We have analyzed a very short channel tunneling field effect transistor which uses new heterostructures (CoSi2/Si/CdF2/CaF2) lattice-matched to the Si substrate. In device operation, the drain current from source (CoSi2) to drain (CoSi2) through tunnel barriers (Si) and the channel (CdF2) is controlled by a gate electric field applied to the barrier between the source and the channel through the gate insulator (CaF2). Theoretical analysis shows that this transistor has characteristics similar to those of conventional metal-oxide-semiconductor field effect transistors even with channel lengths as short as 5 nm. In addition, we have estimated the theoretical response time of this transistor and showed the possibility of subpicosecond response.