Surface integral determination of built-in electric fields and analysis of exciton binding energies in nitride-based quantum dots

We present a simple analytical approach to calculate the built-in strain-induced and spontaneous piezoelectric fields in nitride-based quantum dots (QDs) and then apply the method to describe the variation of exciton, biexciton and charged exciton energy with dot size in GaN/AlN QDs. We first present the piezoelectric potential in terms of a surface integral over the QD surface, and confirm that, due to the strong built-in electric field, the electrons are localised near the QD top and the holes are localised in the wetting layer just below the dot. The strong localisation and smaller dielectric constant results in much larger Coulomb interactions in GaN/AlN QDs than in typical InAs/GaAs QDs, with the interaction between two electrons, J_ee, or two holes, J_hh, being about a factor of three larger. The electron–hole recombination energy is always blue shifted in the charged excitons, X⁻ and X⁺, and the biexciton, and the blue shift increases with increasing dot height. We conclude that spectroscopic studies of the excitonic complexes should provide a useful probe of the structural and piezoelectric properties of GaN-based QDs.     

Optical properties of exciton confinement in wurtzite ZnO/MgxZn1−xO coupled quantum dots

Based on the framework of effective-mass approximation and variational approach, optical properties of exciton are investigated theoretically in ZnO/Mg_xZn_1−xO vertically coupled quantum dots (QDs), with considering the three-dimensional confinement of electron and hole pair and the strong built-in electric field effects due to the piezoelectricity and spontaneous polarization. The exciton binding energy, the emission wavelength and the oscillator strength as functions of the different structural parameters (the dot height and the barrier thickness between the coupled wurtzite ZnO QDs) are calculated with the built-in electric field in detail. The results elucidate that structural parameters have a significant influence on the exciton state and optical properties of ZnO coupled QDs. These results show the optical and electronic properties of the quantum dot that can be controlled and also tuned through the nanoparticle size variation.     

Fine structure splitting and biexciton binding energy in single self-assembled InAs/AlAs quantum dots

We report on photoluminescence investigations of individual InAs quantum dots embedded in an AlAs matrix which emit in the visible region, in contrast to the more traditional InAs/GaAs system. Biexciton binding energies, considerably larger than for InAs/GaAs dots, up to 9 meV are observed. The biexciton binding energy decreases with decreasing dot size, reflecting a possible crossover to an antibinding regime. Exciton and biexciton emission consists of linearly cross polarized doublets due to a large fine structure splitting up to 0.3 meV of the bright exciton state. With increasing exciton transition energy the fine structure splitting decreases down to zero at about 1.63 eV. Differences with InAs/GaAs QDs may be attributed to major dot shape anisotropy and/or larger confinement due to higher AlAs barriers.     

Influence of Mg content on optical properties of exciton confinement in wurtzite ZnO/MgxZn1−xO coupled quantum dots

Based on the framework of effective-mass approximation and variational approach, optical properties of exciton are investigated theoretically in ZnO/Mg_xZn_1−xO vertically coupled quantum dots (QDs), with considering the three-dimensional confinement of electron and hole pair and the strong built-in electric field effects. The exciton binding energy, the emission wavelength and the oscillator strength as functions of the structural parameters (the dot height, the barrier thickness between the coupled wurtzite ZnO QDs and Mg content x in the barrier layers) is calculated in detail. The results elucidate that Mg content have a significant influence on the exciton state and optical properties of ZnO coupled QDs. When Mg content x increases, the strong built-in electric field increases and leads to the redshift of the effective band gap of the Mg_xZn_1−xO layer. These theoretical results are useful for design and application of some important photoelectronic devices constructed by using ZnO strained QDs.     

Size dependence of biexciton binding energy in single InAs/GaAs quantum dots

This paper studies the size dependence of biexciton binding energy in single quantum dots (QDs) by using atomic force microscopy and micro-photoluminescence measurements. It finds that the biexciton binding energies in the QDs show ``binding' and ``antibinding' properties which correspond to the large and small sizes of QDs, respectively. The experimental results can be well interpreted by the biexciton potential curve, calculated from the exciton molecular model and the Heitler--London method.     

