Schottky-Barrier Anomalies and Interface States

The surface‐state energy distribution at the metal‐semiconductor interface of a Schottky barrier has been deduced by combining a general theoretical analysis with one observed fact concerning the anomalous temperature dependence of the forward current on voltage. The fact, empirically found by Saxena, Padovani, and Sumner and by Padovani, is that the exponential terms of the forward‐current characteristic involve the sum of T plus T₀. Here T is the absolute temperature and T₀ is the empirical parameter which is essentially independent of temperature at constant current. This fact leads to the following new theoretical conclusions: (i) The surface‐state energy distribution near the Fermi level is a simple exponential with a characteristic e‐fold energy increase E₀ that can be computed from T₀. (ii) A plot of $T_0^{\text{−1}}$ vs voltage V yields essentially a straight line whose slope and intercept can be used to compute E₀ and the barrier height φ_B. (iii) In reverse bias, φ_B varies as the log of the surface electric field F, and E₀ can be computed from the slope. (iv) Finally, the log of the reverse current is proportional to (E₀/kT)log F. These theoretical predictions have been substantially checked, and E₀ deduced from data on the following diverse Schottky barriers: Au/GaAs, Cr/Si, Ag/ZnS, Zu/SrTiO₃, and ZrSi₂/Si, as measured by Padovani and Sumner, Padovani, Saxena, Wronski, Carnes and Goodman, and Andrews and Lepselter. Furthermore, the forward‐ and reverse‐current temperature anomalies observed by Padovani on the same sample of Au/GaAs lead to the same value of E₀, E₀=0.045±0.005 eV. Also, φ_B as obtained from a plot of $T_0^{\text{−1}}$ vs V on diverse Schottky barriers agrees closely with φ_B as obtained from independent methods. These features demonstrate a measure of self‐consistency in the theory. A derivation of the empirical equation involving T₀ is given and its limits of applicability are stressed.