• ab-initio
• germanium
• surface

Nanostructures have received growing interests in the last decade as consequence of their peculiar and fascinating properties, and applications often superior to their bulk counterparts. In the last few years surfaces and interfaces strongly influenced the electronic properties of semiconductor nanostructures. Nanomembranes (NMs) provide the opportunity for such quantitative investigations; they are two-dimensional crystalline films that can be shaped with precise surface orientations and sizes. My work connects with this widespread focus on two dimensional materials, with the aim of working out a novel understanding of the electronic band-gap engineering of the (2x1)-reconstructed Ge(001) surface, by means of ab-initio density functional theory numerical techniques. The truncation of the germanium crystalline structure along the [001] direction generates the (001)-oriented surface of germanium. At room temperature, this (ideal) surface is energetically unstable so that a process of atomic rearrangement occours which leads to (2x1) reconstructions, where (2x1) means that the surface periodicity is doubled along the [110] or the [$\bar1$10] crystallographic directions. In fact, on ideally-terminated (001) surfaces of the diamond lattice, each surface atom exhibits two dangling bonds, partly occupied. The process of formation of dimers on the Ge (001)-oriented surface is driven by halving the number of surface dangling bonds due to the establishment of a chemical bond between two neighbour Ge atoms on the surface. The angular orientation of the dimer has been longly debated, but eventually it was experimentally observed that it is tilted with respect to the surface plane; the asymmetry of the dimers plays a central role in the electronic properties of the (2x1) Ge (001) surface: the semiconductive character of the surface is the most important effect due to this asymmetry. The termination of a crystal with a surface and the successive rearrangment of surface atoms leads to a change of the electronic band structure with respect to the bulk material. In fact, electronic surface-localized states may exist at the semiconductor surface. In previous works the study of these surface states was confined to the unstrained (2x1) Ge (001) surface. Indeed, for low-dimensional as well as for three-dimensional crystalline materials a rich family of properties and functionalities can be tuned by strain-engineering, i.e., varying structural parameters, because their electronic and geometrical structures are sensitive to strain. In this work I study for the first time, by means of ab-initio techniques, the strain-engineering of the structural and electronic properties of the (2x1)-reconstructed Ge (001) surface. Such techniques have revealed to be invaluable tools to investigate crystalline structures (three or low-dimensional), interpret experimental measurements, give fundamental support in many solid state physics fields and design new devices, also due to the everlasting increase of computational capabilities. Nevertheless, these numerical techniques need to be handled and tuned carefully according to the working situations. For this reason, before focusing on the (2x1) Ge (001) surface electronic band-engineering, we found necessary to start from the study of the Ge bulk crystal, under relaxed or strained conditions, and of the unstrained (2x1) Ge (001) surface. These steps are necessary to rightly tune, by a fair comparison with known experimental results, the choices of the computational and working procedures to be finally used in the study of the strained (2x1) Ge (001) surface. The main conclusion of this work is the evidence that it is possible to manipulate the Ge(001) surface states relative to the bulk band structure. We demonstrate that by appropriate compressive strain it is possible to obtain pure surface states which can be exploited for surface transport experiments and optical transitions. The choice of germanium for the present investigation is that it is an ideal material to achieve integrated optical sources for silicon photonics, in particular on the (001) silicon surface which is at the heart of modern semiconductor devices.