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 Total Downloads : 1319
 Authors : Sanjay.C.Patil, B.K.Mishra
 Paper ID : IJERTV1IS8624
 Volume & Issue : Volume 01, Issue 08 (October 2012)
 Published (First Online): 29102012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Gaas MESFET’s Capacitance Model for the Optically Controlled ShortGate Length using MATLAB
Sanjay.C.Patil 1 , B.K.Mishra 2
1 2 Department of Electronics and Telecommunication Engineering
1 Research Scholar at NMIMS (MUMBAI), Parshvanath College of Engineering, THANE (W), MUMBAI, 400601 INDIA
2 Thakur College of Engineering and Technology, Kandivali (E) MUMBAI, 400101 INDIA
Abstract: For GaAs MESFET the capacitance of optically controlled short Gate length modeled analytically using Gaussian doped channel The photo effects on the short gatelength GaAs MESFET device capacitances have been modeled along with the electrical bias dependencies. The modeling has been done for linear as well as saturation region of device operation. The proposed model has been verified using MATLAB
KeyWords: – Gatesource capacitance, Gatedrain capacitance Vertical GaussianLike doping profile,MATLAB

INTRODUCTION
The microwave characteristics of GaAs MESFET can be controlled by incident light radiation having photon energy greater or equal to the band gap energy of GaAs in the same manner as varying the gate bias By biasing the FET optically, many devices such as highspeed optical detector and converter for interaction of optical and microwave signals have been designed
Optically controlled GaAs MESFET is the considered key device used for the design of photodetector [13]. It is experimentally established fact that optical radiation incident on the transparent or semitransparent gate of the device is used to control the microwave characteristics of the OPFET [45]. It has also been investigated that many of the microwave characteristics of GaAs MESFET like resonant frequency, transit time etc., can be controlled by controlling the internal gatesource and gatedrain capacitances of the device [67]. Here it is worth mention that the level of incident illumination can change the charge distribution under the gate that determines the internal capacitances of the GaAs MESFET. Therefore the internal capacitances of GaAs MESFET can also be controlled by the incident illumination.
In the conventional microwave amplifiers and oscillators using GaAs MESFETs once the circuit is designed for a certain gain or resonant frequency, it cannot be changed except the value of some of the external component of the circuit is changed. But using optically biased GaAs MESFET provides us with means of one control terminal from which the microwave characteristics of the GaAs MESFET can be controlled by changing its internal capacitances.
A number of capacitance models for long channel optically controlled GaAs MESFET have been described [6, 810]. In view of the fact that for high speed and denser integrated circuits the device dimensions are getting smaller and with the reduction in device dimensions two dimensional (2D) effects become prominent. So in order to provide efficient simulations and accurate predictions of photonic microwave integrated system behavior having short gatelength MESFET devices, a careful development of an accurate model taking 2D effects into account is required. Some models for the capacitances of GaAs MESFET are present in the literature [7, 11 12] that considers two dimensional effects.
For internal capacitances of ionimplanted selfaligned short channel GaAs MESFETs under dark and illuminated conditions. But that model ignores the effect of sidewall capacitances since the capacitances due to the sidewalls are negligible in self aligned GaAs MESFET device. Sidewall capacitances can play an important role while determining the internal capacitances of nonself aligned GaAs MESFET device. Therefore in the present work we have considered the sidewall capacitances while determining the overall internal capacitances of nonself aligned GaAs MESFET. The modeling of Gaussian profile introduces the error function which is not fully analytical in nature. The error function is originated because of the nonintegrable nature of the Gaussian function over some finite interval. Thus in the present work , an analytic Gaussianlike analytic function proposed by Dasgupta et al. [13] has been used in place of actual Gaussian profile to make the work fully analytical.

