Absorption and scattering coefficients for metallic nanospheres near a substrate

We determine the amount of light absorbed and scattered by metallic spheres in the presence of a substrate. The analysis is restricted to the spheres whose radius is small compared to the wavelength of the light such that the substrate-particle interactions are adequately described by the electrostatics limit. Results are presented for the absorption and scattering coefficients for: (i) the case when the electric permittivity of the spheres is described by the Drude model and (ii) for specific metals (silver, gold, and copper) for which the data on electrical permittivity as a function of the wavelength are available in the literature. It is found that it is possible to significantly increase the photovoltaic energy collected by a silicon substrate by depositing silver nanospheres on its surface. Mechanisms responsible for this increase are explored in detail in the electrostatics limit. Numerical results for the scattering are also used to derive an approximate formula that can be used to estimate the fractional increase in the photovoltaic energy. The increase predicted by this formula is qualitatively consistent with the literature data on the measured increase in the photocurrent by deposited silver nanospheres.