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.     

Hydrostatic pressure dependence of excitonic optical transitions in strained wurtzite GaN/AlN quantum disks

In the framework of the effective mass approximation, the effects of hydrostatic pressure on optical transitions associated with the excitons confined in strained wurtzite (WZ) GaN/AlN quantum disks (QDisks) with the confinement potential of finite depth are investigated by using a variational technique, with considering the influences of the built-in electric field (BEF) and the biaxial strain dependence of material parameters. The Schrödinger equation via the proper choice of the exciton trial wave function is solved. The behaviors of the excitonic optical transition are examined at different pressures for different QDisk sizes. 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. Numerical results show that the hydrostatic pressure and the QDisk size have a remarkable influence on exciton states. The calculated pressure coefficient of optical transition energy shows a negative value if the QDisk height L > 3.2 nm, in contrast with the positive pressure coefficient of the GaN band gap. The peculiar pressure behavior is related to the pressure-induced increase of the built-in electric field. For a fixed pressure, the optical transition energy has a red-shift if the QDisk height and radius increase and QDisk height has a more obvious influence on E_ph than QDisk radius. Furthermore, the relationship between the radiative decay time and hydrostatic pressure (QDisk height) is also investigated. It is found that the radiative decay time increases with pressure and the increment tendency is more prominent for the large height QDisks. The radiative decay time strongly increases by three orders of magnitude reaching microsecond order if the QDisk height increases from 1 nm to 3 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.     

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.     

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.     

Interband optical absorption in a strained CdxZn1−xO/ZnO quantum dot

Numerical calculations of the excitonic absorption spectra in a strained Cd_xZn_1−xO/ZnO quantum dot are investigated for various Cd contents. We calculate the quantized energies of the exciton as a function of dot radius for various confinement potentials and thereby the interband emission energy is computed considering the internal electric field induced by the spontaneous and piezoelectric polarizations. The optical absorption as a function of photon energy for different dot radii is discussed. Decrease of exciton binding energy and the corresponding optical band gap with the Cd concentration imply that the confinement of carriers decreases with composition x. The main results show that the confined energies and the transition energies between the excited levels are significant for smaller dots. Non-linearity band gap with the increase in Cd content is observed for smaller dots in the strong confinement region and the magnitude of the absorption spectra increases for the transitions between the higher excited levels.     

Band-edge exciton transitions temperature in multiple stacked self-assembled (In1−xMnx)As quantum dot arrays

Multiple stacked self-assembled (In_1−xMn_x)As quantum-dot (QD) arrays were grown on GaAs (100) substrates by using molecular-beam epitaxy with a goal of producing (In_1−xMn_x)As QDs with a semiconductor phase and a high ferromagnetic transition temperature (T_c). Atomic force microscopy, magnetic force microscopy, high-resolution transmission electron microscopy, and energy dispersive X-ray fluorescence measurements showed that crystalline multiple stacked (In_0.84Mn_0.16)As with symmetric single-domain particle were formed on GaAs substrates. Near-field scanning optical spectroscopy spectra at 10 K for the (In_0.84Mn_0.16)As multiple stacked QDs showed that the band-edge exciton transitions were observed. The magnetization curve as a function of the magnetic field at 5 and 300 K indicated that the multiple stacked (In_0.84Mn_0.16)As QDs were ferromagnetic, and the magnetization curve as a function of the temperature showed that the T_c was as high as 400 K. These results provide important information on the optical and magnetic properties for enhancing the T_c of (In_1−xMn_x)As-based nanostructures.     

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.     

Exciton binding energy and the optical absorption coefficient in a strained CdxZn1−xO/ZnO quantum dot

Numerical calculations of the excitonic absorption spectra in a strained Cd_xZn_1?xO/ZnO quantum dot are investigated for various Cd contents. We calculate the quantized energies of the exciton as a function of dot radius for various confinement potentials and thereby the interband emission energy is computed considering the internal electric field induced by the spontaneous and piezoelectric polarizations. The optical absorption as a function of photon energy for different dot radii is discussed. Decrease of exciton binding energy and the corresponding optical band gap with the Cd concentration imply that the confinement of carriers decreases with composition x. The main results show that the confined energies and the transition energies between the excited levels are significant for smaller dots. Non-linearity band gap with the increase in Cd content is observed for smaller dots in the strong confinement region and the magnitude of the absorption spectra increases for the transitions between the higher excited levels.     

