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 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.     

Studies of the third-order nonlinear optical susceptibility for InxGa1−xN/GaN cylinder quantum dots

The resonant third-order susceptibilities at various directions (both parallel and vertical to Z-axis) in self-assembled quantum dots (QDs) have been investigated. The nonlinear susceptibilities associated with the intraband transition in the conduction band are theoretically calculated for wurtzite In_xGa_1−xN/GaN-strained cylinder QDs. The confined wave functions and energies of electrons in the dots have been calculated in the effective-mass approximation by solving the 3D Schrödinger equation, in which a strong built-in electric field effect due to the piezoelectricity and spontaneous polarization has been taken into account. Furthermore, it is shown that the magnitude and the resonant position of the nonlinear susceptibility χ⁽³⁾(3ω) strongly depend on the dots’ size as well as size distribution.     

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.     

Separated AlxIn1−xN quantum dots grown by plasma-reactive co-sputtering

Separated Al_xIn_1−xN quantum dots (QDs) embedded in amorphous AlN films have been produced by radio-frequency co-sputtering technique on silicon (1 1 1) and quartz glass substrates. The mean size and density of Al_xIn_1−xN QDs can be conveniently monitored by deposition parameters. Transparent electron microscope, and X-ray diffraction were used to detect the structure of the Al_xIn_1−xN QDs system; field-emission scanning-electron microscope was adopted to measure the surface morphology and anticipate the size of the QDs; X-ray photoelectronic spectroscopy was used to measure the stoichiometric ratios of the QDs.     

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.     

Band offset calculations applied to III–V nitride quantum well device engineering

Band offset calculations for zinc-blende pseudomorphically strained Al_1−xGa_xN/Al_1−yGa_yN and In_xGa_1−xN/In_yGa_1−yN interfaces have been performed on the basis of the model solid theory combined with ab initio calculations. From the results obtained, we have calculated, separately, the valence and conduction band discontinuities of In_xGa_1−xN/GaN and GaN/Al_1−xGa_xN as a function of the indium and gallium contents respectively. Using the latter results, we have extended our study to simulate band discontinuities for strained Ga_1−xIn_xN/relaxed Al_1−yGa_yN heterointerfaces. Information derived from this investigation will be useful for the design of lattice mismatched heterostructures in modeling optoelectronic devices emitting at ultraviolet to near infrared wavelengths.     

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.     

Semiempirical tight-binding modelling of III-N-based heterostructures

In this work, we present a second nearest neighbour sp³s^* semi-empirical tight-binding theory to calculate the electronic band structure of heterostructures based on group III-N binary semiconductors and their ternaries. The model Hamiltonian includes the second nearest neighbour (2nn) interactions, the spin–orbit splitting and the nonlinear variations of the atomic energy levels and the bond length with ternary mole fraction. Using this sp³s^* tight-binding approach, we investigated the electronic band structure of Al_1−xGa_xN/GaN and In_1−xGa_xN/GaN heterostructures as a function of composition and interface strain for the entire composition range (0≤x≤1). There is an excellent agreement between the model predictions and experiment for the principal bandgaps at Γ, L and X symmetry points of the Brillouin zone for AlN, GaN and InN binaries and Al_1−xGa_xN and In_1−xGa_xN ternaries. The model predicts that the composition effects on the valence band offsets is linear, but on the conduction band offsets is nonlinear and large when the interface strain and deformation potential is large.     

Different temperature dependence of carrier transport properties between AlxGa1-xN/InyGa1-yN/GaN and AlxGa1-xN/GaN heterostructures

The temperature dependence of carrier transport properties of AlxGa1-xN/InyGa1-yN/GaN and AlxGa1-xN/GaN heterostructures has been investigated.It is shown that the Hall mobility in Al0.25Ga0.75N/In0.03Ga0.97N/GaN heterostructures is higher than that in Al0.25Ga0.75N/GaN heterostructures at temperatures above 500 K,even the mobility in the former is much lower than that in the latter at 300 K.More importantly,the electron sheet density in Al0.25Ga0.75N/In0.03Ga0.97N/GaN heterostructures decreases slightly,whereas the electron sheet density in Al0.25Ga0.75N/GaN heterostructures gradually increases with increasing temperature above 500 K.It is believed that an electron depletion layer is formed due to the negative polarization charges at the InyGa1-yN/GaN heterointerface induced by the compressive strain in the InyGa1-yN channel,which e-ectively suppresses the parallel conductivity originating from the thermal excitation in the underlying GaN layer at high temperatures.     

