X-ray detectors based on absorber-junction combinations can combine a large detector area with position resolution and good energy resolution. We plan to use a thick, single crystal Nb or Ta absorber with readout tunnel junctions integrated on top as our next generation X-ray detector. The thickness of the absorber should ensure detection of more than 90% of the impinging photons. Special points of attention in the fabrication of this new detector, like surface preparation, the formation of contacts, and handling of the bulk absorber during the fabrication process are discussed.