[en] Excitons in quantum dots manifest a lower-energy spin-forbidden 'dark' state below a spin-allowed 'bright' state; this splitting originates from electron-hole (e-h) exchange interactions, which are strongly enhanced by quantum confinement. The e-h exchange interaction may have both a short-range and a long-range component. Calculating numerically the e-h exchange energies from atomistic pseudopotential wave functions, we show here that in direct-gap quantum dots (such as InAs) the e-h exchange interaction is dominated by the long-range component, whereas in indirect-gap quantum dots (such as Si) only the short-range component survives. As a result, the exciton dark/bright splitting scales as 1/R² in InAs dots and 1/R³ in Si dots, where R is the quantum-dot radius.

[en] We present a generalized valence-force-field (VFF) model for the ternary III-V alloys (III=Ga, In and V=N, P) to predict the formation energies and atomic structures of ordered and disordered alloy configurations. For each alloy (GaInN, GaInP, GaNP, and InNP) the VFF parameters, which include bond-angle/bond-length interactions, are fitted to the first-principles calculated formation energies of 30 ternary structures. Compared to standard approaches where the VFF parameters are transferred from the individual binary III-V compounds, our generalized VFF approach predicts alloy formation energies and atomic structures with considerably improved accuracy. Using this generalized approach and random realizations in large supercells (4096 atoms), we determine the temperature-composition phase diagram, i.e., the binodal and spinodal decomposition curves, of the (Ga, In) (N, P) ternary alloys

[en] Using the pseudopotential configuration-interaction method, we calculate the intrinsic lifetime and polarization of the radiative decay of single excitons (X), positive and negative trions (X⁺ and X^-), and biexcitons (XX) in CdSe nanocrystal quantum dots. We investigate the effects of the inclusion of increasingly more complex many-body treatments, starting from the single-particle approach and culminating with the configuration-interaction scheme. Our configuration-interaction results for the size dependence of the single-exciton radiative lifetime at room temperature are in excellent agreement with recent experimental data. We also find the following. (i) Whereas the polarization of the bright exciton emission is always perpendicular to the hexagonal c axis, the polarization of the dark exciton switches from perpendicular to parallel to the hexagonal c axis in large dots, in agreement with experiment. (ii) The ratio of the radiative lifetimes of mono- and biexcitons (X):(XX) is ∼1:1 in large dots (R=19.2 (angstrom)). This ratio increases with decreasing nanocrystal size, approaching 2 in small dots (R=10.3 (angstrom)). (iii) The calculated ratio (X⁺):(X^-) between positive and negative trion lifetimes is close to 2 for all dot sizes considered

[en] The temperature dependence of the band gap of hydrogen-passivated Si nanocrystals of radius R=0.7 and 1.1 nm has been calculated from first principles using constant-temperature molecular-dynamics simulations. The band-gap change with temperature ΔE_g(R,T)=E_g(R,T)?E_g(R,0) is obtained by averaging over the configurations sampled during the molecular-dynamics simulation. We find that ΔE_g(R,T) depends strongly on the nanocrystal size. At room temperature, the calculated ΔE_g(R,T) is approximately -150 meV for R=1.1 nm nanocrystals, and -210 meV for R=0.7 nm nanocrystals, significantly larger in magnitude than in the case of bulk Si. We also find that in Si nanocrystals the band-gap deformation potential is positive, but smaller than in bulk Si

[en] The calculation of the optical and electronic properties of semiconductor nanostructures is still based for the most part on highly approximated, continuum-like models such as the effective-mass approximation, which do not take into account the atomistic structure of the nanostructures. We present here an atomistic pseudopotential approach to the calculation of excited states in semiconductor nanostructures. The single-particle Schroedinger equation is solved using O(N) methods. The electronic excited states (such as excitons, charged excitons, multi-excitons, etc.) are then calculated by solving the many-particle Schroedinger equation in a basis set of Slater determinants obtained by promoting one or more electrons from the valence band to the conductions band (configuration interaction expansion). Applications of this method to predict the excitonic fine structure and the optical emission spectra of neutral and charged excitons, bi-excitons, and tri-excitons in CdSe colloidal nanocrystals are presented.

[en] Using atomistic, semiempirical pseudopotential calculations, we show that if one assumes the simplest form of a surface state in a CdSe nanocrystal - an unpassivated surface anion site - one can explain theoretically several puzzling aspects regarding the observed temperature dependence of the radiative decay of excitons. In particular, our calculations show that the presence of surface states leads to a mixing of the dark and bright exciton states, resulting in a decrease of 3 orders of magnitude of the dark-exciton radiative lifetime. This result explains the persistence of the zero-phonon emission line at low temperature, for which thermal population of higher-energy bright-exciton states is negligible. Thus, we suggest that surface states are the controlling factor of dark-exciton radiative recombination in currently synthesized colloidal CdSe nanocrystals.

