Defect Physics of Ternary Semiconductor ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ with a High Density of Anion-Cation Antisites: A First-Principles Study

Anion-cation antisite defects usually have low density in the group III-V (e.g., $\mathrm{Ga}\mathrm{N}$) and ${\mathrm{II}-\mathrm{IV}-\mathrm{V}}_2$ (${\mathrm{Zn}\mathrm{Ge}\mathrm{N}}_2$, ${\mathrm{Zn}\mathrm{Sn}\mathrm{P}}_2$) semiconductors, and thus, have not drawn enough attention in defect studies of ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ since 1976. However, our first-principles calculations based on a hybrid functional show that the anion-cation antisite defects (${\mathrm{Ge}}_{\mathrm{P}}$ and ${\mathrm{P}}_{\mathrm{Ge}}$) can have very high density (${10}^{17}-{10}^{18}{\mathrm{cm}}^{-3}$), making them the dominant defects in ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$. Their calculated photoluminescence (PL) spectra agree well with the 1.4 and 1.6 eV PL peaks observed experimentally, indicating that they may be the origin of defects, which challenges previous assumptions that the $\mathrm{P}$ vacancy ($V_{\rm{P}}$) defect is responsible for the two PL peaks. Although the anion-cation antisites (${\mathrm{Ge}}_{\mathrm{P}}$ and ${\mathrm{P}}_{\mathrm{Ge}}$) and cation-cation antisites (${\mathrm{Ge}}_{\mathrm{Zn}}$ and ${\mathrm{Zn}}_{\mathrm{Ge}}$) both have densities as high as ${10}^{17}{\mathrm{cm}}^{-3}$, ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ suffers from serious donor-acceptor compensation, which results in a low carrier density (below ${10}^{10}{\mathrm{cm}}^{-3}$), and thus, poor electrical conductivity. These results explain the mysterious observation that ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ crystals grown using different methods have a high defect density, but low carrier density and high resistivity, and also indicate that it is challenging to suppress the defect-induced optical absorption in the development of high-power ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$-based optical devices.

Figure 1

(a) Unit cell of chalcopyrite ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ crystal structure. (b) Thermodynamic chemical-potential region (shown in gradient color) stabilizing ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ with respect to competing secondary phases, such as $\mathrm{Zn}$, $\mathrm{Ge}$, $\mathrm{P}$, ${\mathrm{Zn}\mathrm{P}}_2,$ and ${\mathrm{Zn}}_3{\mathrm{P}}_2$ in three-dimensional (µ_Zn, µ_Ge, µ_P) space. (c) Projection of the chemical-potential region on the (µ_Zn, µ_Ge) plane. Six points A, B, C, D, E, and F are selected as the synthesis conditions under which the defect properties will be calculated.

Figure 2

Calculated formation energies of point defects in different charge states as a function of Fermi level under the chemical-potential points (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F shown in Fig. 1. Gray arrows denote the Fermi levels under the corresponding chemical-potential conditions (calculated in Fig. 5).

Figure 3

Calculated charge-state transition levels of point defects in the band gap of ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$.

Figure 4

Norm-squared wave function of the defect eigenstates produced by (a) ${\mathrm{Ge}}_{\mathrm{Zn}}$, (b) ${\mathrm{Zn}}_{\mathrm{Ge}}$, (c) ${\mathrm{P}}_{\mathrm{Ge}},$ and (d) ${\mathrm{Ge}}_{\mathrm{P}}$ in their neutral states. Isovalues of isosurfaces are set to 20% of the maximum. Colors of $\mathrm{Zn}$, $\mathrm{Ge},$ and $\mathrm{P}$ atoms are the same as those in Fig. 1.

Figure 5

Calculated density of all defects, Fermi levels, and hole-carrier density at room temperature (300 K) in ${\mathrm{Zn}\mathrm{Ge}\mathrm{P}}_2$ crystals grown at a high temperature (1300 K) and under different chemical conditions (corresponding to the chemical-potential points from A to F in Fig. 1). Since the allowed range of µ_Ge is narrow in Fig. 1, its influence on the results is small, and thus, the differences between A and F, B and E, or C and D points are not large.

Figure 6

(a) Calculated photoluminescence spectrum of ${\mathrm{Ge}}_{\mathrm{P}}$, ${\mathrm{P}}_{\mathrm{Ge}}$, ${\mathrm{Zn}}_{\mathrm{Ge}}$, ${\mathrm{Ge}}_{\mathrm{Zn}},$ and V_P in comparison with experimental data extracted from Refs. [19, 23, 41]. Solid lines are calculated results and dots are experimental values. Spectral peaks are normalized. (b) Corresponding schematic band diagram of carrier excitation and recombination processes. Fermi level is set to 0.69 eV in the shaded pink area.