**2. General characteristics of the model**

The major features of this study are:

To solve the system of the two dimensional partial differential equations, we based for the works of Chin and Wu (1992, 1993), the Green's function technique is used in these

references to solved the two dimensional Poisson's equation, this technique gives an acceptable distribution of the space charge and a form of the depletion area in agreement with the physical phenomena specific to this device.

Analytical Model and Numerical Simulation

for the Transconductance and Drain Conductance of GaAs MESFETs 261

(4)

(5)

( ,0) 0 *x* (6)

(0, ) *y Vb Vg* (7)

(,) *L y Vd Vb Vg* (8)

*y Ly* (9)

(10)

<sup>0</sup> *<sup>n</sup> <sup>S</sup> <sup>E</sup>* (11)

(,) () (,) *xy Uy xy* (3)

where

and

the two-dimensional equation (Eq. 5).

is the built-in voltage of the Schottky barrier.

**2.2. Boundary conditions** 

conditions expressed as:

following condition:

and

 

<sup>2</sup> ( ) ( ) *<sup>d</sup> eN y U y dy* 

 2 2 2 2 , , <sup>0</sup> *xy xy*

 

In such a way, according to formula (3 – 5) the process of solving the initial Poisson's equation consists of looking-for of solution to one-dimensional equation (Eq. 4) and solving

The above solution of the Poisson's equation has to verify the equations and boundary

where *Vg* is the intrinsic gate-source voltage, *Vd* is the intrinsic drain-source voltage and *Vb*

If the drain voltage is equal to zero, the symmetry between the two gate-sides leads to the

0 0 (0, ) ( , ) *Vd Vd*

At the first point of the pinch-off, the electron velocity attains its maximum and the electric

(,)

*x*

( ,)

The electric field must vanish in the depletion-layer edges at both gate-sides; this field may

*L a x y <sup>E</sup>*

*S*

 

field with drain side's corresponds to the saturation field *ES*.

cause a large current flow. Therefore, it may be written:

 

*x y*

To determine the depletion-layer width, we have considered first the one-dimensional approximation (Sze and Ng, 2007), then we add the corrective which results from the twodimensional analysis.

To determine the electron mobility law in the semiconductor, we have considered that described by Chang and Day (1989).

To calculate the drain current expression as a function of the drain-source and gate-source voltages, we divided the channel under the gate in regions (linear, non-linear and saturated) according to the electric field.

In order to simplify the mathematical study and consequently the numerical simulation, we used some assumptions and approximations.

To determine the *I-V* extrinsic characteristics in different operations regimes, we used the iterative method.

To determine the transconductance and drain conductance as a function of the drain-source and gate-source voltages in different operations regimes, we based also for the numerical simulation methods.
