  Interface states in a silicon/barrier junction break the silicon valley
degeneracy near the interface, a desirable feature for some Si quantum
electronics applications. Within a minimal multivalley tight-binding model in
one dimension, we inspect here the spatial extent of these states into the Si
and the barrier materials, as well as favorable conditions for its spontaneous
formation. Our approach---based on Green's-function renormalization-decimation
techniques---is asymptotically exact for the infinite chain and shows the
formation of these states regardless of whether or not a confining electric
field is applied. The renormalization language naturally leads to the central
role played by the chemical bond of the atoms immediately across the interface.
In the adopted decimation procedure, the convergence rate to a fixed point
directly relates the valley splitting and the spread of the wave function,
consequently connecting the splitting to geometrical experimental parameters
such as the capacitance of a two-dimensional electron gas---explicitly
calculated here. This should serve as a probe to identify such states as a
mechanism for enhanced valley splitting.
