Polaron effects on excitons in parabolic quantum wells: fractional-dimension variational approach

Polaron effects on excitons in parabolic quantum wells are studied theoretically by using a variational approach with the so-called fractional dimension model. The numerical results for the exciton binding energies and longitudinal-optical phonon contributions in GaAs/Al_0.3Ga_0.7As parabolic quantum well structures are obtained as functions of the well width. It is shown that the exciton binding energies are obviously reduced by the electron (hole)-phonon interaction and the polaron effects are un-negligible. The results demonstrate that the fractional-dimension variational theory is effectual in the investigations of excitonic polaron problems in parabolic quantum wells.     

Exciton quantization in parabolic quantum wells

The exciton wavefunction in parabolic quantum wells is calculated using variational techniques and effective mass theory. The influences of the potential shape and of confinement on the exciton binding energies are studied. The results are in good agreement with previous calculations. The oscillator-strength of excitons in GaAs/Ga_1-xAl_xAS quantum wells has a maximum value very close to the cross-over from three to two dimensions.     

Binding energies of wannier excitons in GaAs-Ga1−xAlxAs quantum well structures

Binding energies of Wannier excitons in a quantum well structure consisting of a single slab of GaAs sandwiched between two semi-infinite slabs of Ga_1?xAl_xAs are calculated using a variational approach. Due to reduction in symmetry along the axis of growth of these quantum well structures and the presence of band discontinuities at the interfaces, the degeneracy of the valence band of GaAs is removed leading to two exciton systems, namely, the heavy hole exciton and the light hole exciton. The variations of the binding energies of these two excitons as a function of the size of the GaAs quantum wells for various values of the heights of the potential barrier are calculated and their behavior is discussed.     

强耦合表面激子内部激发态的性质

采用线性组合算符和幺正变换方法,研究极性晶体中强耦合表面激子内部激发态的性质.计算了表面激子的激发态能量、激发能量和平均声子数.     

Quantum well excitons in an electric field: two versus three dimensional behavior

Previous calculations have shown a transition between two dimensional and three dimensional behavior of excitons confined in a semiconducting quantum well structure as a function of electric field. We here present calculations of the exciton binding energy as a function of electric field using a two parameter variational wave function of the form used in the absence of the electric field by Matsuura and Shinozuka. Our calculations were performed using a finite potential barrier model for the confinement of the exciton in the quantum well. The results of our calculations confirm the validity of the conclusion that the variational exciton wave function goes from being of a purely 2D hydrogenic type at small well widths and/or low electric fields to a 3D hydrogenic type in wide wells and/or high electric fields.     

Self-consistent approach for calculations of exciton binding energy in quantum wells

We introduce a computationally efficient approach to calculating characteristics of excitons in quantum wells. In this approach we derive a system of self-consistent equations describing the motion of an electron–hole pair. The motion in the growth direction of the quantum well in this approach is separated from the in-plane motion, but each of them occurs in modified potentials found self-consistently. The approach is applied to shallow quantum wells, for which we obtained an analytical expression for the exciton binding energy and the ground state eigenfunction. Our numerical results yield lower exciton binding energies in comparison to standard variational calculations, while require reduced computational effort.     

Electron-phonon effects on Stark shifts of excitons in parabolic quantum wells: Fractional-dimension variational approach

Electron-phonon effects on Stark shifts of excitons in parabolic quantum wells are studied theoretically by using a fractional dimension method in combination with a Lee-Low-Pines-like transformation and a perturbation theory. The numerical results for the exciton binding energies and electron-phonon contributions to the binding energies as functions of the well width and the electric field in the Al_0.3Ga_0.7As parabolic quantum well structure are obtained. It is shown that both exciton binding energy and electron-phonon contributions have a maximum with increasing the well width. The binding energy and electron-phonon contribution decrease significantly with increasing the electric-field strength, in special in the wide-well case.     

On the binding energies of excitons in polar quantum well structures in a weak electric field

The binding energies of excitons in quantum well structures subjected to an applied uniform electric field by taking into account the exciton longitudinal optical phonon interaction is calculated. The binding energies and corresponding Stark shifts for Ⅲ-Ⅴ and Ⅱ-Ⅵ compound semiconductor quantum well structures have been numerically computed. The results for GaAs/A1GaAs and ZnCdSe/ZnSe quantum wells are given and discussed. Theoretical results show that the exciton-phonon coupling reduces both the exciton binding energies and the Stark shifts by screening the Coulomb interaction. This effect is observable experimentally and cannot be neglected.     

