Fingerprints of carbon defects in vibrational spectra of GaN considering the isotope effect

This work examines the carbon defects associated with recently reported and novel peaks of infrared (IR) absorption and Raman scattering appearing in GaN crystals at carbon ($^{12}C$) doping in the range of concentrations from $3.2*10^{17}$ to $3.5*10^{19} cm^{-3}$. 14 unique vibrational modes of defects are observed in GaN samples grown by hydride vapor phase epitaxy (HVPE) and then compared with defect properties predicted from first-principles calculations. The vibrational frequency shift in two $^{13}C$ enriched samples related to the effect of the isotope mass indicates six distinct configurations of the carbon-containing point defects. The effect of the isotope replacement is well reproduced by the density functional theory (DFT) calculations. Specific attention is paid to the most pronounced defects, namely tri-carbon complexes($C_N=C=C_N$) and carbon substituting for nitrogen $C_N$. The position of the transition level (+/0) in the bandgap found for $C_N=C=C_N$ defects by DFT at 1.1 eV above the valence band maximum, suggest that $(C_N=C=C_N)^+$ provides compensation of ${C_N}^-$. $C_N=C=C_N$ defects are observed to be prominent, yet have high formation energies in DFT calculations. Regarding ${C_N}$ defects, it is shown that the host Ga and N atoms are involved in the defect's delocalized vibrations and significantly affect the isotopic frequency shift. Much more faint vibrational modes are found from di-atomic carbon-carbon and carbon-hydrogen (C-H) complexes. Also, we note changes of vibrational mode intensities of $C_N$, $C_N=C=C_N$, C-H, and $C_N-C_i$ defects in the IR absorption spectra upon irradiation in the defect-related UV/visible absorption range. Finally, it is demonstrated that the resonant enhancement of the Raman process in the range of defect absorption above 2.5 eV enables the detection of defects at carbon doping concentrations as low as $3.2*10^{17} cm^{-3}$.