A substrate layer formed of a first semiconductor material includes adjacent first and second regions. Fin structures are formed from the substrate layer in both the first and second regions. At least the side walls of the fin structures in the second region are covered with an epitaxially grown layer of second semiconductor material. A drive in process is performed to convert the fin structures in the second region from the first semiconductor material to the second semiconductor material. The first semiconductor material is, for example, silicon, and the second semiconductor material is, for example, silicon germanium or silicon carbide. The fin structures in the first region are provided for a FinFET of a first (for example, n-channel) conductivity type while the fin structures in the second region are provided for a FinFET of a second (for example, p-channel) conductivity type.