VLSI
DESIGN
1998,
Vol.
8,
Nos.
(1-4),
pp.
261-264
Rep in s
a ailable
di ec ly
om
he
publishe
Pho ocopying
pe mi ed
by
license
only
(C)
1998
OPA
(O e seas
Publishe s
Associa ion)
N.V.
Published
by
license
unde
he
Go don
and
B each
Science
Publishe s
imp in .
P in ed
in
India.
De elopmen
o
a
Me hod
o
De e mining
he
Dependence
o
he
Elec on
Mobili y
on
he
Longi udinal-Elec ic
Field
in
MOSFETs
J.
B.
ROLDAN
*,
F.
GAMIZ
and
J.
A.
LOPEZ-VILLANUEVA
Depa amen o
de
Elec 6nica
y
Tecnologia
de
Compu ado es,
Uni e sidad
de
G anada,
Facul ad
de
Ciencias,
A d.,
Fuen enue a
s/n,
18071
G anada
Spain
A
new
expe imen al
me hod
o
de e mining
he
dependence
o
he
elec on
mobili y
on
he
longi udinal-elec ic
ield
has
been
de eloped.
The
de elopmen ,
alida ion
and
explana ion
o
his
new
me hod
has
been
ca e ully
ca ied
ou .
We
ha e
applied
his
p ocedu e
o
s anda d
submic on
MOSFETs
and
a e
ha ing
ob ained
he
mobili y
dependence
on
bo h
he
ans e se-
and
longi udinal-elec ic
ields
we
ep oduced
he
expe imen al
ou pu
cu es.
The
sa u a ion
eloci y
has
also
been
calcula ed
using
he
mobili y
cu es
ob ained
by
his
new
me hod.
Keywo ds."
Elec on
mobili y,
longi udinal-elec ic
ield,
sa u a ion
eloci y,
ou pu
cu es,
d i -
di usion
simula ion
1.
INTRODUCTION
The
elec on-mobili y
dependence
on
he
longi-
udinal-elec ic
ield,
o ien ed
along
he
channel,
has
been
s udied
expe imen ally.
A
"closed-loop"
in es iga ion
has
been
pe o med
on
he
alidi y
and
accu acy
o
a
new
me hod
o
de e mining
he
educ ion
o
he
channel
mobili y
connec ed
o
he
inc ease
o
he
longi udinal
ield.
This
me hod
is
applicable
o
s anda d
ansis o s.
An
es ima ion
o
he
sa u a ion
elec on
eloci y
in
he
channel
has
been
accomplished
compa ing
a
widely
used
ex-
p ession
[1].
The
da a
ob ained
wi h
his
p ocedu e
can
be
used
o
de elop
local
models
o
accoun
o
he
mobili y
dependence
on
he
longi udinal-elec ic
ield
in
d i -di usion
simula o s.
2.
DESCRIPTION
OF
THE
METHOD
The
basic
concep
o
idea
o
his
me hod
is
he
compa ison
o
expe imen al
d ain
cu en
e sus
d ain
ol age
cu es
Iz-Vos,
measu ed
in
sho -
channel
ansis o s
o
he
esul s
p oduced
by
a
wo-dimensional
simula o
[2,
3]
in
which
an
*
Co esponding
au ho .
261
262
J.B.
ROLD/N
e
al.
accu a e
low- ield
mobili y
is
used
and
he
mobili y
educ ion
caused
by
he
longi udinal-elec ic
ield
is
included.
The
o al
channel
leng h
L
is
di ided
in
N
subchannels
wi h
leng hs
Li,
1,
2,...,
N,
espec i ely.
Ins ead
o
ixing
he
Li
alues,
he
channel
po en ial
alues
a
he
ends
o
he
i- h
subchannel,
Vi-1
and
Vi,
a e
de ined
as
he
sepa a ion
be ween
he
quasi e mi
le els
a
hese
poin s,
V0
Vs
and
VN
Vz
being
he
po en ials
a
he
o al
channel
ends.
The e o e,
he
sepa a ion
in o
subchannels
is
ob ained
by
di iding
Vz-Vs
in o
e y
small
in e als
and
ixing
he
channel
po en ial
a
he
ends
o
each
subchannel.
The
numbe
o
subchannels
is
high
enough
and
he
di e ence
Vi-Vi_
in
each
subchannel
is
low
enough
ha
he
longi udinal-elec ic
ield
in
each
subchannel
can
be
conside ed
o
be
uni o m.
