Monolithic integration of absorber layer and readout electronics is expected to greatly improve spatial resolution and sensitivity of X‐ray imaging detectors. It requires, however, heteroepitaxial growth of thick, lattice, and thermally mismatched absorber layers on a Si substrate. Wafer bowing and layer cracks induced by temperature changes have so far appeared to be insurmountable obstacles in the way of realizing such a device. Here we present first results on a detector concept which does not suffer from such shortcomings. The absorber consists of closely spaced, tall Ge crystals, typically a few microns in width, each forming a heterojunction diode with the Si substrate. Electrical measurements on such diodes reveal reverse dark currents of the order of 1 mA/cm2, low enough for detector fabrication. We present a preliminary version of such a detector, where the pixel size is determined by the CMOS circuits rather than individual Ge crystals.