The critical role of substrate disorder in valley splitting in Si quantum wells

Motivated by theoretical predictions that spatially complex concentration modulations of Si and Ge can increase the valley splitting in quantum wells, we grow and characterize Si/SiGe heterostructures with a thin, pure Ge layer at the top of the quantum well using chemical vapor deposition. We show that these heterostructures remain hosts for high-mobility electron gases. We measure two quantum wells with approximately five monolayers of pure Ge at the upper barrier, finding mobilities as high as 70,000 cm\(^2\)/Vs, compared to 100,000 cm\(^2\)/Vs measured in samples with no Ge layer. Activation energy measurements in quantum Hall states corresponding to Fermi levels in the gap between different valley states reveal energy gaps ranging from 30 to over 200 \(\mu\)eV, and we extract a surprisingly strong dependence of the energy gap on electron density. We interpret our results using tight binding theory and argue that our results are evidence that atomic scale disorder at the quantum well interface dominates the behavior of the valley splittings of these modified heterostructures.