A Simple Derivation of Field-Effect Transistor Characteristics

In the conventional treatment of the field effect transistor, the first step is the specification of an impurity profile that describes the nature of the gate-channel contact. Solutions for the static and small-signal characteristics are then valid only for the particular impurity profile chosen, and must be repeated from the beginning for different structures. The purpose of this communication is to present a simple, though approximate, development of the characteristics of an FET without specifying the detailed nature of the structure. The charge-control approach is used, and it is shown that in the pinch-off region the relation between the drain current and the gate-source voltage is approximately square law. The results are applicable to all gate-channel structures, including the insulated gate types