Combined optimization and hybrid scalar–vector diffraction method for grating topography parameters determination

We describe a new method for grating characterization using scatterometry. The grating parameters, such as height and width, are obtained in two steps. In the first step, the diffraction efficiencies are calculated using a new renormalized scalar diffraction (SDT) method, and the grating parameters are adjusted using a global optimization method to give the best fit between calculated and measured diffraction efficiencies. In the second step, the diffraction efficiencies are calculated using rigorous coupled wave vector diffraction theory (RCW), and the values of the grating parameters are readjusted using a local optimization method that provides not only the best estimate of the grating parameters but also the associated covariance matrix. The two-step method is tested on a surface relief grating with a known period of 480 nm with two unknown parameters describing the rectangular profile, a height h   and a width ww. It is shown that the renormalization extends the limits of scalar diffraction theory beyond the classical limits of a wavelength to period ratio of 0.1, and that the diffraction efficiencies is predicted with an accuracy usually thought to require rigorous electromagnetic theories. The results also show that the presented two-step method is precise, fast and robust in achieving the best estimates of the grating parameters h   and ww and the associated uncertainties.