Effect of a Coulomb well in (In,Ga)As/GaAs quantum wells

Magnetooptical investigation of exciton transitions in high-quality quantum wells of an (In, Ga)As/GaAs heterosystem has been carried out. Investigation of transmission of free-hanging samples detached from the substrate in the magnetic fields of up to 12 T revealed a rich fine structure associated with various heavy-hole and light-hole exciton transitions. In particular, transitions from the excited states of light holes localized in a Coulomb potential produced by an electron along the heterojunction axis (a Coulomb well) have been detected. Taking into account consistently stresses, formation of Landau levels, the binding energies of excitons (diamagnetic excitons), and the effect of a Coulomb well, we have succeeded to describe the experimental results with the use of a self-consistent variational procedure. As a result, new features in the structure of optical transitions have been explained and the effective masses of electrons and holes of excitons formed by both heavy and light holes have been determined with a high accuracy.     

Excitonic transitions in Be-doped GaAs/AlAs multiple quantum well

A series of GaAs/AlAs multiple-quantum wells doped with Be is grown by molecular beam epitaxy. The photoluminescence spectra are measured at 4, 20, 40, 80, 120, and 200 K, respectively. The recombination transition emission of heavy-hole and light-hole free excitons is clearly observed and the transition energies are measured with different quantum well widths. In addition, a theoretical model of excitonic states in the quantum wells is used, in which the symmetry of the component of the exciton wave function representing the relative motion is allowed to vary between the two- and threedimensional limits. Then, within the effective mass and envelope function approximation, the recombination transition energies of the heavy- and light-hole excitons in GaAs/AlAs multiple-quantum wells are calculated each as a function of quantum well width by the shooting method and variational principle with two variational parameters. The results show that the excitons are neither 2D nor 3D like, but are in between in character and that the theoretical calculation is in good agreement with the experimental results.     

Self-consistent Hartree method for calculations of exciton binding energy in quantum wells

A new computationally efficient and flexible approach to calculating characteristics of excitons in quantum wells based on a self-consistent variational treatment of the electron–hole Coulomb interaction is developed. It is applied to several different quantum well materials and is shown to give much better (lower) values of exciton energies. The iterative scheme used to calculate the energies and respective wave functions is stable and rapidly convergent. The authors believe that the method can be an important computational tool in computing exciton characteristics in shallow quantum wells exceeding currently existing approaches in accuracy and efficiency. The method can also be naturally generalized for quantum wires and dots.     

Interface-related effects on confined excitons in GaAs/AlxGa1−xAs single quantum wells

Confined excitons in non-abrupt GaAs/Al_xGa_1−xAs single quantum wells are studied. The graded interfaces are described taking into account fluctuations in their thickness a and positioning with respect to the abrupt interface picture. Numerical results for confined (0,0),(1,1) and (0,2) excitons in GaAs/Al_0.3Ga_0.7As quantum wells show that while the interfacial fluctuations produce small changes (<0.5 meV) in the exciton binding energies, the confined exciton energies can be red- or blue-shifted as much as 25 meV for wells with mean width of 50 Å and 2 ML wide interfaces.     

Excitons in coupled quantum dots

Properties of excitons in vertically coupled GaAs/AlGaAs quantum dots were investigated using the variational method within the envelope function and effective mass approximations. It was found that when the thickness of the spacer layer becomes less than about one exciton Bohr radius, both the exciton binding energy and the fundamental optical transition energy are reduced compared to those in isolated quantum dots. This is a result of increased space extension of exciton due to the penetration of carrier wave functions into the spacer layer and corresponding reduction in confinement energy which dominates over the Coulomb interaction between the electron and the hole.     

