Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 11
3
~
11
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.9
342
1
13
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Projected Range Dependent Tunn
eling Current of Asymm
e
tric
Double Gate MOSFET
Hak
Kee
Ju
ng
Department o
f
Electronic Eng
i
neering,
Kunsan N
a
tion
a
l Univ
ersit
y
,
Kore
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 19, 2015
Rev
i
sed
No
v 8, 201
5
Accepted Nov 23, 2015
This
s
t
ud
y
is
to anal
yz
e the
changes
of tun
n
eling curr
ent
accord
ing to
projected rang
e, a variab
le of Gau
ssian function
of channel doping functio
n
of As
y
mmetric
Double Gate; A
DG
MOSFET.
In MOSFET with ch
annel
length below 10 nm, tunneling
current
occupies a large per
cen
tage among
off-currents
.
Th
e incr
ease of tunneling
curren
t
has a large effect on
th
e
characteristics of subthreshold such as
threshold voltage movement and the
decl
ine of s
ubthres
hold s
w
ing value
,
s
o
the accu
rate an
al
ys
is
of this
is
bein
g
required
.
To ana
l
yze th
is
, potent
i
al di
stribu
tion o
f
series form wa
s obtained
using Gaussian distribution
fun
c
tion
,
and us
ing
this
herm
eneu
t
i
c pot
enti
al
distribution
,
th
ermionic emission cu
rrent and
tunneling
curren
t
making up
off-current wer
e
obtain
e
d. At
this poi
nt, th
e
effect that the
changes of
projected range, a variable of
Gaussi
an distribution function
,
have on the
ratio of tunnelin
g current among off-curre
nts was analy
zed
. As a result, th
e
smaller projected range w
a
s, th
e lowe
r
the ratio of tunneling
current was.
When projected
range in
creased, tunneli
ng curr
ent incr
eased
larg
ely
.
Also
, it
was observed th
at th
e valu
e of
projected r
a
nge
which the r
a
tio
of tunneling
current in
creased changed acco
rdi
ng to maximum channel doping value,
channel length
,
and chann
e
l width.
Keyword:
Asy
m
m
e
t
r
i
c
dou
bl
e
gat
e
Gaus
si
an f
unct
i
on
Pr
oj
ected
r
a
nge
Therm
i
oni
c c
u
rre
nt
Tu
nnel
i
n
g c
u
rr
ent
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Hak
Kee
J
u
n
g
,
Depa
rt
m
e
nt
of
El
ect
roni
c
En
g
i
neeri
n
g,
Kun
s
an
National
Un
i
v
ersity,
5
5
8
D
a
eh
akro
, G
u
n
s
an
, Jeonbu
k, K
o
r
ea,
573-
701
Em
a
il: h
k
j
u
ng@kun
san.ac.k
r
1.
INTRODUCTION
The large
s
t concerns in sem
i
condu
ct
o
r
i
n
t
e
grat
e
d
ci
rcui
t
s
are hi
g
h
-
s
pee
d
oper
a
t
i
on a
n
d
l
o
w p
o
we
r
co
nsu
m
p
tio
n
.
To
satisfy th
ese two
ch
aracteristics, th
e ef
fo
rt
s t
o
i
m
prove
t
h
e way
o
f
de
s
i
gni
n
g
t
h
e i
n
t
e
grat
e
d
circuits and to
reduce the
size of t
h
e tra
n
sistor
use
d
in
t
h
e
ci
rcui
t
s
are
bei
ng m
a
de.
Ho
w
e
ver
,
re
d
u
ct
i
o
n
i
n
t
h
e
size of transis
t
or shows seri
ous
problem
s
in the ch
aract
eristics of subthres
hol
d suc
h
as the decline of
subt
hre
s
h
o
l
d
s
w
i
n
g val
u
e
,
t
h
resh
ol
d
vol
t
a
g
e
m
ovem
e
nt
, and
drai
n i
n
d
u
c
e
d ba
rri
er l
o
w
e
ri
n
g
(D
IB
L)
by
sho
r
t
channel e
ffects
(SCEs
)
. Es
pec
i
ally, the incre
a
se of
of
f-cu
rren
t
sh
ows t
h
e
p
r
ob
lem
with
th
e in
crease of
p
o
wer
co
nsu
m
p
tio
n
by
cu
rren
t flow wh
ich
can
’
t b
e
ig
no
red
i
n
th
e o
f
f-state
tran
si
sto
r
.
