The Potentials of Infinite Systems of Sources and Numerical Solutions of Problems in Semiconductor Engineering

The "method of images" is a simple but elegant technique for the solution of problems in potential theory. Formal solutions to problems involving plane boundaries and point sources can usually be written down immediately from obvious symmetry considerations. The solutions thus obtained, however, are often infinite series whose convergence is unsatisfactory for numerical calculations. Many techniques have been devised for improving upon the convergence of these infinite sums. It has generally been assumed that the mathematician or engineer must select one of these techniques and apply it to his own special problem. The object of this article is to make such special treatment unnecessary in most cases. To this end, the potentials of certain simple image systems are tabulated. The use of the tabulations is illustrated by numerical solutions of some problems in semiconductor engineering. Transistors and varistors have become famous because of their non-ohmic properties. But solutions to ohmic flow problems can be useful as first approximations in the design of semiconductor devices and can be very accurate approximations for suitably arranged measurements of the equilibrium resistivity of semiconductors. Plane boundaries occur-as the physical boundaries 1,2