Surface quantization effect on the macroscopic characteristics of semiconductor space-charge layers

A numerical study of the dependence of the space-charge density Q_sc on the surface potential Ψ_s in a two-dimensional electron inversion layer on Si(100) is presented. The dependence Q_sc(Ψ)_s being a macroscopic characteristic of semiconductor space-charge layers is found to be considerably influenced by the surface quantization in a wide temperature range up to room temperature. The conditions for the appearance of appreciable differences in the behaviour of the Q_sc(Ψ)_s curves in the quantum-mechanical and quasi-classical cases are determined and discussed.