Disclosed are methods and mask structures for epitaxially growing substantially defect-free semiconductor material. In some embodiments, the method may comprise providing a substrate comprising a first crystalline material, where the first crystalline material has a first lattice constant; providing a mask structure on the substrate, where the mask structure comprises a first level comprising a first opening extending through the first level (where a bottom of the first opening comprises the substrate), and a second level on top of the first level, where the second level comprises a plurality of second trenches positioned at a non-zero angle with respect to the first opening. The method may further comprise epitaxially growing a second crystalline material on the bottom of the first opening, where the second crystalline material has a second lattice constant different than the first lattice constant and defects in the second crystalline material are trapped in the first opening.