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.     

An exciton in a quantum well in the presence of crossed electric and magnetic fields

An analytical approach to the problem of the Wannier–Mott exciton in a semiconductor quantum well (QW) in the presence of external magnetic and electric fields is developed. The magnetic field is taken to lie in the heteroplanes while the electric field is directed perpendicular to the heteroplanes. Explicit dependencies of the energy levels and wave-functions of the exciton on the magnitudes of the fields for a wide range of the width of the QW are obtained. For the narrow QW, the results are valid for arbitrary electron and hole effective masses. In the case of intermediate and wide QWs, the adiabatic approximation implying the extreme difference of the electron and hole masses is used. In the intermediate QW, the states of the relative motion are the standard Coulomb states affected by the external fields while the states of the centre of mass are the size-quantized states in the QW. We focus particularly on the delocalized states caused by the external electric field and the motion of the excitons centre of mass in the magnetic field. These states are localized far away from the Coulomb centre. A strong influence of the boundaries of the wide QW on the delocalized exciton states is found to occur. Estimates of the expected values are made using typical parameters associated with GaAs QW.     

Shake-up intersubband transitions observed in GaAs/AlGaAs quantum wells

Shake-up transitions involving QW hole subbands have been observed as satellites in selective photoluminescence spectra of undoped GaAs/AlGaAs QWs. These shake-up transitions are explained in terms of an interaction between localized exciton and valence-band hole states attached to the QW subbands, in which holes are shaken up from the n=1 heavy hole subband to higher subbands, either the n=1 light hole subband or the n=2 heavy hole subband. The required localization is due to the interface roughness; thus these new transitions are of intrinsic origin. From the observation of the intersubband shake-up processes we derive direct information about the hole inter-subband energies. Furthermore, the satellite intensity is strikingly enhanced in the presence of a magnetic field due to an increasing exciton localization related to the compression of its wave function in the field. The exciton wave function compression continues until its radius in the plane of the well is comparable with the radius of the "flat island" characterized by constant QW width. Accordingly, from the magnetic field dependence of the shake-up satellite intensity we can roughly estimate the size of the "flat islands" and consequently probe the interface roughness.     

Nonresonant radiative exciton transfer by near field between quantum wells

We experimentally observed an increase in the intensity of photoluminescence from a wider quantum well (QW) when an exciton transition was induced in the neighboring narrower QW separated from the former one by a tunneling-nontransparent AlGaAs barrier. The dependence of the efficiency of the near-field radiative transfer of excitons on the distance between QWs was studied in heterostructures without coincidence of exciton resonances in the adjacent QWs. Theoretical results were qualitatively consistent with the available experimental data.     

Partial intermixing of strained InGaAs/GaAs quantum wells

Shallow ion implantation and rapid thermal annealing (RTA) was used to modify the optical properties of strained InGaAs/GaAs quantum wells (QWs). After RTA, QW exciton energies, determined from peak positions of the photoluminescence spectra, shifted significantly to higher energies in the implanted areas, whereas they remained basically unaffected in the unimplanted regions. The magnitudes of the energy shifts depend on the well width, RTA temperature and ion implantation fluence. The shifts were interpreted as arising from modification of the shapes of the as-grown QWs due to diffusion of In out of the well material. This process is enhanced by diffusion of vacancies generated near the sample surface by ion implantation. QWs with compositions near the critical thickness exhibit different behaviour from that of fully pseudomorphic layers, due to the presence of dislocations in these layers.     

Quantum well shape modification using vacancy generation and rapid thermal annealing

The effect of rapid thermal annealing (RTA) on the shapes of GaAs/AlGaAs quantum wells (QWs) has been investigated by monitoring exciton energies using low temperature photoluminescence and photoluminescence excitation spectroscopies. After RTA, large changes in exciton energies were observed only in regions of the samples in which excess surface vacancies were generated, either by capping with a thin layer of SiO₂ or by low-energy ion implantation. These changes were interpreted as resulting from modifications of the shapes of the as-grown QWs from abrupt or square to gradual (rounded) due to enhanced interdiffusion of well/barrier atoms. For single QWs there was an increase in exciton energy whose magnitude depended on the width of the well, its distance from the surface of the wafer, the annealing temperature and the total number of surface vacancies available. From studies of coupled QWs, there was clear evidence of asymmetry in the heterostructure after RTA. Although both techniques of vacancy generation yield substantial QW shape modifications, the ion implantation technique has the advantages of being highly reproducible and of being compatible with any material system.     

