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

Method of Images for the Fast Calculation of Temperature Distributions in Packaged VLSI Chips