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In this thesis, I present a reliable and efficient approach to heterogeneous integration of single-crystalline GaSb semiconductors with highly mismatched materials. The mismatch may refer to the crystalline structure and the thermal expansion coefficient of single-crystalline GaSb and the other materials of interest. The strategy of hetero-integration relies on epitaxial lift-off. This approach prevents the formation of extended structural defects that are detrimental to the performance of optoelectronic devices and preserves GaSb growth substrates for potential reuse. Within my research work, I have overcome some outstanding challenges of epitaxial lift-off of GaSb, and I have demonstrated the operation of single-crystalline GaSb photovoltaic devices with unique architecture on single-crystalline Si substrates. Using the pixelated approach for epitaxial lift-off, I release GaSb epilayers from GaSb substrates with 100% yield. By leveraging release and transfer of GaSb membranes on Si, I have demonstrated the operation of thin-film photovoltaic devices with areas of ~100sx100s um2 (i.e., pixelated solar cells). The photo-conversion efficiency of ~340x340 um2 pixelated devices amounts to ~2.6%, i.e., a comparable efficiency to what I extracted for a ~5 x 5 mm2 homo-epitaxial GaSb cell on a GaSb substrate. I have performed a detailed structure-property relationships study to justify device characteristics in pixelated GaSb solar cells on Si. Specifically, I have determined the origin of non-ideal effects and leakage mechanisms underlying the device behaviour with and without illumination. These effects relate to the chemical and physical structure of surfaces and interfaces in small-area GaSb solar cells transferred to Si. These investigations are crucial to gain understanding and predictive control of performance in devices with unprecedented architecture. In conclusion, I have established a reliable and efficient process to isolate GaSb epilayers without the formation of any extended defects. I have demonstrated thin films and pixelated GaSb photovoltaic devices on single-crystalline Si substrates, and I have performed a detailed structure-property relationship of the novel solar cells architectures. My work will potentially impact a variety of optoelectronic devices that would benefit from the integration of III-Sb device layers with mismatched materials. These devices include high power infrared lasers, thermophotovoltaic cells, infrared detectors, and photovoltaic cells.