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We present the first AlGaN/GaN tunnel-junction FETs (TJ-FETs) featuring a metal-2-D-electron-gas (2DEG) Schottky tunnel junction at the source. The control of the source-to-drain current flow is realized through a gate-controlled tunnel junction instead of a gate-controlled 2DEG channel. The TJ-FETs exhibit normally off operation (Vth = +1.35 V) in an otherwise normally on as-grown sample. The unique high-density 2DEG in AlGaN/GaN heterostructures enables the formation of a Schottky tunnel barrier with nanometer-scale barrier thickness even with a large Schottky barrier height (e.g., ~0.8 eV). In the OFF state, the source Schottky junction provides natural reverse-blocking capability, resulting in significant leakage reduction and low OFF-state current. A drive current of 326 mA/mm, a high ION/IOFF ratio (1010), and a low subthreshold swing (89 mV/dec) are obtained.