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[
1
3
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[
1
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ased
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.
Si
n
ce
t
h
e
1
9
6
0
s
,
MO
S
tr
an
s
i
s
to
r
d
i
m
e
n
s
io
n
s
h
av
e
b
ee
n
s
h
r
in
k
i
n
g
3
0
%
ev
er
y
3
y
ea
r
s
,
as
p
r
ed
icted
b
y
Mo
o
r
e’
s
la
w
[
5
]
.
T
h
e
b
u
lk
-
s
il
ico
n
MO
S
FET
h
as
b
ee
n
th
e
b
ac
k
b
o
n
e
o
f
th
e
s
e
m
ico
n
d
u
cto
r
tr
ad
e
o
v
er
t
h
e
l
ast
f
o
r
t
y
y
ea
r
s
.
Ho
w
e
v
er
,
th
e
s
ca
lin
g
o
f
b
u
l
k
MO
S
FET
s
b
ec
o
m
e
s
p
r
o
g
r
ess
iv
el
y
tr
o
u
b
leso
m
e
f
o
r
g
ate
len
g
t
h
s
b
elo
w
~2
0
n
m
(
s
u
b
-
4
5
n
m
h
a
lf
-
p
itch
tech
n
o
lo
g
y
n
o
d
e)
ex
p
ec
ted
b
y
t
h
e
y
ea
r
2
0
0
9
,
b
ec
au
s
e
t
h
e
g
a
te
le
n
g
t
h
is
r
ed
u
ce
d
,
t
h
e
ele
ctr
ical
p
h
e
n
o
m
e
n
o
n
co
u
p
lin
g
o
f
t
h
e
c
h
a
n
n
el
p
o
ten
tial
to
th
e
s
u
p
p
l
y
a
n
d
d
r
ain
w
ill
in
cr
ea
s
e
r
elativ
e
to
t
h
e
g
ate,
r
es
u
lti
n
g
in
co
n
s
id
er
ab
l
y
d
e
g
r
ad
ed
s
h
o
r
t
-
c
h
an
n
el
e
f
f
ec
t
s
(
SC
E
)
.
T
h
is
m
a
n
i
f
es
ts
its
e
lf
a
s
a)
ex
ag
g
er
ated
o
f
f
-
s
tate
d
is
ch
ar
g
e,
b
)
th
r
esh
o
ld
v
o
lta
g
e
(
VT
H)
r
o
ll
-
o
f
f
,
i.e
.
s
m
al
ler
VT
H
at
s
h
o
r
ter
g
ate
len
g
t
h
s
,
an
d
c)
r
ed
u
ctio
n
o
f
VT
H
w
ith
i
n
cr
ea
s
i
n
g
d
r
ai
n
b
ias
o
w
i
n
g
to
a
m
o
d
u
latio
n
o
f
t
h
e
s
o
u
r
ce
-
c
h
a
n
n
el
p
o
te
n
tial
b
ar
r
ier
b
y
th
e
d
r
ain
v
o
lta
g
e,
ad
d
itio
n
all
y
r
e
f
er
r
ed
to
as
d
r
ain
-
in
d
u
ce
d
b
ar
r
ier
lo
w
er
i
n
g
(
DI
B
L
)
.
to
tak
e
ca
r
e
o
f
th
e
co
m
p
ar
ativ
el
y
s
tu
r
d
y
g
ate
m
an
a
g
e
m
en
t
o
f
th
e
c
h
an
n
el
p
o
ten
tial
in
b
u
l
k
d
ev
ice
s
,
v
ar
ied
tech
n
o
lo
g
ical
en
h
a
n
ce
m
e
n
ts
l
ik
e
u
ltra
-
t
h
in
g
ate
d
ielec
tr
ics,
u
ltra
s
h
allo
w
s
o
u
r
ce
/d
r
ain
j
u
n
ctio
n
s
,
h
alo
i
m
p
lan
t
s
a
n
d
ad
v
a
n
ce
c
h
a
n
n
el
d
o
p
in
g
p
r
o
f
ile
e
n
g
in
ee
r
i
n
g
tec
h
n
iq
u
es
li
k
e
s
u
p
er
-
s
teep
r
etr
o
g
r
ad
e
w
ell
s
ar
e
n
e
ce
s
s
ar
y
.
E
v
er
y
o
f
t
h
o
s
e
tec
h
n
o
lo
g
ies
is
c
u
r
r
en
tl
y
ap
p
r
o
ac
h
in
g
b
asic
p
h
y
s
ical
li
m
ita
tio
n
s
w
h
ic
h
ca
n
,
in
t
u
r
n
,
li
m
it a
n
y
s
ca
li
n
g
o
f
d
ev
ice
d
i
m
en
s
io
n
s
.
1
.
2
.
T
he
P
ro
ble
m
No
w
t
h
e
p
r
o
b
lem
ar
is
e
s
w
h
e
n
w
e
g
o
f
o
r
m
i
n
iat
u
r
izatio
n
o
f
s
ize
o
f
MO
S
FET
.
I
f
w
e
tr
y
to
r
ed
u
ce
th
e
th
ic
k
n
e
s
s
b
elo
w
2
n
m
i
n
s
ilico
n
o
x
id
e
MO
S
FET
th
er
e
w
i
ll b
e
a
f
r
ee
f
lo
w
o
f
d
r
ain
cu
r
r
e
n
t t
h
r
o
u
g
h
th
e
c
h
an
n
el
as
r
ep
o
r
ted
b
y
s
ae
ed
e
t
al
[
1
]
.