Self-consistent calculations of exciton, biexciton and charged exciton energies in InGaN/GaN quantum dots

We present theoretical calculations of the variation of exciton energies in truncated conical InGaN quantum dots (QDs) in a GaN matrix with dot size and indium composition. We compute the built-in strain-induced and spontaneous piezoelectric fields using a surface integral method that we have recently derived, and confirm that the built-in fields can be of the order of a few MV/cm, resulting in a spatial separation of the electrons and holes. The ground state wavefunctions of the exciton (X⁰), biexciton (2X⁰) and the two charged excitons (X⁻ and X⁺) are then calculated in the Hartree approximation, using a self-consistent finite difference method. We find that the electron–hole recombination energy is always blue-shifted for the charged excitons X⁻ and X⁺, with a further blue-shift for the biexciton, and this blue-shift increases with increasing indium content. We describe the trends in interband transition energy and the scale of the blue-shift with dot size, shape and composition. We conclude that spectroscopic studies of the exciton, charged excitons and biexciton should provide a useful probe of the structural and piezoelectric properties of GaN-based QDs.     

Two-photon excitation of confined biexcitons in CuCl quantum dots

We have studied direct creation processes of confined biexcitons in CuCl quantum dots by polarization-dependent resonant two-photon excitation spectroscopy. The two-photon absorption band for the lowest state of the biexciton (total angular momentum J=0) which appears on the lower energy side of confined exciton band was identified from the analysis of the polarization dependence of the photoluminescence excitation spectrum of the biexciton. Furthermore, the two-photon excitation process for the excited state of the biexciton (J=2) was also found with polarization dependence different from the J=0 biexciton state.     

Influence of the built-in electric field on luminescent properties in self-formed single InxGa1−xN/GaN quantum dots

Based on the framework of effective-mass approximation and variational approach, luminescent properties are investigated theoretically in self-formed wurtzite In_xGa_1−xN/GaN quantum dots (QDs), considering the three-dimensional confinement of electron and hole pair and the strong built-in electric field effects due to the piezoelectricity and spontaneous polarization. The exciton binding energy, the emission wavelength and the oscillator strength as functions of the different structural parameters (the height L and the radius R) are calculated with and without the built-in electric field in detail. The results elucidate that the strong built-in electric field has a significant influence on luminescent properties of In_xGa_1−xN/GaN QDs.     

Optical probe of InAs/GaAs self-assembled quantum dots grown using low growth rate and growth interruptions

We have investigated the optical properties of InAs/GaAs self-assembled quantum dots (QDs), grown at 500 °C using a low growth rate (0.014 ML/s), growth interruptions and a two-stage capping process. The samples exhibited large-size dots with densities in the range (3-4.5) × 10⁹ cm⁻². Macro-photoluminescence (macro-PL) measurements revealed the presence of five electronic sub-bands in the dots, with the ground state (GS) emission exhibiting a linewidth of ∼70 meV. Because of the dots large size and composition dispersions, associated with the growth method, it was possible to resolve single dots emissions using micro-PL (μ-PL) excitation in the barrier layers of the as-grown samples. The sharp PL lines were detected 60-140 meV above the GS peak energy. High-resolution resonant optical excitation of the dots PL evidenced that these fine lines originate from exciton complexes confined to the GS of individual dots. Non-resonant power dependence μ-PL spectroscopy results further confirmed the occurrence of both single exciton (X) and biexciton (XX) radiative recombinations. Finally, with increasing lattice temperature up to 95 K, PL emissions from most of these nanostructures suffered the usual thermal quenching, with activation energies (E_a) ranging between 12 and 41 meV. The relatively small values of E_a suggest that the growth technique implemented here favors the formation of defects centers in the vicinity of the QDs.     

