An accelerated monotone iterative method for the quantum-corrected energy transport model

A non-stationary monotone iterative method is proposed and analyzed for the quantum-corrected energy transport model in nanoscale semiconductor device simulation. For the density-gradient equations, it is analytically and numerically shown that the convergence rate of the method is optimal in the sense of Gummel’s decoupling iteration. This is a globally convergent method in the sense that the initial guess can be taken as a lower or an upper solution which is independent of applied voltages. The method integrates the monotone parameters, grid sizes, and Scharfetter–Gummel fitting in an adaptive and automatic way to treat the singularly perturbed nature of the model that incurs boundary, junction, and quantum potential layers in the device.