[en] The rubidium-covered surface of the semiconducting transition metal dichalcogenide tungsten diselenide (WSe₂) is examined using photoelectron spectroscopy (PES) and photoemission electron microscopy (PEEM). Adsorbed Rb is known to induce a variety of effects in this system concerning electronic, structural, and mechanical properties. In this work, the surface potential created by charge transfer upon Rb deposition is examined in thermal equilibrium (band bending) and stationary non-equilibrium (surface photovoltage (SPV) effect), which is induced by the absorption of light. It is shown that combined measurements and numerical simulations of the SPV effect as a function of the photon flux can be exploited for the estimation of many material parameters of the system, especially of the unoccupied adsorbate state. Issues of extending a conventional photoelectron spectrometer setup by a secondary light source will be discussed in the context of simulations and calibration measurements. The customization of an existing theoretical model of the SPV effect for the WSe₂: Rb system is introduced, and a comprehensive validation of the obtained predictions is given in the context of experimental data. In addition, the self-organized formation of Rb domains at room temperature was examined by application of spatially resolved XPS spectroscopy using the PEEM setup at the end station of beamline UE49/PGMa at the BESSY II synchrotron facility. From the obtained results, the arrangement of Rb in surface lattices can be concluded. Furthermore, an X-Ray absorption study of self-organized nanostructure networks, aiming at the chemical characterization, is presented. Based on the interpretation of the examined structures as tension-induced cracks, a statistical approach to analyzing large-scale features was pursued. First accordance with the predictions made by a primitive, mechanical model of crack creation developed here gives gives some evidence for the validity of the proposed structure creation mechanism. A detailed analysis of technical aspects of processing spatially resolved photoemission data was carried out during this work. Several novel methods were developed as compensation for well-known technical limitations of the experimental setup. As will be shown, specific perturbations of PEEM data can be eliminated efficiently hereby, so comparability of all data channels in a detector image is guaranteed. Extensive tests with actual experimental data prove the great applicability of the approaches made here. Though usually having low individual quality, the large number of data channels allows for novel approaches to the classification of spectroscopic data. A concept originating from the field of data mining was ported to work with photoemission spectra and is applied here as an aid to the recognition of spatial structures from spectral features.