Flow of Electrons and Holes through the Surface Barrier Region in Point Contact Rectification

Equations are derived for the flow of electrons and holes through a surface barrier region by using the emission theory. The solution allows for nonequilibrium concentration of carriers on the semiconductor side of the barrier. It also allows for the possibility that part of the applied potential is between the metal surface and the semiconductor surface, as would occur if the surface states do not remain in equilibrium with the metal. The solution for the rectification characteristic is completed for the special case of small currents by combining the barrier region equations with the solution for current flow beyond the barrier region. The resulting equations are compared with those for $p-n$ junctions, and the implications are discussed with regard to the relative roles of diffusion and emission in the flow of electrons and holes. Finally, the small current equations are compared with experiment, with a discussion of the evidence for the existence of an inter-surface potential.