Theory of Tunneling Across Semiconductor Junctions

Abstract

The theory of tunnel diodes is reviewed, and a method developed for calculating the direct tunneling current. The formulation follows Fredkin and Wanier, but since the crystal momentum representation is used, the final details resemble work of Keldysh and of Kane. The method is applicable when the field is not assumed constant throughout the junction region. The calculated transmission probability for an electron between states both sufficiently far from an energy extremum in the Brillouin zone agrees with the usual expressions; but in the case that either the initial or final state nears a band extremum, the transmission probability is found to go continuously to zero.