Size dependence of ’’effective’’ barrier heights of mixed-phase contacts

The literature currently abounds with experimental studies of Schottky barrier heights of various metals upon many semiconductors. Unfortunately, these studies present some puzzling aspects: (1) Commonly, barriers determined by C–V studies are larger than barriers determined by I–V studies, and (2) Results obtained by different workers under apparently identical conditions are not always similar. A possible explanation for such effects is simply that many/most contacts experimentally achieved are in fact multiphase; these different barrier-height regions could result from variations in the metallurgical reactions assumed by many current models of Schottky barrier energetics. The different barrier heights measured by different techniques follow directly from the functional form of the relevant probes (e.g., I–V would more heavily weight a low-barrier region). The lack of reproducibility would follow from kinetic aspects of the relevant metallurgical interactions. A recent publication discusses the functional form for I–V and C–V ’’effective’’ barrier heights from mixed-phase contacts isolated from one another. These results apply directly to mixed-phase contacts only if the linear dimensions of all contact regions are large compared to the Debye length of the substrate (≊0.1 μ for 1015 silicon). In this paper, we examine the effects of contact dimensions upon equilibrium potentials (e.g., band bending) as well as transport studies to infer ’’effective’’ barrier heights for truly mixed-phase contacts of varying dimensions but fixed area ratios.