Methods and systems for x-ray scatterometry measurements employing a machine learning based electromagnetic response model

A method comprising:

• illuminating one or more semiconductor structures formed on a wafer surface by an amount of x-ray illumination radiation generated by an x-ray illumination source;
• detecting one or more images of a plurality of diffraction orders of an amount of radiation scattered from the one or more structures onto an x-ray detector, the amount of radiation scattered from the one or more structures in response to the x-ray illumination radiation incident on the one or more structures;
• and
• estimating values of parameters of interest characterizing the one or more semiconductor structures by regression on the one or more detected images using a trained, machine learning based electromagnetic response model, wherein the trained machine learning based electromagnetic response model maps values of the parameters of interest to values of a plurality of electromagnetic response metrics;
• and
• training the machine learning based electromagnetic response model based on a training data set including sets of Design Of Experiments (DOE) values of the parameters of interest and corresponding DOE values of a plurality of electromagnetic response metrics, wherein the training involves a regression on the training data set to minimize an objective function characterizing errors between the DOE values of the plurality of electromagnetic response metrics and values of the plurality of electromagnetic response metrics determined using the machine learning based electromagnetic response model.

A metrology system comprising:

• an x-ray illumination source configured to generate an amount of x-ray illumination radiation directed to one or more semiconductor structures under measurement formed on a wafer surface;
• an x-ray detector configured to detect one or more images of a plurality of diffraction orders of an amount of radiation scattered from the one or more structures in response to the x-ray illumination radiation incident on the one or more structures;
• and
• a non-transitory, computer-readable medium including instructions that when executed by one or more processors of a computing system cause the computing system to:
• estimate values of parameters of interest characterizing the one or more semiconductor structures by regression on the one or more detected images using a trained, machine learning based electromagnetic response model, wherein the trained machine learning based electromagnetic response model maps values of the parameters of interest to values of a plurality of electromagnetic response metrics;
• and
• train the machine learning based electromagnetic response model based on a training data set including sets of Design Of Experiments (DOE) values of the parameters of interest and corresponding DOE values of a plurality of electromagnetic response metrics, wherein the training involves a regression on the training data set to minimize an objective function characterizing errors between the DOE values of the plurality of electromagnetic response metrics and values of the plurality of electromagnetic response metrics determined using the machine learning based electromagnetic response model.