Crystalline heterostructures including an elevated fin structure extending from a sub-fin structure over a substrate. Devices, such as III-V transistors, may be formed on the raised fin structures while silicon-based devices (e.g., transistors) may be formed in other regions of the silicon substrate. A sub-fin isolation material localized to a transistor channel region of the fin structure may reduce source-to-drain leakage through the sub-fin, improving electrical isolation between source and drain ends of the fin structure. Subsequent to heteroepitaxially forming the fin structure, a portion of the sub-fin may be laterally etched to undercut the fin. The undercut is backfilled with sub-fin isolation material. A gate stack is formed over the fin. Formation of the sub-fin isolation material may be integrated into a self-aligned gate stack replacement process.