Impurity states in a cylindrical quantum dot with the modified Pöschl-Teller potential

We study impurity states in a cylindrical quantum dot with two confining potentials: in the direction of cylinder axis modified Pöschl-Teller potential and in radial direction parabolic potential. Studies of impurity states are performed in the frames of variational method and by using numerical methods, the dependences of the particle energy on the geometrical parameters of the cylindrical quantum dot are derived. Dependences of the electron binding energy on the half-width and depth of the potential wall are revealed.     

Impurity states in a spherical quantum dot with a modified P?schel-Teller potential

Quantum states and energy levels of an electron in a spherical quantum dot with a modified P?schel-Teller potential are studied. Analytical expressions for the wave function and energy of particle in the absence of impurity are obtained. Within the framework of variational method the impurity states are studied and by using numerical methods the dependences of the particle energy on the parameters of the spherical quantum dot are derived. Dependences of the electron binding energy on the half-width and depth of the potential well are revealed.     

Binding energy and photoionizaiton cross-section of hydrogen-like impurity in a Pöschl-Teller quantum well

The effect of the donor impurity position and the form of confining potential on the binding energy and the photoionization cross-section in a semiconductor quantum well with the Pöschl-Teller potential is studied. An analytical expression for the photoionization cross-section is obtained for the case when the polarization vector of light wave is directed along the direction of size quantization. It is shown that the photoionization cross-section has a threshold behavior.     

Dynamics of a cold quantum gas in a δ-split one-dimensional potential well

Dynamics of a wave function in a non-symmetrically split (spatially asymmetric) doublewell potential is considered. We study the dependence of the probability of well-to-well transitions on the degree of spatial asymmetry of well sizes and show that the quantum tunneling between the wells is significantly suppressed by this asymmetry. Practically complete suppression occurs at five-ten percent asymmetry. This is close to the threshold of sensitivity of contemporary experimental schemes for creating two-well potentials. We predict the phenomenon of resonance in quantum tunneling of considered states. We have also shown that an incoherently prepared superposition state tunnels in a double-well potential almost in the same way as a perfectly coherent state.     

On the eigenvalue problem for the schrödinger operator with a confining potential

A new method for the computation of the eigenvalues of the Schrödinger operator proposed recently is applied here to the case of a confining potential. It is shown that one can draw conclusions similar to those in the case of short-range potentials discussed in previous work.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.     

Nonlocal effects on second-harmonic generation in a Pöschl-Teller quantum well

Nonlocal effects on the energy conversion efficiency of the second-harmonic generation (SHG) for a p-polarized incident field in a P?schl-Teller quantum well (PTQW) are investigated in detail. The numerical results show that the spatial distribution of the second-harmonic field is nonuniform, and that there exist two resonance peaks in the second-harmonic energy reflection spectra, and their positions have a notable blueshift because of the nonlocal effects. A very important property is that a maximum blueshift at the second-harmonic resonance can be obtained by adopting a proper quantum-well width and donor concentration, which may be interesting in future precision experiments.     

Influence of electric field,hydrostatic pressure and temperature on the electronic states in a Pöschl-Teller quantum well

Influence of the electric field and hydrostatic pressure on the electronic states in a Pöschl-Teller quantum well is studied. In the framework of variational method the dependences of the ground state energy on the electric field and hydrostatic pressure are calculated for different values of the potential parameters and the temperature. It is shown that the increase in the electric field leads to the increase in the ground state energy, while the increase in the well width leads to the strengthening of the electric field effect. The ground state energy decreases with increasing pressure and increases with increasing temperature.     

Terahertz laser-induced 1D–0D crossover in the density of states for electrons in a cylindrical semiconductor quantum wire

The effects of a linearly polarized, terahertz laser field on the density of states (DOS) for carriers confined in a cylindrical semiconductor quantum wire are investigated here within a nonperturbative scheme, based upon a Green’s function approach. In our model, the functional dependence of the DOS on energy is significantly modified in two ways: (i) an uniform blueshift with respect to the laser-free DOS; and (ii) a strong suppression, with the appearance of Franz–Keldysh-like oscillations. Interestingly, with the increase (decrease) of the laser intensity (frequency) the DOS profile evolves from the usual shape for one-dimensional (1D) systems to a discrete set of sharp peaks that resembles the DOS for quasi-zero-dimensional (quasi-0D) electrons confined in quantum dots.     