Th
e
d
e
v
i
ce
wh
ich
h
a
s
b
e
en d
e
velop
e
d
for red
u
cing
SC
Es is th
e m
u
ltip
le-g
ate MOSFET.
Th
e
m
u
ltiple-gate
MOSFET
is t
h
e
device t
h
at the c
h
aracter
i
s
t
i
c
s of
su
bt
h
r
esh
o
l
d
a
r
e i
m
pr
o
v
ed
by
pr
o
duci
n
g
sev
e
ral
g
a
tes ab
le to
con
t
ro
l t
h
e cu
rren
t
flow in
th
e ch
an
n
e
l
aroun
d th
e chan
n
e
l. Th
e m
u
l
tip
le-g
ate MOSFETs
are l
a
rgel
y
di
vi
de
d i
n
t
o
Fi
n
F
ET,
do
u
b
l
e
-
g
at
e (DG
)
M
O
SFET, a
n
d cy
l
i
ndri
cal
M
O
S
F
ET.
Am
ong
t
h
em
,
DGM
OSFET is b
e
in
g
stud
ied
a lo
t d
u
e
to
its si
m
p
le
st
ructure. DGM
O
SFET, as th
e str
u
ctur
e of
p
r
od
u
c
i
n
g
t
w
o gat
e
s at
t
h
e t
op an
d t
h
e bot
t
o
m
,
i
s
di
vi
ded i
n
t
o
th
e symme
tric DGMOSFET with
th
e stru
ct
u
r
e same at
bot
h si
de
s an
d
asym
m
e
t
r
i
c
DGM
OS
FET
(A
DGM
OSF
ET)
pr
o
duce
d
wi
t
h
t
h
e st
r
u
ct
ure
di
ffe
rent
at
eac
h
si
de
,
an
d
ADGM
OSFET of th
e two
is b
e
ing
st
u
d
ied
a lo
t b
eca
use of t
h
e adva
ntage
of t
h
e increase in the
factor
able to c
o
ntrol
the cha
r
acterist
i
cs of the
subthreshold [5].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
11
3 – 11
9
11
4
Especi
al
l
y
, Di
ng
et
al
. i
n
t
e
r
p
ret
e
d t
h
e
su
b
t
hres
hol
d
or
s
o
m
e
t
h
i
ng by
c
a
l
c
ul
at
i
ng t
h
e
herm
eneut
i
c
p
o
t
en
tial d
i
strib
u
tion
of ADGMOSFET [6]. Differen
t
fr
o
m
Din
g
et al
, th
is stu
d
y
will u
s
e th
e Gau
ssian
d
i
stribu
tio
n fun
c
tio
n as t
h
e ch
arg
e
d
i
stribu
tio
n fun
c
tio
n.
Gaus
si
an di
st
r
i
but
i
o
n fu
nct
i
o
n
i
s
t
h
e di
st
ri
but
i
o
n cha
n
ge
d by
t
w
o vari
abl
e
s, w
h
i
c
h
a
r
e pr
oj
ect
ed
ran
g
e t
o
de
fi
ne
t
h
e m
a
xim
u
m
val
u
e a
n
d st
a
nda
r
d
p
r
oject
e
d
d
e
vi
at
i
o
n t
o
det
e
rm
i
n
e t
h
e wi
dt
h
o
f
di
st
ri
but
i
o
n
.
Eve
n
i
n
t
h
e cas
e of
ha
vi
n
g
t
h
e
l
e
ngt
h
of c
h
a
n
nel
bel
o
w
1
0
n
m
i
n
A
DGM
O
SFET,
t
h
e i
n
cr
ease o
f
of
f-c
ur
rent
i
s
in
ev
itab
l
e. Th
erefo
r
e, th
is stud
y tries to
an
al
yze th
e
rat
i
o
-c
han
g
e
of t
u
n
n
e
l
i
ng cu
rre
nt
ac
cor
d
i
n
g t
o
pr
o
j
ect
ed
ran
g
e,
by
cal
cul
a
t
i
ng t
u
n
n
e
l
i
ng c
u
r
r
ent
and t
h
erm
i
oni
c em
i
ssi
on c
u
r
r
ent
c
o
m
p
ri
si
ng
of
f-
cu
rre
nt
o
f
AD
GM
O
SFET
.
In
ch
ap
ter 2
,
th
e po
ten
tial d
i
stribu
tio
n
o
f
ADGMOSFET an
d
t
u
nn
elin
g
cu
rren
t
m
o
d
e
l will be
expl
ai
ne
d.
