Stochastic thermal simulation considering spatial correlated within-die process variations

In this work, we develop a statistical thermal simulator including the effect of spatial correlation under within-die process variations. This method utilizes the Karhunen-Loeve (KL) expansion to model the physical parameters, and apply the polynomial Chaoses (PCs) and the stochastic Galerkin method to tackle stochastic heat transfer equations. We demonstrate the accuracy and efficiency of our simulator by comparing with the Monte Carlo simulation, and point out that the stochastic thermal analysis is essential to provide a robust estimation of temperature distribution for the thermal-aware design flow.