Biexcitonic absorption in a disk-shaped GaN quantum dot

The present work investigates the nonlinear optical properties of a GaN quantum dot in the disk limit via the exciton and biexciton states using the compact density matrix formalism. Based on this model, we calculate the ground state energy of the exciton and biexciton states by the variation method, within envelope function and effective mass approximations. Linear and nonlinear optical absorption (α ⁽¹⁾, α ⁽³⁾) and oscillator strengths attributed to the optical transitions are obtained. The details of the behaviour of α ⁽¹⁾ and α ⁽³⁾ around the resonance frequencies and for different quantum dot geometries are presented. It is found that the size of quantum dot and the optical intensity have a remarkable effect on the optical absorption, and the biexcitonic two-photon absorption coefficient(K ₂) has also been calculated in this system. The results show that this parameter is strongly affected by the size of the quantum dot.     

Electronic structure and absorption spectrum of biexciton obtained by using exciton basis

We approach the biexciton Schrödinger equation not through the free-carrier basis as usually done, but through the free-exciton basis, exciton–exciton interactions being treated according to the recently developed composite boson many-body formalism which allows an exact handling of carrier exchange between excitons, as induced by the Pauli exclusion principle. We numerically solve the resulting biexciton Schrödinger equation with the exciton levels restricted to the ground state and we derive the biexciton ground state as well as the bound and unbound excited states as a function of hole-to-electron mass ratio. The biexciton ground-state energy we find, agrees reasonably well with variational results. Next, we use the obtained biexciton wave functions to calculate optical absorption in the presence of a dilute exciton gas in quantum well. We find an asymmetric peak with a characteristic low-energy tail, identified with the biexciton ground state, and a set of Lorentzian-like peaks associated with biexciton unbound states, i.e., exciton–exciton scattering states. Last, we propose a pump–probe experiment to probe the momentum distribution of the exciton condensate.     

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.     

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.     

Pressure-induced threshold optical pump intensity in a CdTe/ZnTe quantum dot

Pressure-induced binding energies of an exciton and a biexciton are studied taking into account the geometrical confinement effect in a CdTe/ZnTe quantum dot. Coulomb interaction energy is obtained using Hartree potential. The energy eigenvalue and wave functions of exciton and the biexciton are obtained using the self-consistent technique. The effective mass approximation and BenDaniel-Duke boundary conditions are used in the self-consistent calculations. The pressure-induced nonlinear optical absorption coefficients for the heavy hole exciton and the biexciton as a function of incident photon energy for CdTe/ZnTe quantum dot are investigated. The optical gain coefficient with the injection current density, in the presence of various hydrostatic pressure values, is studied in a CdTe/ZnTe spherical quantum dot. The pressure-induced threshold optical pump intensity with the dot radius is investigated. The results show that the pressure-induced electronic and optical properties strongly depend on the spatial confinement effect.     

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.     

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.     

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.     

Correlated photons from multi-carrier complexes in GaAs quantum dots

We have studied micro-photoluminescence spectra of a self-assembled single GaAs quantum dot under 8 K. With strong pulsed excitation, the micro-photoluminescence spectrum shows bright emission lines originated from an exciton, a positively charged exciton, and a biexciton, together with weak lower energy emissions reflecting multi-excitonic structures with more carriers. We have identified the origins of these weak emission lines, and showed the existence of charged biexciton states, through single photon correlation measurements and excitation power dependence of the photoluminescence intensity. In addition, investigating the radiative recombination process of the charged biexciton, we have determined the electron–hole exchange energy in the GaAs quantum dot.     

Fractional-dimensional approach for biexcitons in GaAs/AlxGa1−xAs quantum wells

The energy of a biexciton in a GaAs/Al_xGa_1?xAs quantum well structure with finite barriers is investigated by using the geometrical model of two-dimensional biexcitons proposed by Singh et al. [J. Singh, D. Birkedal, V.G. Layssenko, J.M. Hvam, Phys. Rev. B 53 (1996) 15909; I.-K. Oh, J. Singh, Phys. Rev. B 60 (1999) 2528]. A fractional-dimensional approach is used to obtain the binding energy of the biexciton in both square quantum wells and parabolic quantum wells. Theoretical results show that the binding energy of a biexciton in a finite quantum well exhibits a maximum with increasing well width. The ratio of the binding energy of a biexciton to that of an exciton in a quantum well structure is found to be sensitive to the electron-to-hole mass ratio and larger than that in the three-dimensional system. The results agree fairly well with previous experimental results. The results of our approach are also compared with those of earlier theories.     

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     

垂直耦合自组织InAs双量子点中激子能的计算

在有效质量近似条件下研究了垂直耦合的自组织InAs/GaAs量子点的激子态.在绝热近似条件下，采用传递矩阵方法计算了电子和空穴的能谱.通过哈密顿量矩阵的对角化，对电子和空穴间的库仑相互作用进行了精确处理.讨论了两量子点间的垂直距离对激子基态能的影响.从基态波函数概率分布的角度，讨论了激子的束缚能.计算了重空穴和轻空穴激子的基态能随外部垂直磁场变化的函数关系.计算了量子点大小（量子点半径）对激子能的影响. 关键词： 量子点 激子 对角化     

A negatively charged exciton in a quantum disc

The properties of the bound states of the negatively charged exciton X⁻ in a quantum disc with a confined parabolic potential are studied using exact diagonalization techniques. The binding energy spectra of the ground state and the first excited state are calculated as a function of the confinement strength and the effective electron-to-hole mass ratio. The results we have obtained show that the binding energies are closely correlated to the strength of the confinement potential and the effective electron-to-hole mass ratio.     

