Tight-Binding Method and Multiband Effective Mass Theory Applied to CdS Nanocrystals:  Single-Particle Effects and Optical Spectra Fine Structure

Abstract

Optical spectra of CdS nanocrystals are interpreted by using both the atomistic tight-binding method and multiband effective mass theory. Both methods correctly describe the energy splitting between the two lowest optically active transitions and their relative strengths, providing the same labeling of the two main absorption peaks of the spectrum. Our calculations unambiguously show that these peaks correspond to the 1S 3/2 f 1s and 1P 3/2 f 1p transitions. Both zinc blende and wurtzite-type structures for CdS nanocrystals are considered. Similar optical spectra are predicted for the two lattice structures. We also study how the spectrum, and in particular, the 1S 3/2 -1S 1/2 splitting, is changed by modifying parameters, within the experimental uncertainties, including size and shape fluctuations, surface passivation and spin-orbit coupling. Our results are robust to small variations in all of these parameters. IntroductionProgress in experimental techniques allows both the synthesis and characterization of high quality, monodisperse nanocrystals with a well-established shape, crystal structure, and a consistent surface derivatization. 1-3 Transmission electron microscopy (TEM) and X-ray powder diffraction (XRD) are used in combination with computer simulations to characterize nanocrystallite structural features. TEM allows imaging of individual nanocrystals and the development of a statistical description of the size and shape of the particles in a sample, whereas XRD determines the crystal structure. Different spectroscopies, such as fluorescence line narrowing and hole burning, are able to eliminate the effects of inhomogeneous broadening due to their size-selectivity so that the near-band-edge electronic fine structure can be observed. 2 Recently, attenuated low-energy photoelectron spectroscopy, A-LEP, has been proposed as a new technique for studying the hole states of the quantum particles (QPs), including the splitting between the light/heavy hole and split-off bands. 4 Both the effective mass method (EMM) and tight-binding (TB) theory have been successfully applied to model the optical properties of quantum dots and nanocrystals. The multiband effective mass theory has correctly predicted a large resonant Stokes shift in small CdS nanocrystals 5 consistent with recent photoluminescence excitation measurements, 6 whereas the atomistic tight-binding theory has provided a detailed description of the excitonic fine structure for multilayer nanocrystals with changes in composition on the monolayer scale. 7-9 In the abovementioned studies, the optical properties and the various observed phenomena are described well in terms of a single isolated dot.In this paper, we present both tight-binding and multiband effective-mass theory to describe the electronic states and optical response of CdS nanocrystals. We determine the effects of

Tight-binding model for semiconductor quantum dots with a wurtzite crystal structure: From one-particle properties to Coulomb correlations and optical spectra

“…͑12͒ has been applied in the past. 16,32,[79][80][81][82][83] In some of this work, the first part, the envelope part, has been neglected, 16,83 whereas in other works parts of the second contribution, the orbital contribution, have been included in addition to the envelope contribution. 32,79,82 However, no general statement has been made, which part is the dominant one for which kind of system.…”

“…The proper calculation of the second part, the orbital contribution, is much more involved, which is the reason why in the available literature several different approximations and assumptions have been proposed. 16,32,79,80,82,83 In the case of the orbital part it is necessary to connect the calculated TB coefficients c R␣ i directly to the underlying set of atomic basis orbitals. A commonly used approach is the use of atomic Slater orbitals, 67 as given in Table III for In, Ga, N, which take into account the influence of the effective screening of inner electron densities on the effective oneparticle wave functions for the bonding orbitals.…”

Radiative lifetimes and orbital symmetry of electronic energy levels of CdS nanocrystals: Size dependence

“…The next higher energy transition involves s-orbital hole levels and is orbital allowed. 27,28,[32][33][34] This electronic level structure has successfully been used to explain the resonant Stokes shift. 17 Interestingly, it has also been predicted that the hole level hierarchy is not universal in CdS NCs but depends on the NC size such that the s-orbital hole levels become ground states for large CdS NCs.…”

One-dimensional embedded cluster approach to modeling CdS nanowires

“…Understanding this process in detail requires accurate predictions of the structures and optical properties of such CdS nanostructures and the nanostructure/substrate interface, and an analysis of the role of defects in the material. [4][5][6][7][8][9][10][11][12] In addition to solar cell applications, 3, 12, 13 recent experimental work on one-dimensional (1D) CdS nanostructures has resulted in a range of other device applications such as waveguides, 14,15 light-emitting diodes, 16 logic gates, 17 lasers, [18][19][20] cathodoluminescence, 21 fieldemitters, 22,23 photodetectors, 23 gas sensors, 24,25 transistors, 26 a) Electronic mail: j.buckeridge@ucl.ac.uk and photoelectrochemistry. 27 Considering the importance of this material, both for its device potential and relevance to the understanding of the fundamental physics of anisotropic quantum confinement, there have been relatively few theoretical studies performed, [28][29][30][31][32] which have concentrated on nanowires of diameter ≤5 nm and, though they have had success in modeling the electronic structure of such nanowires, they have not considered modeling defects, which are key to understanding their optoelectronic properties.…”