A dopant atom in a semiconductor, the solid state analogue of a hydrogen atom, has a Bohr radius of several nanometers. Because this length scale is close to being accessible by modern nanolithography, detection and control of charge and spin in a semiconductor down to the level of individual dopant atoms is within reach and provides the unique opportunity to study, manipulate, and utilize a single atom's wave function. We have performed electrical transport measurements across epitaxial defect-free nanometer-sized Schottky diodes. These were formed by self-assembled CoSi2-islands on Si(111) and contacted with the tip of a scanning tunneling microscope (STM). Greatly enhanced conductance was observed in diodes which were small compared to the Debye length in the semiconductor. The observed behavior can be understood qualitatively from a decreased barrier width for smaller diodes. On highly doped substrates, we find that individual dopant atoms even dominate the transport characteristics of our nanometer sized devices, due to their random distribution in the space charge region. The ability to observe the energy levels of single dopant atoms is essential for experimental studies of individual wave functions in a semiconductor. Preliminary results in a fabrication method for nano-devices approaching the size regime necessary for the observation of single dopants demonstrate the feasibility of our STM-based measurement method for this purpose. The most straightforward means to address an individual impurity is manipulation of its wave function with a gate. As a first approach to this problem, we theoretically studied the effect of a homogeneous electric or magnetic field on the energy levels of shallow impurities in silicon, taking the bandstructure into account. Furthermore, we used a description as hydrogen-like impurities for accurate computation of energy levels and lifetimes up to large electric fields. A similar description was used in a realistic device geometry, in which a small nearby gate influences a single dopant atom. This knowledge is particularly important for the development of a dopant-atom based quantum computer.Applied Science