Gaussian distribution of inhomogeneous barrier height in Si Schottky barriers

Deviations from the ideal characteristics in actual nearly ideal Schottky barriers (SBs) are due to inhomogeneous distributions of the Schottky barrier height (SBH) φ. By assuming the distribution as a Gaussian of the standard deviation σ from the ideal SBH ΦB, the SB characteristics have been qualitatively explained. However, the reason is unknown why the SBH distribution is a Gaussian. From the observed temperature dependence of σ, the distribution is found to exponentially decay more gradually than the Gaussian at large ΦB−φ values. According to our model of the local SBH lowering by ionized donors in Si SBs, the SBH distribution represents the spatial distribution of the ionized donors from the interface. The energy levels of the ionized donor decrease, become broad with approaching the interface, and are in ionization equilibrium with the Fermi level. The Gaussian distribution of the inhomogeneous SBH in Si SBs is consistently understood by our microscopic model.