Image-potential band-gap narrowing at a metal/semiconductor interface

The GW approximation is used to systematically revisit the image-potential band-gap narrowing at metal/semiconductor interfaces proposed by Inkson in the 1970s. Here we have questioned how the narrowing, is calculated from quasiparticle energy spectra for the jellium/Si interface depends on r(s) of the jellium. The gap narrowing is found to only weakly depend on r(s) (i.e., narrowing similar or equal to 0.3 eV even for a large r(s) of 6). Hence we can turn to a smaller polarizability in the semiconductor side as an important factor in looking for larger narrowing.