UNSPECIFIED. (1996) Influence of the surface height distribution on the total integrated scatter (TIS) formula. NANOTECHNOLOGY, 7 (1). pp. 43-46. ISSN 0957-4484

Abstract

The TIS formula, relating the rms surface roughness parameter R(q) to the specularly reflected light by TIS = specularly reflected light/total reflected light = exp [-((pi/lambda)R(q))(2)], has been derived for surfaces with a Gaussian height distribution. This study investigates the validity of this formula for Various realistic and artificial surface height distributions with and without skewness. The specular light intensity is calculated by using a Fourier transform expression for the Kirchhoff formalism of diffraction. The Kirchhoff formalism is valid for gently sloped metallic surfaces producing small scattering angles. In the case where the scattered light is collected by a lens, the light distribution in the focal plane of this lens is proportional to the power spectrum of the optical field close to the scattering surface. This optical input field can be related to the surface height distribution by geometrical optics, resulting in a phase modulation expression for the input field E(i)(x) proportional to exp[i2kyx)] where k = 2 pi/lambda and y(x) is the surface profile. Normal incidence illumination with wavelength lambda is assumed in this study. The theoretical surface profiles under investigation can be divided into profiles with and without skewness. They have the following surface height distributions: (i) zero skewness (can be produced by grinding triangular profile diffraction grating), exponential, Gaussian, uniform, sinusoidal, square wave; Iii) non-zero skewness (can be produced by diamond turning split triangular profile resembling plateau honing): parabolic cusp, pseudo-uniform. The results of this study are: (i) in the surface roughness range R(q) < 0.08 lambda, the percentage error in the roughness value obtained by the TIS formula is limited to 10% and (ii) skewness in the surface height distribution tends to reduce the light scatter for a given surface roughness.

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