Energy Levels In Quantum Wells Research Articles

Resonant electron tunnelling assisted by charged domain walls in multiferroic tunnel junctions.

The peculiar features of domain walls observed in ferroelectrics make them promising active elements for next-generation non-volatile memories, logic gates and energy-harvesting devices. Although extensive research activity has been devoted recently to making full use of this technological potential, concrete realizations of working nanodevices exploiting these functional properties are yet to be demonstrated. Here, we fabricate a multiferroic tunnel junction based on ferromagnetic La0.7Sr0.3MnO3 electrodes separated by an ultrathin ferroelectric BaTiO3 tunnel barrier, where a head-to-head domain wall is constrained. An electron gas stabilized by oxygen vacancies is confined within the domain wall, displaying discrete quantum-well energy levels. These states assist resonant electron tunnelling processes across the barrier, leading to strong quantum oscillations of the electrical conductance.

Effect of spontaneous polarization on the energy levels in quantum wells formed at the contact between cubic and noncubic silicon carbide polytypes

We have studied the effect of spontaneous polarization, which is inherent in noncubic silicon carbide (SiC) polytypes, on the characteristics of quantum wells (QWs) formed in the cubic region at the heterojunction. The analysis is performed for various QW models, including triangular, parabolic, and exponential. Conditions for the appearance of a two-dimensional electron gas at the interface are briefly discussed.

Effect of spatial dispersion on the shape of a light pulse propagating through a quantum well

The reflection, transmission, and absorption of a symmetric electromagnetic pulse are calculated. The carrier frequency of the pulse is close to the frequency of direct interband transitions in a quantum well (QW). The QW energy levels are assumed to be discrete, with two closely spaced excited levels being taken into account. The QW width is assumed to be sufficiently large and comparable to the light wavelength corresponding to the pulse carrier frequency. In this case, the dependence of the momentum matrix element for the interband transition on the light wave vector should be taken into account. The refractive indices of the QW and barriers are assumed to be equal. The problem is solved for an arbitrary relation between the radiative and non-radiative lifetimes of the excited electronic states. It is shown that spatial dispersion considerably affects the shapes of the reflected and transmitted pulses. The greatest changes occur in the case where the inverse radiative lifetime is close to the difference between the frequencies of the interband transitions considered.

Retardation of the relaxation over quantum-well energy levels in CdSe/ZnS quantum dots with increasing number of excited carriers

The differential transmission spectra of CdSe/ZnS quantum dots are investigated. It is revealed that the differential transmission spectra measured upon resonant excitation of electrons into the first excited state 1P(e) exhibit a number of specific features, such as a decrease in transmission at the pump frequency, bleaching in the course of the pump pulse at frequencies corresponding to the fundamental optical transition 1S 3/2(h)-1S(e) and transitions between excited hole states and the 1S(e) electron ground state, and retardation of this process with an increase in the energy of the pump pulse. The observed specific features can be explained by the following factors: (i) the absence of a “phonon bottleneck” for electrons due to the energy transfer from hot electrons to rapidly relaxing holes, (ii) relaxation through intermediate quantum-well energy levels of holes, and (iii) retardation of relaxation with increasing number of excited charge carriers in a quantum dot.

A study on the energy bands of multi-quantum wells in the quantum cascade laser structure by deep-level transient spectroscopy

We have investigated the defect states and confined energy levels of three quantum wells (QWs) in the quantum cascade laser (QCL) structure by capacitance–voltage and deep-level transient spectroscopy methods. Defect states with activation energies in the range of 0.49–0.88 eV were obtained in the GaAs capping layer, and their origins were considered as EL3 and EL2 families, which are well-known deep levels of GaAs materials. The densities of these defects in the GaAs capping layer of the QCL structure were about 3–12% of the donor concentration. The confined energy levels of QWs showed activation energies of about 130 meV and 230 meV from the top of the AlGaAs barrier, and their carrier confinement ability was measured to be about 0.5% of the donor concentration.

