Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
11
,
No.
1
,
Febr
uar
y
2021
, pp.
232
~
239
IS
S
N:
20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v
11
i
1
.
pp
232
-
239
232
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om
Relation
ship
of
d
ra
in in
d
uced bar
rier l
owe
ring and
to
p/b
ott
om
gate oxi
de thick
ness in
asymmet
ric jun
ctionl
ess
doub
le gate MOS
FET
Ha
k
kee
Ju
n
g
Depa
rtment
o
f
E
le
c
troni
c
Eng
ineeri
ng,
Kuns
an
N
at
ion
al
Univ
ersity
,
Repub
li
c
of
Korea
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
pr
10, 202
0
Re
vised
Jun
15
, 2020
Accepte
d
Aug 13
, 202
0
The
re
la
t
ionship
of
dra
in
induc
e
d
bar
rie
r
lower
i
ng
(DIBL)
phen
om
enon
and
cha
nne
l
le
ng
th,
sili
con
th
ic
knes
s,
and
thi
ckn
esses
of
top
and
b
ott
om
gat
e
oxide
fil
m
s
is
der
ive
d
for
as
y
m
m
et
ric
junc
t
io
nle
ss
double
ga
te
(JLDG
)
MO
S
FETs.
The
cha
ra
cteri
sti
cs
bet
wee
n
the dra
in
cur
ren
t
and the
gat
e
vo
ltag
e
is
der
ive
d
b
y
usi
ng
t
he
pote
ntial
distri
buti
on
m
odel
to
propose
in
thi
s
pape
r
.
In
thi
s
c
ase
,
th
e
thre
shold
voltage
is
d
efi
n
ed
as
the
cor
respo
nding
gate
volt
ag
e
when
th
e
dra
in
cu
rre
nt
i
s
(
W/L
)×
10
-
7
A,
and
th
e
DIBL
r
epr
ese
nt
ing
the
cha
ng
e
in
t
he
thre
shold
vo
lt
ag
e
with
resp
ec
t
to
th
e
dra
in
volt
age
is
obta
in
ed.
As
a
r
esult
,
w
e
observ
e
the
DIBL
is
p
roporti
ona
l
to
th
e
neg
at
iv
e
thi
rd
power
of
the
cha
n
nel
length
and
the
se
cond
power
o
f
the
sil
ic
o
n
thi
ckn
ess
and
li
nea
r
l
y
propor
tional
to
the
ge
om
et
ric
m
ea
n
of
the
top
and
bott
om
gat
e
oxi
d
e
thic
knesses
,
and
der
ive
a
r
elation
such
as
DIBL
=25.
15
−
3
2
√
1
∙
2
,
w
her
e
is
a
st
at
i
c
f
ee
db
ac
k
co
ef
fic
i
ent
s
bet
wee
n
0
and
1.
Th
e
is
found
to
be
be
twee
n
0.
5
and
1.
0
in
t
his
m
odel.
The
DIBL
m
odel
of
thi
s
pape
r
has
bee
n
observe
d
to
be
in
good
agr
ee
m
ent
with
t
h
e
r
e
s
u
l
t
o
f
o
t
h
e
r
p
a
p
e
r
,
s
o
i
t
c
a
n
b
e
u
s
e
d
i
n
c
i
r
c
u
i
t
s
i
m
u
l
a
t
i
o
n
s
u
c
h
a
s
S
P
I
C
E
.
Ke
yw
or
d
s
:
Asym
m
et
ric
DI
BL
Dou
ble g
at
e
Ju
nc
ti
on
le
ss
Ox
i
de
thic
knes
s
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Hakkee
Jun
g,
Dep
a
rtm
ent o
f El
ect
ro
nic
Eng
ineerin
g,
Kunsa
n Nati
on
al
U
ni
ver
sit
y,
558 Dae
hak
-
r
o G
un
sa
n Jeoll
a
buk
-
do
5415
0,
Republ
ic of
Korea
.
Em
a
il
:
hk
jung
@ku
ns
an
.ac.
kr
1.
INTROD
U
CTION
In
order
to
re
duce
short
cha
nnel
e
f
fects
(S
C
Es)
kn
own
as
seco
nd
a
ry
e
f
fe
ct
s,
the
str
uctu
res
of
t
hr
ee
-
dim
ension
al
tr
ansisto
r
ha
ve
been
de
velo
pe
d
a
nd
us
e
d.
T
he
FinFE
T
is
th
e
m
os
t
us
ed
c
om
m
ercially
avail
able
three
-
dim
ension
al
MOS
FET
[1
-
4].
The
e
xi
sti
ng
th
ree
-
d
i
m
ension
al
str
uc
ture
m
ai
nly
us
ed
a
n
in
ver
si
on
-
ty
pe
MOSFET
us
i
ng
a
j
unct
io
n
-
ba
sed
str
uctu
re
w
it
h
dif
fer
e
nt
do
ping
ty
pe
a
nd
con
ce
ntrati
on
betwee
n
s
ourc
e/
dr
ai
n
and
c
ha
nnel
,
but
rece
ntly
reached
t
he
li
m
it
of
t
he
te
ch
nolo
gy
of
f
or
m
ing
a
j
unct
io
n
with
decr
ea
sin
g
ch
ann
e
l
le
ng
th
to
na
no
unit
[5
-
8].
