A Laplace sensitivity operator enhances the calculation efficiency of OCD metrology

Abstract

In integrated circuit manufacturing, optical critical dimension measurement is an efficient and non-destructive metrology method. It is also a model-based metrology in which a numerical model of the target device is formed to simulate the optical spectrum. The result is then reconstructed by fitting the simulated spectrum to the experimentally measured optical spectrum. Normally, the measured optical spectrum contains a great deal of data points that consume the storage space, and increase the fitting time. Therefore, it is worth finding an appropriate approach to downsample these data points without losing much accuracy. To quickly and accurately extract critical data with high sensitivity, we propose a Laplace sensitivity operator that is widely used for feature extraction. Compared with traditional sensitivity calculation, the Laplace sensitivity operator focuses more on the correlation and coupling between multiple parameters. Thus, the sensitivity can be properly analyzed from different dimensions. To test the feasibility and correctness of the proposed method, three basic structures were used for single-parameter verification: thin film, one-dimensional grating, and two-dimensional grating, and a vertical gate-all-around device used for multi-parameter analysis. Using the Laplace sensitivity operator, the extracted data showed better results in most cases than those achieved by the traditional sensitivity calculation method. The data volume was compressed by approximately 70%, the result matching loss was not significantly increase in terms of the root mean square error, and the calculation speed was increased by a factor of 2.4. Compared to the traditional sensitivity operator, the Laplace sensitivity operator was able to reduce the RMSE by up to 50%.