A field effect transistor with a heterostructure includes a strained monocrystalline semiconductor layer formed on a carrier material, which has a relaxed monocrystalline semiconductor layer made of a first semiconductor material (Si) as the topmost layer. The strained monocrystalline semiconductor layer has a semiconductor alloy (GexSi1−x), where the proportion x of a second semiconductor material can be set freely. Furthermore, a gate insulation layer and a gate layer are formed on the strained semiconductor layer. To define an undoped channel region, drain/source regions are formed laterally with respect to the gate layer at least in the strained semiconductor layer. The possibility of freely setting the Ge proportion x enables a threshold voltage to be set as desired, whereby modern logic semiconductor components can be realized.