T
h
e
s
o
lu
tio
n
to
t
h
is
p
r
o
b
le
m
is
also
s
u
g
g
este
d
b
y
s
ae
ed
et
al
[
7
]
i
n
t
h
e
s
a
m
e
liter
atu
r
e
th
a
t
f
o
r
o
b
tain
i
n
g
a
p
r
o
p
er
f
lo
w
o
f
d
r
ain
c
u
r
r
en
t
t
h
r
o
u
g
h
c
h
an
n
el
w
e
n
ee
d
to
r
e
p
lace
s
ilica
w
it
h
a
m
ater
ial
h
a
v
i
n
g
h
i
g
h
k
Val
u
e
(
o
r
h
ig
h
Di
-
elec
tr
ic
co
n
s
ta
n
t)
.
W
h
ile
ex
ch
a
n
g
e
th
e
o
x
id
e
w
it
h
a
h
i
g
h
d
i
-
elec
tr
ic
ma
ter
ial
s
o
m
e
f
ac
to
r
s
h
as
g
o
t t
o
b
e
th
o
u
g
h
t o
f
,
th
e
s
e
f
ac
to
r
s
ar
e:
a.
Ma
ter
ial
o
u
g
h
t to
b
e
ab
le
to
co
n
ti
n
u
e
s
ca
li
n
g
to
lo
w
er
eq
u
iv
a
len
t c
o
m
p
o
u
n
d
th
ic
k
n
es
s
.
b.
s
to
p
th
e
g
ate
t
h
r
es
h
o
ld
v
o
ltag
e
in
s
tab
ili
ties
ca
u
s
ed
b
y
t
h
e
h
i
g
h
d
ef
ec
t d
en
s
itie
s
c.
L
i
m
it t
h
e
lo
s
s
o
f
ca
r
r
ier
q
u
ality
w
it
h
in
t
h
e
Si c
h
a
n
n
el
o
n
ce
m
is
tr
ea
t
m
e
n
t H
i
g
h
-
κ
o
x
id
es
d.
W
ar
r
an
t d
ep
en
d
ab
ilit
y
o
f
th
e
g
ate
m
ater
ial
.
1
.
3
.
T
he
P
ro
po
s
ed
So
lutio
n
p
ap
er
s
u
m
m
ar
ized
t
h
e
ch
a
lle
n
g
e
s
a
n
d
p
r
o
b
lem
s
f
ac
ed
o
n
s
ca
lin
g
d
o
w
n
th
e
ch
a
n
n
el
w
i
d
th
o
f
t
h
e
MO
SF
E
T
o
r
u
lti
m
atel
y
s
ca
li
n
g
d
o
w
n
th
e
M
OSFET
s
ize.
T
h
u
s
,
th
e
y
h
av
e
s
u
g
g
ested
v
ar
io
u
s
i
n
s
u
la
tin
g
m
ater
ial
f
o
r
MO
SF
E
T
h
av
i
n
g
h
ig
h
d
ielec
tr
ic
co
n
s
ta
n
ts
w
h
i
ch
ca
n
b
e
a
r
ep
lace
m
en
t
f
o
r
th
e
s
ta
n
d
ar
d
o
x
id
e
la
y
er
alo
n
g
w
ith
t
h
eir
t
h
eo
r
etica
l
ca
lcu
latio
n
.
So
m
e
m
ater
ial
s
lik
e
g
r
o
u
p
I
I
I
A
m
eta
l
o
x
i
d
es
s
u
c
h
as
alu
m
i
n
i
u
m
o
x
id
e
(
A
l2
O3
)
,
g
r
o
u
p
I
VB
Me
tal
Ox
id
es
a
n
d
s
ilicates
s
u
ch
as
ti
tan
i
u
m
o
x
id
e
(
T
iO2
)
,
zir
co
n
iu
m
o
x
id
e
(
Z
r
O2
)
,
zir
co
n
iu
m
s
ilica
te
(
Z
r
SiO4
)
,
Haf
n
i
u
m
o
x
id
e
(
Hf
O2
)
,
h
a
f
n
i
u
m
s
ilicate
(
H
f
Si
x
O
y
)
e
tc
ar
e
r
ep
lace
m
e
n
t
o
f
s
ilico
n
.
2.
L
I
T
E
R
AT
U
RE
SU
RV
E
Y
Saee
d
Mo
h
s
e
n
i
f
ar
,
M.
H.
Sh
a
r
o
k
h
ab
ad
i,
“
Ga
te
s
tac
k
h
i
g
h
-
K
m
ater
ial
s
f
o
r
Si
-
b
ased
MO
s
f
et
s
P
ast,
P
r
esen
t,
an
d
f
u
tu
r
e”
,
Mic
r
o
el
ec
tr
o
n
ics
an
d
s
o
lid
s
tate
E
le
ctr
o
n
ics
2
0
1
5
,
DOI
:1
0
.
5
9
2
3
/
j.
m
s
s
e.
2
0
1
5
0
4
0
1
.
0
3
[
1
]
.
