# Parameter Analysis of the MESFET, Channel Width Calculation

Engineering design regularly involves an analysis of the formulae behind the various parameters of a system one is trying to build or improve. Some parameters are static, such a particular qualities of the materials being used. Perhaps there is a constraint made on the system or a goal, such as achieving function at a certain frequency or to reduce the size as much as possible. Today, many programs exist that can perform complicated calculations for the engineer. To construct a problem or calculation that produces the desired result may need more attention.

The MESFET uses a contact between n-doped semiconductor material with highly n-doped semiconductor material to form a junction field effect transistor. The great advantage of not using a p-doped semiconductor material is that the transistor can be built without using hole transfer. Since hole transfer is much slower than electron transfer, the MESFET can function much faster than other types of transistors.

For the MESFET, it may not be possible to examine all parameters. Consider first the following:

Potential variation along the channel (notice the similarity of the following to Ohm’s law, V=IR):

Where the resistance along the channel is:

Depletion Width (also referenced in the above formula) under the gate:

Pinch-off Voltage:

Threshold Voltage:

Built-in Potential:

The above formulas alone would be enough to put to use. While constructing a MESFET, it was found that the doping concentration of donor electrons in the channel played an important role. N_D, the donor doping concentration is found in most of the above formulas. The doping concentration is of particular importance, since it can be directly manipulated. The pinch-off voltage and the donor concentration are directly proportional. By achieving an estimate (or of the values are known) for other parameters, it would be possible to perform a parameter sweep for the MESFET system for doping concentration. This method may become critical for optimizing semiconductor device designs.

# MESFET Design Problem

Let’s say we want to calculate the channel width of an n-channel GaAs MESFET with a gold Schottky barrier contact. The barrier height (φ_bn) is 0.89 V. The temperature is 300 K. The n-channel doping N_d is 2*10^15 cm^(-3). Design the channel thickness such that V_T = +0.25V.