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

number of transient and steady-state Þnite element formulations of the semiconductor drift-di¤usion equations are studied and compared with respect to their accuracy and e¦ciency 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-di¤usion and PoissonÕs 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 di¤erent time integration methods a¤ect 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