Theory of Electron Tunneling in Semiconductor Junctions

A formalism is developed for calculating the electric current in a semiconductor junction of the Esaki type due to direct tunneling of electrons between the valence and conduction bands. This formalism expresses the current at any temperature and bias in terms of a tunneling amplitude, whose absolute square is essentially the probability that an electron incident on the junction from either side will be seen eventually on the other side. The methods of time-independent perturbation theory are used to calculate the tunneling amplitude for a model in which the junction electric field is piecewise constant and the effective-mass approximation is applicable. The result of this calculation is used to compute explicitly the tunneling current as a function of bias and temperature. The formalism also yields a general variational principle for the tunneling amplitude.