We show that geometric shielding of the reactive flux in chemical vapor deposition by tall neighboring structures obtained by deep substrate patterning, along with short surface diffusion lengths, can provide nearly space filling arrays of high-quality epitaxial crystals despite large mismatches of lattice parameters and thermal expansion coefficients. The density of extended defects is strongly reduced by the method, and wafer bowing and crack formation largely inhibited. The concept is shown to be valid for SiGe/Si ...