Calculations of collector current spreading and low-field avalanche generation in silicon bipolar transistors

The theory for bipolar transistors operated at high collector currents is weak. Controversy exists as to when (or if) lateral current spreading dominates over the Kirk effect. This paper attempts to answer this question. The output characteristics of silicon bipolar transistors in the common emitter configuration are analyzed in detail. The analysis proceeds by extracting the values of transistor generation current (due to small amounts of collector multiplication) from experiment, fitting these values to a model which accounts for the modulation of the collector depletion layer by mobile space charge and the lateral spreading of collector current. It is found that a continuous and gradual increase in collector effective area occurs as the collector current increases. In this manner the deleterious effects of high current density are moderated. By accounting for this effect, cut-off frequency calculations are brought into good agreement with experiment. As an independent check on the validity of the analysis, electron ionization rates are obtained, which are in good agreement with values in the literature. Effects associated with emitter crowding are also shown to be unimportant in the structures investigated.