Influence of spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum well

We have study the simultaneous effect of Rashba and Dresselhaus spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum wells. The linear and cubic contributions of the bulk Dresselhaus spin–orbit coupling and the effects of phonon confinement on electron–optical-phonon interaction Hamiltonians are taken into account. We have found analytical solutions for the polaron energies as well as polaron effective mass within the range of validity of perturbation theory. It is shown that the polaron energy and effective mass correction are both significantly enhanced by the spin–orbit coupling. Wave number dependent phonon contribution on the electron energy has minima and varies differently of the spin-up and spin-down states. Polaron self-energy due to interface optical phonon modes has larger values than of the confined optical phonon modes ones. The polaron effective mass exhibits anisotropy and the contribution of the Dresselhaus spin–orbit coupling term on the polaron effective mass is dominated by Rashba one.     

Relaxation behavior of a supercooled liquid near the bifurcation of α and Johari-Goldstein processes

Many glass formers show the simultaneously existence of two or more relevant elementary processes (α, β, …). The extrapolation of α and β_JG (Johari-Goldstein) processes to higher temperatures leads often to a bifurcation like behavior of these processes. It will be predicted that in general a crossing or a real bifurcation between an α process and β_JG process is excluded. Both processes avoid each other near and above the apparent bifurcation region. Furthermore, the α process shows strong decreasing of the intensity with increasing temperature close to this regime.     

Förster energy transfer from a semiconductor quantum well to an organic material overlayer

We predict an efficient electronic energy transfer from an excited semiconductor quantum well to optically active organic molecules of the nearby medium (substrate and/or overlayer). The energy transfer mechanism is of the F?rster type and, at semiconductor-organic distances of about 50 ?, can easily be as fast as 10-100 ps, which is about an order of magnitude shorter than the effective exciton lifetime in an isolated quantum well. In such conditions, the Wannier-Mott exciton luminescence is quenched and the organic luminescence is efficiently turned on. We consider both free as well as localized quantum well excitons discussing the dependence of the energy transfer rate on temperature and localization length. A similar mechanism for the non-radiative energy transfer to the organic overlayer molecules from unbound electron-hole pairs excited in the 2D continuum is shown to be much less competitive with respect to other relaxation channels inside the inorganic quantum well (in particular, 2D exciton formation). Received 20 July 1998     

Melting line, spinodal and the endpoint of the melting line in the system with a modified Lennard—Jones potential

A molecular dynamics method was used to calculate the pressure p* and the internal energy e* of a liquid and a crystal in stable and metastable states in a system of 2048 particles, which interaction is described by a modified Lennard—Jones potential. For the liquid phase, calculations were performed along 13 isotherms from the range of reduced temperature T* = 0.35–3.0, and for the crystal phase, along 16 isotherms from the range T* =0.1–3.0. The thermal p* = p*(ρ*,T*) and caloric e* = e*(ρ*,T*) equations of state for liquids and crystals have been constructed. The parameters of crystal-liquid phase equilibrium have been determined from the conditions of phases coexistence at positive pressures and in the region of negative pressures, where the coexistent phases are metastable. The spinodal of a stretched liquid has been approximated. It has been found that with a temperature decrease the metastable extension of the melting line meets the spinodal of the liquid phase. The point of their meeting, the endpoint of the melting curve, is the point of termination of crystal-liquid phase equilibrium without the onset of identity of the phases.     

Spin polarization of electrons in a magnetic impurity doped semiconductor quantum dot – The effect of electron–phonon interaction

A theoretical model is presented in this paper for degree of spin polarization in a light emitting diode (LED) whose epitaxial region contains quantum dots doped with magnetic impurity. The model is then used to investigate the effect of electron–phonon interaction on degree of spin polarization at different temperatures and magnetic fields. It is found that magnetic impurity increases the degree of spin polarization irrespective of temperature, while the electron–phonon interaction decreases the degree of spin polarization. Results are found to be in better agreement with experiments.     

Precision solution of the Schrödinger equation with Coulomb and linear confining potentials in momentum space

It is shown that the Schrödinger equation in the momentum representation with linear confining potential and Coulomb and Cornell potentials for the states with zero orbital angular momentum can be solved with high accuracy (far superior to other methods) using special quadrature formulas for singular integrals.     

