Shallow and Deep States of Beryllium Acceptor in GaN: Why Photoluminescence Experiments Do Not Reveal Small Polarons for Defects in Semiconductors

Currently, only one shallow acceptor (Mg) has been discovered in GaN. Here, using photoluminescence (PL) measurements combined with hybrid density functional theory, we demonstrate that a shallow effective-mass state also exists for the ${\mathrm{Be}}_{\mathrm{Ga}}$ acceptor. A PL band with a maximum at 3.38 eV reveals a shallow ${\mathrm{Be}}_{\mathrm{Ga}}$ acceptor level at $113\pm 5\mathrm{meV}$ above the valence band, which is the lowest value among any dopants in GaN reported to date. Calculations suggest that the ${\mathrm{Be}}_{\mathrm{Ga}}$ is a dual-nature acceptor with the “bright” shallow state responsible for the 3.38 eV PL band, and the “dark,” strongly localized small polaronic state with a significantly lower hole capture efficiency.