Unified modeling scheme for semiconductor devices with applications of state-variable analysis

A unified scheme for modeling semiconductor devices is presented. The main feature of this scheme is that it can be directly applied to state-variable analysis. A distributed system based on continuity, current-flow relationship, and Poisson's equations is shown to be approximated by a lumped RC network with arbitrary accuracy. By means of this modeling scheme and state-variable analysis technique, a network composed of semiconductor devices is formulated by a set of ordinary differential equations. The lumped RC network contains some C-only cutsets and circuits, which correspond to Poisson's equation and the conservative nature of the electrostatic field, respectively. From these topological structures, a set of state equations of a minimum number of independent variables is systematically obtained. An example of formulating a set of state equations of a twodimensional transistor model is given as are suggestions for applying the modeling scheme to various kinds of semiconductor devices. The modeling scheme proposed can be efficiently applied to the analysis of both the device itself and a network consisting of many devices over a wide range of conditions.