YbRh2Si2 has advanced to a prototype material for investigating physics related to the Kondo effect. An optimization of the synthesis resulted in single crystals of extraordinary crystalline quality. At the atomic scale, we utilize scanning tunneling microscopy to study the topography of cleaved single crystals. A structural and chemical analysis was conducted by highly accurate x-ray diffraction and wavelength dispersive x-ray spectroscopy measurements. The latter indicate a homogeneity range of the YbRh2Si2 phase between approximately 40.0–40.2 at.% Rh. For our high-quality samples the number of defects found on the atomic scale (of the order of 0.3% of the visible lattice sites) is in quantitative agreement with a very small off-stoichiometry within this homogeneity range. Comparing our results for these samples allows an assignment of the structural defects observed at the cleaved surfaces to Rh occupying Si sites and, even less numerous Si in Rh sites. Such an analysis is hampered for samples of lesser quality, but there seem to be numerous empty Si-sites. Based on these observations the results of scanning tunneling spectroscopy can be analyzed in further detail and provide insight into the Kondo physics.