Extended Curves of the Space Charge, Electric Field, and Free Carrier Concentration at the Surface of a Semiconductor, and Curves of the Electrostatic Potential Inside a Semiconductor

Abstract

This article is an extension of work begun by R. H. Kingston and S. F. Neustadter [J. Appl. Phys. 26, 718 (1955)]. They calculated the space charge, electric field, and change in free carrier concentration for a semiconductor surface. Their results may be expressed as functions of the deviation for the Fermi energy from its intrinsic value in the bulk and at the surface. Curves calculated from their results may be used for any nondegenerate semiconductor at any temperature, provided that the donor and acceptor levels are completely ionized. The curves presented in the above-mentioned article, however, are extensively applicable only to germanium or semiconductors of similar energy gap. The extended curves presented in this article enable computations to be applied to materials of higher energy gap, such as silicon and gallium arsenide, over a wide resistivity range. Also, in this article several curves of electrostatic potential inside a semiconductor have been computed. A few of these curves were presented previously by G. C. Dousmanis and R. C. Duncan, Jr. [J. Appl. Phys. 29, 1627 (1958)]. The curves presented in this article are intended to supplement those previously presented.