Simulation of the electric field strength in the vicinity of metallization edges on dielectric substrates

High electric field strengths at the edge of the metallization of insulated gate bipolar transistor (IGBT) power modules are, besides defects in the substrate or the potting gel, the main reason for partial discharge. These critical electric field strengths occur at the energized contact where it is bordered by the insulating ceramic and the cover (mostly silicone gel). The reduction of high electric field strengths for increasing the threshold voltage for partial discharge has been studied in several publications based on experiments as well as on simulations. Simulations allow the localization of the critical spots and the quantification of the maximum electric field strength. However, a systematic study of the singularities of the electric field strength at the sharp edges is lacking. Such singularities are investigated in this article. The calculation of an absolute electric field strength value is only possible for finite edge radii. For sharp edges, however, the maximum electric field strength returned by simulation depends on the grid size: Through the finite grid size a virtual edge radius is induced that suppresses the singularity at the edge. To get around this problem, a mesh-independent evaluation procedure is introduced. With this procedure it is possible to quantitatively evaluate the electric field strength in the vicinity of the sharp edge. As an example, the influence of the offset between the top and bottom metallization layer on the maximum electric field strength is studied. Moreover, the influence of the thickness of the involved layers and of the shape of the electrodes is discussed. Also, the impact of the material properties of the involved dielectrics is examined. In addition to electrostatic simulations we have carried out electric transient simulations, which show that the ratio of the conductivities of the involved dielectric materials plays a major role for determining the maximum electric field strength.