T
he
transist
or
de
velo
ped
to
s
ol
ve
this
pro
b
le
m
is
a
j
unct
io
nl
ess
MOSF
ET
[9,
10]
.
This
struct
ur
e
is
a
n
accu
m
ula
ti
on
-
ty
pe
MOS
FET
t
hat
ov
e
rc
om
e
s
process
li
m
it
a
ti
on
s
by
do
ping
t
h
e
s
o
u
r
c
e
/
d
r
a
i
n
a
n
d
c
h
a
n
n
e
l
i
n
t
h
e
s
a
m
e
t
y
p
e
a
n
d
c
o
n
c
e
n
t
r
a
t
i
o
n
[
1
1
-
1
3
]
.
I
n
t
h
e
c
a
s
e
o
f
t
h
e
s
y
m
m
e
t
r
i
c
a
l
j
u
n
c
t
i
o
n
l
e
s
s
M
O
S
F
E
T
s
,
m
a
n
y
s
t
u
d
i
e
s
h
a
v
e
b
e
e
n
c
o
n
d
u
c
t
e
d
[
1
4
-
1
6
]
.
H
o
w
e
v
e
r
,
m
a
n
y
s
t
u
d
i
e
s
o
n
t
h
e
asy
m
m
et
ric
j
unct
io
nless
MOSFET
s
ca
pab
le
of
fabri
cat
ing
di
f
fe
rent
top
an
d
bo
tt
om
ox
ide
thic
kn
e
sses
an
d
a
pp
l
yi
ng
dif
fe
re
nt
to
p
and
bott
om
gate
volt
ages
t
o
each
oth
e
r
hav
e
not
been
c
onduct
ed
[
17
-
18]
.
In
t
his
pa
per
,
we
pro
po
se
a
n
a
naly
ti
cal
po
te
ntial
m
od
el
to
a
naly
ze
the
dr
ai
n
in
du
ced
barrier
l
oweri
ng
(
DI
BL
)
of
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Rel
ation
s
hi
p of d
r
ain i
nduce
d ba
r
rie
r loweri
ng an
d
to
p/bott
om gate
oxide
t
hickness
…
(
H
akkee J
ung
)
233
the
sec
onda
ry
ef
fects
in
the
a
sy
m
m
e
tric
junc
ti
on
le
s
s
doubl
e
gate
(
JLD
G)
MOSFE
T
.
T
he
D
IBL
is
a
f
fect
ed
by
channel
le
ngth
,
sil
ic
on
thic
kness
an
d
ox
i
de
s
tructu
re
(t
hick
ness
a
nd
diele
c
tric
const
ant)
.
I
n
ge
ne
ral,
the
DI
BL
is
pro
portiona
l
to
the
ne
gative
thi
rd
powe
r
in
t
he
c
hannel
le
ngth
a
nd
the
seco
nd
powe
r
in
t
he
sil
ic
on
thickne
ss,
a
nd
is
al
so
li
near
ly
pr
op
or
ti
onal
to
the
oxide
fil
m
thickness
[
19,
20
]
.
T
he
relat
ion
s
hip
a
m
on
g
the
to
p
a
nd
bo
tt
o
m
ox
i
de
film
thicknesses
and
the
D
IBL
sh
oul
d
be
re
-
est
ablished
sinc
e
the
t
op
a
nd
bo
tt
om
ox
i
de
fil
m
thickne
sses
m
ay
be
fa
b
ricat
ed
dif
fe
re
ntly
in
the
case
of
the
asym
m
et
ric
s
tructu
re.
Ding
et
al
.
pro
po
se
d
t
he
pote
ntial
m
od
el
of
the
a
sym
m
e
tric
jun
ct
io
n
-
based
double
ga
te
MOSFE
T
a
nd
analy
ze
d
th
e
shor
t
channel
e
f
fect
s
[
21
]
.
Ra
ksh
aram
et
al
.
analy
zed
the
s
hort
c
hannel
ef
fect
us
in
g
t
he
po
te
ntial
m
od
el
of
the
sym
m
et
ric
al
JLD
G
MO
S
FET
[
22]
.
H
oweve
r
,
th
e
res
earch
on
the
a
sy
m
m
e
tric
JLDG
MOS
FET
s
is
ver
y
insuf
fici
ent.
In
this
pa
per
,
we
m
od
ifie
d
the
po
te
ntial
m
od
el
of
Ding
et
al
.
to
be
a
ppli
cab
le
to
the
j
unct
ion
le
s
s
MOSFE
T
,
a
nd
der
i
ved
t
he
po
t
entia
l
m
od
el
of
the
asy
m
m
et
ri
c
JLD
G
MO
S
FET
.
W
e
will
pr
ese
nt
a
n
anal
y
ti
ca
l
m
od
el
o
f DIB
L
for
c
ha
nn
el
di
m
ension and t
op a
nd bott
om
o
xid
e t
hick
ness t
o
ap
ply i
n SP
I
CE.
2.
THRESH
OL
D VOLT
A
GE
AND DIBL
O
F A
S
Y
M
METRIC
J
L
DG M
OSFET
Figure
1
s
hows
a
sc
hem
atic
diag
ram
of
the
asy
m
m
etr
ic
JL
D
G
M
OS
FE
T
us
e
d
in
this
pap
e
r
.
