Analyticity of the phase shift and reflectivity of electrons at a metal-semiconductor interface

The reflection phase shift and reflectivity as a function of electron energy at a metal-semiconductor interface are analytically related. Specifically, conjugate van Hove-type singularities are expected near a semiconductor band edge. These fundamental relations are investigated for the Pb-Si(111) interface by angle-resolved photoemission measurements of thin Pb films on Si(111) as quantum wells. A detailed determination of the reflectivity and phase shift of the Pb valence electrons across the Si valence-band edge is facilitated by using submonolayer amounts of Au as an interfactant to systematically adjust the interface potential.