Properties of carbon impurities in ZnO: A hybrid functional study

The mechanism of the room temperature (RT) ferromagnetism in C-doped ZnO and the trend that the higher the C concentration, the smaller the saturation magnetic moment $({M}_{\mathrm{s}})$, have remained controversial and puzzling for a long time. Using density-functional calculations with hybrid functional, we qualitatively understand these experimental phenomena. The substitutional ${\mathrm{C}}_{\mathrm{O}}$ defects dominate in Zn-rich conditions and $n$-type materials. They carry 1 or $2{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{C}$, depending on the position of the Fermi level. In low C concentrations and at RT, the ${\mathrm{C}}_{\mathrm{O}}$ defects are kept isolated and prefer to couple ferromagnetically, thus the ${M}_{\mathrm{s}}$ is larger. As the C concentration increases, nonmagnetic ${\mathrm{C}}₂$ dimers form through binding of two ${\mathrm{C}}_{\mathrm{O}}$ defects or binding of one ${\mathrm{C}}_{\mathrm{O}}$ defect with one interstitial C, thus decreasing the ${M}_{\mathrm{s}}$. Our results also suggest that the ferromagnetism from ${\mathrm{C}}_{\mathrm{O}}$ defects can be quenched by higher annealing temperatures. Furthermore, the $p$-type conductivity from carbon dopant is not supported in the present study.