The
applica ion
o
he
me hod
is
as
ollows:
1)
S a ing
om
a
e y
small
VDs,
o
which
one
subchannel
is
enough,
he
ga e- o-sou ce
ol-
age
is
a ied
and
he
low- ield
mobili y
as
well
as
i s
dependence
on
he
ans e se-elec ic
ield
is
ob ained.
2)
Vzs
is
inc eased
in
e y
small
s eps
and
he
expe imen al
esul
is
compa ed
o
he
simu-
la ed
esul
calcula ed
by
using
he
low- ield
mobili y
ob ained
in
poin
(1).
New
subchan-
nels
a e
in oduced
i
necessa y.
When
he
expe imen al
and
compu ed
cu en s
de ia e
mo e
han
a
p e ixed
(also
e y
small)
limi ,
6L
a
mobili y
educ ion
is
appa en
a
he
sub-
channel
placed
a
he
d ain
end
o
he
channel.
Then,
he
mobili y
in
his
subchannel
is
mul i-
plied
by
a
ac o
o
<
in
o de
o
ep oduce
he
expe imen al
cu en
again.
The
alues
o
he
ans e se-
and
longi udinal-elec ic
ields
in
his
subchannel
a e
in oduced
in
an
a ay:
E ans
(1)
and
Elong
(1),
espec i ely.
3)
Vzs
is
inc eased
again.
In
all
he
subchannels
o
which
he
longi udinal-elec ic
ield
is
g ea e
han
Elong
(1),
he
low- ield
mobili y
is
mul iplied
by
A
and
he
cu en
hus
ob ained
is
compa ed
o
he
expe imen al
one.
When
he
de ia ion
be ween
he
compu ed
and
expe i-
men al
cu en s
is
again
g ea e
han
61,
a
u he
educ ion
is
assumed
in
he
d ain
end
o
he
channel
and
he
mobili y
is
once
mo e
mul iplied
by
A,
hus
ob aining
a
alue
equal
o
he
low-mobili y
mul iplied
by
A2.
The
ans-
e se-
and
longi udinal-elec ic
ields
in
his
subchannel
a e
in oduced
as
a
new
elemen
o
he
a ay:
E ans
(2)
and
Elong
(2),
espec i ely.
A
he
end
o
his
p ocess,
he
mobili y
alues
o
a
se
o
pai s
( ans,
long
)
is
ob ained.
This
is
schema ized
wi h
he
e ical
solid
line
plo ed
in
Figu e
1.
3.
VALIDATION
PROCEDURE
Once
we
de eloped
he
algo i hm
o
ob ain
he
dependence
o
he
mobili y
on
he
longi udinal-
elec ic
ield
we
p oceeded
o
alida e
i .
To
do
so,
we
simula ed
se e al
ou pu
cu es,
using
ou
d i -di usion
simula o
o
a
MOSFET
and
a
supposed
mobili y
dependence,
a e
applying
ou
me hod
we
we e
able
o
ep oduce
his
depen-
dence,
con i ming
he
co ec ness
o
he
p ocedu e.
(Fig.
2).
2
E
,,,
)2.5
E ec S e
Field
(xlO
V/cm
FIGURE
Tables
(E ans(/)
Elong(/))
used
o
accoun
o
he
mobili y
educ ion
as
he
longi udinal
ield
ises.
They
co espond
o
ou
di e en
ou pu
cu es.
The
solid
line
ep esen s
a
common
chosen
e ec i e
ield
o
all
he
ables.
This
alue
will
be
employed
o
ob ain
he
mobili y
e sus
longi udinal
ield
cu es.
3979, 1998, 1-4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1155/1998/52301 by Uni e sidad De G anada, Wiley Online Lib a y on [12/12/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
A
METHOD
FOR
MOBILITY
DEPENDENCES
DETERMINATION
263
400
200
0
o
5
1o
Longi udinel
Field
(x104
V/cm)
FIGURE
3
Expe imen al
elec on
mobili y
as
a
unc ion
o
he
e ec i e-
and
longi udinal-elec ic
ields
a
oom
empe a u e.
FIGURE
2
Mobili y
cu es
e sus
longi udinal-elec ic
ield
ob ained
wi h
Equa ion
o
simula e
ou pu
cu es
and
alida e
his
me hod.