I
n
th
is
p
ap
er
au
t
h
o
r
s
h
a
v
e
d
is
cu
s
s
ed
t
h
e
c
h
alle
n
g
e
s
a
n
d
p
r
o
b
lem
s
f
ac
ed
o
n
s
ca
l
in
g
d
o
w
n
th
e
ch
a
n
n
el
w
id
t
h
o
f
th
e
MO
SF
E
T
o
r
u
lti
m
atel
y
s
ca
l
in
g
d
o
w
n
th
e
M
O
SF
E
T
s
ize.
As
f
r
o
m
t
h
e
p
ap
er
it’s
b
ee
n
clea
r
t
h
at
Sil
ico
n
m
ater
ial
f
ail
i
n
s
tan
d
ar
d
C
MO
S
tech
n
o
lo
g
y
(
f
o
r
n
an
o
s
ca
le)
,
d
u
e
to
th
e
s
h
o
r
t
ch
an
n
el
ef
f
ec
t
a
n
d
tu
n
n
eli
n
g
e
f
f
ec
t
s
h
o
w
n
b
y
s
ili
co
n
m
ater
ial.
T
h
e
w
o
r
k
i
n
g
o
f
t
h
e
MO
S
FET
ch
an
g
e
s
w
h
en
we
m
o
v
e
to
w
ar
d
s
t
h
e
n
an
o
s
ca
le
r
eg
i
m
e.
I
n
o
r
d
er
to
co
n
tin
u
e
s
ca
li
n
g
th
e
p
la
n
ar
MO
SF
E
T
w
it
h
o
u
t
h
ar
m
f
u
l
S
C
E
’
s
,
th
e
ef
f
ec
ti
v
e
ch
an
n
el
le
n
g
th
n
ee
d
s
to
b
e
4
0
ti
m
es
t
h
e
d
ielec
tr
ic
t
h
i
c
k
n
e
s
s
s
o
th
e
d
ielec
tr
ic
th
ic
k
n
es
s
m
u
s
t
b
e
d
ec
r
ea
s
ed
alo
n
g
w
it
h
t
h
e
p
h
y
s
ical
d
i
m
e
n
s
io
n
o
f
t
h
e
d
ev
ice.
S.Su
t
h
r
a
m
,
J
.
C
Z
eie
g
er
t,
T
.
Nis
h
id
a,
“
P
ieze
o
r
esis
ta
n
ce
c
o
ef
f
icie
n
t
o
f
(
1
0
0
)
Sil
ico
n
n
MO
SF
E
T
m
ea
s
u
r
ed
at
lo
w
an
d
h
i
g
h
(
1
.
5
GP
a)
ch
an
n
el
s
tr
es
s
”,
I
E
E
E
elec
tr
o
n
d
ev
ice
s
let
ter
s
,
Vo
l.
2
8
,
NO.
1
,
J
an
u
ar
y
2
0
0
7
[
2
]
T
h
is
p
ap
er
g
iv
es
a
b
r
ief
id
ea
ab
o
u
t
th
e
m
o
d
eli
n
g
o
f
th
e
h
ig
h
l
y
s
tr
es
s
ed
ch
a
n
n
el
o
f
t
h
e
s
ilico
n
MO
SF
E
T
.
I
n
th
eir
ex
p
er
i
m
en
tal
s
etu
p
t
h
e
y
h
a
v
e
d
esi
g
n
ed
a
n
u
n
a
x
ial
c
h
an
n
el
s
tr
ess
;
t
h
e
w
a
f
er
is
allo
w
ed
to
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An
t
h
o
n
y
G.
O’
Neil
l,
B
ar
r
y
J
.
Gallac
h
er
,
Sar
ah
H
.
Ols
en
,
“Usi
n
g
P
ieze
o
r
esis
ta
n
ce
m
o
d
el
w
it
h
C
-
R
co
n
v
er
s
io
n
f
o
r
m
o
d
ellin
g
o
f
s
tr
ai
n
-
I
n
d
u
ce
d
m
o
b
i
lit
y
”,
I
E
E
E
elec
tr
o
n
d
ev
ice
le
tter
s
,
v
o
l.2
9
.
n
o
.
9
,
Sep
te
m
b
er
2
0
0
8
[
3
]
.
T
h
e
p
ieze
o
r
esis
tan
ce
m
o
d
el
h
av
e
b
ee
n
co
m
m
o
n
l
y
b
ee
n
u
s
ed
to
d
escr
ib
e
m
o
b
ilit
y
en
h
a
n
ce
m
en
t
f
o
r
lo
w
le
v
el
s
o
f
p
r
o
ce
s
s
i
n
d
u
ce
d
s
tr
ai
n
i
n
C
MO
S
tech
n
o
lo
g
y
.
I
n
t
h
i
s
p
ap
er
,
a
co
n
v
er
s
io
n
b
et
w
ee
n
t
h
e
c
h
an
g
e
in
co
n
d
u
ctiv
it
y
a
n
d
r
esi
s
ti
v
it
y
i
s
d
ev
el
o
p
ed
s
u
ch
th
at
a
p
ieze
o
r
esis
t
an
ce
m
o
d
el
ca
n
b
e
ap
p
lied
co
r
r
ec
tly
to
ca
lcu
la
te
th
e
s
tr
ain
-
i
n
d
u
ce
d
m
o
b
il
it
y
ch
a
n
g
es.
