Nearly ideal vertical Al_xGa_1-xN (\(0.7\ \le x<1.0\)) p-n diodes are fabricated on an AlN substrate. Distributed polarization doping (DPD) was employed for both p-type and n-type layers of the p-n junction, instead of conventional impurity doping, to overcome the major bottleneck of AlN-based material: the control of conductivity. Capacitance-voltage measurements revealed that the net charge concentration agreed well with the DPD charge concentration expected from the device layer structure. The fabricated devices exhibited a low turn-on voltage of 6.5 V, a low differential specific ON-resistance of 3 mΩ cm², electroluminescence (maximum at 5.1 eV), and an ideality factor of 2 for a wide range of temperatures (room temperature-573 K). Moreover, the breakdown electric field was 7.3 MV cm^-1, which was almost twice as high as the reported critical electric field of GaN at the same doping concentration. These results clearly demonstrate the usefulness of DPD in the fabrication of high-performance AlN-based power devices.