Multi-Wavelength Angle-Resolved Scattering of Randomly Rough Surfaces Based on the Scalar Diffraction Theory

Abstract

Angle-resolved scattering was measured for four samples of silicon exhibiting different surface roughnesses. The measurements were performed for three wavelengths: 457.9 nm, 514.5 nm, and 647.1 nm. Three approaches were used to evaluate the experimental data. The first approach corresponds to the exact formula derived using the scalar diffraction theory. This formula is quite complicated, and numerical methods must be used for its evaluation. For this reason, another two approaches representing approximations by much simpler formulae were considered. The use of several wavelengths allowed us not only to recover the power spectral density function in a limited interval of spatial frequencies but also to determine the total rms values of the heights, which represent the quantity of roughness for all spatial frequencies. The possibility of recovering the total rms values of the heights using the multi-wavelength approach is the most important result of this work. The results obtained from the scattering experiment and atomic force microscopy are compared.Angle-resolved scattering was measured for four samples of silicon exhibiting different surface roughnesses. The measurements were performed for three wavelengths: 457.9 nm, 514.5 nm, and 647.1 nm. Three approaches were used to evaluate the experimental data. The first approach corresponds to the exact formula derived using the scalar diffraction theory. This formula is quite complicated, and numerical methods must be used for its evaluation. For this reason, another two approaches representing approximations by much simpler formulae were considered. The use of several wavelengths allowed us not only to recover the power spectral density function in a limited interval of spatial frequencies but also to determine the total rms values of the heights, which represent the quantity of roughness for all spatial frequencies. The possibility of recovering the total rms values of the heights using the multi-wavelength approach is the most important result of this work. The results obtained from the scattering experiment and atomic force microscopy are compared.