Space charge regions in semiconductors

Abstract

Poisson's equation is solved for a homogeneous semiconductor in equilibrium and the results are presented in a form which is relatively independent of the impurity concentration. Some convenient analytic forms are given for the dependence of carrier concentration on field and the spatial variation of these quantities. The application of the results to surface field-effect experiments and to abrupt p- n junctions is discussed. In particular, it is shown that the field at an asymmetric junction depends on the impurity concentration on the more heavily doped side. A formula is also given for a critical transistor base width below which the entire base region becomes inverted in equilibrium.