Description of Topography of Surfaces and Thin Films with the use Fourier Transformation, Obtained from Non-Standard Optical Measurements

Abstract

This chapter explains how to interpret the results obtained from optical scattering study to characterize topography surfaces and films. In particular, it focuses on measurement of bidirectional reflectance distribution function (BRDF) and on optical profilometry (PO). These techniques allow to determine two main functions describing surface topography, namely: power spectral density (PSD) and autocorrelation function (ACF). They characterize any real surface quantitatively and qualitatively. The PSD and ACF functions are commonly calculated from Fourier transform (FT) of the surface profiles determined in AFM, SEM or PO) measurements. The optical scattering is directly related to material and surface properties. We can distinguish three types of scatterings base on their features: 1) Topographic scattering resulting fom roughness causing phase fluctuations impressed on the reflected wavefront by the surface height variation [Beckmann and Spizinochino 1963] 2) material scattering created by fluctuations in the composition or density of the surface material [Elson 1984]. Defect scattering is resulting from a presence of sparse distribution of some surface features responsible for scattering, is distributed broadly and continuously over surfaces such as pits or bumps in case of topography and patches of different reflectivity in the case of material scattering [Stover 1995a]. One should emphasize that the roughness is the main source of scattering on surfaces at visible wavelengths range. Topography of real surface may be described using some fundamental parameters described in national and international norms [ANSI/ASME B46.1, ISO 2517] For macroscopic characterization of surface the following terms is applied [Whitehause 2003]): 1) Root mean square roughness σ (rms). It is calculated by the vertical deviations of a real surface from its ideal form. 2) The rms slope s and correlation length which is expressed by the ratio: T = 21/2 σ /s. 3) The power coefficient the type of qualifying statistical distribution of surface heights. The distance between respective surface features is defined as spatial wavelengths. In topographic analysis the term spatial frequency which is a reverse of spatial wavelength is used.