Optical absorption of semiconductor quantum dot solids

Several aspects concerning optical absorption in 3D assemblies of semiconductor quantum dots (QD solids) were studied. Considering the numerically simulated spectral dependences of the absorption coefficient in the case 3D QD assemblies with finite crystal size distribution, described by log-normal probability distribution functions (PDFs), several fundamental predictions were derived. First of all, it is predicted that the band gap energy of the QD solid should exhibit a certain 'red-shift' upon enlargement of the dispersion of the crystal size at a fixed average value thereof when the size-quantization regime in individual QDs has been entered. Furthermore, very large Urbach energy values are predicted, comparable to those characteristic for amorphous materials, for semiconductor QD solids with finite dispersion of the crystal size when the average QD size falls within the size-quantization interval. The Urbach energy in 3D assemblies composed by strongly quantized QDs with large dispersions of the PDFs characterizing the size distributions could be 100 times larger than the values in the non-quantized case (regardless of the size distribution in the latter case). Such large values are not due to the structural disorder inherent to individual QDs constituting the array, but a consequence of the disorder on the superlattice scale. Analogous arguments could be applied to predict large Urbach energies corresponding to the absorption tails in absorption spectra constructed from the spectral response of stationary nonequilibrium conductivity (photoconductivity). All these predictions are in excellent agreement with the available experimental data. Moreover, the presented approach could enable exact prediction of the optical absorption of a semiconductor QD solid if the PDF of the crystal size is known from the experiment. The smearing of excitonic absorption peaks in QD solids induced as a consequence of particle size distribution is considered and analyzed to some extent as well.