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IEEE TRANSACTIONS ON ELECTRON DEVICES,VOL.47,NO.5,MAY 2000
905
An Analytic Model for Estimating the Length of the Velocity Saturated Region in GaAs MESFET’s
Curtis Leifso ,Student Member,IEEE,and James W.Haslett ,Senior Member,IEEE
Abstract—An analytical model is prented for estimating the length of the portion of a FET channel with velocity saturated car-riers.The model is bad on previous work propod by Pucel et al.[1],[2],and has been adapted to remove discontinuities between extreme bias conditions.The need for complicated numerical solu-tions has also been removed making the model suitable for u with circuit simulators.Results obtained from the model agree well with previously propod models over a wide range of bias conditions where velocity saturation can be either dominant or negligible,de-pending on the overall channel length and bias conditions.Index Terms—Gallium arnide,MESFET,modeling,velocity saturation.
I.I NTRODUCTION
K
NOWLEDGE of the length of the velocity saturated re-gion (LVSR)of a FET channel aids in modeling both the dc and noi performance of GaAs MESFET’s.For devices with gate lengths less than
0.5
Publisher Ite
906IEEE TRANSACTIONS ON ELECTRON DEVICES,VOL.47,NO.5,MAY
2000
(5)
(6)
where
Shockley pinch off potential;
[15]
undepleted channel
depth;
overall channel
length;
-field at the pinch off
point;
normalized gate referred channel potentials at
the pinch off point,source,and drain,respec-
tively.
A common t of assumptions were made in this derivation
and are briefly summarized.As shown in Fig.1,it is assumed
that at the pinch off
point
is given by(5).For
all
-field in the channel.For
all-field and
the carrier velocity is saturated at a constant value.
premiThe above model described by(1)–(6)is valid when both re-
gions exist in the channel and(4)gives a value
for
increas until(4)
indicates
as well as
the normalized drain
potential cannot
exceed
,since the
condition
given by
the smallest of
either that
makes
can be easily done using(1)
for a given bias current,however,simulations are more conve-
niently done
when
.This is more uful in dc modeling where the dc
drain current is typically the desired quantity to model.
Determining
must be
found from numerical solution of an extremely nsitive func-
tion in(2).If the channel potential at the pinch off point was
known,(5)could be ud to
calculate
.
缺点英语
Fig.1.Assumed E-field distribution in the channel.
From this,two modifications to the model must be made if it
is to be conveniently ud in a circuit simulator.First,the LVSR
must be an explicit function
of
for all bias conditions that keep the device in saturation.
III.D EVELOPMENT OF A LTERNATIVE M ODEL
A.Explicit Form of LVSR
In order to get the LVSR as a function
of must be
found as an explicit function
of
(7)
a new
function can be defined
that girl什么意思
as
(8)
who roots give the required value
of
is defined
as
(9)
For devices with channel
lengths
m
and
breakingnewsincreas,
.However,for most practical device geome-
tries and bias conditions,the
idiot是什么意思
assumption
(10)
which must be solved
for
values
where
for英文顿号
large
is small
(is large
(
m.In practical
circuits,especially microwave designs,the conditions rarely
occur.Instead submicron process are preferred with minimal
bias voltages.
The conditions result in the LVSR occupying a large frac-
tion of the channel which
caus
for a wide range of bias conditions.This makes it possible to
approximate with a local ries expansion over a bounded
region just before the slope
of increas rapidly,as oppod
to a global ries expansion about some arbitrary point that is not
LEIFSO AND HASLETT:VELOCITY SATURATED REGION IN GaAs MESFET’S
907
Fig.2.Dependence of x(p)on p and L from the original Pucel del. easily determined if the model is to be valid for a wide range of channel lengths.
For a small local region,a common quadratic approximation to a function given in most numerical methods texts,(Powell [16])
海淀翻译公司
is
is found by differentiating(10)to
get
.In order to choo the upper limit of the in-
terval,(4)can be solved for the point at which the entire channel
can be modeled with constant mobility
or
.When the expansion is
done within the limits,the portion
of with large slope is
not modeled as well,which reduces the model’s accuracy
as
that will be valid for all practical op-
erating conditions and FET channel lengths for reasonably
low
expression in(10)and noting that the logarithmic term changes
much slower
than is incread.Rewriting(10)
as
(13)
Fig.3.Plot of x(p)from Pucel del with the approximation~x(p)as p
is varied.
will give a quadratic solution
to
(15)
respectively,
where derived in Sec-
tion IV.Substituting the approximations into(13)and simpli-
fying gives a quadratic summarized in Section III-C that
can be solved to give two roots,one of which will be greater
than1and can be discarded.
Fig.3shows a plot
of calculated from the Pucel et al.
model and the new approximation over a range
of
are ud.The solution
for.
From the clo agreement shown in Fig.3
when and
equal zero,it is clear that a quadratic estimate
of
.
B.Self Limiting Modifications
Limiting the LVSR expression
to
LVSR m
implies has one zero in the open
interval,
where
such
that
is monotonically increasing in the
interval
908IEEE TRANSACTIONS ON ELECTRON DEVICES,VOL.47,NO.5,MAY
2000
Fig.4.Ideal function f (L )for limiting ~x (p ).
the lower limit occurs
when and thus must be nega-tive for the zero to exist.
As discusd,there are two possible upper limits
on ,that would indicate no
velocity saturation within the channel.This solution can take on
any value
between
to determine the actual upper
limit
from
(3),it is easy to show
that
is found from (4)
when
Knowing the upper and lower limits
on
and hence the expression for
the LVSR.The overall expression for the LVSR cannot be di-rectly truncated when it approaches the valid limits
since has no zero within the
range
science怎么读
at
t boundaries and leaves it unaltered when within a valid range.This makes the effect of the limiting function easier to e
since
has a simple linear dependence
on
,
(16)
and
is the unit step function.
C.New Model Summary
couponcodeThe complete explicit model for the LVSR is given as
LVSR
(19)
where
who coefficients
are
with
from the Pucel model is shown in Fig.3for veral different bias conditions.The most common measures of LVSR models
are the dependence
on
.Fig.5shows the plots for veral bias voltages and channel lengths.The actual LVSR es-
graphical
LEIFSO AND HASLETT:VELOCITY SATURATED REGION IN GaAs MESFET’S909 timates given by the Pucel model are also plotted in Fig.5.
The plots show excellent agreement between the two func-
tions when both a velocity saturated and constant mobility re-
gion exist.
When
caus to remain less than zero resulting in the
LVSR to equal m
in is to ensure that a zero exists in the valid interval for
when the channel length
is small and
and
