IC Spatial Variation Modeling: Algorithms and Applications

Rapidly improving the yield of today's complicated manufacturing process is a key challenge to ensure profitability for the IC industry. In this thesis, we propose accurate and efficient modeling techniques for spatial variation, which is becoming increasing important in the advanced technology nodes. Based on the spatial model, we develop algorithms for two applications that help identify the important yield-limiting factors and prioritize yield improvement efforts. Variation decomposition narrows down the sources of variation by decomposing the overall variation into multiple different components, each corresponding to a different subset of variation sources. Wafer spatial signature clustering automatically partitions a large number of wafers into groups exhibiting different spatial signatures, which helps process engineers find important factors that prevent the process from stably maintaining a high yield across different lots and wafers.

An important problem in variation decomposition is to accurately model and extract the wafer-level and within-die spatially correlated variation. Towards this goal, we first develop a physical basis function dictionary based on our study of several common physical variation sources. We further propose the DCT dictionary to discover spatially correlated systematic patterns not modeled by the physical dictionary. Moreover, we propose to apply sparse regression to significantly reduce the over-fitting problem posed by a large basis function dictionary. We further extend the sparse regression algorithm to a robust sparse regression algorithm for outlier detection, which provides superior accuracy compared to the traditional IQR method. Finally, we propose several efficient methods to make the computational cost of sparse regression tractable for large-scale problems.

We further develop an algorithm for the wafer spatial signature clustering problem based on three steps. First, we re-use the spatial variation modeling technique developed for variation decomposition to automatically capture the spatial signatures of wafers by a small number of features. Next, we select a complete-link hierarchical clustering algorithm to perform clustering on the features. Finally, we develop a modified L-method to select the number of clusters from the hierarchical clustering result.