Undoped AlN / GaN heterostructures, grown on sapphire by molecular beam epitaxy, exhibit very low sheet resistances, ~ 150 Ohm/sq, resulting from the 2-dimensional electron gas situated underneath a 4 nm thin AlN barrier. This extraordinarily low sheet resistance is a result of high carrier mobility and concentration (~ 1200 cm2/Vs and ~ 3.5×1013 cm-2 at room temperature), which is ~ 3 × smaller than that of the conventional AlGaN / GaN heterojunction field effect transistor (HFET) structures. Using a 5 nm SiN x deposited by plasma enhanced chemical vapor deposition as gate-dielectric, HFETs were fabricated using these all binary AlN / GaN heterostructures and the gate tunneling current was found to be efficiently suppressed. Output current densities of 1.7 A/mm and 2.1 A/mm, intrinsic transconductance of 455 mS/mm and 785 mS/mm, were achieved for 2 µm and 250 nm gate-length devices, respectively. Current gain cut-off frequency fT of 3.5 GHz and 60 GHz were measured on 2 µm and 250 nm gate-length devices, limited by the high ohmic contact resistance as well as the relatively long gate length in comparison to the electron mean free path under high electric fields.