The
sourc
e
a
nd
dr
ai
n
we
re
he
avily
dope
d
with
n
+
an
d
t
he
cha
nnel
was
al
so
do
ped
w
it
h
N
d
=3.5
×
10
19
/cm
3
.
The
to
p
a
nd b
ot
to
m
gate
volt
ages
a
re
V
gt
a
nd
V
gb
resp
ect
i
vely
,
L
g
is
gate
le
ng
t
h,
t
si
is
sil
ic
on
thick
ness
,
a
nd
t
ox1
and
t
ox2
a
re
the
ox
i
de
thick
nes
ses
of
the
t
op
a
nd
bo
tt
om
,
res
pecti
vely
. T
he
V
s
a
nd
V
d
are
t
he
volt
ages
of
so
urce
and
drai
n,
res
pecti
vely
.
The
po
te
ntial
distr
ibu
ti
on
m
od
ifie
d
usi
ng
the
Po
iss
on
e
quat
ion
a
nd
the
bo
unda
ry
conditi
on of
Di
ng
’
s m
od
el
ca
n be e
xpres
sed
a
s
f
ollow
s
[2
1
].
Figure
1. Sc
he
m
at
ic
cro
ss
-
sect
ion
al
d
ia
gr
am
o
f
the asym
m
e
tric
JLDG M
O
SFET
1
,
s
i
n
d
sn
gg
n
Vx
nx
x
y
V
A
y
LL
,
(1)
nn
k
y
k
y
n
n
n
n
n
A
y
C
e
D
e
f
k
4
,
1
,
3
,
5
,
0
,
2
,
4
,
6
,
d
n
si
qN
n
f
n
n
2
2
1
2
1
2
1
2
2
22
12
(
)
(
)
11
(
)
(
1
)
n
s
i
n
s
i
n
s
i
s
i
n
o
x
n
n
n
ox
kt
o
x
s
i
n
n
n
n
n
kt
o
x
s
i
n
n
kt
o
x
o
x
s
i
n
k
C
f
G
k
C
r
C
k
f
H
k
e
C
C
k
r
e
k
C
C
k
e
,
2
2
1
2
1
2
1
2
2
22
12
(
)
(
)
11
(
)
(
1
)
n
s
i
n
s
i
n
s
i
n
s
i
kt
s
i
n
o
x
n
n
n
kt
ox
o
x
s
i
n
n
n
n
n
kt
o
x
s
i
n
n
kt
o
x
o
x
s
i
n
k
C
f
G
k
e
Ce
r
C
k
f
H
k
D
C
k
r
e
k
C
C
k
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1,
Febr
uar
y
2021
:
232
-
239
234
2
2
1
,
3
,
5
,
0
2
,
4
,
6
,
s
g
t
f
b
t
d
n
V
V
V
V
n
G
n
n
，
，
2
2
,
1
,
3
,
5
,
0
,
2
,
4
,
6
,
s
g
b
f
b
b
d
n
V
V
V
V
n
H
n
n
,
21
,
o
x
o
x
n
g
C
r
C
k
n
L
.
wh
e
re
ε
si
is
t
he
diele
ct
ric
co
nst
ant
of
sil
ic
on
,
V
fbt
is
the
flat
-
ba
nd
vo
lt
age
of
t
he
t
op
gate
,
an
d
V
fbb
is
th
e
flat
-
band
vo
lt
age
of
the
bo
tt
om
gate.
C
ox1
(=
ε
t
ox1
/
t
ox1
)
and
C
ox2
(=
ε
tox2
/
t
ox2
)
a
re
the
gate
oxide
ca
pacit
an
ces
of
t
h
e
t
o
p
a
n
d
b
o
t
t
o
m
s
i
d
e
s
.
S
i
n
c
e
t
h
e
s
i
l
i
c
o
n
d
i
o
x
i
d
e
i
s
u
s
e
d
a
s
t
o
p
a
n
d
b
o
t
t
o
m
g
a
t
e
o
x
i
d
e
m
a
t
e
r
i
a
l
s
,
ε
t
o
x
1
=
ε
t
o
x
2
=
3
.
9
.
In
t
he
case
of
the
j
unct
io
nless
str
uctur
e
,
m
os
t
of
th
e
m
ov
in
g
el
ect
ric
c
harges
i
n
the
channel
a
re
known
t
o
m
ove
thr
ough
the
c
entral
axis
(
y
=
t
si
/2),
a
nd
the
re
la
ti
on
sh
i
p
bet
ween
the
dr
ai
n
curre
nt
an
d
th
e
gate
vo
lt
age
in
t
he
s
ub
t
hr
es
hold
re
gion ca
n be
deri
ved
from
the diffusi
on
-
dr
ift c
urren
t e
quat
io
n o
f
(
2).
0
0
1
e
x
p
1
(
,
)
e
x
p
g
si
d
in
d
L
t
qV
q
n
W
k
T
kT
I
dx
q
x
y
dy
kT
(2)
wh
e
re
k
is
Bolt
z
m
ann
'
s
con
sta
nt,
T
is
abso
l
ute
tem
per
at
ure,
n
i
is
the
el
e
ct
ron
co
ncen
tr
at
ion
of
the
in
trinsic
sem
ic
on
duct
or,
μ
n
is t
he
elec
tr
on m
ob
il
it
y, and
W
is a c
hann
el
w
idth
.
