Optimized spatial modeling for optical CD metrology

A non-transitory machine-readable storage medium having instructions stored thereon which cause a computer to perform a method of evaluating a diffracting structure, the method comprising:

• measuring spectral information for a diffracting structure, measuring the spectral information including illuminating the diffracting structure with an incident beam by a light source and detecting a resulting spectral signal with a detector of the optical metrology;
• and
• receiving and analyzing the measured signal by a processing module of the optical metrology system, including:
• providing a 3D spatial model of the diffracting structure in a simulation domain, the simulation domain being a spatial domain, providing the 3D spatial model including constructing a geometric model of the diffracting structure and determining how to parameterize the geometric model;
• splitting the simulation domain into a plurality of subdomains;
• discretizing the model into a 3D spatial mesh in the simulation domain;
• approximating 3D fields for each element of the 3D mesh using 3D spatial basis functions for each subdomain of the simulation domain;
• generating a matrix comprising coefficients of the 3D spatial basis functions approximating fields in each subdomain of the simulation domain;
• computing the coefficients of the 3D spatial basis functions using the matrix;
• computing spectral information for the model based on the computed coefficients;
• comparing the computed spectral information for the model with the measured spectral information for the diffracting structure;
• and
• in response to a determination of a model fit by the processing module, determining a physical characteristic of the diffracting structure based on the model of the diffracting structure, the physical characteristic being a geometric or material characteristic of the diffracting structure,
• wherein approximating the 3D fields for each element of the 3D mesh comprises:
• approximating first 3D fields for a first element of the 3D mesh on one periodic boundary using one or more first spatial basis functions;
• and
• approximating second 3D fields for a second element of the 3D mesh on an opposite periodic boundary with one or more second spatial basis functions, wherein the one or more second spatial basis functions comprise the one or more first spatial basis functions multiplied by a phase shift factor, wherein the phase shift factor is a function of an angle of incident light and pitch in one or more directions of periodicity.

An optical measurement system comprising:

• a light source to illuminate a diffracting structure with an incident beam and a detector to detect a resulting spectral signal;
• first logic to receive measured spectral information for the diffracting structure;
• and
• second logic to:
• provide a 3D spatial model of the diffracting structure in a simulation domain, the simulation domain being a spatial domain, providing the 3D spatial model including constructing a geometric model of the diffracting structure and determining how to parameterize the geometric model;
• split the simulation domain into a plurality of subdomains;
• discretize the model into a 3D spatial mesh in the simulation domain;
• approximate 3D fields for each element of the 3D mesh using 3D spatial basis functions in the spatial domain
• generate a matrix comprising coefficients of the 3D spatial basis functions approximating fields in a subdomain of the spatial domain;
• compute the coefficients of the 3D spatial basis functions using the matrix;
• compute spectral information for the model based on the computed coefficients;
• compare the computed spectral information for the model with the measured spectral information;
• and
• in response to a determination of a model fit by the second logic, determine a physical characteristic of the diffracting structure based on the model of the diffracting structure, the physical characteristic being a geometric or material characteristic of the diffracting structure,
• wherein the second logic, in approximating the 3D fields for each element of the 3D mesh, is configured to:
• approximate first 3D fields for a first element of the 3D mesh on one periodic boundary using one or more first spatial basis functions;
• and
• approximate second 3D fields for a second element of the 3D mesh on an opposite periodic boundary with one or more second spatial basis functions, wherein the one or more second spatial basis functions comprise the one or more first spatial basis functions multiplied by a phase shift factor, wherein the phase shift factor is a function of an angle of incident light and pitch in one or more directions of periodicity.