Model optimization approach based on spectral sensitivity

A system comprising:

• a fabrication cluster configured to fabricate a semiconductor structure comprising repeating structures on a semiconductor substrate or wafer, according to a specification;
• and
• an optical metrology system comprising
• a non-transitory machine-accessible storage medium having instructions stored thereon which cause a data processing system to perform a method of optimizing parametric models for structural analysis using metrology of repeating structures on a semiconductor substrate or wafer, the method comprising:
• determining a first model of a structure on a semiconductor substrate or wafer, the first model based on a first set of parameters;
• calculating spectra for the first model of the structure for multiple points in parameter space using multiple different rays;
• determining a set of combined spectral sensitivity variations data for the structure for variation of the spectra calculated with respect to the parameters of the first model, wherein combined spectral sensitivity is determined by calculation of derivatives of the calculated spectra for the multiple points in parameter space with respect to the first set of parameters;
• performing a spectral sensitivity analysis based on the set of combined spectral variations data for the structure;
• modifying, based on the set of combined spectral sensitivity variations data for the structure and the spectral sensitivity analysis, the first model of the structure to provide a second model of the structure, the second model of the structure based on a second set of parameters different from the first set of parameters;
• calculating and providing a simulated spectrum derived from the second model of the structure;
• comparing the simulated spectrum derived from the second model to a sample spectrum derived from the structure on the semiconductor substrate or wafer;
• identifying the simulated spectrum that matches the sample spectrum to a predetermined matching criteria;
• and
• employing the identified simulated spectrum in a production environment to determine whether the semiconductor structure has been fabricated according to the specification.

A system to generate a simulated diffraction signal to determine process parameters of a wafer application to fabricate a structure on a semiconductor substrate or wafer using optical metrology, the system comprising:

• a fabrication cluster configured to perform a wafer application to fabricate a structure on a semiconductor substrate or wafer, wherein one or more process parameters characterize behavior of structure shape or layer thickness when the structure undergoes processing operations in the wafer application performed using the fabrication cluster;
• and
• an optical metrology system configured to determine the one or more process parameters of the wafer application, the optical metrology system comprising:
• a beam source and detector configured to measure a diffraction signal of the structure;
• and
• a processor configured to determine a first model of a structure on a semiconductor substrate or wafer, the first model based on a first set of parameters, configured to calculate spectra for the first model of the structure for multiple points in parameter space using multiple different rays, configured to determine a set of combined spectral sensitivity variations data for the structure for variation of the spectra with respect to the parameters of the first model, wherein combined spectral sensitivity for the structure is determined by calculation of derivatives of the spectra for the multiple points in parameter space with respect to the first set of parameters, configured to perform a spectral sensitivity analysis of the set of combined spectral variations data for the structure, configured to modify the first model of the structure to provide a second model of the structure based on the set of combined spectral sensitivity variations data for the structure and the spectral sensitivity analysis, the second model of the structure based on a second set of parameters different from the first set of parameters, configured to calculate and provide a simulated spectrum derived from the second model of the structure, and configured to compare the simulated spectrum derived from the second model to a sample spectrum derived from the structure on the semiconductor substrate or wafer.