Influence of Mg Composition on Optical Properties of Exciton Confinement in Strained Wurtzite ZnO/MgxZn1-xO Cylindrical Quantum Dots

Based on the effective-mass approximation and variational approach, excitonic optical properties are investigated theoretically in strained wurtzite (WZ) ZnO/Mg_xZn_1-xO cylindrical quantum dots (QDs) for four different Mg compositions: x=0.08, 0.14, 0.25, and 0.33, with considering a three-dimensional carrier confinement in QDs and a strong built-in electric field effect due to the piezoelectricity and spontaneous polarization. The ground-state exciton binding energy, the interband emission wavelength, and the radiative lifetime as functions of the QD structural parameters (height and radius) are calculated in detail. The computations are performed in the case of finite band offset. Numerical results elucidate that Mg composition has a significant influence on the exciton states and optical properties of ZnO/Mg_xZn_1-xO QDs. The ground-state exciton binding energy increases with increasing Mg composition and the increment tendency is more prominent for small height QDs. As Mg composition increases, the interband emission wavelength has a blue-shift if the dot height L<3.5 nm, but the interband emission wavelength has a red-shift when L>3.5 nm. Furthermore, the radiative lifetime increases rapidly with increasing Mg composition if the dot height L>3 nm and the increment tendency is more prominent for large height QDs. The physical reason has been analyzed in depth.     

Influence of Mg Composition on Optical Properties of Exciton Confinement in Strained Wurtzite ZnO/Mg_x Zn_(1-x) O Cylindrical Quantum Dots

Based on the effective-mass approximation and variational approach, excitonic optical properties are investigated theoretically in strained wurtzite (WZ) ZnO/Mg x Zn 1-x O cylindrical quantum dots (QDs) for four different Mg compositions: x = 0.08, 0.14, 0.25, and 0.33, with considering a three-dimensional carrier confinement in QDs and a strong built-in electric field effect due to the piezoelectricity and spontaneous polarization. The ground-state exciton binding energy, the interband emission wavelength, and the radiative lifetime as functions of the QD structural parameters (height and radius) are calculated in detail. The computations are performed in the case of finite band offset. Numerical results elucidate that Mg composition has a significant influence on the exciton states and optical properties of ZnO/Mg x Zn 1 x O QDs. The ground-state exciton binding energy increases with increasing Mg composition and the increment tendency is more prominent for small height QDs. As Mg composition increases, the interband emission wavelength has a blue-shift if the dot height L 3.5 nm, but the interband emission wavelength has a red-shift when L 3.5 nm. Furthermore, the radiative lifetime increases rapidly with increasing Mg composition if the dot height L 3 nm and the increment tendency is more prominent for large height QDs. The physical reason has been analyzed in depth.     

Built-in electric field effect on the linear and nonlinear intersubband optical absorptions in InGaN strained single quantum wells

Considering the strong built-in electric field (BEF) induced by the spontaneous and piezoelectric polarizations and the intrasubband relaxation, we investigate the linear and nonlinear intersubband optical absorptions in In_xGa_1-xN/Al_yGa_1-yN strained single quantum wells (QWs) by means of the density matrix formalism. Our numerical results show that the strong BEF is on the order of MV/cm, which can be modulated effectively by the In composition in the QW. This electric field greatly increases the electron energy difference between the ground and the first excited states. The electron wave functions are also significantly localized in the QW due to the BEF. The intersubband optical absorption peak sensitively depends on the compositions of In in the well layer and Al in the barrier layers. The intersubband absorption coefficient can be remarkably modified by the electron concentration and the incident optical intensity. The group-III nitride semiconductor QWs are suitable candidate for infrared photodetectors and near-infrared laser amplifiers.     

Size dependent effective band gap,optical absorption coefficients and refractive index changes in a wide ZnS/Zn1−xMgxS strained quantum well

Exciton binding energy of a confined heavy hole exciton is investigated in a Zn_1−xMg_xS/ZnS/Zn_1−xMg_xS single strained quantum well with the inclusion of size dependent dielectric function for various Mg content. The effects of interaction between the exciton and the longitudinal optical phonon are brought out. The effect of exciton is described by the effective potential between the electron and hole. The interband emission energy as a function of well width is calculated for various Mg concentration with and without the inclusion of dielectric confinement. Non-linear optical properties are carried out using the compact density matrix approach. The dependence of nonlinear optical processes on the well width is investigated for different Mg concentration. The linear, third order non-linear optical absorption coefficients values and the refractive index changes of the exciton are calculated for different concentration of magnesium content. The results show that the exciton binding energy is found to exceed LO phonon energy of ZnS for x>0.2 and the incorporation of magnesium ions and the effect of phonon have great influence on the optical properties of ZnS/Zn_1−xMg_xS quantum wells.     

