  We report transport measurements on Josephson junctions consisting of Bi2Te3
topological insulator (TI) thin films contacted by superconducting Nb
electrodes. For a device with junction length L = 134 nm, the critical
supercurrent Ic can be modulated by an electrical gate which tunes the carrier
type and density of the TI film. Ic can reach a minimum when the TI is near the
charge neutrality regime with the Fermi energy lying close to the Dirac point
of the surface state. In the p-type regime the Josephson current can be well
described by a short ballistic junction model. In the n-type regime the
junction is ballistic at 0.7 K < T < 3.8 K while for T < 0.7 K the diffusive
bulk modes emerge and contribute a larger Ic than the ballistic model. We
attribute the lack of diffusive bulk modes in the p-type regime to the
formation of p-n junctions. Our work provides new clues for search of Majorana
zero mode in TI-based superconducting devices.
