Many-body Green function analysis and first-order perturbation theory are used to quantify the influence of size, surface reconstruction, and surface treatment on exciton transport between small silicon quantum dots. Competing radiative processes are also considered in order to determine how exciton transport efficiency is influenced. The analysis shows that quantum confinement causes small (~1 nm) Si quantum dots to exhibit exciton transport efficiencies far exceeding that of their larger counterparts for the same center-to-center separation. This surprising result offers the prospect of designing assemblies of quantum dots through which excitons can travel for long distances, a game-changing paradigm shift for next-generation solar energy harvesting. We also find that surface reconstruction significantly influences the absorption cross section and leads to a large reduction in both transport rate and efficiency. Further, exciton transport efficiency is higher for hydrogen-passivated dots as compared with those terminated with more electronegative ligands, a result not predicted by Förster theory.

CdTe/CdSe core/shell nanocrystals are the prototypical example of type-II nanoheterostructures, in which the electron and the hole wave functions are localized in different parts of the nanostructure. As the thickness of the CdSe shell increases above a few monolayers, the spectroscopic properties of such nanocrystals change dramatically, reflecting the underlying type-I → type-II transition. For example, the exciton Stokes shift and radiative lifetime increase, while the decreasing biexciton binding energy changes sign from positive to negative. Recent experimental results for CdSe nanocrystals isoelectronically doped with a few Te substitutional impurities, however, have revealed a very different dependence of the optical and electronic properties on the nanocrystal size. Here we use atomistic calculations based on the pseudopotential method for single-particle excitations and the configuration-interaction approach for many-particle excitations to investigate carrier localization and electronic properties of CdTe/CdSe nanocrystals as the size of the CdTe core decreases from a few nm (characteristic of core/shell CdTe/CdSe nanocrystals) to the single impurity limit. We find that the unusual spectroscopic properties of isoelectronically doped CdSe:Te nanocrystals can be rationalized in terms of the change in the localization volume of the electron and hole wave functions as the size of the nanocrystal increases. The size dependence of the exciton Stokes shift, exciton radiative lifetime, and biexciton binding energy reflects the extent of carrier localization around the Te impurities.

Many III-V semiconductor alloys exhibit spontaneous [111] alternate monolayer ordering when grown from the vapor phase. This is manifested by the splitting of the valence-band maximum and by a reduction in the direct band gap. We show here how these features can be used to deduce quantitatively the degree of long-range order in a given sample. Examples are given for Ga0.5In0.5P and Ga0.5In0.5As alloys.

The multiplication rates of hot carriers in CdSe quantum dots are quantified using an atomistic pseudopotential approach and first-order perturbation theory. We consider both the case of an individual carrier (electron or hole) decaying into a trion and the case of an electron-hole pair decaying into a biexciton. The dependence on quantum dot volume of multiplication rate, density of final states, and effective Coulomb interaction are determined. We show that the multiplication rate of a photogenerated electron-hole pair decreases with dot size for a given absolute photon energy. However, if the photon energy is rescaled by the volume-dependent optical gap, then smaller dots exhibit an enhancement in carrier multiplication rate for a given relative photon energy. We find that holes have much higher multiplication rates than electrons of the same excess energy due to the larger density of final states (positive trions). When electron-hole pairs are generated by photon absorption, however, the net carrier multiplication rate is dominated by electrons because they have much higher excess energy on average. We also find, contrary to earlier studies, that the effective Coulomb coupling governing carrier multiplication is energy-dependent.

The drive to make solar energy competitive with conventional energy sources has prompted the investigation of new photoconversion technologies, often referred to as third-generation photovoltaics, which have both lower cost and improved efficiency compared to existing technologies. In that framework, nanostructured materials, such as nanocrystals, nanowires, and nanotubes, occupy a prominent place because of their potential advantages over crystalline or thin-film photovoltaics technologies—high tunability of the bandgap via size control, strong band-edge absorption coefficient, efficient multiple-exciton generation by a single photon, and possibly high up-conversion efficiency. The ability to control the size, shape, composition, and surface termination of nanostructures provides new degrees of freedom that are inaccessible in conventional solar cell architectures. At the same time, the ability to explore this vast configuration space by synthesis and characterization alone is limited, which makes computational interrogation of the electronic and optical properties of nanostructures particularly valuable. In recent years, the convergence of new algorithms and new computational capabilities has made it possible for the first time to perform accurate electronic-structure calculations for large nanostructures. This article reviews recent developments in both semi-empirical and first-principles atomistic electronic structure methods that have led to accurate predictions and to a better understanding of carrier generation, relaxation, and recombination processes in nanostructured materials.

Si nanowires have attracted considerable attention as promising candidates for electronic, thermoelectric, photonic, and photovoltaic devices, yet there appears to be only limited understanding of the underlying electronic and excitonic structures on all pertinent energy scales. Using atomistic pseudopotential calculations of singleparticle as well as many-body states, we have identified remarkable properties of Si nanowires in three energy scales: (i) In the " high-energy" similar to 1-eV scale, we find an unusual electronic state crossover whereby the nature of the lowest unoccupied molecular orbital (LUMO) state changes its symmetry with wire diameters for [001]oriented wires but not for [011]-oriented wires. This change leads to orbitally allowed transitions becoming orbitally forbidden below a certain critical diameter for [001] wires. (ii) In the "intermediate-energy" similar to 10(-1)-eV scale, we describe the excitonic binding, finding that in [001] wires the diameter (D) dependence of excitonic gap scales as 1/D-1.9, not as 1/D-1 as expected. The exciton binding energy increases from 52 meV at D = 7.6 nm to 85 meV at D = 3.3 nm and 128 meV at D = 2.2 nm. (iii) In the "low-energy" similar to 10(-3)-eV scale, we describe dark/bright excitonic states and predict how orbitally allowed transitions [in scale (i)] become spin-forbidden due to the electron-hole exchange interaction, whereas the spin-allowed states in the orbitally forbidden diameter region remain dark. The diameter dependence of the fine-structure splitting of excitonic states scales as 1/D-2.3 in [001] wires and as 1/D-2.6 in [011] wires. Surface-polarization effects are found to significantly enhance electron-hole Coulomb interaction, but have a small effect on the exchange fine-structure splitting. The present work provides a roadmap for a variety of electronic and optical effects in Si nanowires that can guide spectroscopic studies.

