The dislocation trapping mechanism in a patterned Si substrate is utilized to reduce the threading dislocation density (TDD) in a Ge epitaxial film as thick as 1 µm for photonic device applications. In particular, a V-groove pattern is more effective than a rectangular one. An array of submicron-wide grooves is patterned on a Si substrate, followed by an epitaxial growth of Ge by chemical vapor deposition. The trapping of dislocations at the groove regions enables a reduction in the TDD of Ge by approximately one order of magnitude compared to the unpatterned case.