Intersubband transitions in quantum wells under intense laser field

An intense laser field effect on the intersubband transitions in quantum wells is theoretically investigated within the framework of the effective-mass approximation. Results obtained show that intersubbband optical transitions and energy levels in quantum wells can be significantly modified and controlled by an intense laser field.

The Energy Levels in Quantum Wells Formed at the Contacts between Cubic and Hexagonal Polytypes of Silicon Carbide

The energies of the ground (e0) and the first excited state (e1) in a quantum well (QW) are evaluated within the framework of the triangular QW model. It is shown that the e0 level in QWs at the contacts between cubic (3C) and hexagonal (NH, N = 2, 4, 6, 8) polytypes of silicon carbide (SiC) can be effectively controlled only by means of doping a wide-bandgap n-NH-SiC polytype with shallow donors.

Effect of electric fields on the transmission of a double heterostructure based on GaN with a quantum well

The potential-barrier parameters (heights) of the AlGaN/InGaN/GaN structure are determined, and the temperature dependences of these parameters are considered. Using the parameters, the transmission coefficient of the structure is calculated both with allowance for the external and internal fields and with no allowance for the electric field. The quantum-well energy levels are determined using the transmission coefficient; the shift of the transmission-coefficient maxima under the action of external bias voltage is explained.

INTERSUBBAND OPTICAL ABSORPTION IN QUANTUM WELLS UNDER APPLIED ELECTRIC AND INTENSE LASER FIELDS

Within the framework of the effective mass approximation, we have theoretically investigated the linear intersubband optical absorption in a quantum well under external electric and intense laser field. Results obtained show that intersubband optical transition and energy levels in quantum wells can significantly be modified and controlled by the electric field and intense laser field. Generally there is a distinct feature for the case of the intersubband absorption compared with intersubband optical absorption in a quantum well with an applied electric field.

Photocarrier escape time in quantum-well light-absorbing devices: effects of electric field and well parameters

We analyze the dependence of the carrier escape time from a single-quantum-well optoelectronic device on the applied electric field and well width and depth. For this purpose, a new simple and computationally efficient theory is developed. This theory is accurate in the case of electrons, and the assessment of the applicability for holes is given. Semi-analytical expressions for the escape times are derived. Calculations are compared to experimental results and previous numerical simulations. Significant correlations between the position of quantum-well energy levels and the value of the escape time are found. The main escape mechanism at room temperature is established to be thermally assisted tunneling/emission through near-barrier-edge states. The formation of a new eigenstate in the near-barrier-edge energy region is found to reduce the electron escape time significantly, which can be used for practical device optimization.

Characterisation of molecular beam epitaxy-grown InGaAs multilayer structures using photoluminescence

Molecular beam epitaxy-grown InGaAs/GaAs multilayer structures were used to characterise for their indium composition, quantum well widths and energy levels in quantum wells employing low-temperature photoluminescence spectroscopy. The effect of surface segregation and thermal desorption of indium atoms in these structures which changes the intended square well and barrier profiles is demonstrated. These shape changes in the well and barrier must be taken into account to correctly predict the quantum well energy level positions and hence the indium composition and the quantum well width.

Electrostatic model of band-gap renormalization and the photoluminescence line shape in a GaAs/AlGaAs two-dimensional layer at a high excitation level

An electrostatic model for calculating the band-gap renormalization in a two-dimensional (2D) semiconductor layer (quantum well) due to the Coulomb interaction between nonequilibrium charge carriers has been proposed. Consideration is given only to the first quantum-well energy levels for electrons and heavy holes. The exchange and correlation energies are calculated for the first time taking into account the charge-carrier potential energyfluctuations created by electrons and holes along the 2D layer. A relationship for the screened Coulomb potential along the 2D layer is derived, which, within the extremely narrow quantum-well approximation, transforms into the known expression. The band-gap renormalization and the photoluminescence line shape for the GaAs 2D layer in an AlxGa1−xAs matrix are computed depending on the concentration of nonequilibrium electrons and holes. The calculated band-gap renormalization is in agreement with the available experimental data at a high photoexcitation of the quantum well when the electrons and holes form the 2D plasma.