Exciton states and interband optical transitions in wurtzite InGaN/GaN quantum dot nanowire heterostructures

Within the framework of the effective-mass approximation, the exciton states and interband optical transitions in In_xGa_1−xN/GaN strained quantum dot (QD) nanowire heterostructures are investigated using a variational method, in which the important built-in electric field (BEF) effects, dielectric-constant mismatch and three-dimensional confinement of the electron and hole in In_xGa_1−xN QDs are considered. We find that the strong BEF gives rise to an obvious reduction of the effective band gap of QDs and leads to a remarkable electron-hole spatial separation. The BEF, QD height and radius, and dielectric mismatch effects have a significant influence on exciton binding energy, electron interband optical transitions, and the exciton oscillator strength.     

Multiparticle states and the factors that complicate an experimental observation of the quantum coherence in the exciton gas of SiGe/Si quantum wells

The measured stationary and time-resolved photoluminescence is used to study the properties of the exciton gas in a second-order 5-nm-thick Si_0.905Ge_0.095/Si quantum well. It is shown that, despite the presence of an electron barrier in the Si_0.905Ge_0.095 layer, a spatially indirect biexciton is the most favorable energy state of the electron–hole system at low temperatures. This biexciton is characterized by a lifetime of 1100 ns and a binding energy of 2.0–2.5 meV and consists of two holes localized in the SiGe layer and two electrons mainly localized in silicon. The formation of biexcitons is shown to cause low-temperature (5 K) luminescence spectra over a wide excitation density range and to suppress the formation of an exciton gas, in which quantum statistics effects are significant. The Bose statistics can only be experimentally observed for a biexciton gas at a temperature of 1 K or below because of the high degree of degeneracy of biexciton states (28) and a comparatively large effective mass (about 1.3m _e ). The heat energy at such temperatures is much lower than the measured energy of localization at potential fluctuations (about 1 meV). This feature leads to biexciton localization and fundamentally limits the possibility of observation of quantum coherence in the biexciton gas.     

Optical study of single InAs on In0.12Ga0.88As self-assembled quantum dots: biexciton binding energy dependence on the dots size

Single self-assembled InAs quantum dots embedded in a In_0.12Ga_0.88As quantum well and emitting in the near infrared have been optically investigated. The dependence on the excitation power of the single quantum dot photoluminescence has been used to identify the emission of the biexciton complex. The biexciton binding energy, which has been measured for a dozen dots, increases with increasing exciton transition energy for the dot sizes investigated in the present work, as a consequence of stronger confinement in a smaller quantum dot. The obtained data is compared with experimental results available in the literature for InAs quantum dots. PACS 78.67.Hc; 73.21.La; 78.55.Cr     

Time-resolved studies of single quantum dots in magnetic fields

We present time-resolved and time-integrated spectroscopy of single InAs quantum dots grown in a GaAs matrix. We observe a number of interesting features in the spectra, including the zero field splitting of exciton and biexciton lines due to quantum dot asymmetry. By the application of an in-plane magnetic field, the normally optically active and inactive exciton states become mixed, enabling us to optically probe the normally inaccessible ‘dark’ states. Time resolved measurements on the mixed states show decay times several times longer than the exciton lifetime at zero field, which we show to be consistent with a dark exciton lifetime orders of magnitude longer than that for bright exciton.     

Influence of the built-in electric field on luminescent properties in self-formed single-GaN/AlxGa1−xN quantum dots

Based on the framework of effective-mass approximation and variational approach, the luminescent properties are investigated theoretically in self-formed wurtzite GaN/Al_xGa_1−xN single-quantum dots (QDs). Considering the three-dimensional (3D) confinement of electron and hole pair and the strong built-in electric field effects, the exciton binding energy, the emission wavelength and the oscillator strength are calculated with and without the built-in electric field in detail. The results elucidate that the strong built-in electric field has a significant influence on luminescent properties of GaN/Al_xGa_1−xN QDs.     

Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.     