I
n
chapt
e
r 3
,
t
h
e
rat
i
o
-c
ha
nge
of t
u
n
n
e
ling
cu
rren
t t
o
ward
p
r
oj
ect
ed range
calculated by
the
param
e
t
e
rs of t
h
e
m
a
xim
u
m
do
pi
n
g
co
nce
n
t
r
at
i
on, t
h
e l
e
n
g
t
h
o
f
cha
nnel
,
t
h
e t
h
i
c
knes
s
of cha
nnel
,
a
nd t
h
e
v
o
ltag
e
of
g
a
te will b
e
ex
am
i
n
ed. C
h
ap
ter 4
will b
e
a con
c
l
u
sion
.
2.
POTENTI
AL DIST
RIB
U
TIO
N
AN
D T
UNN
ELIN
G CU
RR
EN
T M
O
D
ELIN
G
OF
ASYMMETRIC DOUBLE GATE MOSFET
Schem
a
t
i
c
secti
onal
di
ag
ram
of
AD
GM
O
S
F
E
T
was
p
r
ese
n
t
e
d i
n
t
h
e
Fi
gu
re
1.
As
Fi
g
u
re
1
i
n
di
cat
es
,
th
e vo
ltag
e
of t
o
p g
a
te
V
gf
an
d
t
h
e vol
t
a
ge of bot
t
o
m
gat
e
V
gb
can
be
dif
f
ere
n
tly biased and, in t
h
is case
,
it ca
n
be indicated t
h
at the structural pa
ram
e
ter
able to
c
ont
rol the short c
h
annel e
f
fect increases
becaus
e
the
thickne
ss
of oxidative film
of
top a
n
d
botto
m
can be dif
f
ere
n
tly
appointe
d
in each.
Fi
gu
re
1.
Sc
he
m
a
t
i
c
sect
i
onal
di
ag
ram
of as
ym
m
e
t
r
i
c
do
ub
l
e
gat
e
M
O
SF
ET
Herm
eneut
i
c
p
o
t
e
nt
i
a
l
di
st
ri
b
u
t
i
on
has
bee
n
obt
ai
ne
d
by
c
a
l
c
ul
at
i
ng t
h
e
Poi
s
s
on e
q
uat
i
on
o
f
Eq
. (
1
)
.
In t
h
i
s
case, Ga
ussian function, approxim
ate
t
o
t
h
e expe
ri
m
e
nt
al val
u
e,
has
be
en use
d
as t
h
e
char
ge di
st
ri
b
u
t
i
o
n
fun
c
tion
.
Th
at
is lik
e th
is.
2
22
22
2
()
ex
p
2
pp
si
p
qN
x
R
xy
(1
)
w
h
er
e
s
i
is th
e
perm
i
ttiv
it
y o
f
silico
n
,
N
p
t
h
e
m
a
xim
u
m
do
pi
ng
c
once
n
t
r
at
i
o
n
,
R
p
pr
o
j
ect
ed ra
nge
,
a
n
d
p
th
e
st
anda
rd
p
r
o
j
e
c
t
e
d de
vi
at
i
o
n
.
In t
h
i
s
case,
p
o
t
e
nt
i
a
l
di
st
ri
b
u
t
i
on
o
b
t
a
i
n
e
d
by
usi
ng t
h
e b
o
u
n
d
ary
c
o
n
d
i
t
i
on
of
Ding et al., is t
h
e sam
e
as Eq. (2).
11
2
2
1
(
,
)
(
/2
)
(
/2
)
s
i
n
nn
d
kx
k
x
sn
n
g
g
n
Vn
y
xy
V
y
C
e
D
e
B
e
r
f
b
B
e
r
f
b
LL
(2
)
whe
r
e
V
s
is t
h
e sou
r
ce
vo
ltag
e
,
V
d
t
h
e drai
n v
o
l
t
a
ge,
n
a
fi
xe
d n
u
m
b
er,
k
n
=
n
/
L
g
, an
d t
h
e
ot
he
r c
onst
a
nt
s are
inscribe
d i
n
t
h
e refe
re
nce
[7]
.
On
e six
t
h
o
f
el
ectron
s
m
o
v
i
ng
rando
m
l
y will h
ead toward
d
r
ai
n
fro
m
so
urce, and
,
u
s
ing
th
e nu
m
b
er
of
el
ect
ro
ns a
r
r
i
vi
ng
at
t
si
W
area of
drain pe
r
unit tim
e, the therm
i
oni
c em
ission curre
nt is
as following.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Projected Range Depe
ndent Tunneling
C
u
r
r
en
t
o
f
Asymmetric Doub
le Ga
te MOS
F
ET
(H
a
k
Kee Ju
ng
)
11
5
mi
n
m
i
n
(,
)
2
(/
)
6
ef
f
qx
y
ip
s
i
t
h
th
e
r
qn
N
e
t
W
v
I
(3
)
whe
r
e
x
eff
is t
h
e cen
ter of cond
u
c
tion
,
and
y
min
is
y
val
u
e tha
t
the s
u
rface
potential gets m
i
nimized.
