3D modeling of a smart power device

Solid state devices are increasingly being used in the automobile industry, both as sensors and actuators. An accelerometer for crash detection in automobile, for example, was described in Chapter 20 of this Volume. In this chapter we shall consider a smart power device used for fuel injection. This is a 3D device. The power devices reside within the top few microns of the silicon substrate of the chip, are arranged in interdigitated fingers, as shown in Figure 22.1, and number in the thousands per chip. Heat generated by the devices poses a significant problem and must be conducted away quickly enough to prevent thermal runaway and burnout failure. On June 3, 1993 Leonard Borucki from Motorola described the device and developed a mathematical model. The problem can be formulated as a nonlinear time dependent heat equation with a source term in the fingers. Significant computational resources and time are required to calculate the location and magnitude of the temperature maximum, where failure is likely to occur first. A problem posed by Borucki is whether analytic methods can provide, more quickly, estimates of the maximum temperature.