Nanowires have attracted increasing interest due to their potential applications in electronics, optics and photonics. To understand the properties of nanowires, it is necessary to know their electronic structure. Moreover, it is important to understand how this electronic structure depends on the nanowire composition, crystal structure, orientation and geometry (shape and size), as well as on the eventual presence of some built-in deformation. The aim of this Ph.D. thesis is to develop theoretical models and computational methodologies that are realistic enough but also efficient to study piezoelectric, electronic and optical properties of nanowires. In the first place, we have formulated a consistent two-dimensional (2D) theoretical framework to solve fully-coupled piezoelectric problems with translational symmetry. For these problems all transverse sections of the system are in identical state, and therefore the strain and piezoelectric fields depend only on the in-plane coordinates. With this sole input a very general procedure, able to encompass a wide range of in-plane geometries, compositions, loads, charges, and boundary conditions, is developed. This framework is here called the generalized plane piezoelectric, GPP, problem. This problem is expected to be a good approximation to three-dimensional (3D) systems with high aspect-ratio, such as the nanowires we are interested in. We have further developed an efficient and flexible numerical implementation by means of the finite element method. By means of it, we have examined the strain and piezoelectric fields in various cases of lattice-mismatched core-shell nanowires. In particular, a systematic comparison of the 2D problem with exact 3D calculations in long finite nanowires has been presented. The analysis shows that the behavior of the 3D solutions (strain and electric fields) at distances >1.25D from the end surfaces (where D is the largest size of the cross section) is very well approximated by the predictions of the 2D generalized plane approaches, in both non-piezoelectric and piezoelectric nanowires. In a second research line, a theoretical model for the study of the single-particle electronic structure and linear optical absorption in semiconductor nanowires has been developed. It is based on the envelope function approximation combined with the eight-band k.p (Kane-like) Hamiltonian. If there is a strain distribution in the system, its effects on the electronic structure are included by using the Bir-Pikus Hamiltonian. When the model is applied to nanowires with an axially symmetric (e.g., cylindrical) geometry made of zincblende and wurtzite and oriented along appropriate directions, it is possible to classify the electronic states in terms of the total (envelope plus intrinsic) angular momentum, what facilitates the computation and interpretation of the band structures. The resulting equations have been solved by means of an eigenfunction expansion methodology. The model has been applied to the study of the electronic structure and optical absorption of free-standing (InAs, GaAs, InN, ZnO) and core-shell (AlGaAs/GaAs and GaAs/InAs) nanowires. In each case, a detailed study has been made of the geometry-dependence of the energies and symmetries of the conduction and valence band states, as well as the polarization-dependent optical spectra. In the case of core-shell nanowires, we have investigated the influence of the shell thickness in both lattice-matched and lattice-mismatched nanowires. The impact of an applied uniaxial stress on ZnO nanowires has also been investigated. Various distinctive effects of the confinement have been found in all systems for the range of very narrow nanowires.