[en] An exciton evolving from an m-fold degenerate hole level and an n-fold degenerate electron level has a nominal m x n degeneracy, which is often removed by electron-hole interactions. In PbSe quantum dots, the degeneracy of the lowest-energy exciton is m x n = 64 because both the valence-band maximum and the conduction-band minimum originate from the 4-fold degenerate (8-fold including spin) L valleys in the Brillouin zone of bulk PbSe. Using a many-particle configuration-interaction approach based on atomistic single-particle wave functions, we have computed the fine structure of the lowest-energy excitonic manifold of two nearly spherical PbSe quantum dots of radius R = 15.3 and 30.6 (angstrom). We identify two main energy splittings, both of which are accessible to experimental probe: (i) The intervalley splitting is the energy difference between the two near-edge peaks of the absorption spectrum. We find (delta) = 80 meV for R = 15.3 (angstrom) and (delta) = 18 meV for R = 30.6 (angstrom). (ii) The exchange splitting Δ_x is the energy difference between the lowest-energy optically dark exciton state and the first optically bright exciton state. We find that Δ_x ranges between 17 meV for R = 15.3 (angstrom), and 2 meV for R = 30.6 (angstrom). We also find that the room-temperature radiative lifetime is τ_R ∼ 100 ns, considerably longer than the ∼10 ns radiative lifetime of CdSe dots, in quantitative agreement with experiment

[en] Recent experimental observations of multiexciton recombination in colloidal CdSe quantum dots have revealed a high-energy emission band that has been attributed to the radiative recombination of a p-like electron with a p-like hole in a triexciton complex (three holes + three electrons). The reason for the occupation of p-like hole states in the triexciton, however, has remained elusive. Using atomistic pseudopotential calculations, we show here that p-like hole states are populated even at low temperature because of the relatively small Coulomb repulsion between s-like and p-like hole states, which leads to a non-Aufbau occupation sequence of the hole levels. We also show that the observed temperature dependence of the p-p emission band originates from the dark-bright splitting of the triexciton ground state. Our results provide a consistent explanation of the physical origin of the triexciton emission lines in CdSe quantum dots

[en] Quantum dots can be charged selectively by electrons or holes. This leads to changes in the intensity of interband and intraband optical transitions. Using atomistic pseudopotential calculations, we show that (1) when carriers are injected into dot-interior quantum-confined states, the intensity of interband transitions that have those states as their initial or final states is attenuated ('Pauli blocking') and (2) when carriers are injected into localized states near the surface of the dots, the electrostatic field set up by these charges attenuates all optically allowed interband transitions. We describe and explain these two mechanisms of intensity attenuation in the case of charged PbSe quantum dots. In addition, this study reveals a new assignment of the peaks in the absorption spectrum. The absorption spectrum of charged PbSe dots was previously interpreted assuming that all injected electrons reside in dot-interior states. This assumption has led to the suggestion that the second absorption peak originates from S_h-P_e and P_h-S_e optical transitions, despite the fact that such transitions are expected to be dipole forbidden. Our results show that the observed bleaching of absorption peaks upon electron or hole charging does not imply that the S_h-P_e or P_h-S_e transitions are allowed. Instead, the observed bleaching sequence is consistent with charging of both dot-interior and surface-localized states and with the assignment of the second absorption peak to the allowed P_h-P_e transition

[en] Direct carrier multiplication (DCM) occurs when a highly excited electron-hole pair decays by transferring its excess energy to the electrons rather than to the lattice, possibly exciting additional electron-hole pairs. Atomistic electronic structure calculations have shown that DCM can be induced by electron-hole Coulomb interactions, in an impact-ionization-like process whose rate is proportional to the density of biexciton states ρ_XX. Here we introduce a DCM 'figure of merit' R₂(E) which is proportional to the ratio between the biexciton density of states ρ_XX and the single-exciton density of states ρ_x, restricted to single-exciton and biexciton states that are coupled by Coulomb interactions. Using R₂(E), we consider GaAs, InAs, InP, GaSb, InSb, CdSe, Ge, Si, and PbSe nanocrystals of different sizes. Although DCM can be affected by both quantum-confinement effects (reflecting the underly electronic structure of the confined dot-interior states) and surface effects, here we are interested to isolate the former. To this end the nanocrystal energy levels are obtained from the corresponding bulk band structure via the truncated crystal approximation. We find that PbSe, Si, GaAs, CdSe, and InP nanocrystals have larger DCM figure of merit than the other nanocrystals. Our calculations suggest that high DCM efficiency requires high degeneracy of the corresponding bulk band-edge states. Interestingly, by considering band structure effects we find that as the dot size increases the DCM critical energy E₀ (the energy at which R₂(E) becomes (ge)1) is reduced, suggesting improved DCM. However, whether the normalized E₀/(var_epsilon)_g increases or decreases as the dot size increases depends on dot material