T
h
e
y
co
n
clu
d
e
d
th
at
th
e
lin
ea
r
p
ieze
o
r
es
is
tan
ce
co
n
ce
p
t
f
a
ils
w
h
e
n
t
h
e
ap
p
lied
s
tr
ess
ex
ce
ed
t
h
e
lin
ea
r
li
m
it
w
h
er
e
n
o
n
l
in
ea
r
p
ieze
o
r
esis
tan
ce
e
f
f
ec
t
o
cc
u
r
s
an
d
s
h
o
w
ed
th
at
t
h
e
co
r
r
ec
tio
n
to
th
is
i.e
.
th
e
C
-
R
co
n
v
e
r
s
io
n
d
r
a
m
atica
ll
y
i
m
p
r
o
v
es
t
h
e
ac
cu
r
ac
y
o
v
er
t
h
e
co
m
m
o
n
l
y
u
s
ed
f
o
r
m
u
lati
o
n
o
f
p
ie
ze
o
r
esis
tan
ce
co
n
ce
p
t
w
h
ile
m
a
in
tai
n
i
n
g
its
s
i
m
p
licit
y
.
J
h
o
n
g
-
S
h
e
n
g
W
an
g
,
W
illi
a
m
P
o
-
Nien
C
h
e
n
,
C
h
u
n
-
Hsi
n
g
Sh
is
h
,
C
h
e
n
h
s
i
n
L
ei
n
,
P
in
S
u
,
“
Mo
b
ilit
y
m
o
d
eli
n
g
an
d
its
ex
tr
ac
tio
n
tech
n
iq
u
es
f
o
r
m
a
n
u
f
ac
tu
r
i
n
g
s
t
ar
in
ed
-
Si
MO
SF
E
T
s
”,
I
E
E
E
e
lec
tr
o
n
letter
s
,
v
o
l.
2
8
,
N
O.
1
1
No
v
e
m
b
er
2
0
0
7
[
4
]
.
I
n
th
i
s
letter
,
f
o
r
a
MO
S
FET
ch
an
n
el
t
h
ic
k
n
e
s
s
f
r
o
m
3
2
n
m
to
7
3
n
m
,
a
p
r
ac
tical
ex
tr
ac
tio
n
m
et
h
o
d
is
in
teg
r
ated
an
d
p
r
o
p
o
s
ed
to
d
ec
o
u
p
le
th
e
p
ar
asit
ic
p
ar
am
et
er
s
an
d
to
ev
alu
ate
th
e
m
o
b
ilit
y
o
f
s
h
o
r
t
ch
an
n
el
s
tr
ain
ed
-
Si
d
ev
ice
s
.
T
h
e
ex
tr
ac
tio
n
o
f
p
ar
asit
ic
s
o
u
r
ce
/d
r
ain
r
esis
tan
ce
f
o
llo
w
s
th
e
i
m
p
r
o
v
ed
B
er
k
ele
y
s
h
o
r
t
ch
an
n
el
I
GFET
m
o
d
el
m
et
h
o
d
to
g
et
an
ac
cu
r
ate
d
r
ain
cu
r
r
en
t
w
it
h
o
u
t
p
ar
asit
ic
d
r
ain
r
esis
ta
n
ce
d
e
g
r
ad
atio
n
f
o
r
th
e
cu
r
r
en
t
d
ev
ice.
T
h
e
y
co
n
clu
d
ed
t
h
at,
at
a
r
elati
v
el
y
h
i
g
h
f
ie
ld
,
b
y
ass
u
m
in
g
th
at
a
co
n
s
ta
n
t
b
u
l
k
p
ieze
o
r
esis
tan
ce
co
ef
f
icie
n
t
is
ap
p
lied
f
o
r
s
tr
ess
d
ev
ices
,
th
eir
m
o
d
el
ca
n
p
r
o
p
er
ly
p
r
ed
ict
th
e
m
o
b
ilit
y
en
h
a
n
ce
m
en
t
f
o
r
th
e
v
ar
io
u
s
s
tr
ain
ed
-
S
i
tech
n
o
lo
g
ie
s
an
d
d
ev
ice
d
i
m
e
n
s
io
n
s
b
y
in
cl
u
d
in
g
th
e
co
u
lo
m
b
s
ca
tter
in
g
co
r
r
ec
tio
n
s
.
A
b
etter
d
esc
r
ip
tio
n
o
f
ten
s
ile
-
s
tr
es
s
m
o
b
il
it
y
is
ac
h
ie
v
ed
f
o
r
n
an
o
s
ca
le
s
h
o
r
t c
h
an
n
el
d
ev
ic
es.
Fig
u
r
e
1
I
D
v
s
.
VDD
C
h
a
ra
c
t
e
r
is
tics
o
f
A
c
t
i
v
e
M
O
SF
E
T
fo
r
V
ar
io
u
s
p
r
e
s
s
u
r
es
[9
].
Fig
u
r
e
2
I
D
v
s
.
VD
D
Ch
ar
a
ct
e
r
i
s
t
ics
o
f
Ac
t
i
v
e
MO
SF
E
T
f
o
r
V
a
r
i
o
us
T
h
i
ck
n
e
s
s
o
f
Ox
i
d
e
L
a
y
er
[
1
1
].
3.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
q
u
esti
o
n
ar
is
e
s
h
er
e
is
th
at
h
o
w
th
e
th
ick
n
es
s
o
f
c
h
an
n
el
w
ill
af
f
ec
t
th
e
s
e
n
s
i
tiv
it
y
o
f
MO
SF
E
T
p
r
ess
u
r
e
s
e
n
s
o
r
.
