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

The barrier heights in ideal metal-semiconductor contacts are determined by the continuum of the metal-induced gap states (MIGS). In generalizing Paulingʹs concept, the charge transfer across such interfaces may be modeled by the difference Xm − Xs 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 φBn = φcnl + Sx(Xm − Xs). The zero-chargetransfer barrier heights φcnl were calculated for almost all semiconductors. The slope parameters Sx are determined by the density of states of the MIG states, the thickness of the respective interfacial double layer, and the interface dielectric constant ϵi. 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 Sx to vary proportional to (ϵ∞ − 1)2ϵi where ϵ∞ is the electronic contribution to the static dielectric constant of the semiconductor. This result confirms a previously found semi-empirical rule.