Because, in c
h
annel
with bel
o
w
10nm
length, the
widt
h of energy ba
nd from
the source
to the drai
n
becom
e
s very
nar
r
o
w
, t
u
n
n
e
l
i
ng cu
rre
nt
as wel
l
as t
h
erm
i
oni
c em
i
s
si
on c
u
r
r
ent
c
a
n’t
b
e
i
g
n
o
r
a
b
l
e
as
i
ndi
cat
ed
i
n
Fi
gu
re
1.
T
h
ere
f
ore
,
t
h
i
s
st
u
d
y
has cal
c
u
l
a
ted
tu
nn
elin
g cu
rren
t in ord
e
r t
o
ob
tain
t
h
e
o
f
f cu
rren
t
f
o
r
th
e ADGMO
SFET
w
ith
th
e ch
ann
e
l len
g
t
h
below
10
n
m
.
W
K
B (W
en
tzel
-
K
r
a
m
e
r
s
-
B
r
illo
u
i
n
)
app
r
oxi
m
a
t
i
on i
s
used t
o
o
b
t
a
i
n
t
u
nnel
i
n
g c
u
r
r
ent
.
C
o
m
p
ared wi
t
h
t
h
e ap
pr
oxi
m
a
t
i
on of
q
u
ant
u
m
m
echani
c
s
,
WKB
a
p
pr
o
x
i
m
at
i
on i
s
p
r
o
v
e
d t
o
be
avai
l
a
bl
e o
n
e
beca
u
s
e th
e
d
i
f
f
e
r
e
n
c
e is ig
nor
ab
le
en
oug
h [8
]. Tun
n
e
ling
cu
rren
t
ob
tain
ed
b
y
u
s
i
n
g
WKB app
r
o
x
i
m
a
ti
o
n
is lik
e t
h
is.
2
1
,
,
2
2
63
3
2(
,
)
exp
2
tl
ds
i
t
t
h
l
t
h
tunn
y
tl
e
f
f
f
m
tl
y
qN
t
W
T
v
T
v
I
mq
x
y
E
Td
y
(4
)
whe
r
e sign
t
and
l
m
ean the va
lues of transve
r
sal and longi
t
udi
nal direction respectively. In this,
t
th
v
and
l
th
v
are therm
i
onic velocities
of
t
r
ansversal and longitudinal
direction
re
spectively. Total of
f-current is like
this.
t
o
t
t
her
t
unn
II
I
(5
)
This study will calculate total off-c
urre
nt by usin
g E
q
. (5) and t
h
en calc
u
late tunneling c
u
rrent
rati
o
according
to projected ra
nge, the varia
b
le of Ga
ussian
distribution
function with
the pa
ram
e
ters
such as
the
length
o
f
c
h
a
n
nel, the
thic
kn
ess o
f
c
h
a
nnel,
an
d the
do
pi
ng concentration.
Also the change of t
h
is ratio wil
l
be e
x
am
ined.
3.
CO
NSI
D
ER
A
T
ION OF
T
U
NNELI
NG C
U
R
R
ENT
OF AD
GM
OSFE
T
Because the
validity of E
q
. (3) and
(4) has
already bee
n
proved
in
pre
v
iously
prese
n
te
d the
s
is [9,
10], this st
udy
will calculate
ther
m
i
onic emission curre
nt and
tunneli
ng current
for ADGMOSFET by
usi
ng
Eq.
(
3
)
an
d
(4
),
an
d c
o
n
s
ider
the c
h
an
ge
o
f
tu
nnelin
g c
u
rre
nt
.
At first, the tu
nnelin
g cu
rre
n
t
for p
r
o
j
ected
range
obtaine
d with the pa
r
a
m
e
ter of chan
nel length is
indicated
in Figu
re 2.
Figu
re
2.
The
c
h
an
ge
o
f
tu
n
n
e
ling c
u
r
r
ent
rat
i
o f
o
r
p
r
oj
ected
range
with a
param
e
ter of channel lengt
h
i
n
AD
GM
O
SFET
ha
vin
g
m
a
xim
u
m
channel
d
o
p
in
g c
once
n
tra
tion
of
1
0
19
/
cm
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 6, No
. 1, Feb
r
uar
y
20
1
6
: 11
3 – 11
9
11
6
The calculating condition is
indicated in t
h
e Figure 2.
