Linear and Nonlinear Intersubband Optical Absorptions and Refractive Index Changes in InGaN Strained Single Quantum Wells： Strong Built-in Electric Field Effects

Considering the strong built-in electric field （BEF） effects due to the spontaneous and piezoelectric polarizations, the intersubband optical absorptions and refractive index changes for an InxGa1-xN/AlyGa1-yN strained single quantum well are studied theoretically within the framework of the density matrix method and effective-mass approximation. The linear, third-order nonlinear and total absorption coefficients and refractive index changes are calculated as a function of the incident optical intensity and photon energy. Our results show that both the incident optical intensity and the strong BEF have great influence on the total absorptions and refractive index cllanges. The results are significant for designing some important photodetectors and the photonic crystal devices with adjustable photonic band structures.     

Influence of exciton energy on intersubband transition of chirped superlattice GaAs/AlGaAs quantum cascade laser

The influence of exciton energy on intersubband transition was simulated for a chirped supperlattice quantum cascade laser of GaAs/Al_xGa_1-xAs. Exciton energy was modelled as a function of QW width for alloys of various percentages of constituent elements. The results showed that the exciton energy decreased proportionally with increasing QW width. Models were also generated to study exciton energy as a function of the percent alloy contents of Al_xGa_1-xAs barriers for QWs of various widths. Exciton energy showed characteristics of higher discrete energy when QW width was narrower. Transition energy was also simulated from e₁ and e₂ to the 1s exciton state as functions of applied electric field at various QW widths. Our simulation results showed that the transition energy from e₂ to the 1s exciton state increased proportionally to the increasing strength of the electric field. This transition energy was indicative of THz range radiation.     

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.     

Contactless electroreflectance of GaNyAs1−y/GaAs multi quantum wells: The conduction band offset and electron effective mass issues

Interband transitions in GaN_yAs_1−y/GaAs multi quantum well (MQW) samples with y=0.012 and 0.023 have been studied by contactless electroreflectance spectroscopy (CER). Optical transitions related to absorption in the GaAs barriers and in the GaN_yAs_1−y/GaAs QWs have been observed and analyzed. The GaAs related transition exhibits clear Franz-Keldysh oscillations with the period corresponding to the built-in electric field of 14 and 17 kV/cm for samples with y=0.012 and 0.023, respectively. The portion of the CER spectrum related to absorption in the GaN_yAs_1−y/GaAs QW exhibits two clear resonances which are attributed to optical transitions between the ground and excited states confined in the QWs. The resonance attributed to the ground state transition is associated with absorption between the first light- and heavy-hole subbands and the first electron subband (11L and 11H) while the resonance attributed to the excited state transition is associated with absorption between the second heavy-hole subband and the second electron subband (22H). The energies of the 11H and 22H transitions have been matched with those obtained from theoretical calculations performed within the effective mass approximation. Thus, the GaN_yAs_1−y/GaAs QWs are type-I structures with a conduction band offset, Q_C, between 70 and 80%. Moreover, the incorporation of N atoms into GaAs is found to cause a significant increase in the electron effective mass. The determined values of electron effective mass for GaN_yAs_1−y/GaAs QW with y=0.012 and 0.023 are 0.105m₀ and 0.115m₀, respectively.     

Intersubband absorption in strained AlxGa1−xN/GaN quantum wells with InyGa1−yN nanogroove layers

The intersubband absorption in a four-energy-level system consisting of a strained Al_xGa_1?xN/GaN quantum well with an In_yGa_1?yN nanogroove layer is calculated by considering the strain modification on the material parameters and polarization effect. It is found that the In_yGa_1?yN nanogroove layer in the middle of quantum well can enhance the confinement of electrons and their energy levels which consequently affect the intersubband absorption. With increasing the In composition and the groove thickness or applying a moderate compressive stress, an inflexion of energy levels appears when the lowest energy potentials of the left well and the groove are equivalent. The intersubband absorption spectrum exhibits multiple peaks contributed by different transitions. The position and height of absorption peaks are sensitive to the structural parameters (i.e., In composition and nanogroove thickness) and the strain induced by the groove layer.     

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.     

