Conformal mapping techniques for the analytical, two-dimensional calculation of currents in lateral bipolar transistor structures

Abstract Compact modelling of lateral bipolar transistors (available in CMOS and in bipolar processes) in a circuit designers' environment is still carried out by using theoretical approaches, which were developed for vertical transistors. These models do not reflect the two- or three-dimensionality of the current flow in these devices correctly. In this paper, an analytical theory of two-dimensional current flow in lateral bipolar transistors is presented. This theoretical approach uses conformal mapping techniques extensively. The basic mathematical and physical principles are explained, and a specially developed decomposition strategy for lateral structures is presented. With this background, a two-dimensional description of the current flow at all injection levels in these devices is derived in an analytical closed form. The presented results are in excellent agreement with numerical simulations and reveal significant differences to quasi-one-dimensional models with respect to the prediction of layout- and process-related device behaviour.