If
projected ra
nge increases
, the ratio of tunneling
current am
ong off-c
urre
nt re
aches to alm
o
s
t
100% i
n
the
end
altho
u
gh i
t
is diffe
rent a
ccor
d
in
g to
ch
anne
l
length
.
It is
o
b
ser
v
e
d
that,
as the c
h
an
nel
lengt
h
gets
s
h
o
r
ter,
tu
nneli
ng
cu
rre
nt
in
the sm
aller extent of
proj
ected ra
nge reaches t
o
the satura
ted c
ondition.
Especia
lly, in the case
of
very short chan
nel length a
r
ound
7nm
, the off
-
c
u
r
r
ent is com
pose
d
of
10
0% tun
n
elin
g cu
rre
nt rega
rdless
o
f
pr
o
j
ected ra
n
g
e. H
o
weve
r, the ratio
of t
u
nnelin
g c
u
r
r
ent
gets s
h
arply
decrease
d
in
the
sm
aller exte
nt of
projected
ra
nge if c
h
annel l
e
ngt
h
increases, and
then it can be observed
that the ratio of tunne
ling c
u
r
r
ent
gets saturate
d as pr
ojecte
d
ra
nge
increases
. I
n
t
h
e case o
f
c
h
a
n
nel len
g
th a
r
ou
nd
1
0
n
m
,
the r
a
tio o
f
tu
nneli
ng
cu
rre
nt c
h
a
nge
s s
h
ar
ply
fr
om
0%
to 10
0% in p
r
o
j
ected ra
n
g
e ar
ou
n
d
2.
3 nm
. Like this,
the r
a
tio of tu
nnelin
g cur
r
e
n
t chan
ges sha
r
ply
acc
or
din
g
to the channel lengt
h.
In the case that channel t
h
ickness is the para
m
e
ter,
the c
h
ange
of t
u
nneli
n
g current acc
ording t
o
t
h
e
pr
o
j
ected
ra
ng
e is in
dicated
in Fi
gu
re
3.
A
s
sh
o
w
n
in
Fi
gu
re
3a
), it ca
n
be
o
b
ser
v
e
d
that
whe
n
ch
anne
l
thickness is
big, t
h
e ratio of tunne
ling c
u
rrent
greatly increases e
v
en in
the c
a
se
projected
ra
nge is low.
Howev
e
r,
in
th
e v
e
r
y
th
in
case o
f
ch
ann
e
l th
ick
n
ess arou
nd
1
n
m
,
the r
a
tio
of
tunnelin
g
cu
rr
en
t
gr
eatly
decrease
s
in the s
m
all project
ed ra
nge
. H
o
w
e
ver
,
if pr
o
j
ect
ed ra
nge inc
r
ea
ses o
v
e
r
2n
m
,
t
h
e r
a
tio
of
tunn
elin
g
current inc
r
eases up to
100%
rega
rdless
of c
h
an
nel thick
n
e
ss. I
n
the case of Fi
gu
re 3
b
)
with 1
0
nm
of chan
ne
l
length, the rat
i
o of t
u
nneling curre
nt increases sh
a
r
ply from
0% to 100% acco
rdi
n
g to projecte
d
range
rega
rdless
o
f
c
h
an
nel thickness.
Figu
re
2 a
nd
3 are
the case
s
that the m
a
xim
u
m
channe
l do
pin
g
c
onc
entratio
n is
19
3
10
/
cm
. T
o
obs
er
ve the
ch
ange
o
f
t
h
e rat
i
o o
f
t
u
n
n
elin
g
cu
rre
nt acc
or
d
i
ng t
o
the
ch
an
ge
of
d
o
p
in
g c
once
n
tratio
n,
in th
e
case that cha
n
nel thick
n
ess i
s
the pa
ram
e
ter an
d
the m
a
xim
u
m
dopi
ng
c
once
n
tratio
n
d
ecreases to
1
0
16
/
cm
3
,
the
change of the
ratio of
tunneling
cur
r
e
nt is shown in
Fig
u
r
e
4
.
