Optical properties of dielectric thin films including quantum dots

Depending on the minimum size of their micro/nanostructure, thin films can exhibit very different behaviors and optical properties. From optical waveguides down to artificial anisotropy, through diffractive optics and photonic crystals, the application changes when decreasing the minimum feature size. Rigorous electromagnetic theory can be used to model most of the components, but, when the size is a few nanometers, quantum theory also has to be used. The materials, including quantum structures, are of particular interest for many applications, in particular for solar cells because of their luminescent and electronic properties. We show that the properties of electrons in periodic and nonperiodic multiple quantum well structures can be easily modeled with a formalism similar to that used for multilayer waveguides. The effects of different parameters, in particular the coupling between wells and well thickness dispersion, on possible discrete energy levels or the energy band of electrons and on electron wave functions are given. When such quantum confinement appears, the spectral absorption and extinction coefficient dispersion with wavelength are modified. The dispersion of the real part of the refractive index can be deduced from the Kramers-Kronig relations. Associated with homogenization theory, this approach gives a new model of the refractive index for thin films including quantum dots. The bandgap of ZnO quantum dots in solution obtained from the absorption spectrum is in good agreement with our calculation.