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.     

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.     

Effect of built-in electric field in photovoltaic InAs quantum dot embedded GaAs solar cell

In this paper, three p–i–n GaAs solar cells were grown and characterized, one with InAs quantum dot (QD) layers embedded in the depletion region (sample A), one with QD layers embedded in the n ⁻ base region (B), and the third without QDs (control sample C). QD-embedded solar cells (samples A and B) show broad photoluminescence spectra due to QD multi-level emissions but have lower open-circuit voltages V _oc and lower photovoltaic (PV) efficiencies than sample C. On the other hand, the short-circuit current density J _sc in sample A is increased while it is decreased in sample B. Theoretical analysis shows that in sample B where the built-in electric field in QDs is zero, electrons tend to occupy QDs and strong potential variations exist around QDs which deteriorate the electron mobility in the n ⁻ base region so that J _sc in sample B is decreased. Hole trapping and electron–hole recombination in QDs are also enhanced in sample B, resulting in a reduced V _oc and thus a worse PV effect. In sample A, a strong built-in field exists in QD layers, which facilitates photo-carrier extraction from QDs and thus J _sc is increased. However, QDs in the depletion region in sample A act also as recombination-generation centers so that the dark saturated current density is drastically increased, which reduces V _oc and the total PV effect. In conclusion, a nonzero built-in electric field around QDs is vital for using QDs to increase the PV effect in conventional p–i–n GaAs solar cells.     

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.     

应变纤锌矿GaN/A10.15Ga0.85N柱形量子点的光学性质:流体静压力效应

在有效质量近似下,考虑强的内建电场和应变对材料参量的影响,变分研究了流体静压力对有限高势垒应变纤锌矿GaN/Al_0.15Ga_0.85N柱形量子点中重空穴激子的结合能、发光波长和电子空穴复合率的影响.数值结果表明,激子结合能和电子空穴复合率随流体静压力的增大而近线性增大,发光波长随流体静压力的增大而单调减小.在量子点尺寸较小的情况下,流体静压力对激子结合能和电子空穴复合率的影响更明显.由于应变效应,为了获得有效的电子-空穴复合过程,GaN量子点的高度必须小于5.5 nm.     

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.     

The donor bound exciton states in wurtzite GaN quantum dot

Based on the effective mass approximation, the donor bound exciton states in a wurtzite (WZ) GaN/AlGaN quantum dot (QD) are investigated by means of a variational method, including the strong built-in electric field effect due to the spontaneous and piezoelectric polarizations. Numerical results show that the donor bound exciton binding energy is highly dependent on the impurity position and QD size. In particular, we find that the donor bound exciton binding energy is insensitive to dot height when the impurity is located at the right boundary of the WZ GaN/AlGaN QD with large dot height.     

Donor bound excitons in wurtzite InGaN quantum dots: Effects of built-in electric fields

Within the framework of the effective-mass approximation and variational approach, we present calculations of the bound exciton binding energy, due to an ionized donor, in wurtzite In_xGa_1−xN/GaN strained quantum dots (QDs), considering three-dimensional confinement of the electron and hole in the QDs and the strong built-in electric field induced by the spontaneous and piezoelectric polarizations. Our results show that the position of the ionized donor, the strong built-in electric field, and the structural parameters of the QDs have a strong influence on the donor binding energy. The variation of this energy versus position of the donor ion is in double figures of milli-electron volt. Realistic cases, including the donor in the QD and in the surrounding barriers, are considered.     

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)     

Flying qubits and entangled photons

Efficient generation of polarized single photons or entangled photon pairs is crucial for the implementation of quantum key distribution (QKD) systems. Self organized semiconductor quantum dots (QDs) are capable of emitting on demand one polarized photon or an entangled photon pair upon current injection. Highly efficient single‐photon sources consist of a pin structure inserted into a microcavity where single electrons and holes are funneled into an InAs QD via a submicron AlOx aperture, leading to emission of single polarized photons with record purity of the spectrum and non‐classicality of the photons. A new QD site‐control technique is based on using the surface strain field of an AlO_x current aperture below the QD. GaN/AlN QD based devices are promising to operate at room temperature and reveal a fine‐structure splitting (FSS) depending inversely on the QD size. Large GaN/AlN QDs show disappearance of the FSS. Theory also suggests QDs grown on (111)‐oriented GaAs substrates as source of entangled photon pairs.     

