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After an introduction on the methods used for electronic states calculations, we study electron and hole bound states in a single dot. We initially evaluate the oscillator strength and polarization selection rules for intraband transitions. We show that in a single dot the absorption is very anisotropic, depending on the polarization direction of the incident light. We also develope a model for interpreting some recent STM measurements, which are able to ``image'' single dot wavefunctions. Then we study vertically stacked quantum dot systems. We examine the coupling between the dots of a stack as a function of the barrier thickness. Systems of strongly coupled dots are particularly interesting: we show that the optical anisotropy, typical of single dots, considerably diminishes in this kind of systems. Strongly coupled dots are also interesting when electric field effects are studied. We show that they are as tunable as quantum wells of the same dimensions, when an uniform electric field is applied in the growth direction. In addition to this enhanced Stark tunability, stacked dots present the advantage over quantum wells that no continuum absorption exists. The last part of this work is devoted to a detailed numerical study of the continuum, wetting layer ($2D$) and barrier ($3D$), states. We show that the continuum states have an important role for interband transitions. We show in particular that crossed transitions, which involve bound and continuum states, lead to the appearance of a continuous background in the interband absorption spectrum, in the energy range between the bound-to-bound transitions and the wetting layer absorption edge. The existence of this background, experimentally proved, shows that the ``artificial atom'' model is too simple to describe the features of quantum dot interband spectrum.; Après avoir présenté les méthodes utilisées pour le calcul des états électroniques, nous discutons les états liés d'électrons et de trous dans une boite isolée. Nous calculons la force d'oscillateur et les régles de sélection pour les transitions intrabandes. Nous montrons qu'il faut distinguer entre les excitations polarisées dans le plan et celles polarisées verticalement; notre calcul montre que dans une boite isolée l'absorption est très anistrope. Dans le cadre des boites isolées nous développons également un modèle pour interpréter plusieurs experiences récentes de STM, qui prétendent l'observation directe des fonctions d'onde d'électrons et de trous. Nous étudions ensuite les systèmes de boites empilées. Nous discutons le couplage entre les boites en fonction de l'epaisseur de la barriere qui les separe. Nous nous interessons en particulier au regime de boites fortement couplees. Nous montrons que l'anisotropie typique des boites uniques diminue considerablement dans le cas des systemes de boites fortement couplees. Ces derniers sont particulierement interessants si l'on regarde les effets du champ electrique. Nous montrons ainsi que les systemes de boites fortement couplees sont aussi polarisables que les puits quantiques, avec une proprite en plus: le confinement dans le plan. La derniere partie de ce travail presente une discussion detaille des etats du continuum bidimensionnel (couche de mouillage) et tridimensionnel (barriere). Le role du continuum est particulirement important dans le cas des transitions interbandes: nous montrons que les transitions croisees entre etats lies et etats du continuum sont a l'origine d'un fond continu entre la partie basse energie du spectre (due aux transitions liees) et le seuil de la couche de mouillage. Cet effet, observe exprimentalement, montre de facon claire que le modele ``atome artificiel'' est trop simple pour decrire de facon adequate les propriets des boites quantiques.

The theories used up to now to model theoretically and numerically nanostructures, and more specifically semiconductor heterostructures, do not allow to include efficiently at the envelope function level, in a k · p approach, the effects imposed by a possible symmetry of the problem. The most elaborated techniques available only allow to take into account the existence of a single symmetry plane, or deal with global symmetry, but not with envelope functions. The most important part of this thesis deals with the development of a novel formalism, very general, which allows to study the electronic and optical properties of high symmetry nanostructures. This new Maximal Symmetrization and Reduction (MSR) formalism allows to maximally symmetrize the eigenstates and significantly reduce the size of the spatial domain of solution. The formalism was explicitly developed with the aim to study a C3v quantum wire, with three symmetry planes at 120°, and allowed to analytically justify some numerical result obtained without an adapted theoretical formalism. In addition, some other physical results related to the effects of symmetry were highlighted and understood. To cite a simple example, it is possible to demonstrate a perfect isotropy polarization with respect to two directions in the cross-section of a wire. In addition, for some transitions new analytical expressions were found for the polarization anisotropy between a direction in the plane and a direction along the wire. The new formalism allows also to understand, in much more details, a number of effects in a qualitative and quantitative way, e.g. symmetry breaking effects. For the example of the C3v wire, the conduction and valence bands are treated separately in the k · p approximation, with respectively one (spinless) band and four bands (describing the valence band mixing). For the scalar wavefunction problem of the conduction band, we propose a new systematic Spatial Domain Reduction (SDR) method. For every different symmetry of the problem (irreducible representation), the independent sub-domains can be identified and a reduced Hamiltonian on the minimal domain can be obtained (numerical optimization). For a spinorial problem, the spatial and spinorial (Bloch functions) parts, have to be considered separately (both for operators and the eigenstates) although treated simultaneously. Whatever the number of bands considered, completely symmetrized bases can be chosen according to the symmetry properties of the heterostructure. This approach allows to classify with respect to the symmetry not only any spinorial states, but every one of their spinorial components (envelope functions) separately. The physical understanding as well as subsequent analytical treatment are considerably simplified. Finally we propose to apply the spatial domain reduction technique to the spinorial components, which ensure to solve the spinorial problem on a minimal domain with numerical optimization. The proposed approach is valid in a much larger framework than k · p theory, and is applicable to arbitrary systems of coupled partial differential equations, e.g. strain equations in heterostructures or the Maxwell equations describing an impurity state in a photonic band-gap.