Anisotropic Spin Splitting in Step Quantum Wells

By the method of finite difference, the anisotropic spin splitting of the AlxGa1-xAs/GaAs/Aly Ga1-yAs/AlxGal-xAs step quantum wells （QWs） are theoretically investigated considering the interplay of the bulk inversion asymmetry and structure inversion asymmetry induced by step quantum well structure and external electric field. We demonstrate that the anisotropy of the total spin splitting can be controlled by the shape of the QWs and the external electric field. The interface related Rashba effect plays an important effect on the anisotropic spin splitting by influencing the magnitude of the spin splitting and the direction of electron spin. The Rashba spin splitting presents in the step quantum wells due to the interface related Rashba effect even without external electric field or magnetic field.     

Tunneling time correction to the intersubband optical absorption in a THz laser-dressed GaAs/Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1-</Subscript><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As quantum well

Tunneling effect on the intersubband optical absorption in a GaAs/Al _x Ga_{1- x} As quantum well under simultaneous presence of intense non-resonant laser and static electric fields is theoretically investigated. Based on the shooting method the quasi-stationary energy levels and their corresponding linewidths are obtained. By considering the joint action of the two external fields the linear absorption coefficient is calculated by means of Fermi’s golden rule and taking into account the intersubband relaxation. We found that: (i) the linewidth broadening due to the electron tunneling has an appreciable effect on the absorption spectrum; (ii) a constant relaxation time adopted in the previous studies could not be justified even for moderate electric fields, especially in the laser dressed wells. Our model predicts that the number of absorption peaks can be controlled by the external applied fields. While in the high-electric fields the excited states become unbounded due to a significant tunneling of the electrons, for high laser intensities and low/moderate electric fields the absorption spectrum has a richer structure due to the laser-generated resonant states. The possibility of tuning the resonant absorption energies by using the combined effects of the static electric field and the THz coherent radiation field can be useful in designing new optoelectronic devices.     

Improvement in intersubband optical absorption and the effects of device parameter variations in quantum wells with an applied electric field

The intersubband optical absorption in symmetric and asymmetric, single and coupled, double GaAs/ Ga_{1 − x}Al_xAs quantum wells is calculated. The results have been obtained in the presence of a uniform electric field as a function of the potential symmetry, size of the quantum well, and coupling parameter of the wells. In coupled double quantum wells we obtain a large Stark effect that can be used to fabricate tuneable photodetectors. We show that the effect of an applied electric field on the intersubband optical absorption is similar to changes in the dimensions of the structure. This behaviour in the intersubband optical absorption for different wells and barrier geometries can be used to study these systems in regions of interest, without the need for the growth of many different samples.     

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.     

Properties of InGaN/GaN quantum wells and blue light emitting diodes

We have reported the effects of growth interruption time on the optical and structural properties of high indium content In_xGa_1−xN/GaN (x>0.2) multilayer quantum wells (QWs). The InGaN/GaN QWs were grown on c-plane sapphire by metal organic chemical vapor deposition. The interruption was carried out by closing the group-III metal organic sources before and after the growth of the InGaN QW layers. The transmission electron microscopy (TEM) images show that with increasing interruption time, the quantum-dot-like region and well thickness decreases due to indium reevaporation or the thermal etching effect. As a result the photoluminescence (PL) peak position was blue-shifted and the intensity was reduced. The sizes and number of V-defects did not differ with the interruption time. The interruption time is not directly related to the formation of defects. The V-defect originates at threading dislocations and inversion domain boundaries due to higher misfit strain. Temperature dependent PL spectra support the results of TEM measurements. Also, the electroluminescence spectra of light-emitting diode show that dominant mechanism in InGaN/GaN QWs is a localized effect in the quantum-dot-like regions.     

Effect of position-dependent effective mass on linear and nonlinear optical properties of a cubic quantum dot

In this paper, we first obtain an analytic relation for studying the position-dependent effective mass in a GaAs/Al_xGa_1−xAs cubic quantum dot. Then, the effect of position-dependent effective mass on the intersubband optical absorption coefficient and the refractive index change in the quantum dot are studied. Our numerical calculations are performed using both a constant effective mass and the position-dependent effective mass. We calculate the linear, nonlinear and total intersubband absorption coefficient and refractive index change as a function of the incident optical intensity and structural parameters such as dot length. The results obtained from the present work show that spatially varying electron effective mass plays an important role in the intersubband optical absorption coefficient and refractive index change in a cubic quantum dot.     

