Microscopic calculation of electric field effects in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs tunnel structures

The combined effects of an applied electric field and the inherent crystal band structure on the tunneling of electrons through ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As barriers between field-free regions of GaAs are presented. A microscopic pseudopotential-based calculation is used. It includes the effect of all the higher conduction-band minima. We find that a finite field changes the electron tunneling probabilities and produces intervalley transfers if the energy of the tunneling particle is near a conduction-band minimum. The net result for direct-band-gap barriers is small, but for indirect-band-gap barriers a field-dependent transition region between a Γ behavior and an X behavior is found, with the electron transferred from an evanescent Γ state to a propagating X state in the barrier. The exact rate of transfer and proportion of the Γ and the X states’ contributions to the total wave function is found to be strongly dependent on the exact composition of the barrier material.