Fast computation of the temperature distribution in VLSI chips using the discrete cosine transform and table look-up

Temperature-related effects are critical in determining both the performance and reliability of VLSI circuits. Accurate and efficient estimation of the temperature distribution corresponding to a specific circuit layout is indispensable in physical design automation tools. In this paper, we propose a highly accurate fast algorithm for computing the on-chip temperature distribution due to power sources located on the top surface of the chip. The method is a combination of several computational techniques including the Green function method, the discrete cosine transform (DCT), and the table look-up technique. The high accuracy of the algorithm comes from the fully analytical nature of the Green function method, and the high efficiency is due to the application of the fast Fourier transform (FFT) technique to compute the DCT and later obtaining the temperature field for any power source distribution using the pre-calculated look-up table. Experimental results have demonstrated that our method has a relative error of below 1% compared with commercial computational fluid dynamic (CFD) softwares for thermal analysis, while the efficiency of our method is orders of magnitude higher than the direct application of the Green function method.