Exciton fine structure in semiconductor nanocrystals in the tight‐binding method

Abstract

We present a symmetry-based tight-binding (TB) method for calculating the exciton states and optical spectra in spherical semiconductor quantum dots (QD's). Here we focus on the resonant photoluminescence (PL) Stokes shift between the first optically active level and the ''dark" exciton ground state for nanocrystals (NC's). The method has so far been applied to CdSe and CdTe NC of diameter up to 6 nm. The experimental gaps and Stokes shifts show satisfactory agreement with the theoretical results. We have also investigated two series of quantum dot quantum wells (QDQW's). One of them is based on CdS cores which act as energy barrier; HgS well layers are intercalated between the core an additional CdS clad. The second serie of QDQW's is based on ZnS cores and CdS layers as wells. The experimental absorbance edges in the latter are quantitatively reproduced by our model which allows us to confidently predict the corresponding Stokes shifts.The confinement-induced blueshift of the fundamental gap and the discretization of the energy spectrum were early studied in the effective mass approximation (EMA) [1], progressively refined by taking into account the degeneracy of the valence band [2]. Atomistic approaches based on TB [3] or pseudopotential [4] methods provide a better description in the strong-confinement regime, where the QD radius R is smaller than the bulk exciton Bohr radius a B . It was early recognized that the quantum confinement also increases the overlap between the electron (e) and hole (h) charge distributions leading to an enhanced Coulomb interaction. But this energy scales as 1=R, while the confinement energy increases much faster ($ 1=R 2 in the EMA) with decreasing R. Thus, it seemed adequate to treat the e-h Coulomb interaction perturbatively, yielding a small decrease of the optical gap. More recently, the discovery of resonant PL Stokes shifts [5][6][7], attributed to the e-h exchange interaction, stimulated a strong interest in the theoretical investigation of the excitonic fine structure [7][8][9]. We have developed a symmetry-based TB approach which has been applied to CdTe (Refs. [10,11]) and CdSe (Ref.[12]) NC's as well as CdS/HgS/CdS and ZnS/CdS QDQW's (Refs. [13] and [14]). Here we present a short review.

Zero- versus One-Dimensional Water-Soluble CdTe NanocrystalsSynthesis and Photophysical Characterization

“…Notably, when the CdTe QD and QR were photoexcited above their band gaps (i.e., 420 nm), the nonresonant Stokes shifts, that is, the energetic dispositions of the absorptive and emissive transitions, were calculated from the corresponding absorption and emission spectra (Figure ). For the CdTe QD, the linear trend of nonresonant Stokes shifts versus the emission peak energies resembles that previously reported for comparable systems. − On the other hand, a more shallow slope is seen for the CdTe QR.

10 Nonresonant Stokes shift versus emission peak energy for CdTe QD (left) and QR (right).

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“…For the CdTe QD, the linear trend of nonresonant Stokes shifts versus the emission peak energies resembles that previously reported for comparable systems. [75][76][77] On the other hand, a more shallow slope is seen for the CdTe QR.…”