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.

Figure 1

Evolution of the PL spectrum with temperature for GaN:Be (sample 0408b) at $P_{\mathrm{exc}}=0.13\mathrm{W/}{\mathrm{cm}}^2$. The DAP peaks with the ZPL at 3.375 eV transform to identical in shape eA peaks with the ZPL at 3.395 eV. The LO phonon replicas follow the ZPL. The NBE emission consists of the two-electron satellite (TES), donor-bound exciton (DBE) and free exciton (FE) peaks. The time-resolved PL spectrum is shown with filled circles for the time-delay of $14\mu \mathrm{s}$ at $T=55\mathrm{K}$.

Figure 2

Configuration coordinate diagram for the ${\mathrm{Be}}_{\mathrm{Ga}}$ acceptor in GaN. The adiabatic potentials are obtained by fitting into HSE computed transition energies using the harmonic approximation. Direct HSE calculations are also performed (filled circles). Isosurfaces (at 10% of the maximum values) of the hole spin density for both shallow and deep states are shown (yellow) along with ${\mathrm{Be}}_{\mathrm{Ga}}$ nearest neighbors. Small (gray) atoms are N, medium (orange) atoms are Be, and large (green) atoms are Ga.