Single photon sources have recently attracted significant interest for their potential role in the future applications of quantum cryptography, and in the longer term, quantum computing. Among the different types of single photon emitters, semiconductor quantum dots (QDs) are good candidates as they combine discrete electronic transitions with the possibility of electrical excitation. Self-assembled InAs QDs on GaAs substrate are by far the most studied system as they can easily be grown into a microcavity structure. Embedding these into a microcavity is important as it increases the extraction efficiency, directionality and speeds up the photon emission. Until now, most studies have concentrated on QDs emitting in the λ

We investigate the ground state properties of large atoms and quantum dots described by a d-dimensional N-body Hamiltonian of confinement ZV. In atoms, d = 3 and V is the Coulomb interaction; in dots, d = 2 and V is phenomenologically determined. We express the grand-canonical partition function in a path integral approach, and evaluate its expansion in Z-1. The problem can be seen as that of field theory possessing a saddle point. This saddle point results in a mean-field contribution to the energy, while the fluctuations result in the correlation energy. The mean-field contribution to the energy is self-consistently determined by the Hartree potential and contains an exchange term. Its smooth contribution is evaluated by a semiclassical method, with ε = Z-1/d in the role of ℏ, while its oscillating contribution can be related to the periodic orbits in the corresponding classical Hamiltonian. In the case of atoms, the leading order in ε of the correlation energy contains a term in Z ln Z1/3, which is essential in reproducing the behaviour shown by reference values, and a term in Z. While we have evaluated the contribution to the Z-term provided by the leading fluctuation order, the numerical evaluation of the contributions provided by higher order fluctuations remains an open problem. The self-consistent contribution to the energy corresponds to the statistical atom, composed of Thomas-Fermi and its corrections, comprehensively analysed, including oscillations, by Schwinger and Englert. In the case of dots, the leading order in ε of the correlation energy is a universal contribution of order Z, which we obtain in closed form. We then determine the expansion in ε of the smooth contributions down to this correlation order. We apply the approach to dots of quadratic and quartic confinement, including the oscillating contribution in the case of a chaotic quartic confinement.

This thesis reports measurements concerning quantum size effects of single crystalline metallic islands by using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Different sample systems are presented in the following chapters. In chapter 2, several aspects of quantum well states (QWS) of Pb ultrathin islands grown on Si(111) substrate are reported. The differential conductance spectra of QWS can be understood by discrete energy levels with linewidth broadening because of finite quasiparticle lifetime. Using low temperature scanning tunneling spectroscopy, we studied the linewidth of unoccupied quantum-well states (QWS) in Pb islands, grown on Si(111) on two different Pb/Si interfaces, of thicknesses between 7 and 22 monolayers. A quantitative analysis of the differential conductance spectra allowed us to determine the QWS lifetime broadening as a function of energy, showing agreement with 3D Fermi-liquid theory, as well as the electron-phonon (e-ph) contribution between 5 and 50 K. Layer-dependent ab initio calculations of the e-ph linewidth contributions are in excellent agreement with the data. Importantly, the sum of the calculated e-e and e-ph lifetime broadening follows the experimentally observed quadratic energy dependence. In chapter 3, studies investigating reduction of the superconducting gap of ultrathin Pb islands are presented. The energy gap Δ of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Δ was found to decrease from its bulk value as a function of inverse island thickness. Corresponding Tc values, estimated using bulk gap-to-Tc ratio, are in quantitative agreement with ex situ magnetic susceptibility measurements, however, in strong contrast to previous scanning probe results. Layer-dependent ab initio density functional calculations for free-standing Pb films show that the electron-phonon coupling constant, determining Tc, decreases with diminishing film thickness. In chapter 4, we present preliminary results on single electron tunneling and Coulomb blockade phenomena of metallic islands decoupled from a Ag(111) substrate by dielectric NaCl layers. Using low temperature STM/STS, the geometry of the metallic island can be determined unambiguously and the single electron tunneling properties are characterized. Using orthodox theory of single electron tunneling, the tunneling spectra can be reproduced qualitatively. Despite minor quantitative disagreement between data and simulations, the parameters of the double barrier tunneling junction, including the capacitances and the resistances of both junctions, as well as the residual charge, can be determined.

