Accurate thermal analysis considering nonlinear thermal conductivity

The increase in packing density has led to a higher power density in the chip which in turn has led to an increase in temperature on the chip. Temperature affects reliability, performance and power directly, motivating the need to accurately simulate the thermal profile of a chip. In literature, thermal conductivity is assumed to be a constant in order to obtain a linear system of equations which can be solved efficiently. But thermal conductivity is a nonlinear function of temperature and for silicon it varies by 22% over the range 27-80deg C (McConnell et al., 2001). If the nonlinearity of the thermal conductivity is ignored the thermal profile might be off by 10deg C. Thus to get an accurate thermal profile it is important to consider the nonlinear dependence of the thermal conductivity on temperature. In this work the nonlinear system arising out of considering the nonlinear thermal conductivity is solved efficiently using a variant of Newton-Raphson. We also study the abstraction levels under which the approximation of a periodic source by a DC source is valid