T
h
er
e
ar
e
m
a
n
y
li
ter
atu
r
es
i
n
w
h
ich
i
t
is
r
e
p
o
r
ted
th
at
w
it
h
th
e
d
ec
r
ea
s
e
i
n
th
e
c
h
an
n
el
w
id
t
h
th
e
d
r
ain
cu
r
r
en
t
i
n
cr
ea
s
es,
wh
ich
t
h
er
ef
o
r
e
i
n
cr
ea
s
es
th
e
s
e
n
s
it
iv
i
t
y
o
f
t
h
e
d
e
v
ice
[
9
]
.
I
n
t
h
is
s
ec
tio
n
w
e
w
ill
d
is
cu
s
s
ab
o
u
t
th
e
d
ep
en
d
en
c
y
o
f
s
en
s
i
tiv
it
y
o
f
d
ev
ice
w
ith
ch
an
n
el
t
h
ick
n
e
s
s
an
d
also
th
e
v
ar
io
u
s
liter
at
u
r
es
w
h
ic
h
r
ep
o
r
ted
ab
o
u
t th
e
s
a
m
e
p
r
o
b
lem
.
Var
io
u
s
p
ar
a
m
eter
s
u
s
ed
to
d
esig
n
an
d
s
i
m
u
late
MO
SF
E
T
em
b
ed
d
ed
p
r
ess
u
r
e
s
e
n
s
o
r
a.
Diap
h
r
ag
m
s
h
ap
e,
s
ize
an
d
m
a
ter
ial
-
Sq
u
ar
e,
1
0
0
µm
x
1
0
0
µm
x
5
µ
m
,
Sil
ico
n
b.
u
s
i
n
g
5
µ
m
C
MO
S tec
h
n
o
lo
g
y
f
o
r
n
-
MO
SF
E
T
p
iezo
r
esis
to
r
c.
Di
m
e
n
s
io
n
o
f
n
-
MO
SF
E
T
=
1
.
5
µm
x
1
.
2
5
µ
m
x
1
µ
m
d.
Dr
ain
cu
r
r
en
t I
D(
s
at)
=
2
µA
e.
So
u
r
ce
to
d
r
ain
v
o
ltag
e=
.
5
V
f.
Ou
tp
u
t r
esis
ta
n
ce
=
VSD/ I
D(
s
at)
=
.
2
5
MΩ
g.
R
esi
s
tan
ce
o
f
n
-
MO
SF
E
T
eq
u
iv
ale
n
t p
iezo
r
esit
o
r
=
R
=
r
o
=
2
MΩ
h.
R
esi
s
ti
v
it
y
o
f
n
-
MO
SF
E
T
p
iezo
r
esis
to
r
=,
ρ
=
2
5
Ω
m
i.
R
ef
er
e
n
ce
T
em
p
er
atu
r
e
T
o
=
3
0
0
K
Op
er
atin
g
p
r
in
cip
le
o
f
t
h
e
M
OSFET
p
r
ess
u
r
e
s
en
s
o
r
is
p
r
esen
ted
b
y
z
h
ao
h
u
a
z
h
an
g
et
a
l
[
5
]
.
B
ased
o
n
th
e
s
tr
ess
s
en
s
iti
v
e
e
f
f
ec
t
o
f
MO
S
FET
,
a
n
e
w
MO
SF
E
T
-
b
r
id
g
e
-
cir
cu
i
t
s
tr
u
c
tu
r
e
i
s
d
esi
g
n
ed
,
as
s
h
o
w
n
i
n
Fig
u
r
e
1
.
T
w
o
P
MO
SF
E
T
’
s
a
n
d
t
w
o
p
iezo
r
esis
to
r
s
ar
e
co
n
n
ec
ted
to
f
o
r
m
a
W
h
ea
t
s
to
n
e
b
r
id
g
e.
T
o
o
b
tain
th
e
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1
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r
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19
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22
m
ax
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m
u
m
s
en
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iti
v
it
y
,
t
h
ese
co
m
p
o
n
en
ts
ar
e
p
lace
d
n
ea
r
th
e
f
o
u
r
s
id
es o
f
t
h
e
s
il
ico
n
d
iap
h
r
ag
m
,
w
h
ic
h
ar
e
t
h
e
h
ig
h
s
tr
ess
r
e
g
io
n
s
.
T
h
e
MO
S
FET
’
s
h
as
t
h
e
s
a
m
e
s
tr
u
ct
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r
e
p
ar
am
eter
W
/
L
,
s
a
m
e
th
r
e
s
h
o
ld
v
o
ltag
e
VT
an
d
g
ate
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s
o
u
r
ce
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o
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g
e
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S
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al
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h
e
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e
d
esig
n
ed
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o
r
k
in
th
e
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at
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r
atio
n
r
eg
io
n
.
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h
e
p
iezo
r
esis
to
r
s
also
h
av
e
t
h
e
s
a
m
e
r
esis
tan
ce
R
0
.
(
a)
(
b
)
Fig
u
r
e
1
.
