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.     

Study of correlation effects on stability of many-body complexes in III–V nitride quantum dots

The aim of this work is to analyze theoretically the correlation energies, for neutral, positive and negative excitons and bi-excitons in the III–V nitride In_xGa_1−xN/GaN quantum dot; where x=17.5% denotes the indium concentration. So, we propose a model consistent with experimental observations that is small In_xGa_1−xN truncated pyramids with circular base lying on wetting layer, both buried into GaN matrix. The correlation energies of many-body complexes X, X⁻, X⁺ and XX are investigated as a function of the quantum dot radius r_c and the intrinsic electric field.     

Effects of hydrostatic pressure on ionized donor bound exciton states in strained wurtzite GaN/AlxGa1−xN cylindrical quantum dots

Based on the effective-mass approximation and variational procedure, ionized donor bound exciton (D⁺, X) states confined in strained wurtzite (WZ) GaN/Al_xGa_1-xN cylindrical (disk-like) quantum dots (QDs) with finite-height potential barriers are investigated, with considering the influences of the built-in electric field (BEF), the biaxial strain dependence of material parameters and the applied hydrostatic pressure. The Schrödinger equation via the proper choice of the donor bound exciton trial wave function is solved. The behaviors of the binding energy of (D⁺, X) and the optical transition associated with (D⁺, X) are examined at different pressures for different QD sizes and donor positions. In our calculations, the effective masses of electron and hole, dielectric constants, phonon frequencies, energy gaps, and piezoelectric polarizations are taken into account as functions of biaxial strain and hydrostatic pressure. Our results show that the hydrostatic pressure, the QD size and the donor position have a remarkable influence on (D⁺, X) states. The hydrostatic pressure generally increases the binding energy of (D⁺, X). However, the binding energy tends to decrease for the QDs with large height and lower Al composition (x<0.3) if the donor is located at z₀≤0. The optical transition energy has a blue-shift (red-shift) if the hydrostatic pressure (QD height) increases. For the QDs with small height and low Al composition, the hydrostatic pressure dependence of the optical transition energy is more obvious. Furthermore, the relationship between the radiative decay time and hydrostatic pressure (QD height) is also investigated. It is found that the radiative decay time increases with pressure and the increment tendency is more prominent for the QDs with large height. The radiative decay time increases exponentially reaching microsecond order with increasing QD height. The physical reason has been analyzed in depth.     

Optical spectroscopy of a single InAs/GaAs quantum dot in high magnetic fields

We report on the measurements of the photoluminescence from the s-shell of a single InAs/GaAs quantum dot in magnetic fields up to 23 T. The observed multiline emission is attributed to different charge states of a single dot. Characteristic anticrossing of emission lines is explained in terms of hybridization of final states of a triply charged exciton (X⁻³).     

The trion as an exciton interacting with a carrier

The X⁻ trion is essentially an electron bound to an exciton. However, due to the composite nature of the exciton, there is no way to write an exciton-electron interaction potential. We can overcome this difficulty by using a commutation technique similar to the one we introduced for excitons interacting with excitons, which allows to take exactly into account the close-to-boson character of the excitons. From it, we can obtain the X⁻ trion creation operator in terms of excitons and electrons. We can also derive the X⁻ trion ladder diagram between an exciton and an electron. These are the basic tools for future works on many-body effects involving trions.     

Impurity and exciton effects on the nonlinear optical properties of a disc-like quantum dot under a magnetic field

A detailed investigation of the nonlinear optical properties of the (D⁺, X) complex in a disc-like quantum dot (QD) with the parabolic confinement, under applied magnetic field, has been carried by using the perturbation method and the compact density-matrix approach. The linear and nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wave functions. The competition between the confinement and correlation effects on the one hand, and the magnetic field effects on the other hand, is also discussed. The results show that the confinement strength of QDs and the intensity of the illumination have drastic effects on the nonlinear optical properties. In addition, we note that the absorption coefficients of an exciton in QDs depend strongly on the impurity but weakly on the magnetic field. Furthermore, the light and heavy hole excitons should be taken into account when we study the optical properties of an exciton in a disc-like QD.     

CdSSe quantum dots: effect of the hydrogen RF plasma treatment on exciton luminescence

This work deals with effective passivation of CdS_XSe_1−X quantum dot surface after treating it by low-temperature hydrogen RF plasma. An enhancement of the exciton luminescence was observed, which can be interpreted as consequence of a decreasing number of surface non-radiative traps.     