The
res
ult
of
dr
ai
n
cu
rr
e
nt
-
gate
volt
age
obta
ined
us
i
ng
(2)
is
com
pared
with
t
he
re
su
lt
s
of
2D
si
m
ulat
ion
an
d
Xie’s
m
od
el
[
23
]
i
n
Fi
g
ure
2.
As
a
re
su
lt
,
it
cou
ld
be
ob
s
erv
e
d
t
hat
they
coinci
de
with
eac
h
oth
e
r
in
t
he
re
gion
be
lo
w
the
thres
ho
l
d
vo
lt
age.
T
he
refor
e
,
the
po
te
ntial
distrib
ution
of
(1)
prese
nted
i
n
this
pap
e
r
is
valid,
an
d
the
validi
ty
of
the
drai
n
curre
nt
-
gate
volt
age
r
el
at
ionship
obta
ined
us
in
g
this
pote
ntial
distrib
ution
is
al
so
pr
ov
e
d.
I
n
this
pa
per,
the
thres
hold
vo
lt
age
V
th
is
def
i
ne
d
us
in
g
the
de
finiti
on
of
th
re
sh
ol
d
vo
lt
age
us
e
d
i
n
TCA
D
[
24
-
25]
.
I
n
ot
her
w
ords,
t
he
thr
es
ho
l
d
volt
age
is
def
i
ned
as
t
he
gate
volt
age
a
t
wh
e
n
th
e drai
n cu
rr
e
nt is e
qu
al
t
o
(
3).
7
10
d
g
W
IA
L
(3)
T
he
n,
t
he DIB
L is obtai
ne
d b
y usin
g (4).
(
0
.
0
5
)
(
0
.
5
5
)
0
.
5
t
h
d
t
h
d
V
V
V
V
V
V
D
I
B
L
V
(4)
i
n
this
pa
per
,
the
DI
BLs
obta
ined
us
i
ng
(
4)
will
be
e
xpress
ed
acc
ordin
g
t
o
c
hannel
le
ng
th,
sil
ic
on
thic
kn
e
ss,
and to
p
a
nd bo
tt
o
m
o
xid
e
thic
kn
e
ss.
Figure.
2. Com
par
is
ons
of
t
he drai
n
c
urren
t
-
ga
te
v
olta
ge
c
ha
racteri
sti
cs for
this m
od
el
w
it
h resu
lt
s
of 2D
si
m
ulati
on
and
X
ie
’s
m
od
el
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Rel
ation
s
hi
p of d
r
ain i
nduce
d ba
r
rie
r loweri
ng an
d
to
p/bott
om gate
oxide
t
hickness
…
(
H
akkee J
ung
)
235
3.
E
X
T
R
AC
TI
O
N
O
F
DIBL
MO
DEL FO
R
A
S
Y
MM
ET
RIC J
L
DG M
OSFET
First,
the
asy
m
m
et
ric
ty
pe
ca
n
be
fabrica
te
d
diff
e
re
ntly
in
the
top
a
nd
bo
tt
o
m
ox
ide
film
thickness
,
un
li
ke
t
he
sym
m
et
ric
ty
pe.
Ther
e
fore,
DI
B
L'
s
con
to
ur
c
urves
f
or
the
va
riat
ion
s
of
t
he
top
a
nd
bott
om
gate
o
xi
de
thic
knes
s
are
sho
wn
in
Fi
gure
3.
It
was
fou
nd
tha
t
the
to
p
a
nd
bo
tt
om
gate
oxides
we
re
i
n
inv
e
rse
pro
portion
to
e
ach
oth
e
r
i
n
order
to
m
ai
ntain
a
c
on
sta
nt
DIB
L
as
s
how
n
i
n
Fi
gure
3,
a
nd
the
DI
BL
inc
reased
a
s
t
h
e
o
x
i
d
e
t
h
i
c
k
n
e
s
s
i
n
c
r
e
a
s
e
d
.
F
r
o
m
t
h
e
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
o
f
t
h
e
c
u
r
v
e
,
i
t
c
a
n
b
e
s
e
e
n
t
h
a
t
t
h
e
D
I
B
L
c
h
a
n
g
e
s
a
c
c
o
r
d
i
n
g
t
o
t
h
e
p
r
o
d
u
c
t
o
f
t
h
e
t
o
p
a
n
d
b
o
t
t
o
m
o
x
i
d
e
t
h
i
c
k
n
e
s
s
e
s
,
w
h
i
c
h
i
n
t
u
r
n
c
h
a
n
g
e
s
a
c
c
o
r
d
i
n
g
t
o
t
h
e
g
e
o
m
e
t
r
i
c
m
e
a
n
o
f
t
h
e
t
o
p
a
n
d
b
o
t
t
o
m
g
a
t
e
o
x
i
d
e
t
h
i
c
k
n
e
s
s
e
s
.
I
n
o
t
h
e
r
w
o
r
d
s
,
t
h
e
r
e
l
a
t
i
o
n
s
h
i
p
o
f
(
5
)
w
i
l
l
b
e
est
ablishe
d.
