Algorithms and Large Signal Models for Efficient Simulation of Transients in Bipolar Semiconductor Devices

In this research, the models and algorithms necessary to dynamically display the distribution of carrier densities, currents, and potentials at different points in time in bipolar semiconductor devices were developed. The research objectives are to enhance understanding of the phenomena of importance and to provide a simulator for the behavior of semiconductor devices in circuits. As an example, a student might use the simulator to study the effect of temperature or radiation on the performance of a transistor amplifier. The simulator was designed with students in mind, and the simulation software must function on contemporary personal computers widely available to students. Because the simulator was written for computers in the contemporary personal computer class, device models and computer algorithms incorporated in the simulator must require the minimum number of computations possible. In other words, the models and algorithms must be efficient. Once the efficient algorithms and models are available, the simulator could be used to simulate large circuits on computers more powerful than personal computers. The three formulations of simulation typically used are: the finite difference method for discretization in time and space, the finite element method for discretization in space used with the finite difference method for discretization in time, and the lumped element method for discretization in space used with the finite difference method for discretization in time. These three methods were compared quantitatively, and the lumped element method was selected because of its efficiency. In the lumped element method, neutral transport regions are represented by a tandem connection of sections with parameters that characterize carrier storage, transport, and recombination. In these sections, relationships between variables are linear over a wide range of operation. While models of the junction are essentially nonlinear, they can be idealized and represented compactly. Interpolation is added subsequently to yield distributions of variables over the device. When the finite element method is used to simulate dynamic systems, a lumping approximation is usually employed. A critical comparison of the finite element method with the lumping approximation and the lumped element method shows that they yield identical results under a limited set of conditions.