New Quantum and Electronic Theory of Metal-Semiconductor Contacts

The Schottky, Davydov, Bardeen, and Heine theories of metal-semiconductor contacts are improved and developed by using a new general expression for the junction capacitance and by accounting for quantum-mechanical tunneling of free electrons from the metal into the semiconductor's forbidden energy gap. The Poisson equation for electric field and potential is first solved to obtain general expressions for the junction capacitance, the built-in voltage on the junction capacitance, and the barrier height. The electron wave function is then calculated using effective-mass and WKB approximations and the continuity of probability density and current at the metal-semiconductor interface. Finally, the density of states of electrons which tunnel from the metal into the semiconductor's forbidden energy gap is deduced from the electron wave function. In practice, these calculations are intradependent and cannot be completely separated. For metal—$n$-type semiconductor contacts, the most significant differences between this theory and previous theories are the increases of both the energy barrier height and the built-in voltage of the contact capacitance. For metal—$p$-type semiconductor contacts, tunneling of electrons from the metal to the semiconductor reduces the barrier height and width and built-in voltage of the contact capacitance. As a consequence, the hole-tunneling probability and reverse current are both increased. The results agree with published experimental measurements of capacitance, photoemission, and current.