Chemical trends of barrier heights in metal-semiconductor contacts: on the theory of the slope parameter

Abstract

The barrier heights in ideal metal-semiconductor contacts are determined by the continuum of the metal-induced gap states (MIGS). In generalizing Pauling's concept, the charge transfer across such interfaces may be modeled by the difference X m − X s of the metal and the semiconductor electronegativities. For n-type semiconductors this MIGS-and-electronegativity model describes the chemical trends of the barrier heights as φ Bn = φ cnl + S x ( X m − X s). The zero-chargetransfer barrier heights φ cnl were calculated for almost all semiconductors. The slope parameters S x are determined by the density of states of the MIG states, the thickness of the respective interfacial double layer, and the interface dielectric constant ϵ i. The densities of states and decay lengths of the metal-induced gap states at their charge neutrality level were computed by others for some of the semiconductors. It is demonstrated that these theoretical data predict the slope parameters S x to vary proportional to (ϵ ∞ − 1) 2 ϵ i where ϵ ∞ is the electronic contribution to the static dielectric constant of the semiconductor. This result confirms a previously found semi-empirical rule.