Semiconductor quantum wires (QWRs) are promising structures for optoelectronics applications, since they can provide quantum confinement for charge carriers in two dimensions. The advantage that they offer over conventional quantum wells (QWs) is due to the sharper density of states characteristic of these structures, yielding narrower spectral lines and higher optical gain. However, to exhibit clear confinement characteristics, QWRs must meet stringent requirements in terms of size, uniformity and interfacial quality. Different methods have been explored for QWR fabrication. Techniques based on etching and regrowth suffer from defect incorporation into the lateral interfaces, since they are not formed in situ, and are limited in size by the lithographic features. On the other hand, growth of fractions of monolayers on vicinal substrates, although overcoming the above limitations, gives rise to size nonuniformities and graded interfaces. In this project, (In)GaAs/AlxGa1-xAs QWRs are obtained by organometallic chemical vapor deposition (OMCVD) growth of quantum wells on patterned, V-grooved substrates. In this way, the lithographically defined pattern serves as a seed for QWR formation. The self-ordering properties of OMCVD on nonplanar surfaces ensure the creation of a self-limiting profile at the bottom of the grooves, on which the wires are grown. This method overcomes the size limitations imposed by lithography, allows the in situ formation of interfaces and, thanks to the self-ordering mechanism, yields structures with high uniformity, whose characteristics are determined solely by the growth conditions. Although nonplanar growth has been employed for more than ten years for QWR fabrication, the understanding of the self-ordering mechanisms originating the profiles at the bottom of the grooves has been until now only phenomenological. The attainment of self-limiting profiles takes place via transients of the growth rates at the bottom of the groove. Current models of nonplanar growth can predict the formation, evolution or disappearance of facets at the 100nm-μm size. However, they cannot describe the transient behaviors at the nm scale that lead to self-limiting growth. This thesis project has been aimed at elucidating the physical mechanisms of this self-organized growth. A fundamental part of the project has been the creation of a wide experimental database to understand the dependence of the self-limiting profiles on the materials and growth conditions. The profiles at the bottom of the groove exhibit a faceted structure, consisting of a central (100) plane, surrounded by two {311}A ones. Cross-sectional transmission electron microscopy (TEM) shows that the bottom facets become wider as the growth temperature increases and as the Al mole fraction x of AlxGa1-xAs layers decreases. It appears therefore that surface diffusion is a key element in determining self-limiting growth. TEM cross sections show also that the establishment of self-limiting profiles takes place via self-adjusting growth rates on these facets. In addition to this geometrical self-ordering, AlxGa1-xAs alloys exhibit also a compositional self-ordering at the bottom of the groove. Due to the higher mobility of Ga species, with respect to the Al ones, the facets at the bottom of the groove are Ga rich, with respect to the sidewall planes, giving rise to so-called vertical quantum wells (VQWs). To determine the composition of the VQWs, we have developed a technique employing cross-sectional atomic force microscopy (AFM) in air. This method is based on the dependence of the AlxGa1-xAs oxidation rates on the Al content x. Through a calibration on a reference sample, we were able to measure compositions with an accuracy of ±0.02. The enhanced Ga content of the VQWs follows classical models of segregation, and reaches a maximum of Δx ≅ 0.15 for x ≅ 0.55 at a growth temperature of 700°C. We also studied the three dimensional structure of the self-limiting surface profiles by top-surface AFM in air of the nonplanar samples after cool-down and removal from the OMCVD reactor. Each of the planes composing the groove presents a monolayer step structure that reflects directly the morphology of surfaces of the same orientation found in planar epitaxy. However, on the facets forming on corrugated substrates the step structure exhibits a higher degree of ordering, with respect to planar epitaxy. This is due to a modification of surface diffusion, when the trench width becomes comparable to or lower than the adatom surface diffusion length. In the last part of the project, we have developed a model ascribing the self-ordering phenomena observed above to local variations of the surface chemical potential μ. Since μ becomes lower as the concavity of the surface increases, it induces a curvature-dependent capillarity flux towards the bottom of the groove. In the absence of capillarity, if the growth rate is higher on the sidewall planes than on the bottom facets, the capillarity-enhanced growth rate at the bottom can balance exactly the sidewall growth rate, thus leading to self-limiting growth. The different behavior of nonplanar OMCVD (where self-ordering is usually observed at the bottom of the grooves) and molecular beam epitaxy (where self-ordering rather takes place at the top of the corrugations) can be explained by the different growth rate anisotropies of the two techniques. In a ternary alloy, the composition is locally different at the bottom of the groove, due to the different diffusion lengths of Ga and Al. The resulting entropy of mixing, which is lower than the one for a uniform composition, tends however to oppose this segregation, thus affecting the alloy self-limiting profiles. The predictions of the model have been successfully verified on our OMCVD-grown profiles. They can be used to design and optimize a variety of nanostructures, including VQWs, QWRs and QWR superlattices in the GaAs/A1GaAs system, and can be further extended to the strained InGaAs/AlGaAs system.