Dielectric Theory of the Barrier Height at Metal-Semiconductor and Metal-Insulator Interfaces

The barrier height at metal-semiconductor and metal-insulator interfaces is calculated for a simple model of the system, in which the metal is replaced by a jellium model and the semi-conductor and insulator by a continuum with a static dielectric constant. The spreading out of electronic charge into the dielectric continuum is determined by a variational procedure, which is an extension of the Smith's theory of the work function. Approximately, the calculated barrier height increases linearly with the work function of the metals. The slope increases with the ionicity of the semiconductors. The model, however, cannot explain the abrupt covalentionic transition.