Nanowires, represent the smallest device dimensionality for efficient transport of electrons and other more exotic quasiparticles. Among a plethora of applications identified, research directed towards field-effect transistors (FETs), the building blocks of next-generation computer processors, is of utmost importance considering current 7 nm FET technologies are expected to be the limit of “top-down” manufacturing techniques. Characterisation of the mechanical and electronic properties of nanowires, by conventional electronic structure techniques, have coincidentally reached a limit due to the maximum simulation sizes they are capable of.

CONQUEST is a code capable of simulation of millions of atoms using O(N) methods and thousands of atoms using Hamiltonian diagonalisation with a pseudo-atomic orbital basis. Physical quantities calculated using CONQUEST do not exhibit systematic convergence using PAO basis sets, unlike plane-wave codes, so we quantify PAO basis sizes needed to achieve comparable accuracy to plane-wave calculations for a variety of bulk and molecular systems with varying chemical environments. Implementation of the stress tensor, presented in this thesis, resulted in the discovery of slow stress convergence with respect to density matrix localisation. We quantify the O(N) simulation parameters necessary to achieve stress calculations to a required accuracy.

We present the first study of experimentally relevant, surface reconstructed, Si (core) – Ge (shell) nanowires. Vegard’s law, used to quantify experimental results and as an approximation in theoretical calculations, has been found to poorly describe our nanowires and we assess the relative error due to its usage. Young’s modulus is shown to decrease with increasing shell deposition and dependent on relative nanowire composition. Poisson ratios, also correlated to composition, exhibit anisotropy. Shell deposition induced strain has been mapped by our method and shows strong anisotropy in different bonding directions. Our nanowires exhibit a direct-to-indirect band gap transition with intrinsic uniaxial strains > 0.5% and effective hole masses 50% smaller than similar unreconstructed nanowires. Finally, valence band offsets which are responsible for the formation of hole gases, were found to be double that of unreconstructed models.