Effect of Bandwidth and Numerical Aperture in Optical Scatterometry

We consider the effects of finite spectral bandwidth and numerical aperture in scatterometry measurements and discuss efficient integration methods based upon Gaussian quadrature in one dimension (for spectral bandwidth averaging) and two dimensions inside a circle (for numerical aperture averaging). Provided the wavelength is not near a Wood's anomaly for the grating, we find that the resulting methods converge very quickly to a level suitable for most measurement applications. In the vicinity of a Wood's anomaly, however, the methods provide rather poor behavior. We also describe a method that can be used to extract the effective spectral bandwidth and numerical aperture for a scatterometry tool. We find that accounting for spectral bandwidth and numerical aperture is necessary to obtain satisfactory results in scatterometry.