On the spectrum of Schrödinger operators with a random potential

We investigate the spectrum of Schrödinger operatorsH of the type:H =–+q _i ()f(x–x _i + _i ())(q _i () and _i () independent identically distributed random variables,i ^d ). We establish a strong connection between the spectrum ofH and the spectra of deterministic periodic Schrödinger operators. From this we derive a condition for the existence of forbidden zones in the spectrum ofH . For random one- and three-dimensional Kronig-Penney potentials the spectrum is given explicitly.     

Frequency and density dependent radiative recombination processes in III–V semiconductor quantum wells and superlattices

In this paper we review the radiative recombination processes occurring in semiconductor quantum wells and superlattices under different excitation conditions. We consider processes whose radiative efficiency depends on the photogenerated density of elementary excitations and on the frequency of the exciting field, including luminescence induced by multiphoton absorption, exciton and biexciton radiative decay, luminescence arising from inelastic excitonic scattering, and electron-hole plasma recombination.

Semiconductor quantum wells are ideal systems for the investigation of radiative recombination processes at different carrier densities owing to the peculiar wavefunction confinement which enhances the optical non-linearities and the bistable behaviour of the crystal. Radiative recombination processes induced by multi-photon absorption processes can be studied by exciting the crystal in the transparency region under an intense photon flux. The application of this non-linear spectroscopy gives direct access to the excited excitonic states in the quantum wells owing to the symmetry properties and the selection rules for artificially layered semiconductor heterostructures.

Different radiative recombination processes can be selectively tuned at exciting photon energies resonant with real states or in the continuum of the conduction band depending on the actual density of photogenerated carriers. We define three density regimes in which different quasi-particles are responsible for the dominant radiative recombination mechanisms of the crystal: (i) The dilute boson gas regime, in which exciton density is lower than 10¹⁰ cm^-2. Under this condition the decay of free and bound excitons is the main radiative recombination channel in the crystal. (ii) The intermediate density range (n < 10¹¹ cm^-2) at which excitonic molecules (biexcitons) and inelastic excitonic scattering processes contribute with additional decay mechanisms to the characteristic luminescence spectra. (iii) The high density range (n ?10¹² cm^-2) where screening of the Coulomb interaction leads to exciton ionization. The optical transitions hence originate from the radiative decay of free-carriers in a dense electron-hole plasma.

The fundamental theoretical and experimental aspects of the radiative recombination processes are discussed with special attention to the GaAs/Al _x Ga_1-x As and Ga _x In_1-x As/Al _y In_1-y As materials systems. The experimental investigations of these effects are performed in the limit of intense exciting fields by tuning the density of photogenerated quasi-particles and the frequency of the exciting photons. Under these conditions the optical response of the quantum well strongly deviates from the well-known linear excitonic behaviour. The optical properties of the crystal are then no longer controlled by the transverse dielectric constant or by the first-order dielectric susceptibility. They are strongly affected by many-body interactions between the different species of photogenerated quasi-particles, resulting in dramatic changes of the emission properties of the semiconductor.

The systematic investigation of these radiative recombination processes allows us to selectively monitor the many-body induced changes in the linear and non-linear optical transitions involving quantized states of the quantum wells. The importance of these effects, belonging to the physics of highly excited semiconductors, lies in the possibility of achieving population inversion of states associated with different radiative recombination channels and strong optical non-linearities causing laser action and bistable behaviour of two-dimensional heterostructures, respectively.     

A study of an exciton in a quantum dot with Woods–Saxon potential

A theoretical study of an exciton confined in a quantum dot with the Woods–Saxon potential is presented. The great advantage of our methodology is that it enables confinement regimes by varying two parameters in the model potential. Calculations are made by using the method of the numerical diagonalization of the Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground (L=0$L=0$) and first excited (L=1$L=1$) states are obtained as functions of the dot radius. Based on the computed energies and wave functions, the linear, the third-order nonlinear and the total optical absorption coefficients have been examined between the ground and the first excited states. The results are presented as a function of the incident photon energy for the different values of the dot radius and the barrier slope. It is found that the binding energy and the optical properties of the excitons in a quantum dot are strongly affected by the dot radius and the barrier slope of the confinement potential.