  Thermal aware routing and placement algorithms are important in industry.
Currently, there are reasonably fast Green's function based algorithms that
calculate the temperature distribution in a chip made from a stack of different
materials. However, the layers are all assumed to have the same size, thus
neglecting the important fact that the thermal mounts which are placed
underneath the chip can be significantly larger than the chip itself. In an
earlier publication, we showed that the image blurring technique can be used to
calculate quickly temperature distribution in realistic packages. For this
method to be effective, temperature distribution for several point heat sources
at the center and at the corner and edges of the chip should be calculated
using finite element analysis (FEA) or measured. In addition, more accurate
results require correction by a weighting function that will need several FEA
simulations. In this paper, we introduce the method of images that take the
symmetry of the thermal boundary conditions into account. Thus with only "two"
finite element simulations, the steady-state temperature distribution for an
arbitrary complex power dissipation profile in a packaged chip can be
calculated. Several simulation results are presented. It is shown that the
power blurring technique together with the method of images can reproduce the
temperature profile with an error less than 0.5%.

General Physics