Matlab Based Analytical Model For Short Channel Gaas Mesfet For The Distribution Of Potential And Threshold Voltage Under Dark And Illuminated Conditions

Matlab Based Analytical Model For Short Channel Gaas Mesfet For The Distribution Of Potential And Threshold Voltage Under Dark And Illuminated Conditions

Sanjay.C.Patil

(Research Scholar at NMIMS MUMBAI) Parshvanath College of Engineering, THANE (W),

MUMBAI, 400601 INDIA Mob+9109969634801,

B.K.Mishra

Thakur College of Engineering and Technology,

Kandivali (E) \ MUMBAI, 400101 INDIA

Mob+9109821285825,

ABSTRACT:-

Optoelectronic is one of the thrust areas for the recent research activity. One of the key components of the optoelectronic family is photo detector to be widely used in broadband communication, optical computing, optical transformer, optical control etc. Present paper includes the investigation carried on the basis of the 2 D (two dimensional) mathematical modeling for the potential distribution and threshold voltage of short channel ion implanted GaAs-MESFET operated in the sub threshold. Device is assumed to have the double integrable Gaussian like function as the doping distribution profile in the vertical direction of the channel .The Schottky gate has been assumed to be semi-transparent through which optical radiation is coupled in to the device. Investigation shows the 2D potential distribution in the channel of the short channel device by using 2D Poissons equation and suitable boundary conditions. It also shows that the effect of excess carrier generation due to the incident optical radiation in the channel, the potential function has been utilized to model the threshold voltage of the device under dark and illuminated conditions. Results that theoretical predicted for device and using MATLAB.

Key word: – Gaussian doping profile, Poissons equation, ion Implantation, optical biasing, optically controlled GaAs MESFET

1. INTRODUCTION:-

   Optically controlled microwave devices and systems have some advantages such as size reduction, signal isolation, large bandwidth and immunity to electromagnetic interface. The incident illumination reduces the noise figure but increases the power gain of GaAs OPFET. The properties such as high speed, low cost monolithically integrated

   optically gated GaAs MESFET are presently in the high demand for optical communication in the range of low wavelength high frequency devices.

   GaAs MESFET [metal Semiconductor Field Effect Transistor] have drawn considerable attention in the design of high speed digital/analog integrated circuits and microwave monolithic ICs [1]. The optical effects in MESFET have been studied by number of researchers because of its potential application in optoelectronic, optical communication and optical computing. The GaAs MESFET can be modified by coupling a fraction of optical power radiated by external source in to the channel of the device

   [2] The excess electron- hole pair generation due to optical generation in the channel is utilized to control the device characteristics. Since excess electron-hole pair can be controlled by the radiated power level of the external optical source, the radiated power level has direct control on device characteristics. A MESFET with transparent or semitransparent Schottky metal at the gate to the desired incident radiation is known as optically controlled field effect transistor (OPFET).GaAs MESFET with gate length values in the range of 0.2-0.5micrometer shows high drain source current (output current) and large transconductance values at microwave frequencies .The one dimensional (1D) Poissons equation will fail to provide potential distribution of such MESFET with channel length in above range. Since electrical characteristics of devices influenced by the two- dimensional potential distribution and high electric field effect, thus the 2D Poissons equation is required to solve to obtain the channel potential and threshold voltage of short channel devices which can be utilized for the modeling of the electrical characteristics of the device [4-5].In general various techniques can be used for producing non uniform doping in the channel region of the device .ion implantation is very effective for improved GaAs MESFET performance. Ion-implantation method produces a Gaussian doping profile which is an analytically non integrable

   function i.e. integration of the Gaussian function within the finite limit produces error function which is not analytical in nature. Thus 2D modeling of the potential distribution and threshold voltage of short channel ion implanted GaAs MESFET is a difficult and challenging task. The complexity increased further If the modeling is carried out for short gate length GaAs MESFET operating under illuminated condition .It is assumed that uniformly distributed channel for device and results are not validated by any experimental or numerical simulation data. To the best of our knowledge no work has been reported so far in the literature for two dimensional analytical model of an ion implanted GaAs MESFET under dark and illuminations [8-9].

   In this paper the analytically model the channel potential and threshold voltage of short channel optically biased GaAs MESFET with vertical Gaussian profile to get faster and denser components for photonic ICs .The model uses a Gaussian like analytic function in place of actual non analytic Gaussian function for making the model purely analytical one .model is simplified by assuming that vertical channel doping is Gaussian in nature and it is uniform in lateral direction [10].

