# Semiconductors/MESFET Transistors

## MESFET Operation[edit]

Assume an N channel MESFET with uniform doping and sharp depletion region shown in figure 1.

The depletion region is given by the depletion width for a diode. Where the voltage is the voltage from the gate to the channel, where the channel voltage is given for a position x along the channel as .

- (1)

The current density in the channel is given by:

where:

Therefore,

Substituting from equation 1:

One defines constant Β as the channel conductance with no depletion. And the work function to deplete the channel W_{00} [1]:

We now define V_{to}, the voltage such that the channel is pinched off. d is the ratio of channel depletion to maximum depletion for the drain. s the ratio of channel depletion to maximum depletion for the source.

Substituting:

- (2)

Equation 2 is **Shockley's expression** [2] for drain current in the linear region. When the device enters saturation, one end is pinched off(normally the drain). Thus $d=1$ and one may derive the equation for the saturation region:

## Simpler Model[edit]

### General power law:[edit]

It was found that a general power law provided a better fit for real devices [3].

Where Q is dependent on the doping profile and a good fit is usually obtained for Q between 1.5 and 3. A general power law is approximately equal to Shockley's equation for Q = 2.4. Β is also empirically chosen and is proportion to the previous Β

Modelling the various regions is done though model binning. This however infers that a sharp transition exists from one region to another, which may not be accurate.

## References[edit]

[1] A. E. Parker. Design System for Locally Fabricated Gallium Arsenide Digital Integrated Circuits. PhD thesis, Sydney University, 1990.

[2] W. Shockley. A unipolar field-effect transistor. IEEE Trans/ Electron Devices, 20(11):1365–1376, November 1952.

[3] I. Richer and R.D. Middlebrook. Power-law nature of field-effect transistor experimental characteristics. Proc. IEEE, 51(8):1145–1146, August 1963.