A SOI substrate layer formed of a silicon semiconductor material includes adjacent first and second regions. A portion of the silicon substrate layer in the second region is removed such that the second region retains a bottom portion made of the silicon semiconductor material. An epitaxial growth of a silicon-germanium semiconductor material is made to cover the bottom portion. Germanium is then driven from the epitaxially grown silicon-germanium material into the bottom portion to convert the bottom portion to silicon-germanium. Further silicon-germanium growth is performed to define a silicon-germanium region in the second region adjacent the silicon region in the first region. The silicon region is patterned to define a first fin structure of a FinFET of a first (for example, n-channel) conductivity type. The silicon-germanium region is also patterned to define a second fin structure of a FinFET of a second (for example, p-channel) conductivity type.