Semiconductor-on-insulator (XOI) structures and methods of fabricating XOI structures are provided. Single-crystalline semiconductor is grown on a source substrate, patterned, and transferred onto a target substrate, such as a Si/SiO2 substrate, thereby assembling an XOI substrate. The transfer process can be conducted through a stamping method or a bonding method. Multiple transfers can be carried out to form heterogenous compound semiconductor devices. The single-crystalline semiconductor can be II-IV or III-V compound semiconductor, such as InAs. A thermal oxide layer can be grown on the patterned single crystalline semiconductor, providing improved electrical characteristics and interface properties. In addition, strain tuning is accomplished via a capping layer formed on the single-crystalline semiconductor before transferring the single-crystalline semiconductor to the target substrate.