Despite temperature rise being a first-order design constraint, traditional thermal estimation techniques have severe limitations in modeling critical aspects affecting the temperature in modern-day chips. Existing thermal modeling techniques often ignore the effects of parameter variation, which can lead to significant errors. Such methods also ignore the dependence of conductivity on temperature and its variation. Leakage power is also incorporated inadequately by state-of-the-art techniques. Thermal modeling is a process that has to be repeated at least thousands of times in the design cycle, and hence speed is of utmost importance. To overcome these limitations, we propose VarSim, an ultrafast thermal simulator based on Green's functions. Green's functions have been shown to be faster than the traditional finite difference and finite element-based approaches but have rarely been employed in thermal modeling. Hence we propose a new Green's function-based method to capture the effects of leakage power as well as process variation analytically. We provide a closed-form solution for the Green's function considering the effects of variation on the process, temperature, and thermal conductivity. In addition, we propose a novel way of dealing with the anisotropicity introduced by process variation by splitting the Green's functions into shift-variant and shift-invariant components. Since our solutions are analytical expressions, we were able to obtain speedups that were several orders of magnitude over and above state-of-the-art proposals with a mean absolute error limited to 4% for a wide range of test cases. Furthermore, our method accurately captures the steady-state as well as the transient variation in temperature.

翻译：尽管温度上升已成为一阶设计约束，但传统热估算技术在建模影响现代芯片温度的关键因素方面存在严重局限。现有热建模技术常忽略参数变化的影响，这可能导致显著误差。此类方法亦未考虑电导率随温度及其变化的相关性。最先进的技术对泄漏功率的整合也不够充分。热建模是设计周期中需重复至少数千次的过程，因此速度至关重要。为克服这些限制，我们提出VarSim——一种基于格林函数的超快速热仿真器。已有研究表明，格林函数比传统有限差分法和有限元法速度更快，但极少被用于热建模。因此，我们提出一种新的基于格林函数的方法，以解析方式捕捉泄漏功率和工艺变化的影响。我们给出了考虑工艺、温度和热导率变化影响的格林函数闭式解。此外，我们提出一种新方法，通过将格林函数分解为移变分量和移不变分量，处理由工艺变化引入的各向异性。由于我们的解为解析表达式，在广泛测试案例中，相较于最先进方案实现了数个数量级的加速，且平均绝对误差控制在4%以内。此外，本方法能准确捕捉稳态和瞬态温度变化。