Theory of Surface States

TLDR

Surface states are invoked to explain metal‑to‑semiconductor junctions and free semiconductor surfaces, yet localized states cannot exist in metal contacts and the tail length of metal wave functions has often been neglected. The authors show that virtual or resonance surface states arise from the tails of metal wave functions rather than from separate localized states. They estimate the tail length, demonstrate that these virtual states behave like localized ones, and discuss how oxide layers, metal choice, high doping, and cesium layers affect barrier height and work function.

Abstract

The properties of metal-to-semiconductor junctions and of free semiconductor surfaces are usually explained on the basis of surface states. The theory of the metal contacts is discussed critically, because strictly speaking localized surface states cannot exist in such junctions. However, it is shown that virtual or resonance surface states can exist which behave for practical purposes in the same way. They are really the tails of the metal wave functions rather than separate states. In the past, the length of this tail has often been ignored. Some estimates of its length are made and its consequences pointed out. A semiquantitative discussion is given of various recent data, including the effect of an oxide layer on barrier height, the variation of barrier height with the metal, the work function of a free surface at high doping, and the effect of a cesium layer on the work function.