Two dimensional numerical simulation of negative differential mobility semiconducting devices

A numerical simulation in two spatial dimensions of negative differential mobility semiconducting devices is described. The simulation models time dependent operation of two or three terminal devices in an external circuit is presented. The mathematical model of the semiconductor consists of a set of nonlinear second-order partial differential equations which are solved on a rectangular mesh using explicit finite difference techniques. The external circuit is modeled using lumped linear elements and the resulting equations are solved using implicit techniques. The external circuit equations are coupled to the semiconductor equations by the current flow and potential at the device terminals. The solution of the resulting time dependent boundary value problem is a feature of the simulation which permits more realistic numerical analysis of NDM devices than was previously possible. The simulation is implemented using interactive computer graphics. As the solution evolves, displays of the potential, charge density and current flow in the semiconductor are available via a computer graphic terminal. Sample results of simulations of a negative differential mobility field effect transistor are presented.