Figur
e
3a) and
4 a
r
e the
cases that all
conditions are
sam
e
but j
u
st the m
a
xi
m
u
m
c
h
annel doping
concentration i
s
different. As Figure
4 shows, it
can be obse
rved that the ratio of
tu
nneli
n
g
cur
r
e
n
t, in p
r
o
j
ected ra
n
g
e
arou
n
d
4 nm
, chan
ges fr
om
0% to
10
0%
re
gar
d
le
ss o
f
c
h
a
nnel t
h
ick
n
ess.
Figu
re
3.
The
c
h
an
ge
o
f
tu
n
n
e
ling c
u
r
r
ent
rat
i
o f
o
r
p
r
ojecte
d
range with
a
param
e
te
r of channel thickness in
ADGMOSFET
in the
case
of
a)
L
g
= 8
nm
a
n
d b)
L
g
=
10
nm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Projected Range Depe
ndent Tunneling
C
u
rren
t
of Asymmetric Double Gate M
O
SFET
(Ha
k
Kee Ju
ng
)
11
7
Figu
re
4.
The
c
h
an
ge
o
f
tu
n
n
e
ling c
u
r
r
ent
rat
i
o f
o
r
p
r
ojecte
d
range with
a
param
e
te
r of channel thickness in
AD
GM
O
SFET
ha
vin
g
m
a
xim
u
m
channel
d
o
p
in
g c
once
n
tra
tion
of
1
0
16
/
cm
3
If c
h
a
nnel
doping c
o
ncentration
dec
r
eases, the ratio
of tunneling curre
nt
changes sha
r
pl
y
according
to p
r
o
j
ected
r
a
nge
rathe
r
th
an c
h
an
nel thi
c
kne
ss.
In
co
m
p
arison to
F
i
gu
re 3a
), i
f
the m
a
xim
u
m
do
pi
n
g
conce
n
tration
decrease
s
from
10
19
/
cm
3
to
10
16
/
cm
3
, proj
ected range in
which th
e
r
a
tio
of
tunn
eling cu
rr
en
t
changes sha
r
ply increases
from
2 nm
to 4 nm
. As E
q
.
(3) i
ndicates, this is
because
when the m
a
xim
u
m
chan
nel
do
pin
g
c
once
n
tratio
n
decrease
s
, t
h
erm
i
onic em
is
sion c
u
rre
nt increases a
n
d
m
o
st of t
h
e
off-current
whose projecte
d
range reache
s
up
t
o
4 nm
is
occupied by t
h
erm
i
onic e
m
iss
i
on c
u
rre
nt.
I
n
th
e case th
at th
e m
a
x
i
m
u
m
ch
an
n
e
l dopin
g
con
cen
tr
atio
n is 10
16
/
cm
3
, the c
h
ange
of the rati
o
of
tunneling curr
ent
obtained by the
param
e
ter of channel length is
pr
esen
ted
in Figur
e
5
.
Figu
re
5.
The
c
h
an
ge
o
f
tu
n
n
e
ling c
u
r
r
ent
rat
i
o f
o
r
p
r
oj
ected
range
with a
param
e
ter of channel lengt
h
i
n
AD
GM
O
SFET
ha
vin
g
m
a
xim
u
m
channel
d
o
p
in
g c
once
n
tra
tion
of
1
0
16
/
cm
3
In com
p
arison of Fi
gure
2, t
h
is is
just
the
case
that
t
h
e m
a
xim
u
m
ch
annel
d
o
p
in
g c
once
n
tratio
n
d
ecreases
fr
om
10
19
/
cm
3
to 10
16
/
cm
3
.
If
the m
a
xim
u
m
cha
nnel
d
opi
n
g
c
once
n
tr
ation decreases,
it can be
obse
rve
d
that
the ratio of t
u
nneling curre
nt dec
r
eases
greatly b
eca
use the ratio of therm
i
onic em
ission increa
ses as
pre
v
io
usly
ex
p
l
ained. Es
peci
ally
, if
it is c
o
m
p
ared with
the case of c
h
annel length
of 7 nm
, the ratio of
tun
n
eling c
u
rre
nt occ
upies al
m
o
st 100% in
the cas
e that
m
a
xim
u
m
channel
do
pin
g
c
o
ncent
r
ation is
10
19
/
cm
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJEC
E V
o
l. 6, No
. 1, Feb
r
uar
y
20
1
6
: 11
3 – 11
9
11
8
in 2
nm
of pr
o
j
ected
ran
g
e as
sho
w
n in Fi
g
u
re
2,
but it re
m
a
ins un
der t
h
e ratio ar
ou
n
d
5% w
h
e
n
m
a
xim
u
m
channel dopi
ng concent
r
ation decreases to 10
16
/
cm
3
a
s
k
n
o
w
n
i
n
F
i
g
u
r
e
5
.
