Valley Splitting in Silicon from the Interference Pattern of Quantum Oscillations

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined in silicon metal oxide semiconductor Hall-bar transistors. These silicon metal oxide semiconductor Hall bars are made by advanced semiconductor manufacturing on 300 mm silicon wafers and support a two-dimensional electron gas of high quality with a maximum mobility of 17.6×10^{3}  cm^{2}/Vs and minimum percolation density of 3.45×10^{10}  cm^{-2}. Because of the low disorder, we observe beatings in the Shubnikov-de Haas oscillations that arise from the energy splitting of the two low-lying conduction band valleys. From the analysis of the oscillations beating patterns up to T=1.7  K, we estimate a maximum valley splitting of ΔE_{VS}=8.2  meV at a density of 6.8×10^{12}  cm^{-2}. Furthermore, the valley splitting increases with density at a rate consistent with theoretical predictions for a near-ideal semiconductor-oxide interface.