The Electron－Hole Pair in a Single Quantum Dot and That in a Vertically Coupled Quantum Dot

The energy spectra of low-lying states of an exciton in a single and a vertically coupled quantum dots are studied under the influence of a perpendicularly applied magnetic field. Calculations are made by using the method of numerical diagonalization of the Hamiltonian within the effective-mass approximation. We also calculated the binding energy of the ground and the excited states of an exciton in a single quantum dot and that in a vertically coupled quantum dot as a function of the dot radius for different vaJues of the distance and the magnetic field strength.     

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.     

Fine structure of excitons in self-assembled In0.60Ga0.40As quantum dots: Zeeman-interaction and exchange energy enhancement

The fine structure of the ground state exciton has been studied by magnetophotoluminescence spectroscopy of self-assembled In_0.60Ga_0.40As single quantum dots. This was realized by using lithography for fabricating mesa structures which contain only a single dot. Due to a dot geometry-induced symmetry breaking we are able to observe the dark exciton states in magnetic field besides the bright excitons. From the spin-splitting data values for the corresponding exciton g-factors are obtained. In addition, the electron–hole exchange energies are determined, which are compared to detailed numerical calculations.     

Biexcitons in II–VI crystals: New interpretation of emission spectra

We report detailed magnetooptic studies of the so-called P line in CdS and CdSe crystals at high excitations (10³-10⁴ W cm^-2). The whole complex of experimental data allows to conclude unambiguously that the P line is connected with transitions from the Γ₁ ground state of excitonic molecule to 2P excited state of free exciton. Experimental values of binding energies of biexciton, that is 2.5 meV in CdS and 1.2 meV in CdSe, have been found.     

从头计算研究BCl+基态和激发态的势能曲线和光谱性质

基于相关一致极化4zeta(aug-cc-pVQZ)基组, 应用量子化学从头计算中高水平的多参考组态相互作用方法计算了BCl⁺ 两个离解极限B⁺(¹S_g)+Cl(²P_u)和B (²P_u)+Cl⁺ (³P_g)的14个Λ-S态势能曲线. 在计算中考虑了Davidson修正(+Q)和标量相对论效应, 并首次在计算中考虑了BCl⁺ 的旋轨耦合效应, 获得了由能量最低的4个Λ-S态分裂出的7个Ω 态. 计算结果表明相同对称性的Ω 态的势能曲线存在着非常明显的避免交叉. 通过分析Λ-S态的电子结构, 得到了各态的电子跃迁特性, 并确认了电子态的多组态性质. 使用LEVEL程序通过求解径向的Schrödinger方程得到了束缚Λ-S 和Ω态的光谱参数D_e, R_e, T_e, ω_e, ω_eχ_e和B_e. 通过和已有的Λ-S态X²∑⁺ 的实验数据进行对比发现, 本文所得的计算结果与实验结果非常一致. 而文中其他电子态的光谱参数均为首次报道. 关键词： 势能曲线 光谱参数 多参考组态相互作用方法 旋轨耦合     

Role of localized excitons in the stimulated emission in ultra-thin CdSe/ZnSe/ZnSSe single quantum-well structures

Photo-pumped lasing properties have been investigated in a CdSe/ZnSe/ZnSSE single quantum wells (SQWs) with the well-layer thickness (L_W) of 1, 2 and 3 monolayer (ML). At 20 K, the laser threshold for the SQW withL_W = 1 ML was the lowest in spite of the smallest active layer thickness. The carrier (exciton) sheet density at the threshold (n)_thwas estimated to be as low as 7 × 10¹⁰cm⁻², which is well below Mott's screening density. Time-resolved photoluminescence has revealed that the localized biexciton band, whose peak energy agrees with the lasing peak, appeared on the low-energy side of the main PL peak at this level of carrier concentrations. Theoretical calculation has also shown that the localized biexciton recombination has to be taken into account for the lasing process. On the contrary, then_thvalues of the SQWs with 2 and 3 ML are 1 order of magnitude larger than that of the SQW with 1 ML. This may be due to the smaller oscillator strength of both localized excitons and localized biexcitons because of the larger inhomogeneous broadening, resulting in an increased carrier density for achieving optical gain sufficient to overcome the reflection losses.     

EXCITON STATES IN QUANTUM DISKS

The method of few-body physics is applied to the calculation of the low-lying states of the exciton of a GaAs disk-like quantum dot with a parabolic potential. The binding energy of the exciton in quantum disks is calculated for two different thicknesses as a function of the disk size. The four lowest exciton states dependent on the disk thickness are investigated.