A radiation converter includes a directly converting semiconductor layer having grains whose interfaces predominantly run parallel to a drift direction—constrained by an electric field—of electrons liberated in the semiconductor layer. Charge carriers liberated by incident radiation quanta are accelerated in the electric field in the direction of the radiation incidence direction and on account of the columnar or pillar-like texture of the semiconductor layer, in comparison with the known radiation detectors, cross significantly fewer interfaces of the grains that are occupied by defect sites. This increases the charge carrier lifetime/mobility product in the direction of charge carrier transport. Consequently, it is possible to realize significantly thicker semiconductor layers for the counting and/or energy-selective detection of radiation quanta. This increases the absorptivity of the radiation converter which in turn makes it possible to reduce a radiation dose applied to the patient.