Size Dependence of the Spontaneous Emission Rate and Absorption Cross Section of CdSe and CdTe Quantum Dots

In this paper, the size dependence of the band gap, of the spontaneous emission rate, and of the absorption cross section of quantum dots is systematically investigated over a wide size range, using colloidal CdSe and CdTe QDs as model systems (diameters ranging from 1.2 to 8 nm and from 2 to 9.5 nm, respectively). The size dependence of the band gap is well-described by theoretical models, and is dominated by the quantum confinement contribution (1/d(2) scaling). The spontaneous emission rate increases linearly with the emission frequency for both CdSe and CdTe QDs, in good agreement with theoretical predictions. By extrapolating the frequency dependence of the emission rates to the bulk band gap values, the exciton radiative lifetime in bulk CdSe and CdTe could be estimated for the first time (viz., 18 and 20 ns, respectively). Comparison between the empirical trends and theoretical predictions provides new fundamental insights into the size dependence of the 1S((e))1S(3/2(h)) oscillator strengths of QDs, both for emission and absorption. The results highlight the importance of the balance between quantum confinement and coulomb interaction contributions to the size dependence of the exciton properties in QDs and offer an explanation to the long-standing discrepancies observed between the empirical size-dependent trends and the theoretical predictions. The difference between the size dependence of the radiative decay rates and of the absorption cross sections is shown to be due to the fundamental differences between the emission and absorption transitions (viz., spontaneous versus stimulated). The results are also relevant from a practical viewpoint, since they show that the molar extinction coefficients at energies far above the band gap are better suited for analytical purposes. Moreover, more extended and accurate sizing curves are provided for CdSe and CdTe QDs.