12
o
x
o
x
D
I
B
L
t
t
(5)
To
dem
on
strat
e
the
validit
y
of
(
5),
the
va
r
ia
ti
on
of
DI
B
L
with
res
pect
to
the
geo
m
etr
ic
m
ean
of
the
to
p
a
nd
bo
tt
o
m
gate
ox
i
de
thick
nesses
i
s
sho
wn
with
the
sil
ic
on
thic
kn
e
ss
as
a
pa
r
a
m
et
er
in
Fi
g
ure
4.
As
pr
e
dicte
d
i
n
Fi
gu
re
3,
we
can
obser
ve
that
the
D
IBL
i
s
pro
portio
nal
to
√
1
∙
2
.
The
refo
re
(5)
woul
d
be
valid.
The
ob
s
er
vation
f
or
the
sil
ic
on
th
ic
kn
ess
use
d
a
s
a
par
am
et
er
sh
ows
that
the
D
IBL
inc
reas
es
an
d
the
incre
asi
n
g
rate
(th
e
li
near
slop
e
in
Fi
gur
e
4)
al
so
i
ncr
e
ases
as
the
sil
ic
on
thick
ness
i
ncr
ease
s.
T
his
m
eans
that t
he DIBL
do
e
s
no
t i
ncr
ea
se li
near
ly
whe
n
sil
ic
on thic
kness i
ncr
ease
s
li
near
ly
.
Figure
3. Co
nto
urs
of DIBLs
for
the
to
p
a
nd
bo
tt
om
gate oxide
thic
kn
e
sses
i
n
the
case o
f
c
hanne
l l
eng
th
of 2
0nm
an
d
si
li
con
thic
kness
of
5
nm
Figure
4. Re
la
ti
on
of
DI
BLs
for t
he ge
om
et
ri
c m
ean
of the t
op and
bo
t
tom
g
at
e
oxide thick
ness
es
w
it
h
the sil
ic
on thic
kn
e
ss as
a
par
a
m
et
er
T
h
e
v
a
r
i
a
t
i
o
n
o
f
t
h
e
D
I
B
L
w
i
t
h
s
i
l
i
c
o
n
t
h
i
c
k
n
e
s
s
i
s
s
h
o
w
n
i
n
F
i
g
u
r
e
5
i
n
o
r
d
e
r
t
o
f
i
n
d
o
u
t
t
h
e
re
la
ti
on
sh
i
p
of
D
IBL
an
d
sil
ic
on
thick
ness
.
In
ge
ne
ral,
in
a
doub
le
-
gate
MOSFET
s,
the
DI
BL
is
known
to
be
pro
port
ion
al
to
the
sq
ua
re
of
sil
ic
on
thick
n
ess
[20].
As
ca
n
be
seen
in
Fi
gure
5,
the
DIB
L
is
pr
oport
ion
al
to
the
squ
are
of
sil
ic
on
thick
ne
ss
for
not
on
ly
the
sy
m
m
et
ri
cal
JLDG
MO
SFETs
wit
h
th
e
sa
m
e
top
and
bott
om
gate
ox
i
de
thickne
ss,
but
al
so
the
asy
m
m
et
ric
JLDG
MOSFET
s
with
th
e
top
g
at
e
ox
i
de
thick
nes
s
of
2
nm
and
the
bott
om
g
a
t
e
o
x
i
d
e
t
h
i
c
k
n
e
s
s
o
f
1
n
m
.
N
o
t
e
t
h
a
t
i
n
t
h
e
c
a
s
e
o
f
t
h
e
a
s
y
m
m
e
t
r
i
c
J
L
D
G
M
O
S
F
E
T
,
t
h
e
s
a
m
e
r
e
s
u
l
t
s
a
r
e
o
b
t
a
i
n
e
d
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
3
a
n
d
F
i
g
u
r
e
4
e
v
e
n
i
f
t
h
e
t
o
p
a
n
d
b
o
t
t
o
m
g
a
t
e
o
x
i
d
e
t
h
i
c
k
n
e
s
s
e
s
a
r
e
inte
rch
a
nged
.
As
can
be
see
n
in
Figure
5,
the
DI
BL
ch
ang
e
s
with
ch
ann
el
le
ngth.
Ther
e
f
or
e,
Fi
gure
6
s
hows
the
DI
BL
of
the
JLD
G
MO
SFET
with
th
e
sy
m
m
et
ric
a
nd
asy
m
m
et
ric
ox
ide
thic
kn
e
ss
wh
e
n
the
sil
ic
on
t
h
i
c
k
n
e
s
s
i
s
5
n
m
i
n
o
r
d
e
r
t
o
o
b
s
e
r
v
e
t
h
e
v
a
r
i
a
t
i
o
n
o
f
D
I
B
L
w
i
t
h
r
e
s
p
e
c
t
t
o
c
h
a
n
n
e
l
l
e
n
g
t
h
.
A
s
w
i
t
h
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
C
M
O
S
F
E
T
[
1
7
]
,
w
e
c
a
n
s
e
e
t
h
a
t
t
h
e
J
L
D
G
M
O
S
F
E
T
i
s
p
r
o
p
o
r
t
i
o
n
a
l
t
o
t
h
e
n
e
g
a
t
i
v
e
t
h
i
r
d
powe
r
of
the
c
ha
nn
el
le
ng
th
.