(
a
)
S
c
h
e
m
a
t
ic
o
f
N
o
v
el
M
O
SF
E
T
P
r
ess
u
r
e
S
en
s
o
r
In
c
l
u
d
in
g
Tw
o
M
O
S
FET
a
n
d
T
wo
R
e
s
i
s
t
o
r
s
o
n
t
he
M
e
m
b
r
a
n
e
t
o
F
o
r
m
a
W
h
e
a
ts
to
n
e
B
r
i
d
g
e
,
(
b
)
T
he
M
O
SF
E
T
-
Ba
s
e
d
B
r
id
g
e
Ci
r
cu
it
,
t
h
e
O
u
tp
u
t
V
o
lta
g
e
is
V
ou
t
=
V
o
u
t
1
-
V
ou
t2
,
t
h
e
V
o
lta
g
e
S
o
u
r
c
e
is
VDD
W
h
en
t
h
er
e
is
n
o
f
o
r
ce
d
p
r
ess
u
r
e,
t
h
e
b
r
id
g
e
is
in
b
ala
n
ce
.
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h
e
b
alan
ce
d
o
u
tp
u
t
V0
o
f
e
ac
h
ar
m
is
ca
lcu
lated
b
y
[
6
]
V0
=
.
5
R
0
µ
P
0
C
OX
(
W
/L
)
(
VGS
–
VT
)
(
1
)
As
a
r
es
u
lt,
t
h
e
s
en
s
o
r
o
u
tp
u
t
s
ig
n
al
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u
t
i
s
ze
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o
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h
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r
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i
s
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o
r
ce
d
o
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e
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e
m
b
r
an
e,
th
e
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r
r
en
t
a
n
d
p
iezo
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r
es
is
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n
ce
in
ea
c
h
b
r
id
g
e
ar
m
ar
e
c
h
a
n
g
ed
.
T
h
e
v
ar
iatio
n
o
f
t
h
e
P
MO
SF
E
T
cu
r
r
en
t
is
p
r
o
p
o
r
tio
n
al
to
th
e
ch
an
g
e
o
f
ch
an
n
el
m
o
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il
it
y
Δ
µp
,
co
m
p
u
t
ed
as
[
6
]
:
∆
I
DS /
I
DS =
∆µ
/µo
=
πl
.
σ
l
+
πt
.
σ
t
(
2
)
W
h
er
e,
1
an
d
2
ar
e
th
e
p
ar
allel
an
d
v
er
tical
s
tr
es
s
in
t
h
e
ch
an
n
el;
1
a
n
d
2
ar
e
th
e
p
ar
allel
an
d
v
er
tical
ch
a
n
n
e
l
p
iezo
r
esis
tiv
e
co
ef
f
icie
n
t,
r
esp
ec
tiv
el
y
.
T
h
e
ch
an
g
e
o
f
p
iezo
r
esis
tan
ce
i
s
also
p
r
o
p
o
r
tio
n
al
to
th
e
r
esis
to
r
m
o
b
ilit
y
c
h
an
g
e
Δ
R
,
w
h
ic
h
ca
n
b
e
ex
p
r
es
s
ed
u
s
in
g
a
s
i
m
ilar
f
o
r
m
u
la,
as:
∆
R
/ RO =
∆
µR /
µ
R
O
=
πl
.
σ
l +
πt
.
σ
t
(
3
)
W
h
er
e,
1
an
d
2
ar
e
t
h
e
p
ar
allel
an
d
v
er
tical
s
tr
es
s
i
n
t
h
e
r
esis
to
r
b
ar
,
1
a
n
d
2
ar
e
t
h
e
p
ar
allel
an
d
v
er
tical
p
iezo
r
esis
ti
v
e
co
e
f
f
icien
t,
r
esp
ec
tiv
el
y
.
A
cc
o
r
d
in
g
to
th
e
d
if
f
er
en
t
c
u
r
r
en
t
d
ir
ec
tio
n
p
lacin
g
,
t
h
e
b
r
id
g
e
b
ec
o
m
es
u
n
b
ala
n
ce
.
T
h
e
µP
o
f
M1
an
d
th
e
µR
o
f
R
2
g
et
i
n
cr
ea
s
e
d
w
it
h
th
e
s
tr
es
s
,
i
n
o
p
p
o
s
itio
n
,
t
h
e
µP
o
f
M2
a
n
d
t
h
e
µ
R
o
f
R
1
ar
e
d
ec
r
ea
s
ed
.
T
h
en
th
e
t
w
o
ar
m
s
o
u
tp
u
t
s
b
ec
o
m
e
a
s
[
6
]
:
Vo
u
t 1
,
2
=
(
1
/2
)
(
R
o
+
∆R).
(
µp
o
+
∆µ
p
)
C
OX
(
W
/L
)
(
VGS
–
VT
)
2
(
4
)
T
h
er
ef
o
r
e,
th
e
s
en
s
o
r
o
u
tp
u
t is
o
b
tain
ed
as [
6
]
:
Vo
u
t =
2
(
∆µ
p
/µp
o
+
∆µ
R
/ µ
R
O
)
2
Vo
(
5)
Fo
r
m
u
la
(
5
)
s
h
o
w
s
th
at,
Vo
u
t
is
p
r
o
p
o
r
tio
n
al
to
th
e
s
tr
ess
as
w
ell
a
s
th
e
f
o
r
ce
d
p
r
ess
u
r
e.
