Effect of line and trench profile variation on specular and diffuse reflectance from a periodic structure

I model variations in the profile of a silicon grating consisting of parallel lines or trenches by calculating the reflectance of a superstructure in which the profiles are randomly modulated about the nominal profile. I vary the edge positions, the edge profiles, the line heights, and the trench depths and find that the Stokes reflectance can be modified from its nominal value by a relatively large amount, especially in the case of linewidth variations. I find that the reflected field can be approximated by the mean field reflected by a distribution of periodic gratings and that the field does not represent the field from the average profile. In fitting results to more than one modeled parameter, the changes that are observed can be enough to shift the deduced parameter in some cases by more than the rms variation of that parameter. The diffuse reflectance (the nonspecular diffraction efficiency) is found to increase with the variance of the fluctuations.