Modeling of avalanche effect in integral charge control model

A compact model for bipolar transistors (integral charge control model) which includes many high-level effects has recently been developed. This model has been shown to give much more accurate results than the conventional Ebers-Moll model. However, avalanche effects have not been included previously. Here a simple expression is developed for the avalanche current generated in the collector junction of a transistor. Avalanche current calculated from this expression agrees very well with the results of exact numerical calculations, which solve the Poisson equation and continuity equations for a realistic structure. With this simple expression, avalanche effects can be incorporated into the integral charge control model with the addition of three model parameters. Output characteristics have been calculated with such a modified integral charge control model and compare very well with measured results demonstrating the accuracy of the avalanche modeling.