Maximum surface and bulk electric fields at breakdown for planar and beveled devices

Techniques previously presented for predicting breakdown voltage on planar devices with and without a field ring and in negative beveled devices are greatly extended so that the peak bulk and surface electric fields at breakdown can now be predicted. In addition, new techniques are described which for the first time allow the peak bulk and surface electric fields to be predicted for all positive and double positive beveled devices. Using this paper it becomes possible to predict peak bulk and surface electric fields as well as breakdown voltage for all planar and beveled devices. This is accomplished by the use or normalization procedures which allow dependencies on the substrate doping, junction depth, surface concentration, junction curvature, and bevel angle to be reduced to a single dependence. It is shown that the positive bevel is most effective in reducing surface electric fields with the negative bevel, double positive bevel, and the field ring for planar devices in decreasing order of effectiveness.