The
VSAT
chosen
was
VSaT
1.1X
10
cm/s,
/3
(solid
line),
/3
1.5
(long
dashed
line),
/3
2
(sho
dashed
line).
The
esul s
o
ou
me hod
a e
plo ed
in
squa es
o /3
1,
iangles
o /3
1.5
and
s a s
o
l
2.
4.
EXPERIMENTAL
RESULTS
AND
DISCUSSION
A e
ha ing
alida ed
he
accu acy
o
ou
me hod,
we
applied
i
o
Si
MOSFETs
ab ica ed
by
Lucen
Technologies
wi h
LEFF
0.6
gm,
WEFF
201am,
Tox
157
,
NA
1.2
x
10
l cm
-3
and
RSD
130
.
We
ha e
applied
ou
echnique
o
a
se
o
measu ed
ou pu
cu es
wi h
5I
10
-3
mA
and
A
0.96.
The
esul s
ob ained
can
be
obse ed
in
Figu e
3,
whe e
he
mobili y
e sus
e ec i e
and
longi udinal
ield
su ace
is
shown.
Exp ession
was
used
o
ob ain
he/3
pa ame e
and
he
sa u a ion
eloci y
VSAT.
V(Ell,
E+/-)
/0
(E.l.)
Ell
+/-
(
(#o(E+/-)
x
E]l) l)
lsa
The
alues
ha
ga e
a
be e
i
we e/3
and
VSA
T
1.1
x
107
cm/s.
These
alues
we e
indepen-
den
o
he
e ec i e
ield,
con i ming
he
esul
by
Modelli
and
Manzini
[4].
Using
Tho nbe ’s
exp ession
wi h
hese
pa ame e s
we
ha e
ied
o
ep oduce
he
expe imen al
ou pu
cha ac e is ics.
The
esul
is
shown
in
Figu e
4.
The
da a
p o ided
by
his
new
p ocedu e
a e
e y
use ul
in
o de
o
ob ain
local
mobili y
models
o
d i -di usion
simula o s,
whe e
he
dependence
o
he
longi udinal-elec ic
ield
is
included.
The
in luence
o
he
se ies
esis ance
and
i s
bias
dependence
can
be
aken
in o
accoun
easily.
I
is
also
possible
o
assess
he
in luence
o
elec on
eloci y
o e shoo
e ec s
in
e y
sho
channel
MOSFETs
by
using
a
augmen ed
mobili y
model
[5].
6
0
0.0
0.6
1.2
1.8
2,4
D oin
Vol cge
(V)
FIGURE
4
Expe imen al
and
simula ed
ou pu
cu es
a
T
300
K
o
a
LEFF
0.6
gm
MOSFET.
The
simula ed
cu es
ha e
been
ob ained
by
using
he
mobili y
shown
in
Figu e
3,
whose
dependency
on
he
longi udinal-elec ic
ield
was
ob ained
wi h
his
new
me hod.
3979, 1998, 1-4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1155/1998/52301 by Uni e sidad De G anada, Wiley Online Lib a y on [12/12/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
264
J.B.
ROLD/N
e
al.
5.
CONCLUSIONS
Au ho s’
Biog aphies
A
new
expe imen al
me hod
o
de e mining
he
dependence
o
he
elec on
mobili y
on
he
longi-
udinal-elec ic
ield
has
been
de eloped,
alida ed
and
applied
o
s anda d
submic on
MOSFETs.
This
me hod
can
be
easily
implemen ed
in
a
2D
d i -di usion
simula o .
All
he
di e en
depen-
dencies
o
he
elec on
mobili y
on
he
longi-
udinal-elec ic
ield
can
be
aken
in o
accoun
a
he
same
ime
by
means
o
his
me hod.
A
sa u a ion- eloci y
alue
o
1.1xl0Ycm/s
was
calcula ed
by
compa ing
he
mobili y
cu es
o
Tho nbe ’s
exp ession.
Acknowledgemen s
Juan
B.
Rold in
g adua ed
wi h
a
deg ee
in
physics
in
1993,
and
ecei ed
he
Ph.D.
in
1997
om
he
Uni e si y
o
G anada.
Since
1993
he
has
been
wo king
on
he
MOS
de ice
physics
including
2D
anspo ,
non-local
e ec s
and
Mon e
Ca lo
simula ions.
