Valley splitting in silicon from the interference pattern of quantum oscillations

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

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