A
s
Fi
gure 5 indicates, in the case
that the m
a
xim
u
m
channel
do
pin
g
c
onc
entration is as
relatively low as10
16
/
cm
3
, the
value of projecte
d
range
in whic
h the ratio of tunneli
ng c
u
rren
t gets saturated to 100% cha
nges
greatly accordi
ng to c
h
annel length.
That is, in the
case that the m
a
xi
m
u
m
channel d
o
p
in
g c
once
n
tratio
n is
low, the c
h
an
ge o
f
cha
nnel
length
greatly
af
fects
the cu
rre
nt
bec
a
use the
am
ount o
f
c
h
ar
ge
in
side the act
ual cha
nnel
decre
a
ses. T
h
at is, i
n
E
q
.
(3), in t
h
e case
that
p
N
is s
m
all, therm
i
onic curren
t rises
great
ly, and the
ratio
of
tunneling current decreases
greatly in t
h
e end.
AD
GM
O
SFET
has c
h
aracte
r
istics that volta
ge
of t
op a
n
d
bottom
gate ca
n
be ap
plied
di
ffe
rently
. I
n
Figu
re
6, t
h
e c
h
an
ge
of
tu
nn
eling c
u
r
r
ent
r
a
tio fo
r
pr
o
j
ec
ted ra
ng
e calc
u
lated
by
the
param
e
ter of t
o
p
gate
voltage is presented.
At this,
bottom
gate v
o
ltage is fixe
d a
t
0.5
V
.
As
Fig
u
re
6 in
dicates
, it can be
o
b
s
e
rve
d
that
tunneling current ratio
de
creases if top
gate voltage
inc
r
eases.
Ho
we
ver, if projecte
d
range i
n
crease
s
over
2 nm
, it can be obse
r
ved that
tun
n
eling c
u
rre
nt ratio inc
r
eases to 100% and is satura
te
d r
e
gar
d
less o
f
to
p gate
voltage
.
If t
op
gate
volt
a
ge is fi
xed
at
0.
5 V
an
d
b
o
ttom
gate
voltag
e
gets c
h
an
ge
d
fr
om
0.2
V to
0.
9
V, t
h
e
sam
e
g
r
ap
h
can
also
b
e
ob
tain
ed
. Th
at is,
it can
b
e
f
ound
th
at tunn
eling
cur
r
en
t ratio sho
w
s
symmetr
i
cal
chan
ge f
o
r to
p
and b
o
ttom
gate voltage. A
s
for the c
h
an
ge of tu
n
n
elin
g cur
r
e
n
t in pr
ojecte
d
ra
nge
belo
w 2
nm
, it shows
g
r
eat chan
ge bet
w
een
0.
5 V an
d 0.
7 V
of to
p gate voltage. That is, it can
b
e
f
o
und
th
at tu
nn
eling
current
ratio shows great c
h
ange
in the case t
h
at top and bot
t
om
gate voltage are sim
ilar.
Figu
re
6.
The
c
h
an
ge
o
f
tu
n
n
e
ling c
u
r
r
ent
rat
i
o f
o
r
p
r
oj
ected
range
with a
param
e
ter of top
gate voltage in
AD
GM
O
SFET
ha
vin
g
m
a
xim
u
m
channel
d
o
p
in
g c
once
n
tra
tion
of
1
0
19
/
cm
3
4.
CON
C
LUSIO
N
This st
udy a
n
alyzed the c
h
a
nge
of t
u
nneling cu
rre
nt acc
or
din
g
t
o
pr
o
j
ect
ed range
which is the
varia
b
le o
f
th
e Ga
ussian
f
u
nction
that is
chan
nel
do
pin
g
f
u
nctio
n
of
AD
GM
SF
ET
.
The
ratio c
h
a
nge
o
f
therm
i
onic e
m
ission c
u
rrent
and t
u
nneling
current
wh
ic
h
is com
posing
of
f-c
ur
re
nt in
AD
GM
O
SFET
with
channel le
ngt
h bel
o
w 10 nm
was
observe
d
according t
o
proj
ecte
d
ra
nge
.
At this point,
t
h
e c
h
a
nge
of c
h
annel
size like cha
n
n
e
l length
an
d c
h
an
nel thic
kne
ss,
of t
h
e m
a
xim
u
m
dopin
g
c
once
n
tratio
n,
a
n
d
o
f
to
p
gate
voltage
were
use
d
a
s
p
a
ram
e
ters.