   The 2D potential distribution function is obtained by solving the 2D Poissons equation using superposition

   the substrate surface so that ion distribution profile become 1D Gaussian function described by equation(1)

   Fig.1 schematic of GaAs MESFET

   The undoped substrate is assumed to have a uniform doping and implantation is assumed from an identical beam that scanned uniformly across the substrate, therefore the I D Gaussian Function described by[13].

   method in conjunction with appropriate boundary conditions. Modifications in the Poissons equation to include the photo effect on the device characteristics of GaAs MESFETs under illuminated condition, Since threshold voltage is the key parameter in both dc and

   y

   Q [ [

   N ( y ) e

   2

   R p ]2 ] 2

   y

   [ [

   N p e

   R p ]2 ] 2

   (1)

   microwave circuit design using GaAs MESTFETs ,the effect of optical illumination on threshold voltage of GaAs OPFET has also been investigated[11].Theoretically predicted results are compared with MATLAB results.

2. DEVICE DETAILS:-

   Optically biased GaAs MESFET used for modeling, Structure of fully doped GaAs MESFET shown schematically in the figure.1, where a and L are active layer

   Where Q is the dose , R p is the projected range, is the

   Q

   projected straggle and N p is the peak ion

   2

   concentration in the substrate

   1. The doping distribution in the channel can be

      thickness and gate length respectively

      The substrate of device is assumed to be an un-doped high pure semi-insulating material .The active channel region of

      approximately described by [considering N S

      substrate doping concentration]

      y R p 2

      is the

      the device is an n-GaAs layer which can be obtained by ion implantation of silicon in to semi-insulating substrate

      .monochromatic light of energy greater than or equal to the

      N d ( y ) N s

      ( N p

      [ [ ] ]

      2

      N s ) e

      band gap energy of GaAs is allowed to fall upon the gate area of the device (along y-axis).Indium tin oxide has been

      N s ( N p

      N s ) F y )

      (2)

      used as the Schottky gate metal due to high optical transmittance of incident illumination on gate surface[12]. The un-doped substrate is assumed to have a uniform

      y

      [ [

      Where F ( y ) e

      Rp ]2 ] 2

      (3)

      doping concentration of N s

      The implantation is assumed

      from an infinitesimal beam that scanned uniformly across

      N d ( y) is an analytically non-integrable function of y because of exponential function F(y)

   2. To remove this difficulty we have used an approximate analytic form of F(y) as

   [ { ac ( y R p ) 2 }]

   R is the surface recombination rate

   is the absorption coefficient of GaAs material n and

   p are the life time of electrons and holes respectively And G(y) is photo-generation rate given by

   F ( y )

   Cc [{ac

   2bc

   2

   2

   ( y R p )}

   2 2

   2bc ]e

   (4)

   G ( y )

   ( y )

   0 e

   ( 7 )

   Where

   ac

   1.78571, bc

   0.6460835, cc

   0.28

   where

   1. is thephotonflux density expressed as

      and

      {

      1for y

      in

      R p ,

   2. for y R p

      P T

      m

      in

      0

      h ZL

      (8)

3. THEORETICAL MODEL:

   1. Modeling of 2D channel function:-

      Where P is the incident optical power , Z is the width of the gate material ,L is the gate length ,

      ( x, y) is potential distribution of the channel and it can be determined by solving the following 2D

      Poissons equation in the fully depleted rectangular channel region

      Tm is the optical transmission coefficient for the gate metal,

      h- is the planks constant and is the frequency of the incident light

      2

      d ( x, y )

      2

      2

      d ( x, y )

      2

      qN D ( y )

      (5)

      we can use following boundary conditions for solving equation (5) :

      dx dy s

      ( x ,0) V

      bi

      Vgs

      Vop

      (9)

      Where s is dielectric permittivity of GaAs semiconductor, q- is the electron charge

      ( 0, y ) V

      bi

      ( L , y ) V

      (10)

      V

      (11)

      N D ( y )

      is the net doping concentration in the active

      bi ds

      channel region under illuminated condition which can be expressed as

      ( x , y )

      y 0

      y

      (12)

      N D ( y )

      N d ( y )

      R p

      G ( y ) n

      ( 6)

      gs

      Where V is Schottky barrier potential , V is the

      bi

      Where N d

      (2)

