Efficient Polynomial Chaos Expansion Method based on Tensor Train Decomposition for High-Dimensional Yield Analysis

With the advancement of technology, process variations have a critical impact on key IC designs. Accurately and efficiently estimating circuit failure rates under process variations has become increasingly challenging due to the "curse of dimensionality" introduced by a large number of random variables. Traditional Monte Carlo methods incur prohibitively high computational costs. In this paper, we propose a meta-modeling approach that integrates polynomial chaos expansion (PCE) with low-rank tensor approximation to effectively address these challenges. This method mitigates the "curse of dimensionality", ensuring that computational cost scales linearly with dimensionality. Specifically, we employ tensor train (TT) decomposition to achieve a low-rank approximation of the original tensor, demonstrating superior performance in SRAM column circuit simulations. Compared to CANDECOMP/PARAFAC (CP) decomposition, the TT-based approximation offers greater accuracy and stability. Additionally, we incorporate sensitivity analysis to further reduce computational costs.