Effects of dopant concentrations and firing temperatures on decay kinetics of manganese doped willemite nanopowders

Nanocrystallline willemite, Zn_2−xMn_xSiO₄ (0.5≤x≤5 mol%), doped with variable concentration of divalent manganese ions, phosphor powders were prepared using the simple wet-chemical sol-gel method combined with furnace firing at 800, 900, and 1000 °C. X-ray diffraction (XRD) and high resolution X-ray photoelectron (HR-XPS) scans confirm the presence of willemite phase of Zn₂SiO₄. Laser-induced phosphorescence decay measurements of Zn_2−xMn_xSiO₄ nanophosphors were investigated using high peak power pulsed UV nitrogen laser (λ=337.1 nm). The decay curves show non-single exponential behavior with long term decay rate. Various parameters describing the strength of optical transitions in atoms and molecules such as, Einstein's A and B coefficients, ‘f’, integrated cross-section, and transition dipole moment values have been calculated. The long term decay rate of optical transition parameters was found to be somewhat temperature and concentration dependent.     

Nonlinear optical properties of a D system in a spherical quantum dot

The nonlinear optical properties of a D⁻ system confined in a spherical quantum dot represented by a Gaussian confining potential are studied. The great advantage of our methodology is that the model potential possesses the finite height and range. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. We calculate the linear, third-order nonlinear and total optical absorption coefficients under the density matrix formalism. Numerical results for GaAs − Ga_1 − xAl_xAs QDs are presented. Our results show that the optical absorption coefficients in a spherical QD are much larger than their values for GaAs quantum wells. It is found that optical absorptions are strongly affected not only the confinement barrier height, dot radius, the electron-impurity interaction but also the position of the impurity.     

Electronic states and the resonant optical non-linearity of exciton in a narrow band InSb quantum dot

Binding energy, interband emission energy and the non-linear optical properties of exciton in an InSb/InGa_xSb_1−x quantum dot are computed as functions of dot radius and the Ga content. Optical properties are obtained using the compact density matrix approach. The dependence of non-linear optical processes on the dot sizes is investigated for different Ga concentrations. The linear, third order non-linear optical absorption coefficients, susceptibility values and the refractive index changes of the exciton are calculated for different concentrations of gallium content. It is found that gallium concentration has great influence on the optical properties of InSb/InGa_xSb_1−x dots.     

Exciton characteristics of Tl1−x CuxInS2 single crystals

The absorption spectra of Tl_1?x Cu_xInS₂ single crystals (x=0; 0.005; 0.010; 0.015) are interpreted using experimental data. The allowed interband direct transitions are determined, and the energy gap, binding energy, temperature-shift coefficient, Bohr radius, and reduced effective mass of the exciton are estimated.     

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.     

Indium-incorporation-induced transformation of optical, photoluminescence and lasing properties of InGaN epilayers

A comparative combined study of photoluminescence (PL), PL kinetics, stimulated emission (SE) and photoreflectance (PR) properties in In_xGa_1−xN epilayers is carried out in the composition range 0≤x≤0.19. In-incorporation up to 4% leads to the sufficient longer radiative recombination decay time due to the decrease in non-radiative recombination channels, which are peculiar to GaN, and band-to-band optical transitions predominate the spontaneous PL spectrum. Further In-incorporation (x>4%) leads to the localization of carriers and/or excitons at band-tails in the In-rich areas. Correlation between the position of dominant low-energy PR oscillation due to the main band gap and SE peak position shows that band-to-band transitions are responsible for lasing and dominate the PL spectrum in all highly pumped In_xGa_1−xN samples.     

Photoluminescence quantum and surface states of excitons in ZnSe and CdS nanoclusters

The optical spectra of quantum dots (QDs) of CdS and ZnSe grown in borosilicate glass by the sol-gel method are obtained and analyzed. It is found that at concentrations of the two semiconductors x<0.06% the emission spectra are due to annihilation of free (internal) excitons in quantum states. The mean size of the quantum dots for a given concentration of ZnSe and CdS is calculated and found to be in good agreement with the X-ray data, and the exciton binding energy is calculated with allowance for the dielectric mismatch between the semiconductor and matrix. It is proposed that this mismatch may be the cause giving rise to the exciton percolation level that is observed in QD arrays for both systems at x>0.06%. The emission from the surface level of CdS QDs in the region ~2.7 eV, formed by the outer atoms with dangling bonds, is observed for the first time, as is the emission band from surface localized states. The relation between the position of the maximum of this band and the energy of the 1S state of the free exciton is established. It is shown that the properties of surface localized states are largely similar to the analogous properties of localized states of 3D (amorphous semiconductors, substitutional solid solutions of substitution) and 2D (quantum wells and superlattices) structures.