Two-dimensional finite element modeling of NPN devices

Our program for semiconductor analysis by finite elements has previously been applied to the analysis of IGFET devices. In this paper we describe the application of an experimental program to a state-of-the-art bipolar transistor in inverse active mode. We compute the hole and electron current distributions across the collector-base junction at low forward biases (the base-emitter junction is shorted). Our results show that (a) the injected hole current (from base to collector) is nearly uniform, and (b) the injected electron current (from collector to base) is greatest under the emitter, decreases under the oxide contact, and rises under the base contact. We conclude with a description of a novel method for solving the difficult problem of maintaining current conservation which is valid for finite elements of arbitrary approximation order. This new method employs Gummel's integral formula for the currents, but avoids the nonphysical "gaps" in current flow.