Investigation of stability and migration mechanism of defects in ZnGeP₂ crystals by density functional theory

Abstract

ZnGeP₂ crystals are the frequency conversion materials with the excellent comprehensive performances in a range of 3–5 μm. However, the overlap of the absorption band and the pump wavelength range of optical parametric oscillator at 8–12 μm limits the application performance of the optical parametric oscillator and makes it impossible to achieve a far-infrared laser output. In this work, the formation energy and migration mechanism of six kinds of defects of ZnGeP₂ crystal are discussed by density functional theory. The results show that two defective structures of <inline-formula><tex-math id="M10">\begin{document}$\rm{V_P}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M10.png"/></alternatives></inline-formula>and <inline-formula><tex-math id="M11">\begin{document}$\rm{V_{Ge}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M11.png"/></alternatives></inline-formula> are difficult to form, while four defective structures of <inline-formula><tex-math id="M12">\begin{document}$\rm V_{\rm Zn}^ -$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M12.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M13">\begin{document}$\rm{Z{n_{Ge}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M13.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M14">\begin{document}$ {\rm Ge}_{\rm Zn}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M14.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M15">\begin{document}$\rm{ G{e_{\rm Zn}} + {V_{\rm Zn}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M15.png"/></alternatives></inline-formula> are easy to create. When the number of Ge atoms are slightly more than that of Zn atoms in ZnGeP₂ crystals, the vacancy defects <inline-formula><tex-math id="M16">\begin{document}$\rm V_{\rm Zn}^ -$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M16.png"/></alternatives></inline-formula> form more easily than antistructure defects <inline-formula><tex-math id="M17">\begin{document}$ {\rm Ge}_{\rm Zn}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M17.png"/></alternatives></inline-formula> at 10 K, 500 K and 600 K, but the antistructure defects <inline-formula><tex-math id="M18">\begin{document}$ {\rm Ge}_{\rm Zn}^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M18.png"/></alternatives></inline-formula> are easier to form than the vacancy defects <inline-formula><tex-math id="M19">\begin{document}$ {\text{V}}_{\text{Zn}}^{-} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20220610_M19.png"/></alternatives></inline-formula> at 273 K and 400 K. There is a negative correlation between the volume expansion rate and the defect formation energy of ZnGeP₂ crystal. The larger the volume expansion rate, the lower the defect formation energy is. The differential charge density shows that the electron cloud density among the atoms is enhanced in the defective structures of Ge_Zn and V_Zn+Ge_Zn. The electron cloud density at the lattices of vacancy defects is enhanced when the vacancy defects (V_Zn and V_Ge) and antistructure defects (Ge_Zn and Zn_Ge) form the joint defects. Comparing with the defect-free cells, the charge of Zn atoms increases significantly, that of Ge is significantly reduced, and that of P does not change in the antistructure defect Zn_Ge or Ge_Zn. The absorption spectra of ZnGeP₂ crystal at 10K show that there is the significant absorption in a wavelength range from 0.6 μm to 2.5 μm for the four defective structures: V_Ge, V_Zn, Zn_Ge and Ge_Zn, while the absorption in this range is small for the defective structures V_P and Ge_Zn+V_Zn. The V_Zn has the lowest migration energy, while V_Ge has the highest. The difficulty for V_P to migrate depends on the space resistance, while the difficulty for V_Ge and V_Zn to migrate depend on the inter-atomic distance. This may be related to the small radius and high proportion of P atoms and the large radius and low proportion of Ge and Zn atom in ZnGeP₂ crystal.