We grew heavily Mg-doped GaN using ammonia molecular-beam epitaxy. The use of low growth temperature (740 degrees C) allows decreasing the incorporation of donor-like defects (<3 x 10(17) cm(-3)) responsible for p-type doping compensation. As a result, a net acceptor concentration of 7 x 10(19) cm(-3) was achieved, and the hole concentration measured by Hall effect was as high as 2 x 10(19) cm(-3) at room temperature. Using such a high Mg doping level, we fabricated GaN backward diodes without polarization-assisted tunneling. The backward diodes exhibited a tunneling-current density of 225 A/cm(2) at a reverse bias of -1V at room temperature. (C) 2016 AIP Publishing LLC.