As a result, it was found that
tunneling current ratio
was low as
projecte
d
ra
nge was
sm
all, and that
tunneling current
inc
r
ease
d
greatly as
projected ra
nge
i
n
creas
e
d
. Howeve
r
,
t
h
e tendency
of c
h
ange
was
greatly
di
f
f
e
r
e
n
tiated acc
or
ding
to
pa
ram
e
ters.
That is, in the c
a
se of 10
19
/
cm
3
of the m
a
xim
u
m
channel dopi
ng co
ncentration, w
h
en cha
nne
l length was as
short as 7 nm
, alm
o
st 100% of tun
n
eling curre
nt co
m
posed of
f-c
urre
nt regardles
s
of pr
ojected ra
nge. H
o
we
ver
,
if the
m
a
xim
u
m
channel do
ping
conc
entration decrea
sed to
10
16
/
cm
3
, only
aro
u
n
d
5
% of
of
f-cu
rrent
, whe
n
c
h
annel
length
was 7 nm
, was
com
posed of tunneling cur
r
ent due to the in
crease of ther
m
i
onic em
ission cu
rren
t
. Especially
, projected
range
in
which the tunneling
current
ratio changed sharply showe
d
great
di
f
f
erence accordi
n
g to cha
nnel l
e
ngth,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Projected Range Depe
ndent Tunneling
C
u
rren
t
of Asymmetric Double Gate M
O
SFET
(Ha
k
Kee Ju
ng
)
11
9
channel thickne
ss, and the m
a
xim
u
m
doping concentration.
In
addition, it was observed that curre
nt ratio decreased
greatly
when to
p gate
voltage increased, a
n
d
th
at tunneling
c
u
r
r
ent ratio was
also saturated to
10
0% w
h
en
p
r
o
j
ected
range
increased. Because projected
range
has a
great ef
fect
on tunneling current
ratio like this, i
t
should
be
hee
d
ed in
designing
A
D
G
M
OSFET
.
REFERE
NC
ES
[1]
S
.
M
.
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and
J
.
T. P
a
rk
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E
le
ctri
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ert
i
e
s
of
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channel MugFET at
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ogenic
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,
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,
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[2]
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as
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[3]
S. Jandh
y
a
la
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mpact models for
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-
depleted
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apted
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xide
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imensional An
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ltag
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y
lind
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[5]
S. Mohamm
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m
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e
l eff
ects
in s
y
m
m
e
tri
c
and as
y
mmetr
ic
3-T/4-T double
gate MOSFETs”,
Mi
cr
oel
ectr
oni
cs
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liabi
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l. 51
, pp
. 543-54
9, 2011
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[6]
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Wang and T.
Tang, “An analy
tical model
for
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annel po
tential
and subthreshold
swing of the s
y
mmetric and
as
ymmetric double-
gate MOSFETs”,
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cr
oel
ectr
oni
cs
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, vo
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[7]
Hakkee Jung, “Analy
sis for
Potential
Distr
i
bution of As
y
mmetr
ic Double Ga
te
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[8]
M
.
S
t
ad
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e
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“
In
fluen
c
e of so
urce-
drain tu
nn
elin
g on th
e subthr
esho
ld beh
a
vior o
f
sub
-
10 nm do
ub
le g
a
te MOS
FETs
”,
in
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Eur
.
So
lid-
State Device R
e
s
e
ar
ch
Co
nf
.(
E
S
SDE
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3
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[9]
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1
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06
.
BI
O
G
R
A
P
HY
OF
A
U
T
HO
R
Prof. Hak Kee Jung received th
e B.S. degree fro
m
Ajou University
, Korea, in 198
3, the M.S.
and
Ph.D. degr
ees
from Yonsei University
, Seoul,
Korea,
in 19
85, 1990, respectiv
ely
,
all
in
electronic engin
eering
.
In 1990, he joined K
unsan National Univ
ersity
, Chonbuk, Korea, where
he is currently
a
Professor in department of el
ectr
onic engin
eer
ing
.
From 1995 to 1
995, he held
a
research
positio
n with th
e E
l
e
c
t
r
onic
Engine
erin
g
Departm
e
nt
,
Osaka Universit
y
,
Osaka,
Japan
.
From 2004
to 20
05, he was with
the School of Mi
croelectronic Engineer
ing, Griff
ith University
,
Nathan, QLD, Australia. His res
earch interests include semicondu
ctor device ph
y
s
ics and device
modeling with
a
strong emphasis
on quantum
tr
an
sport and Monte
Carlo simulation
s
.
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