Uncertainty optimization based on sensitivity analysis for TSOM method in multi-measurands metrology

Semiconductor manufacturing usually requires precise measurements on critical geometric parameters of those nano-scaled targets to perform the process control and promote the yields. Theoretically through-focus scanning optical microscopy (TSOM) method enables to extract measurement results with 3D nano-scaled resolution via searching for the solution leading to the minimal errors between simulated and experimented output images (so-called TSOM images) from the possible solution spaces of the measurands. However, the coupling effects among the measurands increase the uncertainties of the results, which hinders TSOM method in the multi-measurands metrology. Since the coupling effects can be decreased via optimizing measurement conditions, this paper proposes an optimization method based upon the sensitivity analysis. This method samples all the measurands to generate the coupling factors that quantitatively characterize the coupling effects and selects the optimized measurement condition which corresponds to the minimal coupling effects. The selected measurement condition is verified by a measurement on three Au lines, and the results prove that this condition leads to nano-scaled measuring errors and uncertainties. Contrary to local optimizations, the proposed method is valid for both linear and nonlinear measurement models, and can be generalized to other model-based metrologies.