An embodiment includes depositing a material onto a substrate where the material includes a different lattice constant than the substrate (e.g., III-V or IV epitaxial (EPI) material on a Si substrate). An embodiment includes an EPI layer formed within a trench having walls that narrow as the trench extends upwards. An embodiment includes an EPI layer formed within a trench using multiple growth temperatures. A defect barrier, formed in the EPI layer when the temperature changes, contains defects within the trench and below the defect barrier. The EPI layer above the defect barrier and within the trench is relatively defect free. An embodiment includes an EPI layer annealed within a trench to induce defect annihilation. An embodiment includes an EPI superlattice formed within a trench and covered with a relatively defect free EPI layer (that is still included in the trench). Other embodiments are described herein.