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Overlay of pattern registration is considered by some to be the most yield critical metrology element monitored in the semiconductor manufacturing process. Over the years, the aggressive demands of competitive chip design have constantly maintained these specifications at the process capability limit. This has driven the lithographer from somewhat simple process control techniques like optically read verniers, to computer automated overlay measurement systems whose outputs are applied to the estimation and correction of full field systematic error sources primarily as modeled wafer and lens pattern distortions. When modeled pattern distortions are used to optimize the lithographic overlay process, the point measurement of registration error is no longer the parameter of interest. Instead the lithographer wishes to measure and minimize the surface modeled pattern distortions such as translation, rotation, and magnification. Yet, often neglected is the fact that estimates of these parameters are influenced by measurement system errors resulting in a loss of precision in the estimate of the distortions and the false introduction of otherwise nonexistent distortions leading to improper determination of the true values for the lens. This paper describes the results of a screening simulation designed to determine the relative effects of measurement system errors on the distortion coefficient estimates produced by a pattern distortion model. The simulation confirms the somewhat obvious result that tool induced shift (TIS) translates directly into the estimate of the offset term of the model. In addition, the simulation indicates that errors in the measurement system pixel scale calibration directly scale all distortion estimates by the same factor. The variance of the measurement system sums with the variance of the stepper and inflates the standard error of the regression as well as the uncertainty of each lens parameter's estimate. Higher order nonlinearities or systematic errors in the response of the registration measurement system do not translate directly into distortion coefficient estimates, rather they also inflate the uncertainty associated with each distortion's estimate. Heuristic analytical considerations are presented which explain the behavior observed in the simulation and are used to demonstrate that these conclusions do apply to the general case.
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