Calculation Of Surface Statistics From Light Scatter

Abstract

The operation of a differential scatterometer developed at Montana State University is briefly described. The scatterometer takes and stores data under computer control. Analysis routines allow calculation of the surface power spectral density (PSD) function for the cases of one-dimensional surfaces [Z(x) - diamond-turned surfaces, for example] and isotropic two-dimensional surfaces [ Z(x,y) - polished surfaces, for example] . In addition, the zero and second moments of the PSD may be taken to provide bandwidth-limited values of the root mean square roughness (cr) and the root mean square slope (m). Results from several samples are used to check the vector perturbation theory [E. L. Church and J. M. Zavada, Appl. Opt. 14, 1788 (1975)] used by the computer to relate the scatter distribution function to the PSD. These experiments take advantage of the fact that the surface - and hence its PSD - remain a constant function during the measurements. Variations in the incident angle and polarization are introduced, and the resulting PSDs are calculated and compared. In another experiment, the min/max scatter angles (or, conversely, the min/max PSD spatial frequencies) are matched to those of a total integrated scatter (TIS) system. Integration over the light scatter data and the PSD allows direct comparison to the TIS and effective rms roughness obtained by the TIS system.