Quantum Monte Carlo simulation of exciton–exciton scattering in a GaAs/AlGaAs quantum well

We present a computer simulation of exciton–exciton scattering in a quantum well. Specifically, we use quantum Monte Carlo techniques to study the bound and continuum states of two excitons in a 10 nm wide GaAs/Al_0.3Ga_0.7As quantum well. From these bound and continuum states we extract the momentum-dependent phase shifts for s-wave scattering. A surprising finding of this work is that a commonly studied effective-mass model for excitons in a 10 nm quantum well actually supports two bound biexciton states. The second, weakly bound state may dramatically enhance exciton–exciton interactions. We also fit our results to a hard-disk model and indicate directions for future work.     

Systematic reduction of the permanent exciton dipole for charged excitons in individual self-assembled InGaAs quantum dots

The nature of the few particle wavefunctions for neutral and positively charged excitons is probed in individual InGaAs quantum dots using Stark-effect perturbation spectroscopy. A systematic reduction of the vertical component of the permanent excitonic dipole (p_z) is observed as additional holes are added to the dot. A comparison with calculations reveals that this reduction (Δp_z/e15–20%) is accompanied by a significant lateral expansion of the hole (2 nm) and contraction (1 nm) of the electron wavefunctions. We suggest that this lateral redistribution of the charged exciton wavefunctions provides an optical means to probe the lateral composition profile of the dot.     

Binding energies of negatively charged excitons in quantum disks

The Hamiltonian of a negatively charged exciton X⁻ (trion) in a quantum disk with parabolic confinement has been diagonalized to obtain the binding eigenenergy values of the L1 states as a function of the electron-to-hole effective mass ratio and the disk radius. It is found that a negatively charged exciton X⁻ in a quantum disk may have the second bound state with orbital angular momentum L=1 and the triplet state of the two bound electrons.     

Exciton-electron interaction in quantum wells with a two dimensional electron gas of low density

II–VI quantum-well structures containing a 2DEG of low density have been investigated by means of polarized photoluminescence, photoluminescence excitation and reflectivity in external magnetic fields up to 20 T. The spin splittings of the exciton X and the negatively charged exciton X ⁻ are measured as a function of the magnetic field strength. The behavior of the magnetic-field-induced polarization degree of the luminescence line related to X ⁻ demonstrates the formation process of negatively charged excitons from excitons and free carriers polarized by the external magnetic field. We have determined the binding energies of the trion formed either with the heavy-hole or the light-hole exciton. The optically detected magnetic resonance (ODMR) technique was applied for the first time to study the optical transition processes in a nanosecond timescale. The electron ODMR was observed with the detection on either the direct exciton or the negatively charged exciton X. Further evidence for the interaction of excitons with the electrons of the two-dimensional gas are demonstrated by a combined exciton-cyclotron resonance line observed in reflectivity and luminescence excitation, shake-up processes observed in photoluminescence, as well as inelastic and spin-dependent scattering processes. Fiz. Tverd. Tela (St. Petersburg) 41, 831–836 (May 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

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.     

Correlation energies of many-body complexes in biased InAs/GaAs quantum dots

The aim of this work is to analyze theoretically the correlation energies for neutral, positively, negatively charged exciton and bi-exciton. So, we propose a model consistent with experimental observations that is small InAs truncated pyramids with circular base lying on wetting layer, both buried into GaAs matrix.In a first step and in contrast to other works, we are able to evaluate coulombic interactions between electron and hole, two electrons and two holes by perturbative method at the second order. In a second step, the correlation energies of many-body complexes X, X^-, X⁺ and XX are investigated as a function of quantum dots basis radius r_c and the applied electric field.Our main goal is to provide realistic estimation for the correlation energies of excitons, charged excitons and bi-excitons while retaining at the same time a transparent formalism, which could easily be transposed to structures of actual interest.The present work provides evidence of the stability of excitons, charged excitons and bi-excitons in InAs/GaAs quantum dots. Calculated correlation energies of many-body complexes are consistent with those reported by recent photoluminescence measurements.     

Coherent dynamics in InGaAs quantum dots and quantum dot molecules

We measure the dephasing time of the exciton ground state transition in InGaAs quantum dots (QD) and quantum dot molecules (QDM) using a sensitive four-wave mixing technique. In the QDs we find experimental evidence that the dephasing time is given only by the radiative lifetime at low temperatures. We demonstrate the tunability of the radiatively limited dephasing time from 400 ps up to 2 ns in a series of annealed QDs with increasing energy separation of 69–330 meV from the wetting layer continuum. Furthermore, the distribution of the fine-structure splitting δ₁ and of the biexciton binding energy δ_B is measured. δ₁ decreases from 96 to with increasing annealing temperature, indicating an improving circular symmetry of the in-plane confinement potential. The biexciton binding energy shows only a weak dependence on the confinement energy, which we attribute to a compensation between decreasing confinement and decreasing separation of electron and hole. In the QDM we measured the exciton dephasing as function of interdot barrier thickness in the temperature range from 5 to 60 K. At 5 K dephasing times of several hundred picoseconds are found. Moreover, a systematic dependence of the dephasing dynamics on the barrier thickness is observed, showing how the quantum mechanical coupling in the molecules affects the exciton lifetime and acoustic-phonon interaction.     

