Valley splitting control in ${\mathrm{SiO}}_2/{\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}\mathrm{O}}_2$ quantum wells in the quantum Hall regime

${\mathrm{SiO}}_2/{\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}\mathrm{O}}_2$ quantum wells fabricated on SIMOX silicon-on-insulator substrates are examined in the quantized Hall regime. An 8 nm quantum well behaves as a single layer of two-dimensional electrons at accessible gate voltages. By using front and back gates, the wave function in the confinement direction can be shifted continuously between two ${\mathrm{SiO}}_2/\mathrm{Si}$ interfaces formed through different processes. We find that this results in a continuous evolution of the valley splitting which is asymmetric with electrical gate bias. Wider quantum wells show bilayer behavior where the valley splitting is different in each layer, demonstrating that its control shown by the 8 nm well arises due to the different properties of the two interfaces. Estimates of the valley splitting are made through Landau level coincidences and activation energies. The coincidence between Landau levels of opposite spin, opposite valley, and like cyclotron indices at $\nu =6\mathrm{}$ shows anticrossing behavior.