4.8 μm vertical emitting PbTe quantum-well lasers based on high-finesse EuTe/Pb1−xEuxTe microcavities

Vertical laser emission at 4.8 μm from PbTe quantum wells in high-finesse Pb0.95Eu0.05Te/EuTe microcavity structures at temperatures between 35 and 85 K is reported. The vertical-cavity laser structure was grown by molecular-beam epitaxy on BaF2(111) substrates, and consisted of a 2λ cavity with four 20 nm quantum wells at the cavity antinodes. Laser emission was excited by optical pumping with a pulsed Nd:YVO4 laser. The comparison of the cavity mode positions with envelope function calculations of the quantum-well energy levels indicates that, in this temperature range, lasing is due to transitions between the ground level of the oblique valleys in the conduction and valence bands.

Formation of interfaces in InGaP/GaAs/InGaP quantum wells

Interfaces (IFs) of In 0.485Ga 0.515P/GaAs/In 0.485Ga 0.515P quantum wells (QWs) grown by LP-MOVPE technology were studied, and a significant influence of growth conditions on properties of the QWs was observed and theoretically analysed. The paper shows that a low-band-gap ternary or quaternary interlayer (IL) between the bottom InGaP barrier and the GaAs well layer is the general reason for the deterioration of the IF quality. Such an IL forms spontaneously during the growth. Its formation can be enhanced using an inappropriate growth switching sequence and temperature. An As-to-P exchange process was found to be the dominant mechanism of the formation of the IL at a growth temperature of 560°C. An In 0.485Ga 0.515As monolayer (ML), created by the P-to-As exchange mechanism, is always present at the InGaP/GaAs IF. Even such an ML can considerably deteriorate properties of the QW. A proper switching sequence with thin GaP ILs grown at the IFs can eliminate the influence of spontaneous intermixing processes. We have calculated the quantized energy levels of QWs, which contained IL of various compositions and thicknesses. The results of calculation were compared with experimentally determined energies obtained from photoluminescence (PL) measurements. Based on this comparison, thicknesses of the ILs were estimated. Only small influence of As interdiffusion into the barriers and a negligible influence of indium carry-over into the GaAs well material were observed. From an analysis of the results it follows that about 1 ML thick ILs are spontaneously formed at the growth conditions used.

Non-monotonic behaviour of the energy levels of quantum wells with a large mass mismatch in the presence of an in-plane magnetic field

We present a theoretical study of the electron states in a quantum well with finite barrier height in a magnetic field applied parallel to the quantum well. For large electron mass mismatch between the quantum well and the barrier, we found the surprising result that the electron energy for zero wave vector decreases with decreasing well width and the energy spectrum has a local minimum at a non-zero wave vector. The influence of well depth, mass ratio and magnetic field are investigated.

Many-body carrier interaction effects in quantum wells

Many-body carrier interaction effects shift the ground- and excited-state subband energy levels of quantum wells. We derive carrier-carrier Coulomb exchange and direct interaction energies as a function of carrier density, quantum well composition, and well width. For values of these parameters of physical interest, the excited-state exchange energy is small compared to the ground-state exchange energy. Our expressions for the ground- and excited-state direct interactions yield considerably smaller energy values than those reported by previous investigators. This is due to the fact that in our derivations we differentiate between quantum well width, carrier doping width, and ground- and excited-state wave function effective confinement lengths. Direct interaction energies increase linearly with carrier density, and for large carrier densities substantially negate exchange interaction effects. We illustrate carrier-carrier interaction effects for the heavy-hole subband of electrically neutral, p-type, isolated strained-layer ${\mathrm{Ge}}_{\mathrm{x}}$ ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ /Si quantum wells.