      ( y) is the doping profile defined by equation

      applied gate bias and Vop is the photo voltage developed at the Schottky junction due to illumination which can be described by

      Vop

      nkT q

      ln(1

      J p ( 0)

      )

      J s

      (13)

      2

      d 1D ( y )

      2

      dx

      qN D ( y )

      s

      (17)

      Where J s – is reverse saturation current density at the gate

      With following boundary conditions

      depletion layer interface, k- is the Boltzman Constant, T- is the room temperature (i.e. 300k) , n -is the ideality factor of Schottky junction

      1D ( y ) y 0 V

      bi

      V V

      gs op

      (18)

      q- is the charge of the electron and J p (0) – is the hole

      1D ( y )

      current density crossing the gate channel Interface is given by

      y a 0

      y

      (19)

      J ( 0 ) qv p (y) y 0

      —(14 )

      The function 1D ( y) can be obtained by integrating

      p p d

      equation (17) twice and can be written as

      Where

      v p is the saturation velocity of hole and

      p d (y) is

      y R y R

      the photo-generated hole density in the depletion region and p d (y) y 0 is described by

      1D ( y )

      2

      q ( 2 )

      [C ( N

      s c p

      [ [ a [

      c

      N ) e

      s

      p

      ] b [

      1. c

      p ]2 ]]

      2

      y R

      R p p 2

      ( )

      ( R ) (

      e p e

      0 n

      ( y R ))

      p

      p (y) y 0 ( 0 p )[1 e (

      a) ]

      a 2

      (15)

      2 ( 2)2

      d 1 v

      N y R y R

      p p s

      2

      p 2 ( )

      2

      p 2

      A( ) B ] 2

      ( 20)

      Applying superposition technique to solve the 2D Poissons

      equation described by(5),

      ( x, y) can be expressed as

      Where A, B are the arbitrary constants expressed as

      ( x , y )

      1D ( y )

      2 D ( x , y )

      (16)

      Where

      1D ( y) is the 1D potential function of the long

      channel MESFET and

      2D ( x, y) is the 2D potential

      function responsible for the short channel effects

      The long -channel potential function

      1D ( y)

      can be

      obtained by solving following 1D Poissons equation

      a R a R

      p p 2

      2 D ( x ,0) 0

      ( 24)

      a R [ [a

      [ ]

      b [ ] ]]

      q 2

      1. [ Cc ( N p

         N s )[a

         2b [

         p c 2 c 2

         ]]e

         ( 0, y ) V

         2 D

         bi

         1D ( y )

         ( 25)

         s c c 2

         a R

         ( L , y ) V V

         2 D

         bi ds

         1D ( y )

         ( 26)

         p

         N [ ]

         s 2

         ( aR ) (

         (a R )

         d 2 D ( x , y )

         y a 0

         dy

         ( 27)

         R a R ( e

         p p 0 n

         [ ]

         p e p

         ] (21)

         Appling the standard technique of separation of variables and using the boundary conditions described by

         a 2 2

         equations(24)-(27),

         2D ( x, y) can be expressed as

      2. [ C ( N

      c p

      [

      N ) e s

      R

      p

      [ a [ ]

      c 2

      R

      b [ p ]2 ]]

      c 2

      N R

      s [ p ] 2 4

      2 D ( x, y )

      Where

      sin( k n y ) sinh( k L )

      R R

      p p 2

      [ ]

      2 a

      n

      n 1

      Bn

      { An sinh[ k n ( L

      x )]

      sinh( k n x )}

      ( 28)

      ( R ) ( R )

      e p e p

      (2n 1)

      0 n

      kn (29)

      2a

      2 ( 2 )2

      R (V V V )

      Cln

      An

      C2n

      C3n

      C4n M n

      C5n

      C6n

      C7n

      (30)

      p s bi

      gs op

      Cln C

      C2n

      C3n

      C4n

      C5n

      C6n

      C7n

      A[ ]

      ] ( 22)

      Bn 1ln

      (31)

      2

      Now,

      q (

      ( x, y)

      2 )2

      the can be obtained by 2D Laplace

      q(2)3 C (N

      c p

      C

      M n

      N )

      s

      [2b

      2

      k ( 2b

      ( 1 a(a

      2

      2

      b a))k

      (32)

      2D ln

      1 3 c n c c c

      n( 2b

      ( 1 a(a

      b a))k

      cos(k a) (a

      2b a)k ) sin(k a)]

      equation

      2

      2

      ( x, y )

