One-dimensional all injection nonquasi-static models for arbitrarily doped quasi-neutral layers in bipolar junction transistors including plasma-induced energy-gap narrowing

Nonquasi-static circuit models accounting for carrier propagation delay in quasi-neutral layers are presented for bipolar junction transistors operating at all injection levels. The models are analytically derived from the Shockley equations for low injection and high injection and are empirically fitted for moderate injection. Large majority current flow in the base, which includes the case of low common-emitter current gain, is also taken into account. The models accommodate all doping profiles via a piecewise-exponential fitting scheme. For very high injection, the resulting electron-hole plasma reduces the energy gap, and this effect is also included. In the simulation of transient or frequency responses, the models provide better accuracy than does the conventional Gummel-Poon (GP) model