Generalized eigenproblem method for surface and interface states: The complex bands of GaAs and AlAs.

A proper calculation of the complex band structure is essential for accurately obtaining the energy levels of quantum wells, or the resonances of resonant tunneling diodes. Most present empirical tight-binding calculations are based upon the nearest-neighbor ${\mathit{sp}}^{3}$s* model, and determine the complex band structure via a transfer-matrix-type equation. This procedure will fail at certain values of the in-plane wave vector ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$ or for certain parameter sets; other methods are unsuitable since they do not fully address this problem. Additionally, the nearest-neighbor ${\mathit{sp}}^{3}$s* model typically does a rather poor job reproducing the X-valley transverse effective mass. More complete calculations thus require an improved method for finding the complex bands and a more complete underlying tight-binding model. Here we develop a method which easily handles those ${\mathbf{k}}_{\mathrm{\ensuremath{\parallel}}}$ at, or parameter sets for, which other approaches fail and implement it in the second-near neighbor ${\mathit{sp}}^{3}$s* model to find the complex bands of GaAs and AlAs. We also give the change of basis necessary to transform the equations into a real system, thus allowing for a more efficient calculation. \textcopyright{} 1996 The American Physical Society.

Analytical formulas for the optical gain of quantum wells

Analytical expressions for the quantized energy levels in quantum wells, the optical gain, the differential optical gain, and the linewidth enhancement factor are presented based on a simple parabolic-band gain model. Explicit formulas show clearly the dependence of these factors on well width, doping, and photon energy. The optical gain in the form of g=g/sub 0/ In(N/N/sub 0/) is derived using explicit approximations in the Fermi functions, where g/sub 0/ is the proportionality constant, N is the injected carrier density, and N/sub 0/ is the transparency carrier density. The approximate formulas are shown to provide not only an efficient way of computing the gain-related parameters but also a convenient way of getting physical insights into the overall interplay of quantum well parameters.

Deformation Potentials in IV-VI Quantum Wells

To analyse the electronic properties of semiconductor superlattices (SLs) or quantum wells (QWs) it is necessary to know the basic parameters of the layers of which the structures are composed: the band gaps, effective masses parallel to the interfaces, etc. In turn, to determine those parameters properly, it is necessary to take into account the strains in the interfaces as well as in the bulk of the layers. The strain induced energy shifts are usually calculated from the corresponding deformation potentials (DPs). For SLs and QWs made of the IV—VI semiconducting materials, the strain induced shifts of energy levels are considered in Refs. [1-4]. It is commonly assumed that the DPs in QWs and SLs are the same as those in bulk crystals. For example, for the DPs of PbTe and SnTe SLs theoretical results of Refs. [5] and [6] are taken as a rule. The purpose of the present contribution is to consider the difference between DPs in QWs and bulk material. We show that such difference does exist for the case of narrow-gap materials with the interband k—p interaction. This is because of pronounced effect of the size quantization on energy levels in QWs made of the narrow-gap materials.

Band nonparabolicity and central-cell corrections for D- centers in GaAs quantum wells.

A one-electron effective Hamiltonian, previously found to describe quite accurately quantum-well energy levels of both free electrons and donor electrons in magnetic fields, is generalized to account for localized two-electron centers. The two-electron effective Hamiltonian derived is applied to the problem of finding energies for optical transitions originating from the ground state of ${\mathit{D}}^{\mathrm{\ensuremath{-}}}$ centers in seven different quantum wells with widths ranging from 9.5 to 52.0 nm. Central-cell corrections for the ${\mathit{D}}^{\mathrm{\ensuremath{-}}}$ centers are included. Comparison with experiments in magnetic fields below 10 T gives agreement to within 2 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for all well widths without any adjustable parameters.