Revisiting the substitutional Mg acceptor binding energy of AlN

Bipolar ($n$- and $p$-type) electric conductivity control is at the heart of semiconductor technologies. However, achieving such control in ultrawide-band-gap semiconductors has been a major challenge because of the very high donor and/or acceptor binding energies of these materials. In the case of aluminum nitride (AlN), which is an ultrawide-band-gap semiconductor and one of the first candidate materials for solid-state deep-ultraviolet emitters, the substitutional magnesium (Mg) acceptor binding energy has been reported to be at least 500 meV; thus, $p$-type electric conductivity control in AlN by Mg doping is believed to be unfeasible. Here, we experimentally and theoretically revisit the substitutional Mg acceptor binding energy of AlN. Our bound exciton luminescence and impurity-related transition spectroscopic studies indicate that the substitutional Mg acceptor binding energy of AlN is well below 500 meV. This statement is supported by variational calculations using anisotropic hole effective masses derived from first-principles calculations. The three independent approaches estimate the substitutional Mg acceptor binding energy of AlN to be $330\ifmmode\pm\else\textpm\fi{}80\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. We find that considering electron-hole exchange interaction, hole anisotropy, and carrier-phonon coupling of AlN leads to a more realistic substitutional Mg acceptor binding energy.