Effects of thermal excitation and quantum-mechanical transmission on photothreshold determination of Schottky barrier height

Abstract

Quantum-mechanical electron transmission effects on photothreshold determination in Schottky barriers with high electric fields are shown to produce a strong effect on apparent photothresholds without a concomitant large change in shape of the photoresponse curve. Quantum-mechanical electron transmission probabilities are determined by numerical integration of the Schroedinger equation for a Schottky barrier model which includes Thomas-Fermi shielding in the metal, image force lowering in the semiconductor, and conservation of transverse momentum at the metal-semiconductor interface. Results are presented for <111> n-type Si and n-type GaAs. In the case of Si, conservation of transverse momentum at the interface produces a discontinuity in the electron kinetic energy associated with motion normal to the interface but does not greatly affect the transmission probability. Using these results, the difference between the true barrier height, qΦ B , and the apparent barrier height, qΦ A , is calculated as a function of temperature, doping, and electric field at the metal-semiconductor interface. qΦ A is defined as the intercept on the hv axis of the slope of a plot of (photocurrent per absorbed photon) 1 2 versus quantum energy, hv. Effects of barrier curvature due to doping are negligible for impurity densities below about 10 18 cm −3 for Si and 10 17 cm −3 for GaAs. Values of q( Φ B - Φ A ) in excess of 50 meV occur in many cases. The corrections derived are used to reinterpret previously reported measurements of the dependence of Schottky barrier height on temperature and impurity concentration.