Comparative study of finite element formulations for the semiconductor drift-diffusion equations

Abstract

A number of transient and steady-state finite element formulations of the semiconductor drift-diffusion equations are studied and compared with respect to their accuracy and efficiency on a simple test structure (the Mock diode). A new formulation, with a consistent interpolation function used to represent the electron and hole carrier densities throughout the set of semiconductor drift-diffusion and Poisson's equations, is introduced. Results highlight the advantages in using consistent interpolation functions showing an increased accuracy in the calculated values and a saving in data storage and execution time. The results also illustrate how the use of different time integration methods affect the number of time steps required during transient simulations. The combination of the fully consistent DFUS with appropriate time integration methods is found to yield a saving of up to 80 per cent of the execution time required for standard spatial/temporal discretization techniques.

Enriched residual free bubbles for semiconductor device simulation

“…This is similar to the special shape functions developed by Machek and Selberherr [12] who combine the functions with an adaptive strategy. There also exists a method that applies a special "hybrid" element within the context of the finite volume technique [7,20], although in one case the authors note themselves that there is no proof that the technique might break down in particular cases.…”