We present a new concept applicable to the epitaxial growth of dislocation-free semiconductor structures on a mismatched substrate with a thickness far exceeding the conventional critical thickness for plastic strain relaxation. This innovative concept is based on the out-of-equilibrium growth of compositionally graded alloys on deeply patterned substrates. We obtain space-filling arrays of individual crystals several micrometers wide in which the mechanism of strain relaxation is fundamentally changed from plastic to elastic. The complete absence of dislocations at and near the heterointerface may pave the way to realize CMOS integrated SiGe X-ray detectors.