Space Charge Calculations for Semiconductors

The electric field at the surface of a semiconductor is obtained as a function of the semiconductor bulk properties and the potential difference across the space charge region. The treatment is general enough to take into account degenerate free carrier distributions and partial ionization of impurities, either in the neutral bulk or the space charge region, or both. A one-dimensional model with a spacially homogeneous impurity distribution is assumed. The density of states in the conduction and valence bands is assumed to be that appropriate for spherical and ellipsoidal energy surfaces. The common model for simple donor and acceptor states is used in the main body of the paper. Conditions under which the equation for the field can be conveniently simplified are discussed, and a particular case is treated numerically. The validity of the free carrier distribution functions in the high fields near the semiconductor surface is discussed in Appendix I. The equation for the electric field at the semiconductor surface where the bulk impurities are described by a general model is given in Appendix II.