A scatterometry inverse problem in optical mask metrology

We discuss the solution of the inverse problem in scatterometry i.e. the determination of periodic surface structures from light diffraction patterns. With decreasing details of lithography masks, increasing demands on metrology techniques arise. By scatterometry as a non-imaging indirect optical method critical dimensions (CD) like side-wall angles, heights, top and bottom widths are determined. The numerical simulation of diffraction is based on the finite element solution of the Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. The inverse operator maps efficiencies of diffracted plane wave modes to the grating parameters. We employ a Newton type iterative method to solve the resulting minimum problem. The reconstruction quality surely depends on the angles of incidence, on the wave lengths and/or the number of propagating scattered wave modes and will be discussed by numerical examples.