Distributed transmission line model for the base transit time of a nonuniformly doped bipolar junction transistor

Abstract

Transit time of a Bipolar Junction Transistor (BJT) is an important parameter. It is required in determining different performance figures of a BJT. In the present work the current-continuity equations for electrons and holes; expressions for Shockley- Reed-Hall and Auger recombination are used in obtaining first order differential equations for voltage and current. These two equations are rearranged in a form that is analogous to the well-known time-independent Telegraphers' equation of transmission line analysis. In this thesis transmission line methods have been employed to construct an iterative procedure to find minority carrier distribution for a particular electron current density. Integration of this distribution over the base width will give the total electron charge for a given electron current density. The ratio of electron charge to current density gives the base transit time. Doping dependence of mobility, velocity saturation effect and bandgap narrowing effect within the base are also incorporated in the analysis. The present approach is easier and conceptually straightforward, in that this work did not lump the RIG's of the transmission line (base). Instead the base is segmented and classical TL analysis has been followed for each segment considering RIG's as strictly distributed element. Thus transmission line model has been employed in a more fundamental way and this is for the first time minority carrier distribution and base transit time of BJT's have been computed. Here both uniform and nonuniform base doping have been considered. Finally many other useful profiles, such as base transit time with base-emitter voltage (for both uniform and nonuniform doping), electron charge with current density and base-emitter voltage etc are obtained. It is observed that base transit time increases strongly with base width, but moderately with peak base-doping. It decreases with increasing slope of base-doping.