Abstract
Fundamental analysis of transistors in one dimension is described. The basic equations are presented in a normalised form together with the data, consisting of example impurity doping profiles of two widely differing real transistors, and comprehensive models for recombination and carrier mobility. These equations are developed in integral and finite-difference form, leading to the computer programs ODESSA and ODETTA. The former is an extensively developed steady-state program now in wide and general use. Examples of its application to the two devices above are given. The program ODETTA is a large signal, voltage driven transient analysis program based on a time-dependent implementation of the Gummel algorithm. The program is stable under all arbitrary driving voltages V[eb] and V[cb], and is shown applied to the same two transistors. One of these is a particularly difficult device to analyse numerically. Under normal operating conditions transient effects dominate its performance, so that its observed behaviour is very different from steady state values. ODETTA handles the problem well and shows how these effects arise.