J.L. Marín

Hydrogenic impurities in spherical quantum dots in a magnetic field

The ground state and binding energies for a hydrogenic impurity in a spherical quantum dot within a uniform magnetic field, are calculated through the variational method in the frame of the effective-mass approximation. The trial wave functions used in the calculation are flexible enough to treat the cases of on-center, off-center, or edge impurities. Overall results show reasonable agreement when compared with other calculations. Interestingly enough, in the case of an off-center impurity, a critical point from which bulk states evolve to surface or edge states is also found. The dependence of this point on the magnetic field strength is discussed and interpreted.

One-phonon-assisted electron Raman scattering in quantum well wires and free-standing wires

The differential cross section for an electron Raman scattering process in a semiconductor quantum well wire (QWW) and in a free-standing wire of cylindrical geometry involving phonon-assisted transitions is calculated for T = 0 K. A complete description of the phonon modes of cylindrical structures embedded in another material, including a correct treatment of the mechanical and electrostatic matching conditions at the surface, is presented. We consider the Frohlich interaction to illustrate the theory for a GaAs/AlAs system. Electron states are considered to be confined within a QWW with finite and infinite potential barriers. We also assume single parabolic conduction and valence bands. The emission spectra are discussed for different scattering configurations and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted.

Electron states in a magnetic quantum ring

Electron states in a magnetic quantum ring are investigated. The electron is assumed to be confined to a plane in the presence of a magnetic field which is zero within the ring a<r<b and has a constant value B0 outside it. In this way, the perturbation caused by this field distribution is found to be quite different from that corresponding to a magnetic quantum disk, as regards electron states and circulating currents. In the case of electron states, the main effect is the splitting of the corresponding Landau levels into a sort of quasi-miniband around them and modulated by the inner radius. It is also found that probability current can change its direction depending on the missing flux quanta, a mechanism that is also governed by the size of the inner radius. Moreover, when the inner radius approaches zero, the results for a magnetic quantum disk are recovered, as expected.

Electron Raman scattering in asymmetrical multiple quantum wells

Optical properties of asymmetrical multiple quantum wells for the construction of quantum cascade lasers are calculated, and expressions for the electronic states of asymmetrical multiple quantum wells are presented. The gain and differential cross-section for an electron Raman scattering process are obtained. Also, the emission spectra for several scattering configurations are discussed, and the corresponding selection rules for the processes involved are studied; an interpretation of the singularities found in the spectra is given. The electron Raman scattering studied here can be used to provide direct information about the efficiency of the lasers.

Two-electron atomic systems confined within spheroidal boxes

The direct variational method is used to estimate some interesting physical properties of the He atom and the Li{sup +} ion confined within impenetrable spheroidal boxes. A comparative investigation f the ground=state energy, pressure, polarizability, dipole, and quadrupole moments with those of the He atom inside boxes with paraboloidal walls is made. The overall results show a similar qualitative behavior. However, for Li{sup +} there are quantitative differences on such properties due to its major nuclear charge, as expected. The trial wave function is constructed as a product of two hydrogenic wave functions adapted to the geometry of the confining boxes.

Optical properties and impurity states in nanostructured materials

Publisher Summary This chapter discusses the optical processes in nanocrystals that can be interpreted in terms of the creation and annihilation of a single electron-hole pair or exciton within a nanostructure. Size-dependent absorption and emission spectra and their fine structures, as well as a size-dependent radiative lifetime, are discussed in the chapter for different nanostructured systems. Optical spectroscopy of semiconductors has been a lively subject for many decades. In spectroscopic terms, the size of the energy gap is the key difference among metals, insulators, and semiconductors. In both intrinsic luminescence and near-gap absorption, the main features of the spectrum can be associated with the magnitude of the energy gap because the photons reflect the energy spacing between the states taking part in the optical process. The states involved in optical transitions must be allowed states, and hence an understanding of the density of allowed states and their correlation with optical transitions is helpful.

