In Dirac materials, like graphene or topological insulators, massless pseudorelativistic electrons promise new, very fast electronic devices by utilizing the partial suppression of backscattering. However, the semimetal nature of graphene makes the realization of practical field effect transistors difficult, due to small on-off current ratios. Here, we propose a new concept, based on Dirac states inside the conduction (or valence) band of a lightly doped wide band gap semiconductor. With the application of a gate voltage, the Dirac states become populated; that is, the Fermi level is switched between the "classical" high-resistivity semiconducting and the relativistic high-mobility metallic range. We demonstrate by theoretical calculations that such a transition can be realized, for example, in thin anatase nanowires, which have been synthesized before. Ta-doped anatase nanowires offer an excellent possibility to build field effect transistors with high speed and good on-off ratio. Guidelines for finding similar "Dirac semiconductors" are provided.