Properties of an Arbitrarily Doped Field-Effect Transistor

Citation

Richer, Ira (1964) Properties of an Arbitrarily Doped Field-Effect Transistor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/E5RR-2P55. https://resolver.caltech.edu/CaltechETD:etd-09272002-160258

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The properties of p-n junction field-effect transistors (FET's) are formulated on a general basis, in terms of an arbitrary doping profile (i.e. arbitrary gate-channel impurity distribution). The external behavior is shown to be quite insensitive to the doping profile, provided that the profile satisfies certain weak restrictions. Essentially all practical structures are included in the restricted theory. A theoretical basis is thus provided for the much-used empirical conclusion that widely different types of FET's exhibit similar functional behavior. More specifically, upper and lower bounds are obtained on the normalized transconductance, drain current, input capacitance, and bias point for zero temperature coefficient of the drain current, and on the voltage-dependent parts of various figures of merit. In each case the bounds represent the solutions of two analytically simple structures, a step-junction FET and a delta-junction FET. Many practical implications stem from these results. Finally, a complete, small-signal, low-frequency equivalent circuit for an arbitrarily doped FET is developed by considering the capacitive current that flows between the channel and the gate. Beyond pinch-off a "new" element, the forward transfer capacitance, is present in the circuit. Below pinch-off the theory predicts that the output capacitance [C22] and the reverse transfer capacitance [C12] differ, and in fact that [C22 - C12 < 0], whereas earlier theories and intuition indicate that [C22 - C12 = 0]. Measurements on a wide variety of FET's substantiate these theoretical results. The frequency limitations of the equivalent circuit and, indeed, of all the results obtained are shown to arise from the breakdown of the gradual approximation.

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