Calculation of the dynamic response of Schottky barriers with a continuous distribution of gap states

Abstract

A full numerical analysis has been developed of the thermal transient and ac dynamic response of a Schottky-barrier space-charge region for a semiconductor with an arbitrary continuous density of gap states $g(E)$. These techniques are applied specifically to a calculation of current and capacitance deep-level transient spectroscopy as well as complex admittance versus temperature. We illustrate our methods on a host of hypothetical examples with densities of states similar to those obtained from studies of crystalline and amorphous semiconductors. A detailed comparison is made between the usual discrete-level case for material with a large dominant dopant level and the case of a material with a large and continuous density of deep-gap states. We also discuss the case of spatially nonuniform material and consider the case of fairly insulating material for which the equilibrium Fermi level lies near midgap. The application of our methods to actual analysis of experimental data of amorphous Si-H alloys to obtain a detailed picture of $g(E)$ is given in an experimental companion paper.