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.     

Photoluminescence linewidth broadening due to alloy/thickness fluctuation of CdxZn1 − xSe/ZnSe triple quantum wells

Photoluminescence (PL) linewidth broadening of Cd_xZn_{1 − x}Se/ZnSe triple quantum wells, grown on GaAs substrates by molecular beam epitaxy (MBE), has been investigated. Various quantum well (QW) samples have been prepared with different QW thickness and composition (Cd-composition). Measured and calculated PL linewidth are compared. Both composition and thickness fluctuations are considered for the calculation with the parameters such as the volume of exciton, nominal thickness and composition of QWs. Surface roughness measured by atomic force microscopy (AFM) is used to estimate the interface roughness. Results show that when Cd-composition increases additional linewidth broadening due to Zn/Cd interdiffusion is enhanced.     

Excitonic optical absorption in wurtzite InGaN/GaN quantum wells

Within the framework of the effective-mass and envelope function theory, exciton states and optical properties in wurtzite (WZ) InGaN/GaN quantum wells (QWs) are investigated theoretically considering the built-in electric field effects. Numerical results show that the built-in electric field, well width and in composition have obvious influences on exciton states and optical properties in WZ InGaN/GaN QWs. The built-in electric field caused by polarizations leads to a remarkable reduction of the ground-state exciton binding energy, the interband transition energy and the integrated absorption probability in WZ InGaN/GaN QWs with any well width and In composition. In particular, the integrated absorption probability is zero in WZ InGaN/GaN QWs with any In composition and well width L > 4 nm. In addition, the competition effects between quantum confinement and the built-in electric field (between quantum size and the built-in electric field) on exciton states and optical properties have also been investigated.     

Thermally induced quantum well shape modification in strained heterostructures

We have demonstrated that shallow ion (⁷⁵As⁺) implantation and rapid thermal annealing (RTA) of strained InGaAs/GaAs quantum well (QW) structures can modify the optical properties of these epitaxial semiconductor heterostructures in a spatially selective manner. After RTA, QW exciton energies, determined from peaks in the photoluminescence spectra, shifted significantly to higher values only in the implanted regions. The magnitudes of the shifts were dependent on QW widths, RTA temperatures, and ion implantation fluences. The shifts were interpreted as arising from the modification of the shapes of the as-grown QWs from square (abrupt interfaces) to rounded (gradual interfaces) due to enhanced indium diffusion out of the well layers in irradiated areas as a consequence of the in-diffusion of vacancies generated near the surface by the implantation. Except for QWs near the critical thickness boundary, the presence of strain in the quantum well layers due to the difference in the lattice constant of the well and barrier layers had negligible effect on the QW shape modification due to thermal processing.     

Interaction between an electron and optical phonons in polar semiconductor heterostructures

Interface phonons and bulk-like longitudinaloptical (LO) phonons and their interaction with an electron are studied for a finite four-layer heterostructure (FFLHS). An analysis of the field eigenvectors shows that, in the vicinity of the Brillouin-zone center, an interface transverse-optical (TO) mode oscillates at the bulk LO frequency, and an interface LO mode oscillates at the bulk TO frequency. Analytic expressions and numerical illustrations for dispersion relations of interface modes and for electron-phonon coupling functions and scattering rates are obtained for finite, semi-infinite and infinite quantum well (QW) structures which are important special cases of an FFLHS. It is shown that the scattering rates depend strongly on the well width of a QW structure, and that interface modes are much more important than bulk LO modes when the well width is small. The calculated results also show that the usual selection rules for intersubband and intrasubband transitions break down in asymmetric heterostructures. Moreover, we have found an interesting result. That is, in comparison with the negligibly small interaction between an electron and the lowest-frequency interface-mode in symmetric single QWs and commonly used step QWs, this interaction may be very large in asymmetric single QWs and general step QWs.     

Effect of Quantum Well Width Reduction for GaInNAs/GaAs Lasers

We investigated the function of the quantum well (QW) width for laser characteristics especially for reduction of the well width. We pointed out that such reduction has almost no influence on the optical gain or the carrier overflow for a large conduction band offset system, such as GaInNAs QWs. A thin QW is advantageous for suppression of the carrier overflow to the higher quantized energy levels which results in good temperature and gain characteristics. Thin GaInNAs QWs is a good candidate for an active layer structure of the lasers utilized in the next optical communication systems.     