Multiphonon resonant Raman scattering in the semimagnetic semiconductor Cd1−xMnxTe: Fröhlich and deformation potential exciton–phonon interaction

A theory describing multiphonon resonant Raman scattering (MPRRS) processes in wide-gap diluted magnetic semiconductors is presented, with Cd1−xMnxTe as an example. The incident radiation frequency ωl is taken above the fundamental absorption region. The photoexcited electron and hole make real transitions through the LO phonon, when one considers Frohlich (F) and deformation potential (DP) interactions. The strong exchange interaction, typical of these materials, leads to a large spin splitting of the exciton states in the magnetic field. Neglecting Landau quantization, this Zeeman splitting gives rise to the formation of eight bands (two conduction and six valence ones) and ten different exciton states according to the polarization of the incident light. Explicit expressions for the MPRRS intensity of second and third order, the indirect creation and annihilation probabilities, the exciton lifetime, and the probabilities of transition between different exciton states and different types of exciton as a function of ωl and the external magnetic field are presented. The selection rules for all hot exciton transitions via exciton–photon interaction and F and DP exciton–phonon interactions are investigated. The exciton energies, as a function of B, the Mn concentration x, and the temperature T, are compared to a theoretical expression. Graphics for creation and annihilation probabilities, lifetime, and Raman intensity of second and third order are discussed.

Electro-optical and transport properties of quasi-two-dimensional nanostructured materials

Publisher Summary The study of the quasi-two-dimensional systems, also called “semiconductor heterostructures by layers,” has acquired a special significance because of the development of growing techniques, which allow the setting of systems with a totally quantum character. These techniques allow the growth of extremely thin layers, controlling the process with great detail—specifically the thickness of the layers, the content of impurities, and the abruptness of the interfaces. The chapter explains confined systems, also called a “low-dimensional system” that is any quantum system in which the carriers are free to move in only two, one, or even zero dimensions. They could be real and/or ideal systems. In these systems, the spatial dimensions are of the order of the De Broglie wavelength of the carriers whose movement becomes quantized. Several methods for obtaining the confined systems exist—namely, the reduction of some spatial directions to quantum scale by the application of any kind of fields or by limiting the borders in the synthesis of the materials.

Confined systems and nanostructured materials

Publisher Summary The general importance of the confined systems and nanostructure materials has been widely suggested as a key in the future of nanotechnology and of interest in diverse fields including pharmaceuticals, aerospace, nanoelectronics, and optoelectronics. Several forms of classifying confined systems exist, and the most universal classification is by considering the number of directions where the particle could move freely—for example, quasi-2D systems have two directions for the free movement of the carriers and one spatial direction of confinement. Four types of quasi-2D systems are investigated in the chapter: (1) single heterostructure, (2) double heterostructure or quantum well, (3) multiple heterostructures or multiple quantum wells, and (4) superlattices. There are many methods for the synthesis and production of nanostructured materials in a laboratory scale; however, the most important are those where high-quality quantum nanostructures are achieved. The effect of an external electric field on the electronic structure of a spherical quantum dot is studied in the chapter by applying the effective-mass envelope function theory.

Scattering and Lifetime of Hot Excitons Interacting with LO-Phonons in InBr and InI Polar Semiconductors

Scattering probabilities and lifetime for a hot Wannier-Mott exciton which interacts with LO-phonons in InBr and InI polar semiconductors are obtained for T = 0. The calculations were performed for exciton states with principal quantum number n = 2 in the states l = 1, m = 0 and l = 1, m = ±1, when electron and hole effective masses are equal (m e = m h ). The results obtained can be used to explain the special characteristic of secondary radiation emission spectrum measured by Yoshida et al. in 1985. In the latter work, the scattering lines show an alterating intensity which can be accounted for only if the electron and hole effective masses are nearly equal. All computation was performed for different scattering probabilities of the excitons, namely: intraband (W s ), inter-exciton band (W 2→1 ), disintegration into the continuous spectrum (W d ), as well as the lifetime of the exciton in both states. The results show that W s is larger than W 2→1 , even in the case m e = m h , for a wide range of kinetic energy of the excitons. A comparison of these results with those for the case of excitons in the state n = 1 is also made.