Symmetry in Nonlinear Mathematical Physics - 2009

Rita Tracina (University of Catania, Italy)

Nonclassical symmetry reductions for the quantum drift-diffusion model of semiconductors

For the description of charge carrier transport in semiconductors, continuum models have interested in the last years applied mathematicians and engineers on account of their applications in the design of electron devices. Simple macroscopic models widely used in engineering applications are the drift-diffusion ones. They are constituted by the balance equation for electron density and the Poisson equation for the electric potential. However, with shrinking dimensions of submicron semiconductor devices, the quantum effects are no longer negligible. One way to include them is based on the Bohm potential. The resulting quantum drift-diffusion (QDD) model consists of a further-order nonlinear parabolic equation for the electron density. New symmetry reductions and exact solutions are presented for the one-dimensional QDD model. The symmetry reductions are derived by using the nonclassical method developed by Bluman and Cole.

This is a jointly work with J. Ramírez (Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Spain).