Artificially ordered quantum dot (QD) arrays, where confined carriers can interact via direct exchange coupling, may create unique functionalities such as cluster qubits and spintronic bandgap systems. Development of such arrays for quantum computing requires fine control over QD size and spatial arrangement on the sub-35 nm length scale. We employ electron-beam irradiation to locally decompose ambient hydrocarbons onto a bare Si (001) surface. These carbonaceous patterns are annealed in ultra-high vacuum (UHV), forming ordered arrays of nanoscale SiC precipitates that have been suggested to template subsequent epitaxial Ge growth to form ordered QD arrays. We show that 3C-SiC nanodots form, in cube-on-cube epitaxial registry with the Si substrate. The SiC nanodots are fully relaxed by misfit dislocations and exhibit small lattice rotations with respect to the substrate. Ge overgrowth at elevated deposition temperatures, followed by Si capping, results in expulsion of the Ge from SiC template sites due to the large chemical and lattice mismatch between Ge and C. Maintaining an epitaxial, low-defectivity Si matrix around the quantum dots is important for creating reproducible electronic and spintronic coupling of states localized at the QDs.