Determination of the state density at the Si-SiO2 interface

The problem of determining the density of surface states at the Si-SiO₂ interface from the quasi-static capacitance of a MOS capacitor is reconsidered in full detail. The errors introduced by the usual zero kelvin approximation are evaluated, an improved semiclassical approximation is proposed and its limits are estimated, an exact formula is found, and a numerical method is developed.The discussion of this formula reveals the existence of fundamental difficulties which are concealed by the approximate methods. These difficulties are common to several problems in solid state physics.