Gaas MESFET’s Capacitance Model for the Optically Controlled Short-Gate Length using MATLAB

Gaas MESFET’s Capacitance Model for the Optically Controlled Short-Gate 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 gate-length 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

Key-Words: – Gate-source capacitance, Gate-drain capacitance Vertical Gaussian-Like doping profile,MATLAB

1. 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 high-speed 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 photo-detector [1-3]. 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 [4-5]. 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 gate-source and gate-drain capacitances of the device [6-7]. 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, 8-10]. 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 gate-length 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 ion-implanted self-aligned 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 non-self aligned GaAs MESFET device. Therefore in the present work we have considered the sidewall capacitances while determining the overall internal capacitances of non-self 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 non-integrable nature of the Gaussian function over some finite interval. Thus in the present work , an analytic Gaussian-like analytic function proposed by Dasgupta et al. [13] has been used in place of actual Gaussian profile to make the work fully analytical.

2. 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 semi-insulating 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 n-GaAs layer which is assumed to be obtained by ion implanting Si into the semi-insulating 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 photo-generated 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

   photo-generated 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 ate-channel

     a

     exp [ c

     2

     ( y R

     p

     b

     ) c ( y R

     2 2 p

     ) 2 ] (3)

     interface[18].

3. 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 gate-source and gate-drain 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 drain-source 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 )

           1. 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

              gate-source 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,

   1. 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

      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)

         1. [K (h( L

            ) h(0))

            2 2

            A

            1 [ s

            s K n

            ( 1 1 )

            sinh( K1L) sinh( K1L)

            3 1 3

         2. (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

      2. 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

        [

   2. 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 gate-Source 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

4. 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 gate-source and gate-drain 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 gate-drain

     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 gate-source capacitance C and

     gs

     internal gate-drain 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 gate-source 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 gate-source 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 gate-source capacitance has been plotted as a function of drain-source voltage V .It can be seen that

   ds

   gate-source capacitance becomes larger for illuminated condition. It can also be observed that gate-source 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 drain-source voltage

   V .Gate-drain

   ds

   capacitance increases with the increase in V in the linear

   ds

   region and becomes nearly constant in the saturation region. Similar to the gate-source capacitance gate-drain capacitance is more under illuminated condition.

   Fig.6: Plot of gate-source capacitance vs. V of GaAs

   ds

   MESFET under dark and illuminated conditions

   Fig. 7: Plot of gate-drain capacitance vs. V of GaAs

   ds

   MESFET under dark and illuminated conditions

   1. 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 photo-detectors.

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