Finite difference numerical solution of Poisson equation in a Schottky barrier diode using maple

In the present study, we determine using Maple software [1] the exact numerical solution of Poisson's equation in a Schottky barrier junction according to three different approaches. First, we consider the simple case where the space charge zone is depleted and the doping impurities are fully ionized. Then we treat the case where the space charge zone is non-depleted and the doping impurities are fully ionized. Finally, we solve rigorously the more general case where the space charge zone is non-depleted and the doping impurities are partially ionized. We use two different methods to solve the problem. In the former one, the distance of each point to the junction is calculated as a function of its potential. In the second one, we use a finite difference scheme to solve the Poisson's equation. The calculations may be integrated into a course on semiconductor devices to show the use of Maple capabilities in the resolution of the second order non-linear differential equation governing the potential in electronic devices.