Method and Apparatus for Measuring a Structure on a Substrate, Models for Error Correction, Computer Program Products for Implementing such Methods and Apparatus

摘要

A reconstruction process includes measuring structures formed on a substrate by a lithographic process, determining a reconstruction model for generating modeled patterns, computing and minimizing a multi-variable cost function including model errors. Errors induced by nuisance parameters are modeled based on statistical description of the nuisance parameters' behavior, described by probability density functions. From the statistical description model errors are calculated expressed in terms of average model errors and weighing matrices. These are used to modify the cost function so as to reduce the influence of the nuisance parameters in the reconstruction, without increasing the complexity of the reconstruction model. The nuisance parameters may be parameters of the modeled structure, and/or parameters of an inspection apparatus used in the reconstruction.

主权项

1. A method of measuring parameters of a structure on a substrate, comprising:
(a) defining a mathematical model in which shape and material properties of said structure, are represented by a plurality of parameters including at least one parameter of interest; (b) illuminating said structure with one or more beams of radiation and detecting a signal arising from interaction between said radiation and said structure; (d) calculating a plurality of model signals by simulating interaction between said radiation and said mathematical model while varying the parameter of interest and while not varying at least one other parameter; (e) calculating a model of influence for said other parameter by simulating interaction between said radiation and said mathematical model while varying the other parameter in accordance with an assumed statistical behavior; (f) calculating degrees of matching between the detected signal and at least some of the model signals calculated in step (d), while using the model of influence to suppress an influence of variations of said other parameter that are not represented in the model signals; and (g) reporting a measurement of said parameter of interest based on the calculated degrees of matching.