The rigorous integral equation method (viz MIM) in which the border structure is represented by a multilayer 1-D grating working at small wavelength-to-period ratios is used for taking into account electromagnetic scattering from different-types of nano-irregularities, such as periodical, random, self-organized, and their combinations. An example of the third type is multiple quantum dot (QD) ensembles and quantum molecules. The borders may contain a few or a large number of asperities of any kind. The program deals with a structure that is a grating from a mathematical point of view but that can model a rough surface if the groove spacing becomes large compared with the width (or correlation length) of asperities. This classical model for scattered light computation of bulk or few-border rough mirrors and gratings at visible and IR wavelengths is applied in PCGrate^(R)-SX v.6.2 software based on the MIM to calculate multilayer structures in the X-ray-VUV range, which is a very difficult problem for any rigorous method, even for 1-D surfaces. Border profiles of most realistic types including real ones (e.g. AFM-measured) have both periodical and random components, and some ensemble averaging is required to obtain exact specular and nonspecular (diffuse) scattering intensities. The PCGrate results are compared with the data obtained by approximated approaches and measurements. Calculated intensities of scattering from gratings and rough mirrors as well as multiple QD structures can differ from those obtained for ideal and average border profiles or from approximations by a few percent up to a few orders of magnitude. The method can be applied both to forward computations of efficiencies over a wide range of angles and to fitting of the border metrological performance by comparing to measured data.

Date Published: 18 June 2007
PDF: 12 pages
Proc. SPIE 6617, Modeling Aspects in Optical Metrology, 661719 (18 June 2007); doi: 10.1117/12.726038

Published in SPIE Proceedings Vol. 6617:
Modeling Aspects in Optical Metrology
Harald Bosse; Bernd Bodermann; Richard M. Silver, Editor(s)