Properties of and Improvements to Time-Domain Dynamic Thermal Analysis Algorithms

Temperature has a strong influence on integrated circuit (IC) performance, power consumption, and reliability. However, accurate thermal analysis can impose high computation costs during the IC design process. We analyze the performance and accuracies of a variety of time-domain dynamic thermal analysis techniques and use our findings to propose a new analysis technique that improves performance by 38-138 x relative to popular methods such as the fourth-order globally adaptive Runge-Kutta method while maintaining accuracy. More precisely, we prove that the step sizes of step doubling based globally adaptive fourth-order Runge-Kutta method and Runge-Kutta-Fehlberg methods always converge to a constant value regardless of the initial power profile, thermal profile, and error threshold during dynamic thermal analysis. Thus, these widely-used techniques are unable to adapt to the requirements of individual problems, resulting in poor performance. We also determine the effect of using a number of temperature update functions and step size adaptation methods for dynamic thermal analysis, and identify the most promising approach considered. Based on these observations, we propose FATA, a temporally-adaptive technique for fast and accurate dynamic thermal analysis.