Theoretical analysis of the electronic structure of truncated-pyramidal GaN/AlN quantum dots

We present a theoretical analysis of the electronic structure of GaN/AlN quantum dots (QD) with a hexagonal, truncated-pyramidal shape. We use a Fourier-transform technique that we had previously developed to calculate the 3D strain and built-in electric fields due to the QD structure. The electron and hole energy levels and wavefunctions are then calculated in the framework of an 8-band k·P model (with zero spin–orbit splitting), using an efficient plane-wave expansion method. We show that because of the large built-in piezoelectric and spontaneous polarization fields, the calculated transition energy is sensitive to variations in the wetting layer width, pyramid top diameter and also to the values chosen for the piezo-electric constants and spontaneous polarization values of bulk GaN and AlN. Numerical results are presented for a set of GaN/AlN QD structures that have been studied experimentally and described in the literature. We find that the calculated value of the ground-state optical transition energy for these structures is in good agreement with experiment.     

Interband Optical Transitions due to Donor Bound Excitons in Wurtzite InGaN Strained Coupled Quantum Dots： Strong Built-in Electric Field Effects

Considering the three-dimensional confinement of the electrons and holes and the strong built-in electric field （BEF） in the wurtzite InGaN strained coupled quantum dots （QDs）, the positively charged donor bound exciton states and interband optical transitions are investigated theoretically by means of a variational method. Our calculations indicate that the emission wavelengths sensitively depend on the donor position, the strong BEF, and the structure parameters of the QD system.     

Exciton states and optical transitions in InGaN/GaN quantum dot nanowire heterostructures: Strong built-in electric field and dielectric mismatch effects

Considering the strong built-in electric field (BEF), dielectric-constant mismatch and 3D confinement of the electron and hole, the exciton states and interband optical transitions in [0 0 0 1]-oriented Ga-rich wurtzite In_xGa_1−xN/GaN strained quantum dot (QD) nanowire heterostructures are investigated theoretically using a variational approach under the effective mass approximation. 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 radiative decay time. Our calculations show that the radiative decay time of the redshifted transitions is large and increases almost exponentially when the QD height increases, which is in good agreement with the previous experimental and theoretical results.     

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.     

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.     

GaN/AlN quantum dot photodetectors at 1.3–1.5 μm

We have demonstrated GaN/AlN quantum dots (QD) photodetectors, relying on intraband absorption and in-plane carrier transport in the wetting layer. The devices operate at room temperature in the wavelength range 1.3–1.5 μm. Samples with 20 periods of Si-doped GaN QD layers, separated by 3 nm-thick AlN barriers, have been grown by plasma-assisted molecular-beam epitaxy on an AlN buffer on a c-sapphire substrate. Self-organized dots are formed by the deposition of 5 monolayers of GaN under nitrogen-rich conditions. The dot height is 1.2±0.6 to 1.3±0.6 nm and the dot density is in the range 10¹¹–10¹² cm⁻². Two ohmic contacts were deposited on the sample surface and annealed in order to contact the buried QD layers. The dots exhibit TM polarized absorption linked to the s–p_z transition. The photocurrent at 300 K is slightly blue-shifted with respect to the s–p_z intraband absorption. The responsivity increases exponentially with temperature and reaches a record value of 10 mA/W at 300 K for detectors with interdigitated contacts.     

应变纤锌矿GaN/A10.15Ga0.85N柱形量子点的光学性质：流体静压力效应

在有效质量近似下,考虑强的内建电场和应变对材料参量的影响,变分研究了流体静压力对有限高势垒应变纤锌矿GaN/Al0.15Ga0.85N柱形量子点中重空穴激子的结合能、发光波长和电子空穴复合率的影响.数值结果表明,激子结合能和电子空穴复合率随流体静压力的增大而近线性增大,发光波长随流体静压力的增大而单调减小.在量子点尺寸较小的情况下,流体静压力对激子结合能和电子空穴复合率的影响更明显.由于应变效应,为了获得有效的电子-空穴复合过程,GaN量子点的高度必须小于5.5 nm.     

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.     

Exciton binding energies in GaN/AlxGa1 − xN pseudomorphic quantum wells

Interband transitions of pseudomorphic GaN/Al_xGa_1 − xN quantum wells are analysed theoretically with respect to the piezoelectric field utilizing a 6  ×  6 Rashba–Sheka–Pikus (RSP) Hamiltonian. Band structure modifications due to the built-in Stark effect explain a shift of the emission peak in GaN/Al_0.15Ga_0.85N of up to 400 meV. Quantum well exciton binding energies are calculated by the variational method and are discussed in terms of spatial separation of electrons and holes by the built-in electric field, as well as the interaction between valence subbands.     

有限元法计算GaN/AlN量子点结构中的电子结构

根据有效质量理论单带模型，采用有限元方法(FEM)计算了GaN/AlN量子点结构中的电子结构，分析了应变和极化对电子结构的影响，计算了不同尺寸的量子点的能级，分析了量子点的大小对电子能级的影响. 结果表明，形变势和压电势提升了电子能级，而且使简并能级分裂. 随着量子点尺寸的增大，量子限制能减小，而压电势能起到更显著的作用，使电子的能级降低，吸收峰发生红移. 关键词： GaN/AlN量子点结构 有效质量理论 电子能级