Potentials induced by the electron-optical-phonon interaction in a quantum well

The potential induced by the electron-optical-phonon interaction in a quantum well (QW) is investigated by means of the perturbation theory. We consider the interactions of an electron with both bulklike confined longitudinal optical (LO) phonons and four branches of interface optical (IO) phonons. The spatial distributionV _i(z) of the induced potential for QW structures with different heterolayer compositions and different well widths is calculated in detail. The numerical results show that the heterolayer composition of the QW plays an important role in determining the shape ofV _i(z) and that the existence of IO-phonons is important to the electronic states in QWs.     

Arnold resonances and quantum states

The dynamics of one electron interacting with a linear chain of heavy atoms bears a strong similarity with the propagation of a classical wave in a periodic non linear medium. Arnold resonances of the dynamical system play a central role. Some of the quantum states associated with these resonances are delocalized and contribute to phenomena such as Peierls dimerization while other ones are localized and are similar to the gap solitons of the classical wave theory, we call them Braggons. Complex Braggons containing several electrons inside the same localized profile are also described.     

Revisiting the theory of large polarons

We extend the theory of large polarons in the frame of a semi classical model. We analyse two physical effects in which the discreteness of the periodic lattice plays a major role: i) In addition to standard Holstein polarons, we show the existence of braggons which are polarons whose energy lies in a lattice gap. According to the type of gap considered, some of the them are ordinary solitons, some others are vector-solitons. ii) The pinning (or Peierls Nabarro) effect of the lattice on the polarons. We show that the coupling of the electrons with acoustic phonons is able to produce polarons or bipolarons in crystallographic situations where the coupling with optical phonons does'nt. The existence of multidimensional polarons and bipolarons is investigated, and we find interesting possibilities in dimension D=2. The binding energy and effective mass of the polarons are determined in the frame of the model, and their dynamical stability is analysed. We also show the existence, for D=1, of tripolarons in which two energy levels are occupied in the potential well created by the electron-lattice interaction. Finally the conditions of validity of the semi-classical approximation are given.     

Optical phonon modes in a free-standing quantum wire with ring geometry

The confined longitudinal-optical (LO) phonon and surface-optical (SO) phonon modes of a free-standing quantum wire with ring geometry are discussed within the dielectric continuum (DC) approximation. Two branches of SO phonon modes have been investigated. The frequencies of the SO phonons are found to be dispersed and radius dependent for small size systems. When the wave vector qz→∞, the frequencies of each SO modes converge to the frequency values of the single planar heterostructure.     

A double quantum well in a driving laser field

The dynamic effect of electrons in a double quantum well under the influence of a monochromatic driving laser field is investigated. Closed-form solutions for the quasienergy and Floquet states are obtained with the help ofSU (2) symmetry. For the case of weak interlevel coupling, explicit expressions of the quasienergy are presented by the use of perturbation theory, from which it is found that as long as the photon energy is not close to the tunnel splitting, the electron will be confined in an initially occupied eigenstate of the undriven system during the whole evolution process. Otherwise, it will transit between the lowest two levels in an oscillatory behavior.     

Neutron scattering study of the intermolecular vibrations in solid C60

We present a detailed account of an inelastic neutron scattering study of the intermolecular vibrations in solid C₆₀ above and below the structural phase transformation. Assignment of the observed phonon peaks to modes of translational and librational character is discussed on the basis of lattice dynamical calculations using phenomenological intermolecular potentials. A new bond charge model is presented which reproduces the observed phonon branches very well. However, the apparently small influence of the orientational disorder on the librational excitations remains to be understood.     

Electron-LO-phonon interaction in wurtzite GaN quantum wells under a magnetic field

We calculate the electron-LO-phonon relaxation rates in wurtzite GaN quantum wells in the presence of a magnetic field parallel to the growth direction. Using the dielectric continuum model (DCM), we are able to include contributions from both the interface and the quasi-confined phonon modes. The relaxation rate expression takes the phonon dispersion into account, and is applicable to all phonon modes. We find that the relaxation rates show strong oscillations as a function of the applied magnetic field. In relatively wide (8 nm) quantum wells, the inclusion of interface phonon mode decreases this oscillation amplitude. But in thin wells (5 nm), the interface phonon mode is of the same importance as the quasi-confined mode, and it strongly modifies the oscillation behavior.     

Electron-interface-phonon interaction in wurtzite multilayer heterostructures

Within the framework of the dielectric-continuum model and Loudon's uniaxial crystal model, the equation of motion for the p-polarization field in a wurtzite quasi-two-dimensional multilayer heterostructure is solved exactly for the interface optical-phonon modes. The eigenvector, the dispersion relation and the electron-interface-phonon interaction Fröhlich-like Hamiltonian are derived using the transfer-matrix method. The analytical formulas are universal and can be applied to single heterojunctions, single/multiple quantum wells and superlattices.     

Donor binding energies and spin-orbit coupling in a spherical quantum dot

The ground state and a few excited state energies of a hydrogenic donor in a spherical quantum dot (GaAs in a GaAlAs matrix) are computed. While the 1s and the 2s-state energies behave normally for dots of all radii, the 2p₀ and 2p_± states are unbound for most of the radii of interest. It is predicted that a semiconductor quantum dot with a hydrogenic donor will exhibit photoconductivity for a low threshold wavelength ∼12 μm. The spin-orbit coupling gives a contribution of the order of 10⁻⁵ meV for both 2p₀ and 2p_± states.     

