BIPOLAR THEORY OF METAL–SEMICONDUCTOR CONTACTS UNDER ARBITRARY INJECTION LEVELS

Abstract

Metal–semiconductor contacts have been known empirically to obey a modified diode equation I = Is (exp qV/akT −1), where the parameter a often took values greater than the theoretical limit of two. Previous theories could not simply account for this anomaly. The model presented in this paper considers one-dimensional bipolar flow of carriers with zero recombination in a homogeneous semiconductor filament with a rectifying and an ohmic contact at opposite ends. The zero-electron-current theory by Borneman et al. (1955), valid for low injection levels, is extended to arbitrary injection levels by the use of the Misawa junction relations (1955). Then the nonzero-electron-current theory is developed. This theory shows that a is unity for low injection into extrinsic semiconductors and that a = (3b − M)/(b − M) for arbitrary injection into intrinsic semiconductors and for high injection into extrinsic semiconductors; M is the electron-to-hole current ratio and b is the electron-to-hole mobility ratio. Thus a can take any value depending on the magnitude of M/b.