High injection in epitaxial transistors

An analysis of base widening and the current dependence of the cutoff frequency f
T
has been given previously by Kirk. His approximate analysis is based on the location of the edges of transition regions, whose definition becomes problematic in transistors having nonuniform base doping and at high current levels. An alternate theory of f
T
falloff at high currents has recently been given with the implication that base widening does not occur. This paper presents numerical solutions based on a one-dimensional model (with realistic doping profile) of an npn epitaxial transistor at low reverse collector bias at various current densities ranging from low level injection to high level injection. Solutions for electric field, hole and electron densities as functions of distance are shown. At low-injection levels, a high-field region exists near the transition between base and expitaxial layer. This high-field region is relocated to the interface between epitaxial layer and substrate under high injection conditions. Numerical solutions of delay time as a function of current density, calculated frown a charge control point of view, are also given. The results show that the delay time increases sharply in the current range where "field relocation" takes place. Whether "base widening" occurs is a matter of semantics. However, the physically observable effects predicted by Kirk for a one-dimensional structure are shown to occur.