Phonon-assisted intersubband transitions in wurtzite GaN/InxGa1-xN quantum wells

A detailed numerical calculation on the phonon-assisted intersubband transition rates of electrons in wurtzite GaN/In_xGa_1-xN quantum wells is presented. The quantum-confined Stark effect induced by the built-in electric field and the ternary mixed crystal effect are considered. The electron states are obtained by iteratively solving the coupled Schrödinger and Poisson equations and the dispersion property of each type of phonon modes is considered in the derivation of Fermi's golden rule to evaluate the transition rates. It is indicated that the interface and half-space phonon scattering play an important role in the process of 1-2 radiative transition. The transition rate is also greatly reduced by the built-in electric field. The present work can be helpful for the structural design and simulation of new semiconductor lasers.     

InAs/AlAs quantum dots with InGaAs insertion layer: dependence of the indium composition and the thickness

We have systematically studied the effect of an In_xGa_1−xAs insertion layer (IL) on the optical and structural properties of InAs quantum dot (QD) structures. A high density of 9.6×10¹⁰ cm⁻² of InAs QDs with an In_0.3Ga_0.7As IL has been achieved on a GaAs (1 0 0) substrate by metal organic chemical vapor deposition. A photoluminescence line width of 25 meV from these QDs has been obtained. We attribute the high density and high uniformity of these QDs to the use of the IL. Our results show that the InGaAs IL is useful for obtaining high-quality InAs QD structures for devices with a 1.3 μm operation.     

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.     

Blue cathodoluminescence from thulium implanted AlxGa1−xN and InxAl1−xN

Room temperature cathodoluminescence (RTCL) was obtained from Tm implanted Al_xGa_1−xN with different AlN contents (in the range 0≤x≤0.2) and from implanted In_xAl_1−xN with different InN contents (x=0.13 and 0.19) close to the lattice match with GaN. The Tm³⁺ emission spectrum depends critically on the host material. The blue emission from Al_xGa_1−xN:Tm peaks in intensity for an AlN content of x0.11. The emission is enhanced by up to a factor of 50 times with an increase of annealing temperature from 1000 to 1300 C. The blue emission from In_0.13Al_0.87N:Tm, annealed at 1200 C, is more than ten times stronger than that from Al_xGa_1−xN:Tm, x≤0.2. However, the intensity decreases significantly as the InN fraction increases from 0.13 to 0.19.     

About some optical properties of AlxGa1−xN /GaN quantum wells grown by molecular beam epitaxy

Wurtzitic nitride quantum wells grown along the (0001) axis experience a large Stark effect induced by the differences of spontaneous and piezoelectric polarizations between the well and barrier materials. In Al_xGa_1−xN/GaN quantum wells, due to the adverse actions of quantum confinement, that blue-shifts transition energies, and of the Stark field, that red-shifts them, the transition energies are nearly independent of barrier compositions at a particular well thickness (L₀2.6 nm), at least for x≤0.3. The effect of alloy fluctuations is then minimal, as reflected by a minimum in the quantum well luminescence linewidth when LL₀ for wells grown by molecular beam epitaxy on silicon or sapphire substrates. We use this effect to estimate the average variances of well widths and alloy composition fluctuations. Both results are in good agreement with, respectively, a scanning tunneling microscopy study of GaN (0001) surfaces, and estimates based on the lateral extent of the quantum well excitons.We then discuss the optical properties of the Al_xGa_1−xN barrier material, with particular emphasis on the symmetry of the valence band maximum (Γ₉ or Γ₇). We show that it may play an important role in the apparent barrier luminescence efficiency. We analyse the possible consequences of the barrier Γ₉–Γ₇ crossover on the Al_xGa_1−xN/GaN quantum well properties.     

Built-in-polarization and thermal conductivity of InxGa1-xN/GaN heterostructures

The effect of built-in-polarization (BIP) field on thermal properties of In_xGa_1−xN/GaN heterostructure has been investigated. The thermal conductivity k of In_xGa_1−xN alloy has been estimated using Callaway's formula including the BIP field for In content x = 0, 0.1, 0.3, 0.5 and 0.9. This study reports that irrespective of In content, the room temperature k of In_xGa_1−xN/GaN heterostructure is enhanced by BIP field. The result predicts the existence of a characteristic temperature T_p at which both thermal conductivities (including and excluding BIP field) show a crossover. This gives signature of pyroelectric nature of In_xGa_1−xN alloy which arises due to variation of polarization with temperature indicating that thermal conductivity measurement can reveal pyroelectric nature. The pyroelectric transition temperature of In_xGa_1−xN alloy has been predicted for various x. The composition dependent nature of room temperature k for x = 0.1 and 0.5 are in line with prior experimental studies. The result can be used to minimize the self heating effect in In_xGa_1−xN/GaN heterostructures.     