DEVICE ANALYSIS
The device under consideration has been shown in Fig.(1) where a is the active channel thickness and L is the gate length. Indium Tin Oxide (ITO) has been assumed as the gate metal because of its higher optical transmittance [15]. The monochromatic light is incident on the Schottky gate metal with photon flux density .The substrate of the device is assumed to be an undoped high pure semiinsulating GaAs material.
When the light is incident on the gate metal carriers are generated within the semiconductor material. The generated electrons move towards the channel region and holes move towards the surface where they recombine with surface traps. Considering these effects of generation and recombination the net doping concentration can be given as [18]
R p
N D ( y )
N d ( y ) G( y ) n
(4)
a
Where
N d ( y )
represents the doping profile defined by
Fig.1.Schematic of GaAs MESFET
The active channel region of the device is an nGaAs layer which is assumed to be obtained by ion implanting Si into the semiinsulating substrate
The ion distribution profile in the channel region can be given as [15]
equation (2)
R is the surface recombination rate is the absorption coefficient of GaAs material
n and p are life time of electron and holes. Respectively
,G(y) is the photon generation rate
Under illumination, the optical radiation penetrates into the active layer of the MESFET which results in the generation
N ( y )
y R
p
2
N p exp [( )
2
] (1)
of the excess electronhole pairs in the active region of the MESFET. The excess holes generated due to illumination in the depletion region are swept out towards the metal side
Where R p
is projected range and is the projected
whereas the photogenerated holes generated in the neutral region are diffused into the depletion region. These excess
straggle and
N p
Q
2
is the peak Ion concentration
photogenerated holes in the neutral region as well as in the depletion region are finally swept out towards the metal at
the Schottky gate. [10].This gives rise to a photocurrent
in the substrate .Q is the dose The doping concentration in
the channel can be given as [17]
N d ( y) N s ( N p N s ) F ( y) (2)
flowing from the semiconductor layer into the metal side that develops a photo voltage across the Schottky junction to make the junction forward biased. This photo voltage can be given as [18].
Where N s is the substrate doping concentration and
Vop
nkT
ln(1
J p (0)
) (5)
F ( y )
y R p
[exp (
)2 ]
q J s
2 Where J s
is reverse saturation current density at the
2
Since F(y) cannot be integrated analytically. We have to use an approximate analytic form of F(y)as[13]
gate depletion layer interface, n is the ideality factor of the Schottky junction, K is the Boltzmann constant, T is room temperature(i.e., 300K),q is the charge of an electron, and
F ( y )
Cc [{ac
2bc
2
( y R p )}

2bc ]
J p (0)
is the hole current density at the atechannel
a
exp [ c
2
( y R
p
b
) c ( y R
2 2 p
) 2 ] (3)
interface[18].


CAPACITANCE MODELING
We have assumed so far that the depletion region is confined only in the channel region below the Schottky gate and we have computed the 2D potential function accordingly.
Where a c =1.7857142,
bc =0.6460835,
However, in practice, the depletion region below the gate has
a very complicated structure and has extensions towards
C 0.28
c
and
{1for y R & 1for y R
p p
both the source and drain sides in a very complex manner depending on the bias conditions of the GaAs MESFET [7, 19].
we write the onset of velocity saturation given as[22].Following the
L h( x) x
1
0 (6)
same assumption of linear region the lengths of depletion region extensions towards source and drain in saturation region can be given as
L2 h( x) x L (7)
L h( x)
x
0 (12)
Where h(x)is the depletion region height under the gate same as Ref.[12].
The heights of the depletion region in the Regions IV and V can respectively be described as
2
4
L5 h( x)
sat
x
sat
L (13)
h(x)
L1 x 2 2
for L1 x 0 (8)
Where h( x) is the depletion region height under the
sat
h(x)
L 2 x 2
for L x
L L
2
(9)
gate in saturation region same as Ref.[19]. The depletion
region heights are given as
It may be noted that the onset of velocity saturation of the electrons has been assumed to be occurred at
h(x)
L2 x 2 for L
x
0 – (14)
x L L . Thus, the region L x L L
3 3 3 s
sat 4 4
(i.e. Region II) represents the portion of the saturation region confined below the gate and the region
h(x)
sat
L2 ( x – L) 2 5
for
L x L
L L x L ( L L ) L L
3 s 3 s ex 3 sat
L – (15) 5
(Region III) represents the extension of the velocity
saturation region beyond the gate with
Now, the gatesource and gatedrain capacitances of the
GaAs OPFETs can be defined as [7]
L L L representing the total length of the
sat s ex
C gs
Q t
V
(16)
velocity saturation region in the channel [20]. The
Vs gd constant
expressions for the
given by [20].
L and
s
L can respectively be
ex
C gd
Q t
V
Vgs constant
(17)
s (V V ) ds
L 2.06 K
( ds sat )1/ 2
(10)
Where Q is the total charge in the depletion under the gate
s d
q ncr
N D ( y )
t
of the device. Since depletion region charges are different for linear and saturation region due to the different structures
L 2.06(1 K
(V
s
)( ds

Vsat
) 1/ 2
)
(11)
of depletion region.
The total charge Q t
in the depletion region under the linear
ex d
q ncr
N D ( y )
region of operation of the device can be obtained by the addition of the charges contained in region I, IV, V respectively. The charge in various regions of depletion can be evaluated using following relation [7]
where K d
is a domain parameter, ncr is the characteristic
Q qZ N D (h(x))dxdh (x) (18)
doping density of GaAs (typically n cr
3X1021 / m 3
and
Q Q
t a
Q (19)
b
and Vsat is the minimum drainsource voltage required for
Where Q
a
and
Q are
b
Q qZ[L [ K
(h(0) h( L
)) M
2 2
(h (0) h ( L )
qN sinh[k (h x)]
sinh( K x)
A'' x
a 1 1 1 1
1 A' ( s )1[
1 ] 1
2
(27)