I
n
ad
diti
on
,
it
can
be
s
een
that
not
only
the
sy
m
m
e
tric
ty
pe
bu
t
al
so
the
asy
m
m
etr
ic
JLD
G
MO
SFETs
hav
i
ng
diff
e
re
nt
top
and
bo
tt
om
g
at
e o
xid
e thick
nesses
are
equ
al
ly
p
r
oport
ion
al
to
the n
e
gative thir
d
po
wer
of
the
channel
le
ngth.
I
n
this
pa
pe
r,
the
D
IBL
is
ob
se
rv
e
d
f
or
t
he
JLD
G
MOS
FET
with
cha
nnel
le
ng
th
of
m
or
e
than
10
nm
.
For
the
JL
DG
M
OS
FE
T
s
with
channel
le
ng
t
hs
bel
ow
10
n
m
,
ad
diti
on
al
sec
onda
ry
ef
fects,
su
c
h
a
s
tunneli
ng,
ha
ve
to
be
a
n
al
yz
ed
qua
ntu
m
m
echan
ic
al
ly
[26,
27
]
.
Ta
ke
n
tog
et
her
t
he
ab
ov
e
res
ults,
th
e
DI
B
L
can
be
e
xpress
ed
as
the
fo
ll
owin
g (6).
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1,
Febr
uar
y
2021
:
232
-
239
236
Figure
5.
DI
B
Ls for si
li
con thick
nesses
w
it
h
c
hannel
le
ng
th
and
oxi
de
thic
kn
e
ss as
p
a
ram
et
ers
Figure
6. D
IB
Ls for cha
nnel
le
ng
th
in
t
he
ca
se of
sil
ic
on
thic
kn
e
ss of
5
nm
w
it
h o
xid
e
thickne
ss as
a
par
am
et
er
32
12
g
s
i
o
x
o
x
D
I
B
L
A
L
t
t
t
(6)
wh
e
re
A
is
the
pro
portio
nal
c
on
sta
nt
an
d
is
the
SP
ICE
para
m
et
er
known
as
the
sta
ti
c
fe
edb
ac
k
c
oe
ff
ic
ie
nt.
To
obta
in
A
,
th
e
value
of
A
is
firstly
ob
ta
ine
d
from
the
fo
ll
owin
g
(
7)
b
y
us
i
ng
t
he
cha
nnel
siz
e
and
t
he
ox
ide
fil
m
thickn
ess
us
e
d
to
calc
ula
te
the DIBL.
32
12
/
g
s
i
o
x
o
x
A
D
I
B
L
L
t
t
t
(7)
The
m
axi
m
u
m
value
obta
ine
d
us
i
ng
(
7)
is
25.15,
a
nd
A
i
s
set
to
25
.
15
t
o
obta
in
a
reas
on
a
ble
ra
ng
e
of
the
sta
ti
c
f
eedb
ac
k
c
oeffici
ents.
The
sta
ti
c
feed
bac
k
c
oeffici
ents
thus
ob
ta
ine
d
are
sh
ow
n
in
Fig
ur
e
7.
Figure
7
(a
),
(
b),
an
d
(c)
show
a
case
in
wh
ic
h
the
to
p
a
nd
bott
om
gate
oxide
la
ye
rs
ha
ve
th
e
sam
e
sy
m
m
e
tric
al
s
tructu
re.
H
ow
ever,
the
sam
e
ty
pe
of
relat
ion
s
hip
grap
hs
can
be
de
rive
d
in
the
case
of
the
asy
m
m
et
ri
c
JLD
G
MOS
FETs
i
f
the
to
p
a
nd
bo
tt
om
gate
ox
i
de
thic
kn
e
ss
es
a
re
a
dj
us
te
d
to
ha
ve
t
he
sam
e
geo
m
et
ric
m
ea
n
for
the
to
p
a
nd
bott
om
gate
oxide
t
hick
nes
ses
as
desc
ribe
d
a
bove.
T
he
r
easo
n
f
or
this
i
s
tha
t
they
sh
ow
the
sam
e
DI
BL
res
ults.
As
ca
n
be
seen
in
Fi
gure
7,
it
can
be
ob
serv
e
d
that
as
t
he
ge
om
et
ric
m
ean
of
the
to
p
a
nd
bo
tt
om
oxide
thick
nesses
inc
reases,
the
ra
nge
of
the
sta
ti
c
feed
bac
k
coe
f
fici
ent
increas
es
and
the
c
hange
acc
ordin
g
t
o
t
he
si
li
con
t
hick
ness
al
so
increa
ses.
I
n
ge
ner
al
,
the
SP
ICE
par
am
et
er,
sta
ti
c
feed
back
coeffic
ie
nt,
ha
s
a
value
between
0
a
nd
1,
so
the
D
IBL
m
od
el
is
rea
so
na
ble
f
or
th
e
asym
m
e
tric
JLD
G
MOSFET pres
ented
in
t
his
pa
per.
I
n
ot
her
words,
t
he
D
IBL
m
od
el
of
t
he
a
sy
m
m
e
tric
JLDG
M
OS
F
ET can
be
expresse
d by t
he follo
wing
(
8) d
e
pe
nd
i
ng on th
e
ch
a
nnel
l
eng
t
h,
sil
ic
on
t
hick
ness, an
d o
xid
e
film
th
ic
kn
ess.
