Numerical analysis of heterostructure semiconductor devices

A numerical method for analyzing heterostructure semiconductor devices is described. The macroscopic semiconductor equations for materials with position-dependent dielectric constant, bandgap, and densities-of-states are first cast into a form identical to that commonly used to model heavily doped semiconductors. Fermi-Dirac statistics are also included within this simple, Boltzmann-like formulation. Because of the similarity in formulation to that employed for heavily doped semiconductors, well-developed numerical techniques can be directly applied to heterostructure simulation. A simple one-dimensional, finite difference solution is presented. The accuracy of the numerical method is assessed by comparing numerical results with special-case, analytical solutions. Finally, we apply numerical simulation to two heterostructure devices: the heterostructure bipolar transistor (HBT) and the modulation doped field-effect transistor. The influence of a conduction band spike on the current-voltage characteristics of the HBT emitter-base junction is studied, and the variation with gate bias of the two-dimensional electron gas in a field-effect device is also investigated.