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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.