The dielectric breakdown problem

The dielectric breakdown problem can be solved very easily from the solution of the fuse problem in two dimensions using the concept of duality. This concept is largely used in the case of composite materials and in percolation for problems in d = 2 or with cylindrical symmetry (Mendelson 1975, Bowman and Stroud 1989). Here we follow the derivation of Bowman and Stroud. 

We mentioned this concept when we introduced the electromigration fuse model (Section 2.2.5). We recall it in the present context of the dielectric breakdown problem. Above we considered a walker which jumps from bond to bond since the problem was to break bonds until failure. Here, we adopt a slightly different definition specific to the present problem. 

Recently, Sen and Kar-Gupta (1994) and Kar-Gupta and Sen (1995) proposed a new percolation model to mimic the properties of nonlinear composites. However, it can also be interpreted as a special model for the dielectric breakdown problem. 

Fig. 2.18. Breakdown susceptibility as a function of the applied voltage in the dielectric breakdown problem for several sample sizes (from Acharyya and Chakrabarti 1996a). The inset shows that AF b, the difference of E y estimates from the peak position in x tnd from the percolation of the broken cluster, decreases with increasing system size.

This book presents three particular cases of failure Chapter 2 is on electrical failures like the fuse and dielectric breakdown problems and Chapter 3 is on mechanical fracture, both essentially in static models of solids containing random defects. We start with the electrical failures, because it helps to introduce several crucial concepts perhaps more easily. The last chapter is devoted to the recent model studies of dynamic failures like the earthquakes. If we insist more on the statics, rather than on the dynamics, that is merely because the dynamic problems, being more complex, have yielded less to solutions. We introduce in Chapter 1 the general concepts that we have employed in the subsequent chapters. We have made some attempts not to make the chapters totally interdependent, and, unlike the well-organised people, we did not try to avoid some repetitions when we thought some repetitions might help smooth reading of the book. 

The third problem associated with water based varnishes is poor electrical insulation properties of the laminate after moisture conditioning. This problem is probably the most critical problem because insulation failures of the laminate can lead to electrical failure of the finished printed circuit board. This property is measured by conditioning the finished laminate in a high moisture environment and then testing the dielectric breakdown strength. ED24574 has excellent insulation resistance. This was achieved by a proprietary resin composition. 

These lead-based materials (PZT, PLZT, PMN) form a class of ceramics with either important dielectric, relaxor, pie2oelectric, or electrooptic properties, and are thus used for appHcations ia actuator and sensor devices. Resistive properties of these materials ia film form mirror the conduction processes ia the bulk material. Common problems associated with their use are low dielectric breakdown, iacreased aging, and electrode iajection, decreasiag the resistivity and degrading the properties. 

A serious potential problem related to the use of high-k gate dielectrics in SiC power MOSEETs can be encountered due to the much smaller (sometimes-negative) conduction band offsets between SiC and high-k metal oxides compared with silicon dioxide (see Table 5.1). Time-dependent dielectric breakdown (TDDB) and hot... 

---