Using ab initio all-electron methods, we investigate the evolution of effective masses, deformation potentials and pressure coefficients with the degree of long-range order in spontaneously ordered Ga0.5In0.5P alloys. We find that (i) the electron effective mass in the ordering direction increases significantly with the degree of order, while the effective mass in the perpendicular direction decreases; this produces a strong anisotropy of the electron effective mass which is not present in the disordered alloy; (ii) the band-gap deformation potential for (001) epitaxial strain decreases with increasing degree of order, reflecting the extent, of the ordering-induced Γ - L coupling; (iii) the band-gap pressure coefficient decreases from 8.4 meV/kbar in the disordered alloy to 6.6 meV/kbar in the ordered CuPt structure; interpolation to partial degrees of order leads to good agreement with recent high-pressure experiments.

Large GaAs domains embedded in an A1„Gai „As matrix act as potential wells for both electrons and holes, resulting in a direct band-gap system. When the GaAs domains become small, however, quantum-confinement effects may push the I -like conduction-band state localized on GaAs above the X-like conduction-band state of the Al Gai As alloy, leading to an indirect band-gap system. Using a pseudopotential band-structure method, as well as the conventional one-band effective-mass approximation, we investigate the nature of the direct~indirect (I —+X) transition in GaAs/A1„Gal „As quantum films, wires, and dots. In the case of an isolated GaAs quantum structure embedded in A1As, we 0 find that the critical size for the onset of the I ~X transition increases from —31 A in a two0 ~ ~ ~ ~ ~ ~ 0 dimensional film through -56 A in a one-dimensional cylindrical wire to -80 A in a zero-dimensional spherical dot. The interaction between GaAs quantum structures tends to reduce the critical size for the I ~X transition. We further study the effect of the alloy composition on the I —+X transition, finding that the critical size decreases when the Ga concentration of the alloy increases. In the case of spherical GaAs quantum dots embedded in an Al„Ga& As alloy, we show that, as a function of the dot radius and the alloy composition, different alignments of the band-edge states lead to different regimes of the lowest-energy optical transition.

A simple model-the single-configuration perturbation theory-has traditionally been used to explain the main features of the multiexcitonic spectra of quantum dots, where an electron and a hole recombine in the presence of other N(e)-1 electrons and N(h)-1 holes. The model predicts the (N(h),N(e)) values for which such spectra consist of a single line or multiple lines and whether singlet lines of different (N(h),N(e)) values are energetically aligned. Here we use a nonperturbative, correlated approach that shows when such simple rules work and when they fail, thereby establishing a basis for the appropriate use of such rules.

The concepts of (1) Carrier-Multiplication (CM - “two electron-hole pairs from one photon”) and (2) Intermediate Band Solar Cell (IBSC) based on nanostructures, have created significant interest and excitement, but, at the same time, raised questions pertaining to the approaches used to argue their validity. In part, confusion arose because the initial arguments made were based on rather qualitative, if not naïve, physical models. Here we propose to use the tools of modern theory of nanostructures for examining these concepts. Simple but surprising physical pictures emerge from such complex atomistic calculations. We will review and discuss the underlying concepts and experiments surrounding CM and quantum dot-based IBSC, delineating fact from fiction, and pointing to some new, important unanswered questions.

We report on the electronic structure of the band-edge biexciton in colloidal CdSe quantum dots using femtosecond spectroscopy and atomistic many-body pseudopotential calculations. Time-resolved spectroscopy shows that optical transitions between excitonic and biexcitonic states are distinct for absorptive and emissive transitions, leading to a larger Stokes shift for the biexciton than for the single exciton. The calculations explain the experimental results by showing that there is a previously unobserved electronic substructure to the band-edge biexciton which yields two distinct families of transitions.

The dark/bright exciton splitting Delta(X) in semiconductor nanocrystals is usually caused by electron-hole exchange interactions. Since the electron-hole wave-function overlap is enhanced by quantum confinement, it is generally assumed that Delta(X) increases monotonically as the quantum-dot size decreases. Using atomistic pseudopotential calculations, we show that in GaAs nanocrystals Delta(X) scales nonmonotonically with the nanocrystal size. By analyzing the nanocrystal wave functions in terms of contributions from different k points in the bulk Brillouin zone, we identify the origin of such nonmonotonic behavior in a transition of the lowest conduction-band wave function from Gamma like to X like as the nanocrystal radius decreases below 19 A. The nonmonotonicity arises because the long-range component of the electron-hole exchange interaction all but vanishes when the electron wave function becomes X like. We also show that the direct/indirect transition induced in GaAs nanocrystals by external pressure results in a sudden reduction in Delta(X).

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.