Nonlinear discretization scheme for the density-gradient equations

Density-gradient theory enables engineering-oriented analyses of electronic devices in which quantum confinement and tunneling phenomena are significant (Ancona and Tiersten, 1987; Ancona, 1990; Ancona et al, 1999). A nonlinear three-point discretization of the density-gradient equations is presented. The new method, an exponential-fitting scheme, is evaluated using numerical examples involving both quantum confinement and tunneling. The nonlinear discretization is shown to perform far better than the conventional linear version allowing for a substantial easing in the mesh refinement, especially in tunneling problems.