Cu en
in e es s
a e
also
ela ed
o
SiGe
and
SiC
de ices.
He
is
a
Teaching
Assis an
a
he
Uni e si y
o
G anada.
F ancisco
G imiz
g adua ed
wi h
a
deg ee
in
physics
in
1991,
and
ecei ed
he
Ph.D.
in
1994
om
he
Uni e si y
o
G anada.
Since
1991
he
has
been
wo king
on
he
cha ac e iza ion
o
sca e ing
mechanisms
and
hei
in luence
on
he
anspo
p ope ies
o
cha ge
ca ie s
in
semiconduc o
he e os uc u es.
His
cu en
esea ch
in e es
includes
he
e ec s
o
many-ca ie s
on
he
We
would
like
o
hank
Jos6
Ldpez
Se ano
om
elec on
mobili y
and
he
in e p e a ion
o
he
Lucen
Technologies
(Spain)
o
p o iding
he
in luence
o
high
longi udinal
elec ic
ields
ha e
MOSFETs
(0.9
lam
echnology)
we
ha e
used
in
on
MOS
ansis o s.
Cu en
in e es
a e
also
ou
s udy.
This
wo k
has
been
ca ied
ou
ela ed
o
SiGe
and
SiC,
and
SCI
de ices,
and
wi hin
he
amewo k
o
esea ch
p ojec
TIC
quan um
anspo .
He
has
coau ho ed
se e al
95-0511,
suppo ed
by
he
Spanish
Go e nmen
pape s
in
all
hese
subjec s.
He
is
an
Associa e
(CICYT).
P o esso
a
he
Uni e si y
o
G anada.
Juan
A.
Ldpez- illanue a
g adua ed
in
1984,
Ph.D.
in
1990
(Uni e si y
o
G anada)
wi h
a
Re e ences
hesis
on
he
deg ada ion
o
MOS
s uc u es
by
[1]
Tho nbe ,
K.
K.
(1980).
"Rela ion
o
d i
eloci y
o
low-
Fowle -No dheim
unneling.
Since
1985
he
has
ield
mobili y
and
high- ield
sa u a ion
eloci y",
J.
Appl.
been
wo king
on
deep-le el
cha ac e iza ion
and,
Phys.,
51,
2127.
[2]
Rold in,
J.
B.,
G imiz,
F.,
L6pez-Villanue a,
J.
A.
and
mainly,
MOS
de ice
physics,
including
Fowle -
Ca celle ,
J.
E.
(1995).
"Mon e
Ca lo
simula ion
o
a
No dheim
and
di ec
unneling,
quan um
e ec s,
submic on
MOSFET
including
in e sion
laye
quan iza-
2D
anspo ,
e ec s
o
nonpa abolici y,
sca e ing
ion",
4 h
IWCE,
p.
37.
[3]
Rold/m,
J.
B.,
G/ miz,
F.,
L6pez-Villanue a,
J.
A.
and
mechanisms
and
Mon e
Ca lo
simula ion
o
Ca celle ,
J.
Eo
(1997).
"Dependence
o
he
elec on
cha ge
anspo .
He
has
coau ho ed
se e al
mobili y
on
he
longi udinal
elec ic
ield
in
MOSFETs",
Semieond.
Sci.
Technol.,
12,
321-330.
pape s
in
all
hese
subjec s.
His
cu en
esea ch
[4]
Modelli,
A.
and
Manzini,
S.
(1988).
"High- ield
d i
in e es
includes,
simula ion
and
modelling
o
eloci y
o
elec ons
in
silicon
in e sion
laye s",
Solid-S a e
Elec on.,
31,
99.
elec on
de ices.
His
educa ional
ac i i ies
also
[5]
Rold/ n,
J.
B.,
G imiz,
F.,
L6pez-Villanue a,
J.
A.
and
include
analog
sys ems
o
elec onic
ins umen a-
Ca celle ,
J.
E.
(1997).
"Modeling
e ec s
o
elec on
ion
and
powe
elec onics
He
is
an
Associa e
eloci y
o e shoo
in
a
MOSFET",
IEEE
T ansc.
on
Elec on
De ices,
44,
841-846.
P o esso
a
he
Uni e si y
o
G anada.
3979, 1998, 1-4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1155/1998/52301 by Uni e sidad De G anada, Wiley Online Lib a y on [12/12/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License