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Interface states in a silicon/barrier junction break the silicon valleydegeneracy near the interface, a desirable feature for some Si quantumelectronics applications. Within a minimal multivalley tight-binding model inone dimension, we inspect here the spatial extent of these states into the Siand the barrier materials, as well as favorable conditions for its spontaneousformation. Our approach---based on Green's-function renormalization-decimationtechniques---is asymptotically exact for the infinite chain and shows theformation of these states regardless of whether or not a confining electricfield is applied. The renormalization language naturally leads to the centralrole played by the chemical bond of the atoms immediately across the interface.In the adopted decimation procedure, the convergence rate to a fixed pointdirectly relates the valley splitting and the spread of the wave function,consequently connecting the splitting to geometrical experimental parameterssuch as the capacitance of a two-dimensional electron gas---explicitlycalculated here. This should serve as a probe to identify such states as amechanism for enhanced valley splitting.

Splitting Valleys in Si/SiO$_2$: Identification and Control of Interface States