2 R
p
(h( L
1
) h(0))] L[K
1
(h( L) h(0))
sinh(k L)
s
1
sinh( K1L)
''' x
A

M (h 2
( L) h 2
(0) 2 R
(h(0) h( L))] (20)
A,A are
2qN
sinh[k
( L x)]
sinh( K x)
1 p ''
A
[ s ( 1 1 )
Qb qZL2 [ K1 (h( L L2 ) h( L) M1
s K1 sinh( K1L) sinh( K1L)
2 2 4qN s ]x1
X (h
( L L2 ) h
(h) 2 R p (h( L) h( L L2 ))] (21)
x2 (28)
s
Where K , M and N can be given as
'''
A
[(( D D 2 R
) 2 2qN s X
1 1 1
2
1 2 p
s K1
1
K ac Cc ( N p N s ) 2bcCc ( N p

N s ) N s
(sinh[ K1 ( L x) sinh( K1 x)
R p
0
a
n exp( R p ) (22)
sinh( K1L)
sinh( K1L)
)Vgs
'
' A ( D D
'

2 R p ) A
' ' '
A

2 B
1 2 (30)
M 2a b C ( N N )( 2 )

c c c p s
(23)
qN s 2
2( )
s
exp( R )
0 n p
N a C ( N
N ) (24)
Similarly, the gate drain capacitance ( (C gd ) under the
1 2
a c p s
linear region of operation of the optically controlled GaAs MESFET can be obtained using equation (18)in
Now, using Q (Eq.(19)) in Eq.(16) the expression for the
equation(16)as
t
gatesource capacitances
C gs
in the linear region of
C gd
P L
4 1





P L P L
5 6 2
(31)
1' 1'
operation can be given by
Where P is the value of P with A and B calculated
4
Where P is the value of P with A and B calculated using
.
1
using
x
1
0, x
2
L
1
x 0, x
1 2
L
1
Where P
Similarly,

and
P
5 6
are the values of P with
A ' and B '
P qZ
2[ (K1 M1R p (
2 ) 2 ) M B' ] (26)
calculated using
x L, x 0 1 2
and
A'
A
2
1
Similarly the values of P and
2
P are values of P with A
3
x L L , x
L respectively. And
1' and
and B calculated using respectively A and B are
x L L
1 2
, x 2
L.
1 2 2
B
1' are
1' qN 1
sinh[ k ( h x)]
sinh( K x)
Where Q , Q
and Q
are
A ( s )
s
''
[sinh( k1L)
1 sinh( K1L)
Qc
c
qZ[L
d
4 [K1
e
(h(0) h( L4
)) M 1 X
1
A
'''
1

A
1 (32)
]
x
x2
(h 2 (0) h 2
( L
4
) 2 R
p
(h( L
4
) h(0))]
'' 2qN
sinh[k ( L x)]
sinh( K x)

[K (h( L
) h(0))
2 2
A
1 [ s
s K n
( 1 1 )
sinh( K1L) sinh( K1L)
3 1 3

(h
1
( L ) h (0) 3
sinh[ k ( L x)] sinh( K x)
2 R (h(0) h( L
p 3
))]] (37)
2( D D

2 R
)( 1 1 )
1 2 p
sinh( K L)
1
sinh( K L)
1
Qd qZLs [k1 (h( L3 Ls ) h( L )
3
4qN s ]x1 2 2
x2 (33)
s
M (h
1
( L3

Ls ) h
( L )] 2 R



[K (h( L

p
(h( L
3
) h( L
3
L ))]s
'''
1
A
[((D

D2
2

2 R p )


2qN s X
s K n
qZL
ex
1
2
( K (h( L L
1 3 s

L ) h( L
ex 3
2
L )
s
sinh[K ( L x ) sinh(K x )
2qN
M (h ( L L L ) h ( L L )
( 1 1 )V

s
1 3 s ex 3 s
sinh(K1L )
gs
sinh(K1L ) s
x
2 R (h( L
p 3

L ) h( L L s 3 s
L ))] (38)
ex
X (ch
( x ) D (V
bi

Vgs

Vop
1 / 2 1
V ))) ]
ds x
2
(34)
e
[



qZL K
5 1
(h( L
3

Lex

L ) h( L
5 3

Lex
L ))
5
'
'
1
1 A ( D D
'
p A
2 R ) 1
' ' '
1
A
2
M1 (h ( L

Ls L
L ) p ( L

L L )
B 1 2 (35)
3 ex 5
3 s ex
qN s 2
2( )
s
2R X (h(L L L ) h( L L L L ))] (39)
p 3 s ex 3 s ex 5
In saturation region the total charge in the depletion region can be obtained using similar methodology of linear region and can be used as
Now, the gateSource capacitance in saturation of the OPFET can be evaluated using equation (36) in equation.(15) and can be given as
Qt Qc

