Disentangling parallel conduction channels by charge transport measurements on surfaces with a multi-tip scanning tunneling microscope

Within this thesis, both position-dependent charge transport measurements with a multi-tip scanning tunneling microscope (STM) are performed, and theoretical models for describing these measured data are developed. Only a combination of both allows for actually disentangling multiple current transport channels present in parallel, in order to reveal the physical properties of the investigated systems, i.e. the conductivity of the individual channels. In chapter 2, the instrumental setup for the multi-tip STM is shown in general and the specific methods used for tip positioning are discussed. An introduction into the theory of distance-dependent four-point resistance measurements is given in chapter 3. Here, the relations between four-point resistance and conductivity influenced by the chosen probe geometry are discussed for both a pure two-dimensional and a pure three-dimensional system. Furthermore, also anisotropic conductance in two dimensions is considered. Chapters 4-7 depict actual measurements with the multi-tip STM on different sample systems, as semiconductors and topological insulators. First, in chapter 4 the conductivity of the Si(111)-(7x7) surface and the influence of atomic steps of the underlying substrate are investigated. In order to interpret the measured resistances, a 3-layer model is introduced which allows for a description by three parallel conductance channels, i.e. the surface, the space charge region and the bulk. Such a model enables to extract a value for the surface conductivity from the measurements. Moreover, by a measurement of the conductance anisotropy on the surface, the conductivity of a single atomic step can be disentangled from the conductivity of the step-free terraces. In chapter 5, the 3-layer model is extended to an N-layer model in order to model the strongly depth-dependent conductivity of the near-surface space charge region in semiconductors in a more precise way. In order to demonstrate the universal applicability of the N-layer model, it is used to extract values for the surface conductivity of Ge(100)-(2x1) and Si(100)-(2x1) reconstructions from data already published in the literature, but not evaluated in terms of the surface conductivity. Chapter 6 depicts a further combined experimental and theoretical approach in order to reveal parallel conductance channels in topological insulators thin films, i.e. the interface channel at the boundary to the substrate and the interior of the film itself, which are both in parallel to the transport channel through the topological surface states at top and bottom surface of the film. From measurements on specific surface reconstructions, the conductivity of the interface channel can be revealed, while the interior of the thin film is approached by band bending calculations in combination with results from angle-resolved photoemission spectroscopy measurements (ARPES). Here, it turns out that in the thin-film limit the charge carrier concentration inside the film is only governed by the position of the Fermi level at the surface, as it is revealed by ARPES, but not influenced by the actual dopant concentration inside the film material which is usually unknown, thus allowing for a reliable estimate of the film conductivity. Finally, in chapter 7, the weak topological insulator Bi_14Rh_3I_9 is investigated by means of scanning tunneling spectroscopy and scanning tunneling potentiometry, in order to reveal the presence and the transport properties of the one-dimensional edge state at step edges on the dark surface. From the spectroscopy and thermovoltage measurements, it turns out that the topological channel can indeed be found at step edges of the 2D TI-layer, as it has been already reported in literature, and additionally at artificially created scratches into the surface. However, it is not located directly at the Fermi energy, and thus cannot substantially contribute to current transport. Additionally, it turns out that the surrounding so-called dark surface is very conductive itself due to unintentional surface doping, as deduced from potentiometry with applied transport field and distance-dependent four-point measurements. Both facts prevent to directly reveal the transport properties of the edge channels for the studied Bi_14Rh_3I_9 crystals, but nevertheless in principle the depicted measurement method should be capable of revealing direct transport through an edge channel on more sophisticated samples