A pertinent approximation of the electrostatic potential in a quantized electron accumulation layer induced at a nonideal surface of a narrow-gap semiconductor

Quantitative analysis of the electron accumulation layer formed near nonideal (actual) semiconductor surface causes considerable difficulties. In the present article, for the accumulation layers induced in the subsurface region at the real narrow-gap semiconductor-insulator interface, an effective algorithmic approach providing a simplified self-consistent solution of the Poisson and Schrödinger equations is proposed and discussed. The physical model takes into account the conduction band nonparabolicity, electron gas degeneration, and other dominant features of solids in question; special attention is paid to the existence of semiconductor-dielectric intermediate layer. A novel approximation for the surface electrostatic potential in the form of a modified Кratzer potential is proposed and substantiated. It allows us to obtain the electron wavefunctions and energy spectrum in the analytical form. It is shown that the modified Кratzer potential is a good approximation function applicable at least to subsurface electron accumulation layers induced at the A³B⁵ narrow-gap semiconductor boundary surface allowing for the existence of a semiconductor-insulator intermediate layer. For the n-InSb nonideal surface, as an example, spatial distribution of electron potential energy, discrete energy spectrum of electrons in the broad range of surface densities (up to 10¹³ cm^-2), and some other physical characteristics are calculated using the proposed algorithm.