Extending the numerov process to the semiconductor transport equations

Some classes of differential equations are amenable to a numerical solution based on the Numerov process (NP), whose accuracy can be up to two orders of magnitude superior with respect to the standard finite-difference or box-integration methods, with a negligible increase in the computational cost. The paper shows that the equations describing charge transport in solid-state devices can suitably be manipulated to make the application of NP possible. Also, thanks to a specifically-tailored algebraic solver, the 1D Poisson equation is fully decoupled from the transport equation, this reducing the procedure to the solution of a single non-linear equation. The example of an Ovonic device is considered, used as selector in phase-change memory applications.