Numerical model for degenerate and heterostructure semiconductor devices

A one-dimensional finite-difference numerical model appropriate for devices which require degenerate statistics to describe the carrier concentrations is reported. The Joyce–Dixon approximations [Appl. Phys. Lett. 31, 354 (1977)] to Fermi–Dirac statistics were used and found to be efficient and accurate methods to determine carrier concentrations, to calculate derivatives required in the iterative solution of the equations in the numerical model, and to compare to nondegenerate (i.e., Boltzmann statistics) models. For degenerate carrier statistics and heterostructure devices the Scharfetter–Gummell equations [IEEE Trans. Electron Devices ED-16, 64 (1969)] for the current densities must be modified to include the degenerate Einstein relations and variation of the density of states with position. These modifications, as well the possibilities of using the thermodynamic formulation of current density, are described.