Valley splitting in the disordered and deterministic regimes

We show that there are two distinct ways to influence valley splitting in Si/SiGe devices: deterministically, using sharp features in the heterostructure, and through disorder, where valley splitting arises due to the random distribution of Ge atoms in the crystal lattice structure. Most current devices operate in the disordered regime: to give rise to significant deterministic valley splitting, the sharp features of the interface must be thinner than 3 monolayers. While difficult to construct, devices in the deterministic regime, like the recently-proposed wiggle well, can achieve high valley splittings with 100% yield. In the disordered regime, the average valley splitting can be enhanced by increasing the average Ge concentration. While this strategy does not require sharp heterostructure features and is not significantly affected by interface steps, it is statistical in nature, so there is always a nonzero probability of low valley splitting. We show that the ability to reposition a dot makes it possible to achieve high valley splittings with high yield.