Uncertainty quantification with high-dimensional correlated process variations for an in-situ thermal expansion coefficient test structure

Abstract

The impacts of process variations on the π-shaped thermal expansion coefficient (TEC) in-situ test structure are analyzed. Correlations among high-dimensional design parameters have to be taken into account for this type of structure, while the widely studied polynomial chaos expansion (PCE) technique is incapable of solving such problems. This paper presents a novel method for high-dimensional uncertainty quantification problems with non-Gaussian correlated variants. As a pre-processing method, the Spearman correlation coefficient and generalized lambda distribution are merged to eliminate the correlation. Then a compressed-sensing based Legendre-sparse solver is applied benefiting from the uniformly distributed parameters derived from the pre-processing and thus the cost of rebuilding correlated basis functions is eliminated. This method has demonstrated superior performance over existing methods in the analysis of TEC in-situ test structures. This analysis shows that the measurement accuracy of the test structure demonstrates good performance and is insensitive to process errors, which is consistent with experimental data. The presented technique has the potential to be applied in the design of various microelectromechanical system (MEMS) devices.