POTENTIAL BARRIERS NEAR THE JUNCTION OF 2 BOUNDARIES

The present paper deals with the junction of two charged boundaries in a polycrystalline, semiconducting film (e.g. two crossing grain boundaries or a surface and a grain boundary). The overlap of the depletion layers near the crossing point is considered in a two-dimensional Schottky approximation and the resulting electrical potential is calculated using an appropriate shape for the space charge region. The potential at the crossing point is calculated exactly using the Green formula in flat space. It turns out that for the symmetric case (2Q(s) = Q(i); Q(s), surface charge density; Q(i), interface charge density) the potential at the crossing point is 3.4 times as great as the one-dimensional unperturbed potential due to the same surface charge density. On the basis of the Ritz variational method for partial differential equations a numerical solution of the two-dimensional potential is calculated for the whole space charge region. The good agreement between the variational values both for the potential at the crossing point (the deviation is smaller than 5%) and for the boundary potentials demonstrates the efficiency of the variational method.