Study of optical properties in a cubic quantum dot

In this paper, the effect of hydrostatic pressure on both the intersubband optical absorption coefficients and the refractive index changes is studied for typical GaAs/Al _x  Ga_1?x As cubic quantum dot. We use analytical expressions for the linear and third-order nonlinear intersubband absorption coefficients and refractive index changes obtained by the compact-density matrix formalism. The linear, third-order nonlinear, and total intersubband absorption coefficients and refractive index changes are calculated at different pressures as a function of the photon energy with known values of box length (L), the incident optical intensity (I), and Al concentration (x). According to the results obtained from the present work, we have found that the pressure plays an important role in the intersubband optical absorption coefficient and refractive index changes in a cubic quantum dot.     

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.     

Exciton effects on the refractive index and optical absorption in wurtzite quantum wells via a fractional-dimensional space approach

The optical refractive index changes and absorption coefficients of quantum wells (QWs) are theoretically investigated with considering exciton effects within the framework of the fractional-dimensional space approach. The exciton wave functions and bound energies are obtained as a function of spatial dimensionality, and the dimension increases with the well width increasing. Then optical properties are obtained by using the compact-density matrix approach and an iterative method. Numerical results are presented for wurtzite ZnO/Mg_xZn_1−xO QWs. The calculated results show that the changes of refractive index and absorption coefficients are greatly enhanced due to the quantum confinement of exciton. And the smaller the QW width (dimension) is, the larger influence of exciton on the optical properties will be. Furthermore, the exciton effects make the resonant peaks move to a lower energy. In addition, the optical properties are related to the QW width, the incident optical intensity and carrier density.     

Coulomb effects in spatially separated electron and hole layers in coupled quantum wells

We report on the (magneto-) optical study of many-body effects in spatially separated electron and hole layers in GaAs/Al_xGa_1?x As coupled quantum wells (CQWs) at low temperatures (T = 1.4 K) for a broad range of electron-hole (e-h) densities. Coulomb effects were found to result in an enhancement of the indirect (interwell) photoluminescence (PL) energy with increasing the e-h density both for a zero magnetic field and at high fields for all Landau level transitions; this is in contrast to the electron-hole systems in single QWs where the main features are explained by the band-gap renormalization resulting in a reduction of the PL energy. The observed enhancement of the ground state energy of the system of the spatially separated electron and hole layers with increasing the e-h density indicates that the real space condensation to droplets is energetically unfavorable. At high densities of separated electrons and holes, a new direct (intrawell) PL line has been observed: its relative intensity increased both in PL and in absorption (measured by indirect PL excitation) with increasing density; its energy separation from the direct exciton line fits well to the X ^? and X ⁺ binding energies previously measured in single QWs. The line is therefore attributed to direct multiparticle complexes.     

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.     

First principles study on electronic and optical properties of Al<Subscript>x</Subscript>Ga<Subscript>1−x</Subscript>N and In<Subscript>y</Subscript>Ga<Subscript>1−y</Subscript>N

The band structure, density of states of Al_xGa_1?xN and In_yGa_1?yN was performed by the first-principles method within the local density approximation. The calculated energy gaps of the AlN, Al_0.5Ga_0.5N, GaN, In_0.5Ga_0.5N and InN were 5.48, 4.23, 3.137, 1.274 and 0.504 eV, which were in agreement with the experimental result. The dielectric functions, absorption coefficient and loss function were calculated based on Kramers–Kronig relations. Further more, the relationships between electronic structure and optical properties were investigated theoretically. For Al_xGa_1?xN and In_yGa_1?yN materials, the micromechanism of the optical properties were explained.     

Intersubband transition in symmetric AlxGa1 − xN/GaN double quantum wells with applied electric field

Influence of the applied electric field (AEF) on the intersubband transitions (ISBTs) in symmetric Al_xGa_1 − xN/GaN double quantum wells (DQWs) is investigated by self-consistent calculation. It is found that three- and four-energy-level DQWs can be realized when suitable electric field is applied. When the AEF is 0.93 MV/cm, the 1_odd-2_even ISBT has a comparable absorption coefficient with the 1_even-2_odd ISBT, and the four-energy-level DQWs are realized. The wavelengths of the 1_odd-2_even and 1_even-2_odd ISBTs are located at 1.31 and 1.62 μm, respectively. When the AEF is 1.10 MV/cm, the 1_odd-2_even and 1_odd-2_odd ISBTs have comparable absorption coefficients, and the three-energy-level DQWs are realized. The wavelengths of the 1_odd-2_even and 1_odd-2_odd ISBTs are located at 1.30 and 1.55 μm, respectively. The results suggest promising application to two-color optoelectronic devices operating within optical communication wavelength band, and this study also provides a method for realizing the two-color optoelectronic devices by using the AEF.