NanoTherm: An Analytical Fourier-Boltzmann Framework for Full Chip Thermal Simulations

Abstract

Temperature simulation is a classic problem in EDA, and researchers have been working on it for at least the last 15 years. In this paper, we focus on fast Green's function based approaches, where computing the temperature profile is as simple as computing the convolution of the power profile with the Green's function. We observe that for many problems of interest the process of computing the Green's function is the most time consuming phase, because we need to compute it with the slower finite difference or finite element based approaches. In this paper we propose a solution, NanoTherm, to compute the Green's function using a fast analytical approach that exploits the symmetry in the thermal distribution. Secondly, conventional analyses based on the Fourier's heat transfer equation fail to hold at the nanometer level. To accurately compute the temperature at the level of a standard cell, it is necessary to solve the Boltzmann transport equation (BTE) that accounts for quantum mechanical effects. This research area is very sparse. Conventional approaches ignore the quantum effects, which can result in a 25 to 60% error in temperature calculation. Hence, we propose a fast analytical approach to solve the BTE and obtain an exact solution in the Fourier transform space. Using our fast analytical models, we demonstrate a speedup of 7-668X over state of the art techniques with an error limited to 3% while computing the combined Green's function.