      ( x, y )

      V

      C ds

      k

      K

      s n

      V cosk a

      ds n

      k

      c c c n

      (33)

      n c c n n

      2 D

      2

      x

      2 D

      2 0

      y

      ( 23)

      1ln

      n n

      q( 2)3 N

      C s

      2 2

      [ 2 (2 a k

      ) cos(ak ) 2ak cos(ak )

      (34)

      by using the following boundary conditions derived from equation(9)-(12) in conjunction with equation (18)-(19)

      2n 3 n

      2k

      s n

      n n n

      q ( 2 )

      n ( Rp

      2a )

      k e(

      2a ) k

      cos( ak )

      2 sin( ak )

      Thus from resultant expression

      ( x, y) can be obtained by

      2

      C 0 e X [ n n n n ] 3n

      2

      using the expression

      1D ( y ) and 2 D

      ( x , y )

      from

      V V cos( ak )

      ( 2 ) k

      n

      equation (20) and equation (28) in equation (16) respectively

      [ bi k n

      bi n ]

      k n

      3

      (35)

      Note that equation (28) is an infinite series and hence impossible to use for computation of the values of

      2D ( x , y ) by taking all the terms in to consideration .it

      may be mentioned that any hyperbolic sine function ,say sinh(z) ,decreases exponentially with the increase in z ,Thus

      C4n

      q( 2)

      R p

      3 [ 2

      2

      (2 a k

      2

      ) cos(ak

      ) 2ak

      cos(ak )]

      (36)

      both sin(k n ( L

      x)) and sin(k n L)

      In equation (28) decreases

      2a s k n

      n n n n

      very rapidly with increase in n since k nis increased with n

      2

      Aq (

      4

      2) (

      ak n ) cos(ak n )

      sin(ak n )

      Further it may be verified that both An and Bn are also

      C 5n

      R Aq2 (

      p

      2)3 ( 1

      2 2

      k n s

      cos(ak )

      n

      (37)

      decreased with the increase in n

      Therefore it maybe a quite reasonable assumption to consider only the fundamental term for n=1

      Of the series to approximately express as

      1 2

      K ( x , y )

      ( y )

      sin( k y )

      1 { A

      sinh[ k ( L

      x )] B

      sinh( k x )}

      ( 41)

      n s 1D

      1 1 1 1

      sin( k1L )

      2 6

      q ( 2 ) C ( N

      c p

      N )( 1 cos(ak ))

      s n

      Where k , A and B

      can be determined by using n=1 in

      C 6n

      2 1 X [[a

      1 1 1

      s

      a R [

      k n

      a R

      p

      a ( )

      c

      a R

      b ( p )2 ]

      (38)

      equations (29)-(31) respectively.

   2. Modeling of Threshold Voltage:-

   p 2

   2b ( )]

   c 2

   2

   2b ]e c c

   2 c 2

   R

   p

   [ a ( )

   R

   b ( p )2 ]

   The Threshold voltage V of a short channel optically

   th

   biased MESFET can be obtained as

   C 7 n

   q( 2) (1

   2

   cos ak n )

   [C ( N

   c 2 c 2

   N )e k L

   N

   s ( 2

   s k

   R

   R p 2 p

   ) (

   2 a

   c

   R p 2

   )

   2

   1. s

      ( R ) ( R )

      e p e p

      0 n ]

      ( 2 )2

      V V

      th tho

      sec(

      1 ) A

      1

      2

      ( 42)

      Where k and A are obtained from equation (29) and

      (Vbi

      Vgs

      Vop )(1

      cos k n a)

      1 1

      (39)

      k n equation(30) with n=1 respectively, and

      V is the

      tho

      2 ak n

      M n

      sin( 2 ak n )

      ( 40)

      threshold voltage of the long channel MESFET which can be obtained as

      4 k n

      V

      tho

      V V V

      po

      op

      bi

      ( 43)

      Where V po is the pinch -off voltage defined as

      6

      10 S

      n n

      8 6

      10 S 10

      / m ,

      0

      8700 A and

      Vpo

   2. a

   N ( y )ydy

   0 D

   s

   ( 44)

   T 0.9 ;

   m

   q[C

   ( N p

   N s )

   2 (C

   C C )]

   Vpo

   1 2 3 4

   s

   ( 45)