T
h
is
is
t
h
e
o
p
er
atin
g
p
r
in
cip
le
o
f
t
h
e
n
o
v
el
MO
SF
E
T
-
b
r
id
g
e
-
cir
c
u
it p
r
ess
u
r
e
m
icr
o
s
en
s
o
r
.
Sev
er
al
li
ter
atu
r
es
h
a
s
b
ee
n
r
e
p
o
r
ted
th
e
s
en
s
iti
v
it
y
o
f
t
h
is
p
r
ess
u
r
e
s
en
s
o
r
to
b
e
in
cr
ea
s
in
g
u
p
to
1
0
0
m
icr
o
m
eter
o
f
c
h
a
n
n
e
l
th
ic
k
n
ess
co
n
cl
u
d
ed
th
at
t
h
e
s
e
n
s
iti
v
it
y
o
f
t
h
e
MO
SF
E
T
s
en
s
o
r
w
il
l
also
in
cr
ea
s
e
w
i
th
r
ed
u
ctio
n
in
c
h
a
n
n
el
t
h
ic
k
n
e
s
s
w
it
h
t
h
e
in
cr
ea
s
e
i
n
d
r
ain
c
u
r
r
en
t
[
4
]
,
[
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
S
tu
d
y
o
f D
iffer
en
t P
a
r
a
metric V
a
r
ia
tio
n
s
o
f MOS
F
E
T P
r
ess
u
r
e
S
en
s
o
r
(
S
h
r
u
ti B
h
a
r
g
a
va
)
23
T
h
er
e
ar
e
also
s
o
m
e
liter
at
u
r
es
h
as
r
ep
o
r
ted
th
at
th
e
d
r
a
in
c
u
r
r
en
t
o
f
MO
S
FET
in
cr
ea
s
es
w
it
h
r
ed
u
ctio
n
i
n
th
ic
k
n
es
s
o
f
c
h
an
n
el
[
9
]
.
W
ith
ab
o
v
e
f
o
r
m
u
las
a
n
d
t
h
e
li
ter
atu
r
e
m
e
n
tio
n
ed
ab
o
v
e
w
e
ca
n
co
n
clu
d
e
t
h
at
t
h
e
s
e
n
s
iti
v
it
y
o
f
th
e
MO
SF
E
T
p
r
ess
u
r
e
s
en
s
o
r
s
h
o
u
ld
i
n
cr
ea
s
e
i
f
w
e
g
o
b
elo
w
1
3
0
n
m
th
ic
k
n
e
s
s
o
f
ch
a
n
n
el.
I
n
t
h
i
s
p
ap
er
w
e
w
ill
p
r
ese
n
t
t
h
e
co
m
p
ar
is
o
n
o
f
s
en
s
iti
v
it
y
o
f
M
OSF
E
T
p
r
ess
u
r
e
s
e
n
s
o
r
h
av
i
n
g
th
ick
n
es
s
f
r
o
m
1
3
0
n
m
to
2
0
n
m
.
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
Af
ter
s
i
m
u
lati
n
g
MO
S
FET
f
o
r
v
ar
io
u
s
t
h
ic
k
n
e
s
s
e
s
an
d
ap
p
l
y
i
n
g
a
f
o
r
ce
o
f
2
b
ar
w
e
h
a
v
e
o
b
tain
ed
th
e
I
-
V
c
u
r
v
e
i.e
.
t
h
e
d
r
ain
cu
r
r
en
t
a
n
d
d
r
ain
v
o
lta
g
e
c
u
r
v
e
(
Fi
g
u
r
e
1
)
a
n
d
p
lo
tted
t
h
e
t
h
ic
k
n
e
s
s
v
er
s
u
s
r
esis
ta
n
ce
cu
r
v
e.
Fig
u
r
e
2
.
3
-
D
M
od
e
l
&
Pl
o
t
of
E
lectr
o
n
C
o
nc
e
n
tr
at
io
n
in
t
h
e
M
o
d
el
at
T
i
m
e
=
0
o
f
p
-
ch
a
n
n
e
l M
O
SF
E
T
w
i
th
Si
l
i
c
o
n
M
at
e
r
i
al
Fig
ur
e
3
.
3
-
D
i
m
ens
i
onal
p
C
hanne
l
MOS
FE
T
o
f
3x3x.
7 nm
,
D
oped
n
-
R
eg
i
on
of
A
r
ea
1x3
nm
Each
Side
w
i
t
h
a p
-
cha
nnel
Wi
d
t
h
of
1nm
Fig
ur
e
4
.
E
l
ec
t
r
o
n
D
ens
i
t
y
of
Mo
del
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
10
,
No
.
1
,
A
p
r
il 2
0
1
8
:
19
–
26
24
T
h
e
th
eo
r
etica
l
ca
lc
u
latio
n
f
o
r
in
cr
ea
s
i
n
g
t
h
e
s
en
s
iti
v
it
y
o
f
t
h
e
s
e
n
s
o
r
w
e
ca
n
r
elate
t
h
e
s
e
n
s
it
iv
i
t
y
o
f
th
e
s
e
n
s
o
r
to
th
e
r
esi
s
ta
n
ce
,
l
o
w
er
th
e
r
es
is
ta
n
ce
i
n
th
e
c
h
a
n
n
el
g
r
ea
ter
th
e
m
o
b
ilit
y
o
f
t
h
e
ca
r
r
ier
an
d
h
en
ce
th
e
s
e
n
s
iti
v
it
y
in
cr
ea
s
es
as
th
e
v
ar
iatio
n
i
n
t
h
e
c
u
r
r
en
t
w
i
ll
b
e
s
en
s
ib
le.
