A method for bipolar semiconductor device modeling implementable in circuit simulators

Abstract

This paper presents a method for modeling power semiconductor devices based on the unidimensional solution of the diffusion equation describing the behavior of charge in low doped zones. The method uses a variational approach, and the finite elements method, which allows one to transform a partial differential equation in space and time into a finite set of differential equations in time only. As the used functional is quadratic the matrices associated with this set of differential equations are tridiagonal and symmetric which enables a network analogy and the solution to be tried oriented to circuit simulator. This electrical network model is then linked with other circuits, modeling the remaining zones of the device, in order to make a circuit representation of the same one. Modular models for the circuit simulation of generic p-i-n diodes and bipolar junction transistors are presented as well as some simulation results.