Valley Splitting in V-Shaped Quantum Wells

The valley splitting energy difference between the states of the lowest doublet in strained silicon quantum wells with a V-shaped potential is calculated variationally using a two-band tight-binding model. The approximation is valid for a moderately long approximately 5.5 – 13.5 nm quantum well with a V-shaped potential which can be produced by a realistic delta-doping on the order of nd 1012 cm−2. The splitting versus applied field steepness of the V-shaped potential curves show interesting behavior: a single minimum and for some doublets, a parity reversal as the field is increased. These characteristics are explained through an analysis of the variational wave function and energy functional