Modification of upwind finite difference fractional step methods by the transient state of the semiconductor device

The mathematical model of the three‐dimensional semiconductor devices of heat conduction is described by a system of four quasi‐linear partial differential equations for initial boundary value problem. One equation of elliptic form is for the electric potential; two equations of convection‐dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Upwind finite difference fractional step methods are put forward. Some techniques, such as calculus of variations, energy method multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates and techniques are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008