Molecular beam epitaxy shall be applied to fabricate semiconductor heterostructures with large spin-orbit interaction. In the C modulation-doped GaAs/AlGaAs material system one focus lies on the design and exploration of tailored band-structure profiles. This should lead to adjustable Rashba induced spin-splittings of the resulting two-dimensional hole systems as a result of the structure inversion asymmetry. The other goal for this material system is to further increase the sample quality with respect to low-temperature hole mobilities and achievable densities. Among the optimisation of other growth parameters, here the implementation of reproducible substrate temperature profiles is planned. In the second part of the proposal we plan to introduce Sb as a group-V element in our molecular beam epitaxy system. This will allow the growth of InAs/GaAlSb and InSb/InAlSb heterostructures in which two-dimensional electron systems form at the corresponding interfaces. These semiconductor heterostructures are of particular importance for spintronic applications due to their peculiar properties, however, are much more demanding in the fabrication process compared to the GaAs-based heterostructures.