Effect of temperature on (TV) statics characteristics of GaAs Mesfet

The GaAs metal semiconductor field effect transistors called mesfets are the most active components used in microwave applications. To better exploit the performance of these components circuits, it is necessary to develop techniques for sophisticated numerical computation based on physical mechanisms that govern the operation of these devices. The static properties of GaAs MESFET could be determined from an original analytical study based on the resolution of the semiconductor fundamental equations. Then we will study the equation of thermal resistance as a function of the physical parameters of MESFETs by analogy electric thermal resistance RTH will be determined as the ratio of the difference of temperature on the thermal dissipation. The model took into account the difference between the temperature of the component and the ambient temperature and the effect of temperature on the parameters of the component.


1-Introduction:
The GaAs MESFETS are attractive devices for the used in microwave applications because of their relatively simple processing and they high-speed and low noise performance. The principal object in the paper is to propose a physical and analytical model of the characteristics current voltage of these devices with different laws of temperature. In the first ,we calculate the potential in the depletion layer due to the electrical charge formed under the gate which can be obtained by resolving the Poisson's equation by the conventional approximation ,Then we determine the drain current Id, the characteristic I-V obtained by this model, using effect of temperature on IV characterisation.

2-Calculation of the potential and the current in the channel:
To calculate the potential and the electric field under the gate, the channel is divided into two principal regions [1] as shown in figure (1): (2) Not controlled by the gate.
The electric potential due to the electrical charge Formed under the gate can given by [2]: With Nd(x,y) is the density of the donors,Vbi is the built in potential of Schottky barrier gate and ε is the permittivity.It should be noted that the approximations in (1) is based on the fact that the depletion layer thickness under the gate h(x) is a slowly varying function in the channel an is giving by: The channel potential is obtained by integration limits with y=h(x) The equation of the potential take a maximum of values in diffusion potential Vb i ( h y = ): The dimensional potential of the channel under the gate is given as follows: To calculate the drain current expression as a function of the drain voltage, we must make some approximations [3]: One neglects the current flow in the y-direction; this approximation is valid for the components with the length short gate.
An abrupt Schottky barrier junction.
is the electron mobility which depends of the electric field.
The drain current Id is considered positive in the drain source is obtained by integrating the current density Jx over the conducting channel section: The calculations made above don't take into account the contribution of the space charge region located below the gate contact. In order to consider this contribution we introduce the pinch off voltage V P at drain voltage equation and the saturation current Ip as following: Then the expression final of the current Id:

3.Effect of temperature .
The current characteristics are strongly related to the temperature. However, most simulations assume that the temperature of the component is constant, usually equal to the ambient temperature (300 ° K). A rigorous thermal model requires solving the equation of heat [4] ( The saturation velocity varies with temperature as according to Conger [3] the dependence of the threshold voltage may be approximately given by: The value of VT α is in the order of 1.2mV/°C.

Results and discussion
To show the effect of temperature on the characteristics (I-V), we perform the numerical simulation with the laws of mobility, velocity saturation and the threshold voltage as a function of temperature: As the diffusion voltage of the junction " bi V " varies with temperature as follows: The structure used for the calculation is shown in Figure (1 In table 1.we give the characteristic of our MESFET. The Figures (2) and (3)    The Figures (4) and (5) shows the variation of the mobility of electrons as a function of electric field for various values of temperature. We find that mobility is higher as the temperature decreases.  The same manner when the mobility varies, we present in Figures (7) and (8), the influence of temperature on the I-V characteristics of transistors "GAT1». We choose five values of temperature "T = 100 K ," "T = 170K " and "T = 240 K ","T = 310 K ","T = 380 K ",. From these figures, we find that the performance and reliability of the transistors are strongly influenced by temperature. Conduction along the channel is due to the majority carriers (electrons), it will be affected by the temperature variation for certain parameters (electron mobility, the Schottky barrier height, the saturation velocity, the dielectric constant and the same the specific resistance of ohmic contacts). If the temperature increases, thermal motion of the carriers also increases and hence the electron mobility of the channel decreases from expression (5), which causes a decrease in the current "Ids". Similarly the height of the potential barrier increases with increasing temperature from expression (8), therefore the width of the space charge region increases against the conductive channel narrows, and thus the drain current decreases.

5.Conclusion
In this study we have developed an analytical model to calculate the I-V characteristics of short gate length GaAs MESFET which takes into account the one-dimensional analysis of the charge distribution in the active region and incorporates the effect of temperature on field electron mobility, velocity saturation and effect of this parameter to the temperature expressions. Moreover, comparisons between the analytical models with different values of temperature showed the effect the output characteristics (I-V) of GaAs MESFET,then the MESFET structure allows very significant improvement in performance when it is operated at low temperatures.