   N a2 a

   (1 (1

   a ) e( a )

   C s

   1 2

   p [ 0 n ] 2

   ( 46)

   C 2C [ e

   1. c

      a ( a R )

      c p

      [

      2

      ( a R

      b (

      c 2

      )

      p ) 2 ]

      a ( R )

      c p

      [

      2

      e

      ( R )

      b ( p ) 2 ]

      c 2

      ]

      ( 47)

      Fig.2.Comparision of Gaussian and New Gaussian like function curves

      ( a R )

      1. ( a R )

         c p

         [

         ( a R

      2. (

      )

      p ) 2 ]

      C C ( a

   2. c

      p

      R )[a 2b ]e

      p c c 2

      2 c 2

      C ( R

      )[a

      ( a R p

      2b

      a ( R )

      c p

      ) [

      2

      ]e

      ( R )

      b ( p ) 2 ]

      c 2

      ( 48)

      c p c c 2

      ( a R )

      1. ( a R )

         c p

         [

         ( a R

      2. [

         p ) ]2 ]

         p

         C R C [[a 2b ]e

   3. p c c c 2

   2 c 2

   [ a 2b

   1. c

   ( R )

   p

   ]e

   2

   a ( R )

   c p

   [

   2

   ( R )

   b [ p ]2 ]

   c 2

   ] ( 49)

4. RESULT AND DISCUSSION:-

   The value of parameter used for modeling results are a=0.4m, Vgs=0.2v, Rp=0.06m, Vbi=0.6v, =0.05m,

   Fig.3. Variation of channel Potential along the Channel Length for dark and illuminated conditions

   Fig.3 shows the variation of channel potential with gate length (L) in dark and illuminated conditions for different

   23 3

   N p 1X 10 m ,

   21 3

   Ns 1X 10 m ,

   gate to source voltage(Vgs).it can be seen that for a given gate voltage ,the source channel potential barrier is reduced due to the incident optical radiations on the device .this due to the fact that the photo voltage developed across the junction due to illumination forward biased the Schottky gate channel junction and hence decreasing the source channel potential this results that the height of depletion

   region below gate is decreased with increase in the level of incident illumination on the device.

   Fig.4.Va

   Fig.6.Variation of Threshold Voltages

   V with incident

   th

   riation of channel Potential along the Channel length for different standard deviation ()for dark and illuminated conditions

   Fig.4 shows the channel potential variation as a function of channel Length (L), for different values of projected straggle . It is observed that source channel barrier height is decreased with the increase in the value of due to the increase in the average implanted ion density in the active channel region of the MESFET with increase in a of the

   profile for the constant peak doping N p

   Fig.5.Threshhold Voltage V variation with gate length(L)

   th

   for dark and illuminated conditions

   Fig.5shows the threshold voltage variation with gate length for dark and illuminated conditions .it has been observed that, for gate length less than 0,2m drain induced barrier lowering (DIBL) effect becomes prominent which intern, reduces the threshold voltage of the device, It is also found that the threshold voltage under illuminated condition is smaller than that obtained under dark condition of the device. This is due to development of photo voltage at the Schottky gate, as optical radiation make junction forward biased

   optical power (Pin)for different gate length (L)

   Fig.6 shows the variation of the threshold voltage with incident optical power on the device, as the threshold voltage is decreased with increase in the incident optical power, for smaller change in the threshold voltages at 0.1mW is due to fact that developed photo voltage is too small to make a change in the device characteristics below the mentioned power level .Once the optical power increased beyond the active level ,the photo-generated carriers become sufficient in number to develop significant amount of photo voltage which forward biases the gate channel junction and reduce the threshold voltage of the device

   Fig.7. Variation of Threshold voltage ( V ) With gate length

   th

   (L) for different channel thickness

   Fig.7 shows the variation of threshold voltage with gate length under illuminated condition of the device for different thickness (a) it is observed that threshold voltage degradation due to short channel effect can optimized by reducing the channel thickness.

5. CONCLUSIONS:-

In this paper a 2D channel potential has been modeled for optically depleted GaAs MESFET device with a Gaussian like doping profile in the vertical direction

The potential distribution has been derived by solving 2D Poissons equation using superposition method .optical radiation dependent on threshold voltage have been derived and compare with dark condition .The observed threshold voltage degradation due to short channel effects can be minimized by reducing channel thickness of GaAs MESFET .The proposed model results are found to be match with MATLAB

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