High-efficiency green function-based thermal simulation algorithms

Due to technology scaling trends, the accurate and efficient calculations of the temperature distribution corresponding to a specific circuit layout and power density distribution will become indispensable in the design of high-performance very large scale integrated circuits. In this paper, we present three highly efficient thermal simulation algorithms for calculating the on-chip temperature distribution in a multilayered substrate structure. All three algorithms are based on the concept of the Green function and utilize the technique of discrete cosine transform. However, the application areas of the algorithms are different. The first algorithm is suitable for localized analysis in thermal problems, whereas the second algorithm targets full-chip temperature profiling. The third algorithm, which combines the advantages of the first two algorithms, can be used to perform thermal simulations where the accuracy requirement differs from place to place over the same chip. Experimental results show that all three algorithms can achieve relative errors of around 1 % compared with that of a commercial computational fluid dynamic software package for thermal analysis, whereas their efficiencies are orders of magnitude higher than that of the direct application of the Green function method.