32
12
2
5
.
1
5
g
s
i
o
x
o
x
D
I
B
L
L
t
t
t
(8)
It
ca
n
be
seen
f
ro
m
Fig
u
re
7
t
hat
the
sta
ti
c
fee
dback
c
oe
ff
ic
ie
nt
is
a
ppr
oxim
a
te
ly
0.
5
<
<
1.
0
i
n
the
cha
nnel
di
m
ension
a
nd
ox
i
de
thic
kn
e
s
s
ra
ng
e
cal
c
ul
at
ed
in
t
his
pa
per.
I
n
orde
r
to
ver
ify
the
va
li
dity
of
(
8),
the
D
I
BL
values
obt
ai
ned
f
ro
m
R
aks
har
am
’s
m
od
el
[
22]
and
t
he
analy
ti
cal
DI
BL
m
od
el
of
(
8)
pr
ese
nted
i
n
this
pa
per
a
re
com
par
ed
i
n
Figure
8.
A
s
can
be
see
n
i
n
Fig
ur
e
8,
it
can
be
obser
ved
t
hat
the
DI
BL
obta
ined
us
i
ng
Ra
ks
ha
ram
'
s
m
od
el
fall
s
within
the
range
w
he
n
the
sta
ti
c
feed
bac
k
coe
ff
ic
i
ent
i
s
betwee
n
0.5
a
nd
1.0
in
(
8)
.
Ther
e
f
or
e,
the
DI
B
L
ca
n
be
obta
ined
acc
ordi
ng
to
t
he
c
hannel
dim
ension
a
nd
the
top
a
nd
bo
tt
o
m
ox
ide
thi
ckn
e
ss
by
a
djust
ing
the
sta
ti
c
feedbac
k
coe
f
fici
ent.
As
ca
n
be
seen
i
n
Fig
ur
e
8,
the
cha
nge
of
DI
BL
with
re
s
pect
to
the
c
ha
ng
e
of
the
st
at
ic
feed
bac
k
coeffic
ie
nt
is
s
m
al
l
as
the
chan
nel
le
ng
th
i
ncr
ea
s
es,
but
the
DIB
L
changes
si
gn
i
ficantl
y
with
th
e
c
hange
of
t
he
sta
ti
c
feed
bac
k
c
oeffic
ie
nt
as
the
channel
le
ng
t
h
dec
reases
.
Ther
e
f
or
e,
t
he
sh
ort
er
the
c
hannel
le
ngth,
the
m
or
e
care
m
us
t
be
ta
ken
wh
e
n
determ
ining
th
e stat
ic
f
eed
ba
ck
c
oeffici
ent.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Rel
ation
s
hi
p of d
r
ain i
nduce
d ba
r
rie
r loweri
ng an
d
to
p/bott
om gate
oxide
t
hickness
…
(
H
akkee J
ung
)
237
(a)
(b)
(c)
Figure
7. Stat
ic
f
ee
db
ac
k
c
oe
f
fici
ents for
cha
nn
el
le
ng
t
h wit
h
sil
ic
on thic
kness a
nd
ox
i
de t
hickn
e
ss as
par
am
et
ers
in t
he
case
of
(a)
t
ox1
=
t
ox2
=1
nm, (
b)
tox
1
=
tox
2
=2
nm
, and (c)
tox1
=
tox
2
=
3
nm
Figure
8. Com
par
is
ons
of
t
he DIBL
m
od
el
of (8
)
a
nd Raks
har
am
’s
m
od
el
4.
CONCL
US
I
O
N
In
t
his
pa
pe
r,
t
he
relat
io
nship
am
on
g
the
de
vice
dim
ension
su
c
h
as
c
ha
nnel
le
ng
th
,
sil
ic
on
thick
ness
,
and
t
op
a
nd
bo
tt
o
m
ox
ide
thi
ckn
e
ss
an
d
DIB
L
of
the
a
sym
m
e
tric
JLDG
MOSFET
is
de
rive
d.
I
n
gen
e
ral,
f
or
sy
m
m
e
tric
al
do
uble
gate
MO
SFETs,
D
IBL
is
pro
portion
al
to
the
ne
gativ
e
third
po
wer
of
t
he
c
hannel
le
ng
th
,
the seco
nd po
wer
of
t
he
sil
ic
on
t
hick
n
ess, a
nd
li
nea
rly
to
oxide thic
kness.
I
n
t
he
case o
f a
sy
m
m
e
try
, h
oweve
r
,
t
h
e
r
e
l
a
t
i
o
n
s
h
i
p
t
h
a
t
t
h
e
D
I
B
L
i
s
l
i
n
e
a
r
l
y
p
r
o
p
o
r
t
i
o
n
a
l
t
o
t
h
e
o
x
i
d
e
l
a
y
e
r
m
u
s
t
b
e
c
o
r
r
e
c
t
e
d
s
i
n
c
e
the
thic
kn
es
s
es
of
the
oxid
e
la
ye
rs
at
t
he
to
p
and
the
bott
om
can
be
fa
br
ic
at
ed
dif
f
ere
nt
ly
.
As
a
res
ul
t,
it
was
fou
nd
that
the
asy
m
m
et
ri
c
JLD
G
MOS
FET
is
pro
port
ion
al
to
the
ge
om
et
ric
m
ean
of
the
gate
oxi
de
thick
ness
at
the
top
and
bott
om
.
