The one-electron (Bethe-Sommerfeld) model of electron tunneling is formulated to describe tunneling when the curvature (electron mass) and centroid of the one-electron constant-energy surfaces vary across the junction. The conductance for an abrupt GaAs $p-n$ tunnel diode is calculated and shown to exhibit minima near zero bias for highly asymmetrical doping ratios. The conductance of metal-oxide-semimetal (M-O-SM) tunnel junctions is evaluated both with and without the inclusion of space-charge effects and of surface states. All calculations are performed using solvable models for which the WKBJ approximation is not imposed. Neither the removal of the WKBJ approximation nor the space-charge effects give rise to maxima in the conductance of the M-O-SM junctions near a band edge.

• Received 2 June 1966

DOI:https://doi.org/10.1103/PhysRev.152.683