Formation of nanoscale spatially indirect excitons: Evolution of the type-II optical character of CdTe/CdSe heteronanocrystals

Abstract

In this work, the evolution of the optical properties of nanoscale spatially indirect excitons as a function of the size, shape, and composition of the heteronanostructure is investigated, using colloidal CdTe/CdSe heteronanocrystals (2.6 nm diameter CdTe core and increasing CdSe volume fraction) as a model system. Emphasis is given to quantitative aspects such as the absorption cross section of the lowest-energy exciton transition $({\ensuremath{\mu}}_{SS})$, Stokes shift, linewidths, and the exciton radiative lifetime. The hole wave function remains confined to the CdTe core while the electron wave function is initially delocalized over the whole heteronanocrystal ($type\text{\ensuremath{-}}{I}^{1/2}$ regime), and gradually localizes in the CdSe segment as the growth proceeds, until the spatially indirect exciton transition becomes the lowest-energy transition (type-II regime). This results in a progressive shift of the optical transitions to lower energies, accompanied by a decrease in the oscillator strengths at emission energies and an increase in the exciton radiative lifetimes. The onset of the type-II regime is characterized by the loss of structure of the lowest-energy absorption band, accompanied by a simultaneous increase in the Stokes shift values and transition linewidths. This can be understood by considering the dispersion of the hole and electron states in $k$ space. The ${\ensuremath{\mu}}_{SS}$ values decrease rapidly in the ${\text{type-I}}^{1/2}$ regime but only slightly in the type-II regime. This shows that the indirect exciton formation leads primarily to redistribution of the oscillator strength of the lowest-energy transition over a wider frequency range. The total absorption cross section per ion-pair unit (i.e., integrated over all the exciton transitions) remains essentially constant during the heteronanocrystal growth, demonstrating that ${\ensuremath{\mu}}_{SS}$ is redistributed from higher-energy transitions of both the CdTe and the CdSe segments, in response to the reduction in the electron-hole wave-function overlap. Two radiative decay rates are observed and ascribed to exciton states with different degrees of localization of the electron wave function (an upper state with a faster decay rate and a lower state with a slower decay rate). The results presented here provide fundamental insights into nanoscale spatially indirect exciton transitions, highlighting the crucial role of a number of parameters (viz., electron-hole spatial correlation, exciton dispersion and exciton degeneracy, shape effects, and electronic coupling).