Identifying multi‐excitons in quantum dots: the subtle connection between electric dipole moments and emission linewidths

The emission linewidths of excitonic complexes confined in quantum dots (QDs) mirror their interaction with a defect‐induced, fluctuating charge environment, a phenomenon known as spectral diffusion. Interestingly, extended excitonic complexes that comprise several interacting excitons exhibit significantly smaller emission linewidths if compared to the optical fingerprint of their building block, a sole exciton. Hence, it is not the absolute, but the relative electric dipole moment that governs the directly accessible emission linewidths. Exemplarily we investigate this matter based on differing exciton and biexciton emission linewidths of single GaN QDs with varying emission energies, i.e. QD dimensions. Our results establish the full width at half maximum (FWHM) or any other linewidths criterion for the identification of excitonic complexes, a technique that can directly be applied to polar but even non‐polar QD materials. Additionally, we find an emission energy dependent trend for the FWHM ratios of the biexciton and the exciton (XX_FWHM/X_FWHM) in perfect agreement with their relative dipole moment ratios as derived from our 8‐band‐ k · p based treatment of the Coulomb and exchange interaction within these multi‐particle complexes. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Relaxation and dephasing of multiexcitons in semiconductor quantum dots

We measure the dephasing time of ground-state excitonic transitions in InGaAs quantum dots under electrical injection in the temperature range from 10 to 70 K. Electrical injection into the barrier region results in a pure dephasing of the excitonic transitions. Once the injected carriers fill the electronic ground state, the biexciton to exciton transition is probed and a correlation of the exciton and biexciton phonon scattering mechanisms is found. Additional filling of the excited states creates multiexcitons that show a fast dephasing due to population relaxation.     

Multiple exciton generation in silicon quantum dot arrays: density functional perturbation theory computation

We use the density functional theory (DFT) combined with the many-body perturbation theory to derive expressions for the rates of the optical photon→exciton and photon→bi-exciton processes in nanoparticles, and for quantum efficiency, all to the leading order in the screened Coulomb interaction between Kohn–Sham quasiparticles. Also, we calculate exciton→bi-exciton rates due to the impact ionisation (II) mechanism in Si₂₉H₃₆ quantum dots (QDs) with both crystalline and amorphous core structures, and in quasi-one dimensional (1-D) arrays constructed from these QDs. We observe significant dependence of the carrier multiplication rates on the structure’s morphology and structural disorder. Amorphous silicon QD arrays are predicted to have more efficient bi-exciton generation rates as a function of exciton energy compared to their crystalline counterparts, and the isolated QDs of both kinds.     

Exciton in wurtzite GaN/AlxGa1−xN coupled quantum dots

Based on effective-mass approximation, we present a three-dimensional study of the exciton in GaN/Al_xGa_1−xN vertically coupled quantum dots (QDs) by a variational approach. The strong built-in electric field due to the piezoelectricity and spontaneous polarization is considered. The relationship between exciton states and structural parameters of wurtzite GaN/Al_xGa_1−xN coupled QDs is studied in detail. Our numerical results show that the strong built-in electric field in the GaN/Al_xGa_1−xN strained coupled QDs leads to a marked reduction of the effective band gap of GaN QDs. The exciton binding energy, the QD transition energy and the electron-hole recombination rate are reduced if barrier thickness L^AlGaN is increased. The sizes of QDs have a significant influence on the exciton state and interband optical transitions in coupled QDs.     

Exciton tunnelling in ZnCdSe quantum well/CdSe quantum dots

Exciton tunnelling through a ZnSe barrier layer of various thicknesses is investigated in a Zn_0.72Cd_0.28Se/CdSe coupled quantum well/quantum dots (QW/QDs) structure using photoluminescence (PL) spectra and near resonant pump-probe technique. Fast exciton tunnelling from quantum well to quantum dots is observed by transient differential transmission. The tunnelling time is 1.8, 4.4 and 39 ps for barrier thickness of 10, 15 and 20 nm, respectively.