T
h
u
s
t
h
e
eq
u
atio
n
b
elo
w
d
e
f
i
n
es
t
h
e
r
esis
ta
n
ce
o
f
th
e
c
h
a
n
n
el
R
=
(
VDD
–
VGS)
/ I
G
(
6
)
W
h
er
e,
VDD
is
d
r
ain
v
o
lta
g
e,
VGS
is
g
ate
to
s
o
u
r
ce
v
o
lta
g
e,
I
G
is
g
ate
cu
r
r
en
t.
Af
ter
s
i
m
u
lati
n
g
MO
S
FET
i
n
2
Di
m
e
n
s
io
n
al
s
tr
u
ct
u
r
e
f
o
r
v
ar
io
u
s
t
h
ic
k
n
e
s
s
es
o
b
tai
n
e
d
th
e
I
-
V
cu
r
v
e
i.e
th
e
d
r
ai
n
cu
r
r
e
n
t
a
n
d
d
r
ain
v
o
lta
g
e
cu
r
v
e
(
Fi
g
u
r
e
.
2
0
)
an
d
p
lo
tted
th
e
th
ic
k
n
e
s
s
v
er
s
u
s
r
esis
tan
ce
cu
r
v
e
(
Fi
g
u
r
e
3
)
.
(
a)
I
d
-
V
d
C
ur
v
e
f
o
r
Ch
a
n
n
e
l
T
h
ic
k
ne
ss1
0n
m
(
b
)
I
d
-
V
d
Cu
r
v
e
f
o
r
C
ha
n
n
e
l
T
h
i
ck
nes
s
o
f
6
0
nm
(
c
)
I
d
-
Vd
Cu
r
v
e
fo
r
T
h
ick
n
es
s
1
3
0n
m
(
d
)
I
d
-
Vd
Cu
r
v
e
f
o
r
T
h
ick
n
es
s
20
0
n
m
Fig
u
r
e
3
.
T
h
e
I
d
-
Vd
C
u
r
v
e
f
o
r
Dif
f
er
en
t
C
h
a
n
n
el
T
h
ick
n
es
s
e
s
w
ith
v
g
C
o
n
s
ta
n
t
at
.
5
,
.
7
5
a
n
d
1
v
o
lt
f
o
r
Ox
id
e
T
h
ick
n
ess
o
f
1
0
n
m
,
6
0
n
m
,
1
6
0
n
m
a
n
d
2
0
0
n
m
T
h
u
s
f
r
o
m
f
i
g
u
r
e
i
t’
s
b
ee
n
v
i
s
ib
le
th
a
t
w
h
en
w
e
m
o
v
e
f
r
o
m
2
0
0
n
m
to
w
ar
d
s
1
0
n
m
t
h
e
r
esis
ta
n
ce
in
itial
l
y
i
n
cr
ea
s
e
s
till
1
3
0
n
m
b
u
t
b
elo
w
it
t
h
e
r
esi
s
ti
v
it
y
d
ec
r
ea
s
es
h
en
ce
th
e
s
en
s
iti
v
it
y
in
cr
ea
s
es
f
o
r
th
e
ch
an
n
el
t
h
ic
k
n
e
s
s
o
f
M
OSFE
T
b
elo
w
1
3
0
n
m
to
1
0
n
m
f
o
r
th
e
co
n
v
e
n
tio
n
al
s
i
lico
n
m
ater
i
al.
5.
CO
M
P
ARATI
VE
ANA
L
YS
I
S
C
u
r
v
e
b
elo
w
2
n
m
h
a
s
b
ee
n
p
lo
tted
f
o
r
th
e
th
r
ee
d
i
f
f
er
en
t
m
ater
ial
s
t
h
at
is
f
o
r
Z
ir
co
n
i
u
m
O
x
id
e
(
Z
r
2
O
3
)
,
L
a
n
t
h
an
u
m
O
x
id
e
(
L
a
2
O
3
)
an
d
Haf
n
i
u
m
O
x
id
e
(
H
f
O
2
)
.
I
n
o
r
d
er
to
co
m
p
ar
e
t
h
e
s
e
m
ater
ial
s
i
n
t
h
is
s
ec
tio
n
a
co
m
p
ar
ati
v
e
I
-
V
c
u
r
v
es
h
a
s
b
ee
n
d
r
a
w
n
b
elo
w
2
n
m
f
o
r
an
al
y
s
is
o
f
t
h
e
b
est
m
ater
ial
a
m
o
n
g
th
e
r
esp
ec
tiv
e
th
r
ee
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
S
tu
d
y
o
f D
iffer
en
t P
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r
a
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a
r
ia
tio
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E
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ess
u
r
e
S
en
s
o
r
(
S
h
r
u
ti B
h
a
r
g
a
va
)
25
Fig
u
r
e
5
.
I
d
-
Vd
C
u
r
v
e
at
2
n
m
f
o
r
Dif
f
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ater
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Dif
f
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ater
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ch
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m
p
ar
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f
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r
s
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n
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Ha
f
n
i
u
m
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x
id
e,
L
a
n
th
a
n
u
m
O
x
id
e
a
n
d
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ased
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Vo
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29
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No
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8
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0
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