A two-dimensional numerical analysis of a silicon N-P-N transistor

First-order transistor theory leads to conclusions that do not compare well with experimental results obtained for today´s transistors fabricated with sophisticated technology. In an effort to overcome this situation, Gummel [1] for the first time used a digital computer to give a unified exact treatment of one-dimensional device performance. This paper treats the two-dimensional case that must be considered in order to account for lateral current effects. A set of 3 nonlinear partial differential equations describing the flow of carriers within the transistor under steady-state conditions is formulated and solved iteratively. The potential distribution and the hole and electron distribution within the transistor are calculated, and two-dimensional plots of these quantities are given.