Electric field effect on the donor impurity states in zinc-blende symmetric InGaN/GaN coupled quantum dots

Based on the effective-mass approximation, the donor binding energy in a cylindrical zinc-blende (ZB) symmetric InGaN/GaN coupled quantum dots (QDs) is investigated variationally in the presence of an applied electric field. Numerical results show that the ground-state donor binding energy is highly dependent on the impurity positions, coupled QDs structure parameters and applied electric field. The applied electric field induces an asymmetric distribution of the donor binding energy with respect to the center of the coupled QDs. When the impurity is located at the center of the right dot, the donor binding energy has a maximum value with increasing the dot height. Moreover, the donor binding energy is the largest and insensitive to the large applied electric field (F?400 kV/cm) when the impurity is located at the center of the right dot in ZB symmetric In_0.1Ga_0.9N/GaN coupled QDs. In addition, if the impurity is located inside the right dot, the donor binding energy is insensitive to large middle barrier width (Lmb?2.5 nm) of ZB symmetric In_0.1Ga_0.9N/GaN coupled QDs.     

The effects of GaN capping layer thickness on two-dimensional electron mobility in GaN/AlGaN/GaN heterostructures

In this paper we present a study of the effect of GaN capping layer thickness on the two-dimensional (2D)-electron mobility and the two-dimensional electron gas (2DEG) sheet density which is formed near the AlGaN barrier/buffer GaN layer. This study is undertaken using a fully numerical calculation for GaN/Al_xGa_1−xN/GaN heterostructures with different Al mole fraction in the Al_xGa_1−xN barrier, and for various values of barrier layer thickness. The results of our analysis clearly indicate that increasing the GaN capping layer thickness leads to a decrease in the 2DEG density. Furthermore, it is found that the room-temperature 2D-electron mobility reaches a maximum value of approximately 1.8×10³ cm² /Vs⁻¹ for GaN capping layer thickness grater than 100 Å with an Al_0.32Ga_0.68N barrier layer of 200 Å thick. In contrast, for same structure, the 2DEG density decreases monotonically with GaN capping layer thickness, and eventually saturates at approximately 6×10¹² cm⁻² for capping layer thickness greater than 500 Å. A comparison between our calculated results with published experimental data is shown to be in good agreement for GaN capping layers up to 500 Å thickness.     

Built-in electric field effect on cyclotron mass of magnetopolarons in a wurtzite In_xGa_（1-x）N/GaN quantum well

The cyclotron mass of magnetopolarons in wurtzite In x Ga 1 x N/GaN quantum well is studied in the presence of an external magnetic field by using the Larsen perturbation method.The effects of the built-in electric field and different phonon modes including interface,confined and half-space phonon modes are considered in our calculation.The results for a zinc-blende quantum well are also given for comparison.It is found that the main contribution to the transition energy comes from half-space and interface phonon modes when the well width is very small while the confined modes play a more important role in a wider well due to the location of the electron wave function.As the well width increases,the cyclotron mass of magnetopolarons first increases to a maximum and then decreases either with or without the built-in electric field in the wurtzite structure and the built-in electric field slightly reduces the cyclotron mass.The variation of cyclotron mass in a zinc-blende structure is similar to that in a wurtzite structure.With the increase of external magnetic field,the cyclotron mass of polarons almost linearly increases.The cyclotron frequency of magnetopolarons is also discussed.     

Phonon and electron-hole plasma effects on binding energies of excitons in wurtzite GaN/In<Subscript>x</Subscript>Ga<Subscript>1−x</Subscript>N quantum wells

The binding energy of an exciton screened by the electron-hole plasma in a wurtzite GaN/In _x Ga_1−x N quantum well (in the case of 0.1 < x < 1 within which the interface phonon modes play a dominant role) is calculated including the exciton-phonon interaction by a variational method combined with a self-consistent procedure. The coupling between the exciton and various longitudinal-like optical phonon modes is considered to demonstrate the polaronic effect which strongly depends on the exciton wave function. All of the built-in electric field, the exciton-phonon interaction and the electron-hole plasma weaken the Coulomb coupling between an electron and a hole to reduce the binding energy since the former separates the wave functions of the electron and hole in the z direction and the later two enlarge the exciton Bohr radius. The electron-hole plasma not only restrains the built-in electric field, but also reduces the polaronic effect to the binding energy.