A silicon containing fin is formed on a semiconductor substrate. A silicon oxide layer is formed around the bottom of the silicon containing fin. A gate dielectric is formed on the silicon containing fin followed by formation of a gate electrode. While protecting the portion of the semiconductor fin around the channel, a bottom portion of the silicon containing semiconductor fin is etched by a isotropic etch leaving a body strap between the channel of a finFET on the silicon containing fin and an underlying semiconductor layer underneath the silicon oxide layer. The fin may comprise a stack of inhomogeneous layers in which a bottom layer is etched selectively to a top semiconductor layer. Alternatively, the fin may comprise a homogeneous semiconductor material and the silicon containing fin may be protected by dielectric films on the sidewalls and top surfaces of the silicon containing fin.