r
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8
:
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5
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962
[1
1
]
S
.
Ka
rm
a
lk
a
r
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n
d
G
.
Ra
m
e
sh
,
"
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si
m
p
le
y
e
t
c
o
m
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re
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h
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l
m
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tro
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s
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ig
h
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o
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il
it
y
tran
sisto
rs,"
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E
T
ra
n
sc
a
ti
o
n
o
n
El
e
c
tro
n
De
v
ice
s
,
v
o
l.
4
7
,
p
p
.
1
1
–
2
3
,
2
0
0
0
.
[1
2
]
S
.
S
e
n
,
e
t
a
l,
"
T
e
m
p
e
ra
tu
re
a
n
d
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lu
m
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m
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o
m
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siti
o
n
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e
p
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n
d
e
n
t
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rrier co
n
c
e
n
tratio
n
a
t
A
lGa
A
s/
Ga
As
in
terfa
c
e
,
"
J
o
u
rn
a
l
o
f
P
h
y
sic
s D: A
p
p
l
ied
P
h
y
sic
s
,
v
o
l
.
3
3
,
p
p
.
1
8
–
2
3
,
2
0
0
0
.
[1
3
]
S
.
H.Ng
,
e
t
a
l,
"
A
tw
o
-
d
ime
n
sio
n
a
l
se
lf
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o
n
siste
n
t
n
u
m
e
rica
l
m
o
d
e
l
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o
r
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ig
h
e
lec
tro
n
m
o
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il
it
y
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sisto
r,
"
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E
T
ra
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sc
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ti
o
n
o
n
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tro
n
De
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ice
s
,
v
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l.
3
4
,
p
p
.
8
5
2
–
8
6
1
,
1
9
9
1
.
[1
4
]
A
.
De
n
is,
e
t
a
l
,
"
G
a
ll
iu
m
n
it
rid
e
b
u
lk
c
ry
st
a
l
g
ro
w
th
p
ro
c
e
s
se
s:
A
re
v
ie
w
,
"
M
a
ter
ia
ls
S
c
ien
c
e
a
n
d
En
g
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n
e
e
rin
g
,
R
5
0
,
p
p
.
1
6
7
–
1
9
4
,
2
0
0
5
.
[1
5
]
J
Ku
z
m
ik
,
"
In
A
lN/(In
)G
a
N
h
ig
h
e
lec
tro
n
m
o
b
il
it
y
tran
sisto
rs:
so
m
e
a
sp
e
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ts
o
f
th
e
q
u
a
n
tu
m
w
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ll
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stru
c
tu
re
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ro
p
o
sa
l"
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e
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u
c
t
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e
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n
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T
e
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y
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l
.
1
7
,
p
p
.
5
4
0
–
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4
4
,
2
0
0
2
.
[1
6
]
O.
Am
b
a
c
h
e
r,
e
t
a
l
,
"
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o
-
d
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m
e
n
ti
n
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l
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tro
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se
s
in
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c
e
d
b
y
sp
a
n
tan
e
o
u
s
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n
d
p
iez
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e
lec
tri
c
p
o
lariz
a
ti
o
n
c
h
a
rg
e
s in
N
-
a
n
d
G
a
-
f
a
c
e
A
l
G
a
N/G
a
N h
e
tero
stru
c
tu
re
s,
"
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o
u
r
n
a
l
o
f
A
p
p
li
e
d
P
h
y
sic
s
,
v
o
l.
8
5
,
1
9
9
9
.
[1
7
]
I.
V
u
rg
a
f
t
m
a
n
a
n
d
J.
R.
M
e
y
e
r,
"
Ba
n
d
p
a
ra
m
e
ters
f
o
r
n
it
ro
g
e
n
-
c
o
n
tain
i
n
g
se
m
ico
n
d
u
c
to
rs,"
J
o
u
rn
a
l
o
f
Ap
p
li
e
d
Ph
y
sic
s
,
Vo
l.
9
4
,
p
p
.
3
6
7
5
-
3
6
9
6
,
2
0
0
3
.
[1
8
]
P
.
Ca
rrier
a
n
d
S
.
W
e
i,
"
T
h
e
o
re
ti
c
a
l
stu
d
y
o
f
th
e
b
a
n
d
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g
a
p
a
n
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m
a
ly
o
f
In
N,"
J
o
u
rn
a
l
Of
A
p
p
li
e
d
Ph
y
sic
s
,
v
o
l.
9
7
,
2
0
0
5
[1
9
]
G
.
A
t
m
a
c
a
,
e
t
a
l
,
"
Nu
m
e
ric
a
l
i
n
v
e
stig
a
ti
o
n
o
f
th
e
2
DE
G
p
ro
p
e
rti
e
s
o
f
A
l
Ga
N/
A
lN/
G
a
N
HEM
T
stru
c
tu
re
s
w
it
h
In
G
a
N/
G
a
N M
QW
b
a
c
k
-
b
a
rrier s
tru
c
tu
re
"
,
Ph
y
sic
a
E
,
v
o
l
.
6
5
,
p
p
.
1
1
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–
1
1
3
,
2
0
1
5
[2
0
]
M
.
Ch
a
rf
e
d
d
in
e
,
e
t
a
l,
"
2
-
D
T
h
e
o
re
ti
c
a
l
M
o
d
e
l
f
o
r
Cu
rre
n
t
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Vo
lt
a
g
e
Ch
a
ra
c
teristics
in
A
l
G
a
N/
Ga
N
HEM
T
’s,
"
J
o
u
rn
a
l
o
f
M
o
d
e
rn
Ph
y
sic
s
,
v
o
l.
3
,
p
p
.
8
8
1
-
8
8
6
,
2
0
1
2
Evaluation Warning : The document was created with Spire.PDF for Python.