The
sam
e
relat
i
on
s
hi
p
can
be
us
ed
f
or
sym
m
et
rical
JLDG
MOS
FETs
with
the
sam
e
ox
i
de
thickne
ss
at
th
e
top
a
nd
b
ott
om
.
In
add
it
ion,
we
can o
bse
r
ve
that
the
DI
B
L
m
od
el
prese
nted
in
t
his
pa
per
is
in
good
ag
reem
e
nt
with
the
m
od
el
pr
esent
ed
in
oth
e
r
pa
per.
The
sta
ti
c
feedback
c
oeffici
ent,
w
hi
ch
i
s
a
par
am
et
er
use
d
in
t
he
S
PI
C
E
DI
B
L
m
od
el
of
CM
OS
F
ET
,
is
know
n
to
be
ab
ou
t
0.7.
In
the
D
IBL
m
od
el
of
the
asy
m
m
et
ri
c
JLD
G
M
OSFET
pr
ese
nted
in
this
pa
per,
the
sta
ti
c
fee
dback
coe
ff
ic
ie
nt
ha
s
a
value
betwee
n
0.5
an
d
1.0.
It
is
belie
ved
th
at
this
m
od
el
can
be
us
e
d
s
uffici
ently
in
ci
rcu
it
si
m
ulati
on
program
s
su
c
h
as
SPI
CE.
T
hese
resu
lt
s
will
serve as
the
basis
fo
r fu
t
ur
e
fa
br
i
cat
ion
of the a
s
ymm
et
ric JLD
G
MO
SFET
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1,
Febr
uar
y
2021
:
232
-
239
238
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r
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m
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r
a
n
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i
s
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o
r
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g
a
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e
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e
v
e
l
,
”
I
n
t
e
r
n
a
t
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n
a
l
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o
u
r
n
a
l
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l
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i
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u
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i
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r
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uss
ia
n
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c
ti
onle
ss
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DG
-
JL)
tra
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ncl
uding
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n
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ngth:
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ati
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ula
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ouble
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e
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,
”
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R
o
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“
Geom
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ri
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proc
ess
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ult
r
a
-
th
in
junc
ti
on
le
ss
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ert
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SF
ET
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urnal
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Elec
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E
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i
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m
et
ric
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SF
ET
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urnal
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ATE
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r
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t
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-
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y
m
m
et
ric
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ubl
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a
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n
a
n
a
l
y
t
i
c
m
o
d
e
l
f
o
r
c
h
a
n
n
e
l
p
o
t
e
n
t
i
a
l
a
n
d
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t
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l
d
s
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n
g
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f
t
h
e
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m
m
e
t
r
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c
a
n
d
a
s
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m
m
e
t
r
i
c
d
o
u
b
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e
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g
a
t
e
M
O
S
F
E
T
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,
”
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i
c
r
o
e
l
e
c
t
r
o
n
i
c
s
J
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u
r
n
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l
,
v
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4
2
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n
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.
3
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1
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5
1
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1
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N:
20
88
-
8708
Rel
ation
s
hi
p of d
r
ain i
nduce
d ba
r
rie
r loweri
ng an
d
to
p/bott
om gate
oxide
t
hickness
…
(
H
akkee J
ung
)
239
BIOGR
AP
H
I
ES
OF
A
UTH
ORS
Pr
of.
Hak
Kee
Jun
g
rec
ei
ved
t
he
B.
S.
deg
ree
f
rom
Ajou
Univer
sit
y
,
Korea
,
in
1983,
the
M.S
.
and
Ph.D.
degr
e
es
from
Yon
sei
Univer
sit
y
,
Se
oul,
Korea
,
in
1
985,
1990,
resp
ec
t
ive
l
y
,
all
in
el
e
ct
roni
c
engi
n
ee
ring
.
In
1990,
he
joi
ned
Kuns
an
Nati
onal
Univ
ersity
,
Chonbuk,
Korea
,
wher
e
he
is
cur
ren
t
l
y
a
Profess
or
in
depa
rtment
of
elec
troni
c
eng
ineeri
ng.
From
1995
t
o
1995,
he
hel
d
a
rese
a
rch
posit
ion
with
th
e
Elec
tron
ic
Eng
ineeri
ng
Depa
r
tme
nt,
Os
aka
Univ
ersity
,
Os
ak
a,
Japa
n.
From
20
04
to
2005
,
an
d
2016
to
2017
,
he
was
with
t
he
School
o
f
Microe
l
ec
tron
ic
Engi
ne
eri
ng,
Griffi
th
Univ
ersity
,
Nath
an,
QL
D,
Aus
tra
lia.
His
rese
arc
h
in
te
rests
in
cl
ud
e
sem
ic
onduct
or
d
evi
c
e
p
h
y
s
i
c
s
a
n
d
d
e
v
i
c
e
m
o
d
e
l
i
n
g
w
i
t
h
a
s
t
r
o
n
g
e
m
p
h
a
s
i
s
o
n
q
u
a
n
t
u
m
t
r
a
n
s
p
o
r
t
a
n
d
M
o
n
t
e
C
a
r
l
o
s
i
m
u
l
a
t
i
o
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.