Semiconductor quantum wires (QWRs) and quantum dots (QDs) represent important classes of low-dimensional quantum nanostructures, useful for studies and applications of quasi one- and zero-dimensional systems. Recently, considerable efforts have been devoted to developing QWRs and QDs of high optical quality for studying the properties of these low dimensional structures. However, realization of QWRs and QDs in a highly reproducible and controllable manner remains challenging. The present thesis systematically investigated a novel QWR-QD system self-formed in inverted tetrahedral pyramids due to capillarity induced alloy segregation effect during metallorganic vapor phase epitaxy (MOVPE). Growth of an otherwise homogenous AlGaAs layer inside the pyramid results in formation of a Ga-enriched vertical QWR (VQWR) running through the center of the pyramid, along the growth axis, and three vertical QWs (VQWs) at the three wedges of the pyramid. Since the VQWR forms along the growth direction, the structure and the composition can be adjusted via the growth conditions and parameters, offering possibilities of achieving QWR structures with controlled potential. In particular, the composition and/or structure of these wires can be tailored with monolayer accuracy, opening the way for a new generation of complex low dimensional nanostructures of different functionalities. Moreover, these QWRs are embedded in a semiconductor matrix, so that high quality interface can be achieved. This feature offers opportunities for integrating these QWRs in electronic and optical devices. As a starting point, we studied the formation mechanisms involved in the pyramid system, particularly the alloy segregation effect. This forms the basis for the entire project, giving useful guidance in structural design for the more complex structures investigated later. The Ga-Al segregation is evidenced by high resolution electron microscopy images and photoluminescence (PL) spectroscopy. A simple diffusion model was developed to interpret the effect qualitatively and quantitatively. Quantum confinement of electrons and holes in these wires is evidenced by peculiar transitions observed in the PL spectra at high excitation levels and confirmed by theoretical modeling of these structures. The wires are also connected to a set of higher bandgap, self-ordered VQWs that promote carrier capture into the wire. The temperature dependence of the PL spectra clearly reveals efficient carrier capture into the VQWR from the surrounding VQWs, particularly at an intermediate temperature range (∼ 100 Κ) where the carrier mobility is enhanced. Cathodoluminescence spectroscopy is applied to identify the individual structures and to investigate the carrier transfer within the structures. In the next step, we systematically shortened the VQWR to bring the structure into the QD regime, simply by decreasing the grown layer thickness from nearly one micron to several nanometers. Thus, a continuous transition from two-dimensional to three-dimensional quantum confinement was realized in the very same system, revealing the impact of dimensionality on the electronic and optical properties of the nanostructures. Several advanced measurement techniques were employed in this study, including polarization-resolved and time-resolved PL spectroscopy. Three main evidences for the QWR-QD transition were observed experimentally and confirmed theoretically: (i) strongly blue-shifted ground state emission, accompanied by increased separation of ground and excited transition energies; (ii) change in the orientation of the main axis of linear polarization of the PL, from parallel to perpendicular with respect to the growth axis; and (iii) prolonged exciton radiative lifetime. The optical properties of the single QDs were also studied. Single- and correlated photon emission from single QD were demonstrated by photon correlation measurements. The success in fabrication of QDs with controlled potential inside the pyramids stimulated the development of QD molecules by stacking several QDs on top of each other. In our QD molecule systems, QDs are tunnel-coupled via connected QWRs. The stronger tunnel coupling in this integrated QD-QWR system allows the hybridization of both electron and hole states, yielding direct-real-space excitonic molecules. Evidence for this hybridization was provided by polarization-resolved PL spectroscopy confirming the formation of delocalized hole states, and by photon correlation spectroscopy showing photon bunching for bonding- and anti-bonding QD-molecule transitions. The QD molecule configuration could be modified intentionally for probing local electron/hole probability density, by insertion of very thin barriers as perturbations in the given structure at specified positions. In conclusion, the controlled growth in inverted pyramids provides considerable freedom in designing complex nanostructures that are difficult to achieve with purely self-assembly approaches. The investigated structures provide new information on low-dimensional systems and hold promise for the development of nano-photonic devices for quantum information processing applications.