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 on the bottom portion to produce a silicon-germanium 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.