Binding energy of an off-center hydrogenic donor in a spherical Gaussian quantum dot

The energy levels of an off-center hydrogenic donor confined by a spherical Gaussian potential have been calculated as a function of the potential radius for different donor position by exact diagonalization method. The results have clearly demonstrated the so-called quantum size effect. The binding energy is dependent on the dot radius R, the impurity ion distance D, and the confining potential depth V₀.     

Exact manipulations to Bloch states of a particle in a double cosine potential

For a single particle held in a double cosine potential with suitable parameters it is demonstrated that the Schrödinger equation has two sets of exact and simple Bloch solutions which are associated with the different boundary conditions. The corresponding eigenenergies can be positive or negative that depend on the amplitude and wave-vector of the laser potential. The results supply possibility for exactly manipulating the quantum motional states of the particle by using the laser beams.     

Formation and charge control of a quantum dot by etched trenches and multiple gates

We have fabricated a GaAs/InGaAs/AlGaAs-based single-electron transistor (SET) formed by etched trenches and multiple gates. Clear Coulomb-blockade oscillations have been observed when the gate biases are scanned. By self-consistently solving three-dimensional Schr?dinger and Poisson equations, we have studied the energy-band structure and the carrier distribution of our SET. General agreement between numerical simulation results and measurement data has been obtained, thus indicating the effectiveness of our SET-device design as well as the necessity of a complete three-dimensional quantum-mechanical simulation. Received: 18 October 2001 / Accepted: 6 January 2002 / Published online: 20 March 2002     

Effects of electric field and hydrostatic pressure on donor binding energies in a spherical quantum dot

The binding energies of a hydrogenic donor in a GaAs spherical quantum dot in the Ga_1−xAl_xAs matrix are presented assuming parabolic confinement. Effects of hydrostatic pressure and electric field are discussed on the results obtained using a variational method. Effects of the spatial variation of the dielectric screening and the effective mass mismatch are also investigated. Our results show that (i) the ionization energy decreases with dot size, with the screening function giving uniformly larger values for dots which are less than about 25 nm, (ii) the hydrostatic pressure increases the donor ionization energy such that the variation is larger for a smaller dot, and (iii) the ionization energy decreases in an electric field. All the calculations have been carried out with finite barriers and good agreement is obtained with the results available in the literature in limiting cases.     

Phonon-assisted auger recombination in quantum well semiconductors

Phonon-assisted Auger recombination (AR) is shown to be an important loss mechanism in a quantum well semiconductor in addition to the direct AR. Theoretical investigations demonstrate that it is of the same order of magnitude and has the same temperature dependence as in bulk material, just as direct AR, provided that the material parameters and the carrier concentrations are the same as in the bulk.     

Tight-binding calculations of the subband structures of zincblende-semiconductor [001] quantum wells

The scattering-theoretic T-matrix method is used to calculate the subband structures of GaAs−ZnSe and ZnSe−ZnS_xSe_1−x [001] quantum wells within an empirical tight-binding model, that includes the bulk Г₆, Г₇ and Г₈ valence- and conduction bands. The resulting confinement energies for vanishing lateral crystal momentumk _‖ are compared with those, that are obtained from a simple effective mass model and effects are found and predicted which the effective mass model cannot account for. The effect of the band nonparabolicity and the influence of the microscopic sequence of atomic layers, which determines the symmetry properties of a quantum well, are studied for the GaAs−ZnSe wells.     

Two interacting electrons in a Gaussian confining potential quantum dot

Two interacting electrons in a Gaussian confining potential quantum dot are considered under the influence of a perpendicular homogeneous magnetic field. The energy levels of the low-lying states are calculated as a function of magnetic field. Calculations are made by using the method of few-body physics within the effective-mass approximation. A ground state behavior (singlet→triplet state transitions) as a function of the strength of a magnetic field has been found in the weak confinement case as a two-electron quantum dot with parabolic confining potential.     

Density and well width dependences of the effective mass of two-dimensional holes in (100) GaAs quantum wells measured using cyclotron resonance at microwave frequencies

Cyclotron resonance at microwave frequencies is used to measure the band mass (m_b) of the two-dimensional holes (2DHs) in carbon-doped (100) GaAs/ Al_xGa_1−xAs heterostructures. The measured m_b shows strong dependences on both the 2DH density (p) and the GaAs quantum well width (W). For a fixed W, in the density range (0.4×10¹¹ to 1.1×10¹¹ cm⁻²) studied here, m_b increases with p, consistently with previous studies of the 2DHs on the (311)A surface. For a fixed , m_b increases from 0.22m_e at to 0.50m_e at , and saturates around 0.51m_e for .     

Model calculations of diffusion limited trapping dynamics in quantum well laser structures

We present a phenomenological theoretical model to treat the trapping of carriers into quantum wells of semiconductor laser structures. We consider explicitely the transport within the barrier layers by solving the continuity equation with the appropriate boundary conditions taking into account surface recombination, radiative and nonradiative recombination in the barrier layers and trapping of carriers into the quantum wells. The experimental findings for the trapping dynamics in GaAs/AlGaAs quantum well structures can be consistently interpreted by the model calculations.