The Field Singularity at the Edge of an Electrode on a Semiconductor Surface

Beneath a charged electrode situated on the surface of a semiconductor, at points far from the electrode edge, the electrostatic field is regular and quasi-one-dimensional, with its maximum value at the electrode. Near the electrode edge, however, the field may become very large because of the accumulation of surface charge at the sharply curved electrode edge.1 Also, the jump in dielectric constant between the semiconductor and the surrounding insulating material may produce a large local field intensity. Such a field may be so large as to cause avalanche breakdown near the edge, but, in any case, the presence of such an edge effect makes the behavior of a semiconductor device difficult to predict. * On leave from the Technion-Israel Institute of Technology, Haifa, Israel, when this work was performed. 1183 1184 T H E BELL SYSTEM TECHNICAL J O U R N A L , J U L Y - A U G U S T 1970 In this paper we consider a simple mathematical model of an electrode edge-semiconductor-insulator configuration, namely a sharp-edged electrode on top of a semiconductor mesa, as in Fig. 1. We study the behavior of the potential, or rather its singular part, in the two wedgeshaped semiconductor and insulator regions shown in the inset circle of Fig. 1, assuming that the potential is locally planar and that its singular part satisfies Laplace's equation, both in the insulator and in the semiconductor. Since the treatment is local and the electrode edge and mesa corner are replaced by mathematically sharp wedges, our analysis can only predict the existence or nonexistence of a singular field at the edge and cannot produce an estimate of local field strength, which depends on conditions far from the edge.