Laser field induced interband absorption in a strained GaAs/GaAlAs double quantum well system

Effect of laser field intensity on exciton binding energies is investigated in a GaAs/ GaAlAs double quantum well system. Calculations have been carried out with the variational technique within the single band effective mass approximations using a two parametric trial wave function. The interband emission energy as a function of well width is calculated in the influence of laser field. The laser field induced photoionization cross-section for the exciton placed at the centre of the quantum well is computed as a function of normalized photon energy. The dependence of the photoionization cross-section on photon energy is carried out for the excitons. The resulting spectra are brought out for light polarized along and perpendicular to the growth direction. The intense laser field dependence of interband absorption coefficient is investigated. The results show that the exciton binding energy, interband emission energy, the photoionization cross-section and the interband absorption coefficient depend strongly on the well width and the laser field intensity. Our results are compared with the other existing literature available.     

Exciton interaction potential in polar crystals

The problem whether polaron effects can lead to a repulsive barrier in the exciton interaction potential is reinvestigated, because this effect is crucial for the possibility of a Bose-Einstein condensation of excitons (rather than of excitonic molecules). The energy for two excitons is calculated accurately as a function of their mean distance in the case of a heavy hole mass by using an integral expansion method of molecular physics. The resulting interaction potential shows for certain polaron radii a very weak repulsive barrier. Taking into account corrections to the Haken potential which have been introduced by Pollmann and Büttner, it is shown that the interaction potential between two excitons in the relative singlet state is always attractive, so that the exciton system is also in polar materials unstable against exciton molecule formation.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Excitons in GaAs quantum wells

This paper attempts to summarize some of the salient properties of excitons in GaAs quantum wells and in doing so it will emphasize work at AT&T Bell Labs with which the authors have been associated. Although the text relies heavily on published material, an effort has been made to stress new material, and where feasible, unpublished aspects, e.g., figures, related to earlier work. Topics discussed on the quasi-2D excitons in GaAs quantum well include: their inherent tendency for intrinsic free-exciton emission, exciton binding energies, bound and localized excitons including biexcitons and excitons bound to neutral impurities, effects of n- and p-type modulation and antimodulation doping, and the developments leading to a proposed set of quantum well parameters that results in acceptable fits to the observed exciton transitions for GaAs quantum wells with both square and parabolic potential profiles.     

半导体量子点中弱耦合激子的性质

研究了抛物型半导体量子点中弱耦合激子的性质,在有效质量近似下,采用线性组合算符和幺正变换的方法,导出了抛物型半导体量子点中激子的基态能量。讨论了量子点半径和受限强度对半导体量子点中弱耦合激子的基态能量的影响。以GaAs半导体为例进行了数值计算,结果表明:在弱耦合情况下,重空穴激子和轻空穴激子的基态能量随量子点半径的减小而增大,随受限强度ω₀的增强而增大。     

The effects of indium segregation on exciton binding energy and oscillator strength in GaInAs/GaAs quantum wells

We solve analytically the Schrödinger equation taking into account the shape changes of GaInAs/GaAs quantum wells due to indium segregation during the MBE growth by using transfer matrix method. The indium compositional profiles of the quantum wells are provided using the phenomenological model. The fundamental transition energy, binding energy and oscillator strength of excitons as a function of indium segregation coefficient R$R$ and well width are studied. For narrow wells (less than 40 ML), the exciton binding energy and oscillator strength decrease, but for wide wells (larger than 40 ML), increase with increasing the segregation coefficient R$R$. It is shown that indium segregation degrades the optical properties and results in a blue-shift of exciton transition energy in GaInAs/GaAs quantum wells.     

非对称方势阱中的激子及其与声子的相互作用

采用类LLP(Lee-Low-Pines)变换和分数维变分法,在讨论有限深非对称方势阱Ga_1－xAl_xAs/ GaAs/Ga_0.7Al_0.3As的分数维基础上,计算了其中激子的基态能量以及声子对其影响,随着势阱宽度增加,激子能量先减小后增大,出现一个最小值.讨论了一侧势垒高度变化对分数维、激子基态能量的影响,并发现声子作用使得激子能量明显增大.另外,非对称方势阱中的激子结合能随阱宽的减小而增     

A Simple Method for Calculating Exciton Binding Energies in Semiconductor Quantum wires

We present a simple, general method for calculating the binding energies of excitons in semiconductor quantum wires. The binding energy is given by an integral (over the electron and hole two-dimensional coordinates perpendicular to the wire) of a prescribed function weighted by the squares of the electron and hole subband envelope functions. Taking as an example, we calculate the binding energy of exciton in quantum wires assuming an infinite confining potential. This method should be applicable to a variety of more complex systems.