Qd

Qe
(36)
C gssat
P L
7 4

P L
8 3

P L
s
9

P L
ex
10
5

P L
11
(40)
' '
Where P is the value of P with A and B calculated using
ds
7
respectively A1 and B1 are same as given in equation (32)
the x 0, x L similarly P , P , P and P
1 2 1 8 9 10 11
equation(35). With
V Vsat .
are the values of P with A and B values calculated using




RESULTS AND DISCUSSION
x 0, x
1 2
L , x
4 1
L , x
3 2
0 ,
To demonstrate the validity of the proposed model the theoretical results obtained for the internal gatesource and gatedrain capacitances of the GaAs OPFETs under dark and
x L
1 3

L , x
s 2
L ,
3
illuminated conditions have been obtained by MATLAB. The values of parameters used for computation of model
x L L
1 3 s

L , x
ex 2
L3

L and
s
results are
R p
0.1m , V
bi
1V
L 0.3m ,
x L L L L , x L Ls

Lex
a 0.25m
, T 0.9
m
,
p
0.02 m ,
1 3 s ex 5 2 1
6
870nm
ds
Respectively A and B are same as given in equation(27)to equation(30) with V Vsat .similarly the gatedrain
capacitance ( (C gd sat ) under the saturation region of
10
, N
p
/ m ,
23
4 X 10
m 3 N
s
and
1X 10 21 m 3 .
operation of the optically controlled GaAs MESFET can be modeled using equation(36) in equation(17) and can be written as
Variation of the internal gatesource capacitance C and
gs
internal gatedrain capacitance C with V for linear
C P L

P L

P Ls P
Lex
gd gs
gd sat
12 4
13 3 14
15 region of operation under dark and illuminated condition is shown in Fig. 2 and Fig. 3. It is seen that both the
5

P L
16
(41)
capacitances increased with increasing incident illumination for a fixed gatesource voltage. This may be accounted by
' 1' the fact that the depletion region width reduces under the
Where
is the value of P with
P
12
A1 and B calculated
illuminated condition
using x
1
0, x2
L
1
similarly P P
P and
Figure 4 and 5 shows the gatesource capacitance
C
13 14 15
' '
and gate drain capacitance C
in the
P are the values of P with A1 and B1 calculated using
16
gs sat
saturation region.
gd sat
x 0, x
1 2
L
,
x
4 1
L , x 0
3 2
It has been found that C
and C
x L
1 3

L , x L
s 2 3 ,
gs sat
gd sat
x L L
1 3 s

L , x ex 2
L3 L
s ,
increases under illuminated condition. This may be due to the reduction in depletion width due to the photo voltage
x L L L
1 3 s ex

L , x
5 2
L L
s
1

Lex developed across the Schottky metal gate.
Fig.4.Plot of
C VS
gs sat
V GaAs MESFET
gs
operated in saturation region for dark and illuminated conditions
It can also be observed that C
gs sat
increases with the
increase in
V because depletion region width decreases
gs
with the increase in gate bias (i.e. more positive V ).From
gs
Fig.2.Plot of C VS
gs
V GaAs MESFET operated in
gs
Fig.5 It can also be observed that
C
gd sat
decreases
Linear region for dark and illuminated conditions
with the increase in V like the conventional long channel
gs
Fig.3.Plot of C VS V GaAs MESFET operated in
device [23].
gd gs
linear region for dark and illuminated conditions
Fig.5.Plot of
C VS
gd sat
V GaAs MESFET
gs
operated in saturation region for dark and illuminated conditions
In Figure .6 gatesource capacitance has been plotted as a function of drainsource voltage V .It can be seen that
ds
gatesource capacitance becomes larger for illuminated condition. It can also be observed that gatesource capacitance decreases with the increase in V in the linear
ds
region and becomes nearly constant in the saturation region. Figure .7 shows the variation of gate drain capacitance
against the drainsource voltage
V .Gatedrain
ds
capacitance increases with the increase in V in the linear
ds
region and becomes nearly constant in the saturation region. Similar to the gatesource capacitance gatedrain capacitance is more under illuminated condition.
Fig.6: Plot of gatesource capacitance vs. V of GaAs
ds
MESFET under dark and illuminated conditions
Fig. 7: Plot of gatedrain capacitance vs. V of GaAs
ds
MESFET under dark and illuminated conditions

CONCLUSION
A model for internal capacitances of GaAs MESFET has been developed .The charge for each part of the depletion region has been derived analytically for linear and saturation regions. and above results are obtained using MATLAB. The developed model may be suitably implemented for the design of photodetectors.

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