Effect of the structure of smooth copper surfaces on the accuracy of determination of the optical constants of copper

The accuracy of determination of the optical constants of smooth copper surfaces produced by different technologies is analyzed, with particular attention paid to the consideration of the influence of scattered radiation (which is ignored by many authors) on the retrieval of the optical constants of copper surfaces from reflected radiation. The neglect of scattered radiation can lead to errors as high as 50% in determining the optical constants for bulk copper. For thin films, the errors are much lower. The influence of surface oxidation during measurements in air and surface features of studied objects on the parameters to be determined is analyzed as well. It is shown that errors in determination of the constants are maximal in the plasma resonance region of copper.

     

A scalar model of the angular and spectral dependence of scattering from a smooth metal surface: Direct and inverse problems

Analytical formulas describing the scalar characteristics of scattering (the scattering indicatrix and the diffuse reflectance spectrum) have been derived in the Rayleigh approximation for a smooth metal surface with randomly oriented roughnesses, taking into account their shapes and the correlation in distribution over the surface. Experimentally measured optical characteristics that can provide information necessary for selecting a proper theoretical model are indicated. The efficacy of the proposed theoretical model is demonstrated in its application to a smooth copper surface prepared by optical polishing. It is shown how topological characteristics can be determined from scattering experiments with this system.     

Erratum: “Simulation of Scattering of Optical Radiation by a Metal Surface with Nanometer Irregularity”

Optics and Spectroscopy -     

Optical constants of nanostructured layers of copper,nickel, palladium,and some oxides in the UV and visible spectral regions

It is found that a significant spread in the optical constants of metals reported by different authors is caused by differences in the sample preparation methods, measurement conditions, and methods of calculation of sought parameters, as well as by the oxidation effect. It is shown that the optical constants of metals in films 80–120 nm thick on silicon substrates with scattering below 10⁻⁴ are determined with minimal errors. The reflectance of these mirrors calculated from the optical constants found by the most accurate ellipsometric method coincides with the experimental value within the measurement accuracy. Low values of k(λ) obtained for thin layers in some works using the methods based on the measurement of the coherent transmittance and regular reflectance are explained by disregarded scattering and luminescence. The spectra of the imaginary part of the complex refractive index of copper, nickel, and copper oxide determined by us by the proposed methods for thin nanostructured layers taking into account the scattering and luminescence coincide with the most correct data for thick films in the spectral range of 325–633 nm. For thin palladium and palladium oxide layers, the variations in k(λ) are caused by the oxidation of metal granules and disregarded luminescence for thick oxide layers in the long-wavelength spectral region. The maximal difference in the imaginary part of the complex refractive index of copper and nickel for thin nanostructured layers are observed in the region of plasmon resonances, whose positions and amplitudes depend on the degree of asphericity, the shape, and the degree of order of particles and their aggregates, which shift the plasmon resonances of films to longer wavelengths with respect to spherical particles.     

Simulation of scattering of optical radiation by a metal surface with nanometer irregularity

Within the framework of the model of a limited electron free path, the scattering indicatrix for spherical nanoparticles was calculated. The calculations were made by an example of silver and supersmooth surfaces, which were modulated by a monolayer of spherical nanoparticles taking into account the correlation in the distribution of particles and the size effect within the framework of the interference approximation. As follows from the calculations, the inclusion of the size effect into consideration leads to a noticeable change of the scattering intensity, both for separate particles and a surface, near the plasma resonance wavelength. Because of this, the spectral dependences of the refractive index calculated with and without allowance for the size dependence of optical constants differ in the resonant region by more than an order of magnitude.