Methods and systems for model-less, scatterometry based measurements of semiconductor structures

A metrology system comprising:

• an illumination source configured to generate a beam of narrowband illumination light incident on a structure under measurement;
• a specimen positioning system configured to orient the structure under measurement with respect to the incident illumination beam at each of a first plurality of angular orientations and one or more of a second plurality of angular orientations, each of the first plurality of angular orientations associated with a different measurement instance of a first plurality of measurement instances, each of the one or more of the second plurality of angular orientations associated with a different measurement instance of one or more of a second plurality of measurement instances;
• an imaging detector configured to detect an image of light scattered from the structure under measurement in response to the incident illumination beam at each of the first plurality of measurement instances and each of the one or more of the second plurality of measurement instances, each detected image including a plurality of diffraction orders of scattered light;
• and
• a computing system configured to:
• estimate a value of tilt of the structure under measurement with respect to the incident illumination beam based on the detected images at each of the first plurality of measurement instances;
• determine the one or more of the second plurality of orientations of the structure under measurement with respect to the incident illumination beam based on the measured tilt;
• and
• determine a value of a parameter of interest characterizing a shape of the structure under measurement based on the detected images at each of the one or more of the second plurality of measurement instances.

A method comprising:

• generating a beam of narrowband illumination light incident on a structure under measurement;
• orienting the structure under measurement with respect to the incident illumination beam at each of a plurality of angular orientations, each of the plurality of angular orientations associated with a different measurement instance of a plurality of measurement instances;
• detecting an image of light scattered from the structure under measurement in response to the incident illumination beam at each of the plurality of measurement instances, each detected image including a plurality of diffraction orders of scattered light;
• determining a plurality of discrete values of a scalar function, wherein each of the plurality of discrete values is based on the detected image at each of the plurality of measurement instances, wherein the scalar function includes a weighting function, wherein the weighting function scales the detected image at each of the plurality of measurement instances;
• determining values of parameters characterizing a continuous mathematical function fit to the plurality of discrete values of the scalar function;
• and
• estimating a value of a parameter of interest characterizing the structure under measurement based on one or more characteristics of the mathematical function.