The phase plane method for the solution of equations applied to semiconductor device modelling

Abstract

SUMMARYA new method is introduced for solving the sets of discretized non-linear equations which arise in the modelling of semiconductor microwave devices. The technique involves writing the functions to be solved as the right-hand sides of damped differential equations. Following the solution path of these equations in phase space leads to the equilibrium point which corresponds to the solution of the original set of equations. An error analysis is made of the method, and the method is illustrated by applying it to a model of a four-layer HEMT with two recesses and a fieldplate. In the early stages of developing the modelling equations for a new device, it is necessary to be able to add or subtract features into the equations; the main benefit of the method introduced here is that the minimum amount of preparation needs to be done in order to discretize the amended equations.

Integral evaluation in semiconductor device modelling using simulated annealing with Bose–Einstein statistics

“…The equations of Poisson, current continuity, energy transport and Schro¨dinger were solved numerically using the phase plane method [29]. In this method, the modelling equations can be changed easily without having to calculate the partial derivatives needed for the Newton method, although this leads to longer simulation times.…”