Effect of size dispersion on the optical absorption of an ensemble of semiconductor quantum dots

The linear optical absorption of an ensemble of semiconductor quantum dots randomly positioned in an insulating matrix is studied theoretically and experimentally for the CdTe/glass system. The calculation of the effective dielectric function of the system, whose imaginary part determines the absorption, is based on a modified Maxwell-Garnett formalism using a diagram technique to calculate the average renormalized polarizability of spherical quantum dots. This approach takes into account both the fluctuations of the polarization interaction due to the random positions of the spheres and their size dispersion. A comparison of the theoretical and experimental spectra permits determination of the mean quantum dot size and concentration. The dependence of these parameters on the postgrowth annealing time of the samples is not consistent with the existing theories on the spinodal decomposition of solid solutions.