Quasi‐Classical Quantization for Potentials with an Infinite Surface Barrier. Subbands in Inversion Layers

Abstract

Abstract For potentials with a high surface barrier, quasi‐classical quantization schemes are investigated. WKB and other previous approximations provide good results for the lower eigenvalues in special cases only. Here a modified local density approximation is used for the calculation of the density of states. From the integral density of states a quantization expression is derived where the ground state constant depends explicitly on the shape of the potential. It yields the whole eigenvalue spectrum very precisely for quite different potentials with surface barrier. The application to subband energies in inversion layers is discussed.