Calculation of the Space Charge, Electric Field, and Free Carrier Concentration at the Surface of a Semiconductor

In the study of the surface properties of semiconductors, it is valuable to know the relation between carrier density at the surface and the shift in electrostatic potential from the bulk to the surface. By a solution of Poisson's equation utilizing Boltzmann statistics, the space charge, electric field, and change in free carrier concentration have been calculated for a semiconductor surface. The results are expressed as a function of the deviations of the Fermi energy from its intrinsic value in the bulk and at the surface. The calculated curves may be used for any nondegenerate semiconductor at any temperature, provided that the donor and acceptor levels are completely ionized. Numerical values are given for germanium and silicon at room temperature.