1D Physical Non-Quasi Static BJT Circuit Model Based on the Equivalent Transmission Line Analysis

Abstract

We describe a novel physically based non-quasi-static (NQS) bipolar junction transistor (BJT) model derived from theoretical analysis of the equivalent transmission line representing the one-dimensional minority carrier transport trough silicon quasi-neutral regions (QNRs). The NQS BJT model holds for arbitrarily doped BJTs operating at all injection levels. It also incorporates most important high-injection effects (Webster effect, Kirk effect, Early effect) and heavy-doping effects (position-dependant mobility, life-time, and band-gap narrowing). Novel NQS BJT model is compact since it allows the DC, AC and transient circuit analysis to be performed with single BJT model representation. In addition, it includes for the first time the influence of momentum relaxation time term appearing in DD equations. The advantages of the proposed NQS BJT model over the standard quasi-static Gummel-Poon model are demonstrated with simulations of Si BJT and SiGe HBT devices as well as with stability analysis of bipolar differential amplifier.