A parametric study of the surface potential and band bending in silicon

Abstract

A unified approach to band bending is described, and the macroscopic electronic potential through the silicon surface is calculated as a function of temperature in the ranges 300–500°K and 100–1600°K, externally applied electric field, for zero field and for 10 3 to 10 5 V/cm, and donor and acceptor concentrations, from 10 12 to 10 18 cm −3. The results, presented in graphical and tabular forms, are intended to serve the convenience of researchers in a wide area of surface and high temperature silicon physics such as in thermionic, field, and photoelectric emission work and in high temperature, and field modulated transport studies. The calculations are based on an essentially classical approach to the solution of the electrostatic band bending problem, using the surface state density for silicon proposed by Allen and Gobeli on the basis of their photoelectric investigations. The cases considered were limited to nondegenerate, intrinsic, and n- and p-doped silicon in which all impurity states are fully ionized.