Magneto-optical properties and exciton dynamics in diluted magnetic semiconductor nanostructures

Nanostructures of diluted magnetic semiconductors were fabricated to study novel magneto-optical properties that are derived from quantum confined band electrons interacting with magnetic ions. Quantum dots (QDs) of Cd_0.97Mn_0.03Se were grown by the self-organization on a ZnSe substrate layer. QDs of Zn_0.69Cd_0.23Mn_0.08Se and quantum wires (QWRs) of Cd_0.92Mn_0.08Se and Zn_0.69Cd_0.23Mn_0.08Se were fabricated by the electron beam lithography. A single quantum well (QW) of ZnTe/Zn_0.97Mn_0.03Te and double QWs of Cd_0.95Mn_0.05Te–CdTe were grown by molecular beam epitaxy. Magneto-optical properties and the formation and relaxation dynamics of excitons were investigated by ultrafast time-resolved photoluminescence (PL) spectroscopy. Excitons in these nanostructures were affected by the low-dimensional confinement effects and the interaction with magnetic ion spins. The exciton luminescence of the Cd_0.97Mn_0.03Se QDs shows the confined exciton energy due to the dot size of 4–6 nm and also shows marked increase of the exciton lifetime with increasing the magnetic field. The QDs of Zn_0.69Cd_0.23Mn_0.08Se fabricated by the electron beam lithography display narrow exciton PL spectrum due to the uniform shape of the dots. The exciton luminescence from the QWRs of Cd_0.92Mn_0.08Se and Zn_0.69Cd_0.23Mn_0.08Se shows the influence of the one-dimensional confinement effect for the exciton energy and the luminescence is linearly polarized parallel to the wire direction. The transient PL from the ZnTe/Zn_0.97Mn_0.03Te QWs displays, by the magnetic field, the level crossing of the exciton spin states of the nonmagnetic and magnetic layers and the spatial spin separation for the excitons. Cd_0.95Mn_0.05Te–CdTe double QWs show the injection of the spin polarized excitons from the magnetic well to the nonmagnetic QW.     

The exciton luminescence in Zn(Cd)Se/ZnMgSSe quantum wells

We study exciton states in Zn(Cd)Se/ZnMgSSe quantum wells (QWs) with various degrees of diffusion blurring in the interfaces by the methods of optical spectroscopy. We show that at low temperatures the QW emission spectra are determined by free and neutral donor-bound excitons. Blurring of the heterointerfaces leads to the increase in the energy shift between the emission line maxima of free and bound excitons. We explain the nonlinear dependence of the steady-state photoluminescence intensity on the excitation-power density in terms of the neutralization of charged donors at the photoexcitation of heterostructures. We observed a complex long-time dynamics of the reflection coefficient, evoked by the charge-redistribution processes in the heterostructure, near the QW exciton resonances under the irradiation.     

Restricted Three Body Problem in Semiconductor Heterostructure

The three-body restricted problem for X ^? and X ⁺ trions when a spatially separated exciton and electron or hole are located in the parallel quantum wells (QW) is reduced to the 2D three body problem for the exciton and the projection of the electron or hole on the plane of the excitonic QW. In the limit of a large spatial separation of the QWs the eigenfunctions and energy spectrum for X ^? and X ⁺ trions are obtained analytically. The 2D Wigner crystallization of the trions in the coupled QWs is discussed.     

Energy and effective mass of a polaron in asymmetric semiconductor quantum well structures

In this paper, the correct electron extended states wave functions and the density of states in asymmetric single quantum wells (QWs) are given for the first time, we put right mistakes from some previous papers of some other authors. Within the framework of the secondorder perturbation theory, the ground-state polaron binding energy and effective mass correction in asymmetric single QWs are studied including the full energy specturm, i.e., the discrete energy levels in the well and the continuum energy spectrum above the barrier, and all possible optical-phonon modes. The effects of the finite electronic confinement potential and the subband nonparabolicity are considered. The relative importance of the different phonon modes is investigated. Our results show that the polaron energy and effective mass are sensitive to the asymmetry of the structure and have a close relation to the interface phonon dispersion. When well width and one side barrier height of asymmetric QWs are fixed and identical with those of symmetric QW, the polaron binding energy and effective mass in asymmetric QWs are always less than those in symmetric QW. It is necessary to include the continuum energy spectrum as intermediate states in the study of polaron effects in QWs in order to obtain the correct results. The subband non-parabolicity has little influence on the polaron effects. The polaron energies given in this paper are excellent agreement with our variational results.     

