Method and apparatus for optimizing models for extracting dose and focus from critical dimension

A method for monitoring a photolithography system, comprising:

• defining a reference model of the photolithography system for modeling top and bottom critical dimension data associated with features formed by the photolithography system as a function of dose and focus, the reference model having a plurality of terms;
• generating a reference fit error metric for the reference model;
• generating a set of evaluation models each having one term different than the reference model;
• generating an evaluation fit error metric for each of the evaluation models;
• replacing the reference model with a selected evaluation model responsive to the selected evaluation model having an evaluation fit error metric less than the reference fit error metric;
• repeating, based on the replaced reference model, the generating of the reference fit error metric, the generating of the set of evaluation models, the generating of the evaluation fit error metrics, and the replacing of the reference model until no evaluation model has an evaluation fit error metric less than the reference fit error metric;
• training the reference model for which no evaluation model has an evaluation fit error metric less than the reference fit error metric using the top and bottom critical dimension data;
• receiving a top critical dimension measurement and a bottom critical dimension measurement of a feature formed by the photolithography system using a commanded dose parameter and a commanded focus parameter;
• employing the trained reference model using the top and bottom critical dimension measurements to determine values for a received dose parameter and a received focus parameter;
• and
• comparing the received dose and focus parameters to the commanded dose and focus parameters to characterize the photolithography system.

A system, comprising:

• a photolithography tool operable to generate a feature on a wafer using a commanded dose parameter and a commanded focus parameter;
• a metrology tool operable to measure a top critical dimension of the feature and a bottom critical dimension of the feature;
• a photolithography solver operable to define a reference model of the photolithography tool for modeling top and bottom critical dimension data associated with features formed by the photolithography tool as a function of dose and focus, the reference model having a plurality of terms, the photolithography solver being further operable to generate a reference fit error metric for the reference model, generate a set of evaluation models each having one term different than the reference model, generate an evaluation fit error metric for each of the evaluation models, replace the reference model with a selected evaluation model responsive to the selected evaluation model having an evaluation fit error metric less than the reference fit error metric, repeat, based on the replaced reference model, the generating of the reference fit error metric, the generating of the set of evaluation models, the generating of the evaluation fit error metrics, and the replacing of the reference model until no evaluation model has an evaluation fit error metric less than the reference fit error metric, and train the reference model for which no evaluation model has an evaluation fit error metric less than the reference fit error metric by using the top and bottom critical dimension data;
• and
• a photolithography monitor operable to receive the top critical dimension measurement and the bottom critical dimension measurement, employ the trained reference model using the top and bottom critical dimension measurements to determine values for a received dose parameter and a received focus parameter, and compare the received dose and focus parameters to the commanded dose and focus parameters to characterize the photolithography system.