A Fast Leakage-Aware Green’s-Function-Based Thermal Simulator for 3-D Chips

In this article, we propose a fast thermal modeling tool, 3DSim, using a Green’s-function-based approach. Green’s-function-based approaches have been shown to be faster than the traditional finite-difference-based techniques. Our proposed tool can model steady-state and transient thermal profiles for both 2-D and 3-D chips, which may contain multiple active layers and fluid-carrying microchannels for heat removal. The unique advantage of our tool is that it models leakage power analytically using a piecewise-linear leakage model, thereby eliminating the need to iterate multiple times through the leakage–temperature feedback loop. We use several algebraic techniques and transforms to compute the thermal profile analytically and thereby speedup the process of calculation. To the best of our knowledge, transform-based approaches have not been used before to model the temperature in 3-D chips with microchannels. Our approach provides a $150\times $ speedup over state-of-the-art thermal simulators, with an error limited to 5%.