Internal transitions of two-dimensional charged magneto-excitons X: theory and experiment

Internal spin-singlet and spin-triplet transitions of charged excitons X⁻ in magnetic fields in quantum wells have been studied experimentally and theoretically. The allowed X⁻ transitions are photoionizing and exhibit a characteristic double-peak structure, which reflects the rich structure of the magnetoexciton continua in higher Landau levels (LLs). We discuss a novel exact selection rule, a hidden manifestation of translational invariance, that governs transitions of charged mobile complexes in a magnetic field.     

Nonlinear optical properties of an exciton bound to an ionized donor impurity in quantum dots

In this study, a detailed investigation of the nonlinear optical properties of the (D⁺,X) complex in a disc-like parabolic quantum dot has been carried out by using the matrix diagonalization method and the compact density-matrix approach. First, the numeric calculations and analysis of the oscillator strength of intersubband quantum transition from the ground state into the first excited state at the varying confinement frequency have been performed. Second, the linear, third-order nonlinear, and total absorption coefficients and refractive indices have been investigated. It is observed that the confinement frequency of QDs and the intensity of the illumination have drastic effects on the nonlinear optical properties. In addition, we find that all kinds of absorption coefficients and refractive indices of an exciton in QDs shift to lower energies and their peak values have considerably decreases induced by the impurity.     

Effect of a buffer layer between the shell and ligand on the optical properties of an exciton and biexciton in type-II quantum dot nanocrystals

In this study, we have investigated the effect of the buffer layers on the electronic and optical properties of an exciton (X) and a biexciton (XX) in a type-II CdTe/CdSe quantum dot nanocrystal. In an experimental study, it has been reported that when a CdTe/CdSe quantum dot nanocrystal is coated by a ZnTe material as a buffer layer, the photoluminescence quantum yield is growing from 4 to 20%. We have confirmed theoretically this improvement and extended the calculations to an XX structure. In the calculations, two different semiconductor materials, CdS and ZnTe, have been considered for the buffer layer. We have theoretically shown that the buffer layer causes an increase in the radiative oscillator strength of both X and XX. When the ZnTe is used as the buffer layer, the oscillator strength becomes stronger when compared to CdSe buffer material because of higher conduction band offset between CdSe and ZnTe.     

Localized exciton dynamics in AlInGaN alloy

Carrier recombination dynamics in AlInGaN alloy has been studied by photoluminescence (PL) and time-resolved PL (TRPL) at various temperatures. The fast red-shift of PL peak energy is observed and well fitted by a physical model considering the thermal activation and transfer processes. This result provides evidence for the exciton localization in the quantum dot (QD)-like potentials in our AlInGaN alloy. The TRPL signals are found to be described by a stretched exponential function of exp[(−t/τ)^β], indicating the presence of a significant disorder in the material. The disorder is attributed to a randomly distributed QDs or clusters caused by indium fluctuations. By studying the dependence of the dispersive exponent β on temperature and emission energy, we suggest that the exciton hopping dominate the diffusion of carriers localized in the disordered QDs. Furthermore, the localized states are found to have 0D density of states up to 250 K, since the radiative lifetime remains almost unchanged with increasing temperature.     

The effects of indium segregation on exciton binding energy and oscillator strength in GaInAs/GaAs quantum wells

We solve analytically the Schrödinger equation taking into account the shape changes of GaInAs/GaAs quantum wells due to indium segregation during the MBE growth by using transfer matrix method. The indium compositional profiles of the quantum wells are provided using the phenomenological model. The fundamental transition energy, binding energy and oscillator strength of excitons as a function of indium segregation coefficient R$R$ and well width are studied. For narrow wells (less than 40 ML), the exciton binding energy and oscillator strength decrease, but for wide wells (larger than 40 ML), increase with increasing the segregation coefficient R$R$. It is shown that indium segregation degrades the optical properties and results in a blue-shift of exciton transition energy in GaInAs/GaAs quantum wells.     

The nonlinear optical rectification of a confined exciton in a quantum dot

An exciton in a disc-like quantum dot (QD) with the parabolic confinement, under applied electric field, is studied within the framework of the effective-mass approximation. The nonlinear optical rectification between the ground and the first-excited states has been examined through the computed energies and wave functions in details for the excitons. The results show that the optical rectification susceptibility obtained in a disc-like QD reach the magnitude of 10⁻² m/V, which is 3-4 orders of magnitude higher than in one-dimensional QDs. It is found that the second-order nonlinear optical properties of exciton states in a QD are strongly affected by the confinement strength and the electric field.