GaAs/AlAs super-flat interfaces in GaAs/AlAs and GaAs/(GaAs) (AlAs) quantum wells grown on (4 1 1)A GaAs substrates by MBE

Effectively atomically flat GaAs/AlAs interfaces over a macroscopic area (“super-flat interfaces”) have been realized in GaAs/AlAs and GaAs/(GaAs) (AlAs) quantum wells (QWs) grown on (4 1 1)A GaAs substrates by molecular beam epitaxy (MBE). A single and very sharp photoluminescence (PL) peak was observed at 4.2 K from each GaAs/AlAs or GaAs/(GaAs) (AlAs) QW grown on (4 1 1)A GaAs substrate. The full-width at half-maximum (FWHM) of a PL peak for GaAs/AlAs QW with a well width ( ) of 4.2 nm was 4.7 meV and that for GaAs/(GaAs) (AlAs) QW with a smaller well width of 2.8 nm (3.9 nm) was 7.6 meV (4.6 meV), which are as narrow as that for an individual splitted peak for conventional GaAs/AlAs QWs grown on (1 0 0) GaAs substrates with growth interruption. Furthermore, only one sharp peak was observed for each GaAs/(GaAs) (AlAs) QW on the (4 1 1)A GaAs substrate over the whole area of the wafer (7 7 mm ), in contrast with two- or three-splitted peaks reported for each GaAs/AlAs QW grown on the (1 0 0) GaAs substrate with growth interruption. These results indicate that GaAs/AlAs super-flat interfaces have been realized in GaAs/AlAs and GaAs/(GaAs) (AlAs) QWs grown on the (4 1 1)A GaAs substrates.     

Contactless electroreflectance spectroscopy of optical transitions in low dimensional semiconductor structures

The authors present the application of contactless electroreflectance (CER) spectroscopy to study optical transitions in low dimensional semiconductor structures including quantum wells (QWs), step-like QWs, quantum dots (QDs), quantum dashes (QDashes), QDs and QDashes embedded in a QW, and QDashes coupled with a QW. For QWs optical transitions between the ground and excited states as well as optical transitions in QW barriers and step-like barriers have been clearly observed in CER spectra. Energies of these transitions have been compared with theoretical calculations and in this way the band structure has been determined for the investigated QWs. For QD and QDash structures optical transitions in QDs and QDashes as well as optical transitions in the wetting layer have been identified. For QDs and QDashes surrounded by a QW, in addition to energies of QD and QDash transitions, energies of optical transitions in the surrounded QW have been measured and the band structure has been determined for the surrounded QW. Finally some differences, which can be observed in CER and photo-reflectance spectra, have been presented and discussed for selected QW and QD structures.     

Finite barrier width effects on exciton states and optical properties in wurtzite InGaN/GaN quantum well

Exciton states and optical properties in wurtzite (WZ) InGaN/GaN quantum well (QW) are investigated theoretically, considering finite barrier width and built-in electric field effects. Numerical results show that when the barrier width increases, the ground-state exciton binding energy, the interband transition energy and the integrated absorption probability increase first and then they are insensitive to the variation of the barrier width. For any barrier width, the ground-state exciton binding energy and the integrated absorption probability have a maximum when the well width is 1 nm; moreover, the integrated absorption probability goes to zero when the well width is larger than 6 nm. In addition, the competition effects between the built-in electric field and quantum confinement are also investigated in the WZ InGaN/GaN QW.     

Exciton states in wurtzite InGaN/GaN quantum wells: Strong built-in electric field and interface optical-phonon effects

Considering the strong built-in electric field (BEF) effects and large exciton–phonon interactions, we investigate the exciton states confined in an InGaN/GaN single quantum well (QW) by using the Lee–Low–Pines variational method. We find that the exciton state modification caused by the exciton–phonon interactions is remarkable. The exciton energy shift due to exciton–phonon interactions increases monotonically if the well width increases. With increasing the In fraction, the exciton energy shift firstly increases to a maximum, then decreases. The BEF has a significant influence on the exciton states in a QW with large well width. The physical reasons have been analyzed in detail. Good agreement for the zero-phonon peak energies and the Huang–Rhys factor has been obtained between our numerical results and the corresponding experimental measurements.