A method of making a structurally stable SiGe-on-insulator FinFET employs a silicon nitride liner to prevent de-stabilizing oxidation at the base of a SiGe fin. The silicon nitride liner blocks access of oxygen to the lower corners of the fin to facilitate fabrication of a high-concentration SiGe fin. The silicon nitride liner is effective as an oxide barrier even if its thickness is less than about 5 nm. Use of the SiN liner provides structural stability for fins that have higher germanium content, in the range of 25-55% germanium concentration.