Introduction

In the past several years, ZnO has been considered as an attractive material, given its unique physical properties, such as a wide direct band gap of 3.37 eV and high exciton binding energy (60 meV) at room temperature1. These properties make it suitable for a wide variety of applications, such as ultraviolet (UV) emittion and detection, surface acoustic wave (SAW) devices, gas sensors and transparent conducting electrodes2,3. In these desired applications, high-efficient ZnO-based light-emitting devices are particularly important. Mixing ZnO-based semiconductor alloys with other materials which possess even wider band gaps, allows for the fabrication of quantum wells and superlattices4,5. Alloying is an effective approach to fine-tune the band gap in the range of blue-green and ultraviolet wavelengths, which greatly promotes the band-gap engineering and heterojunction design6,7. For different desired band gaps, there are several candidates, such as MgO, BeO and CaO8,9,10. The MgZnO alloy, which has high solubility, has been widely investigated11,12,13,14,15,16,17. However, phase segregation between ZnO and MgO was observed for Mg concentrations x ≥ 0.36 due to the different crystal structures and large lattice mismatch between ZnO and MgO. Specifically, MgO is cubic and ZnO is hexagonal. BeO (Eg = 10.6 eV) is another good alternative and it has the same crystal structure as ZnO. However, at increased pressures, the BeO remains in the hexagonal wurtzite structure and ZnO transforms into cubic structure at ~9 GPa. In the past years, some theoretical researches have been done to seek a stable BeZnO alloy18,19,20,21,22,23, yet not fully successful because the large difference in the ionic radii of Be and Zn usually causes the structure of BeZnO thermodynamically unstable.

CaO is an IIa-IVa compound with a rock-salt structure and a wide band-gap of 7.2 eV24,25 and CaxZn1–xO alloys are also candidates for wider band-gap materials. A number of first-principle calculations on CaxZn1–xO with wurtzite structures have been performed26,27,28, however, no stable structure has yet been found. Previous theoretical studies focused on creating alloys in a wurtzite structure by replacing Zn with Ca. For instance, the existence of metastable states at Ca concentrations of x = 0.25, 0.50 and 0.75 has been shown, however, these kinds of consequences are not stable. Bulk ZnO prefers the hexagonal wurtzite structure (B4) under ambient pressure and transforms into a cubic rocksalt structure (B1) at 9 GPa1, while CaO is in a rocksalt structure under 60 GPa. Generally, there is a large difference in the crystal structure between wurtzite hexagonal ZnO (B4) and rock salt cubic CaO (B1) that can cause unstable phase-mixing, as shown by Nazir’s et al.26. In this paper, we investigate the stable structures of CaxZn1–xO alloy under high pressure using first principles calculations. We examine the stability, structural and electronic properties of the CaxZn1–xO alloys with different Ca concentrations. These structural and electronic properties are crucial for hetero-structural design and optimized growth of the related quantum wells and superlattices.

Results and discussion

In this work, we report four stable ground state structures of CaxZn1–xO. The formation enthalpy of CaxZn1–xO alloy is calculated using a fractional representation of CaxZn1–xO (0 ≤ x ≤ 1) with respect to its decomposition into CaO and ZnO, as

where x is the concentration of CaO. B1−CaO transits to B2 at 58 GPa in our calculation, similar to previous results24,29. In the condition of ZnO, the transition from B4 to B1 takes place at 9 GPa in our calculation, consistent with the experimental findings Pt ≈ 8.7 GPa30, Pt ≈ 9.1 GPa31, or Pt ≈ 10 GPa32 and first-principles calculations Pt = 8.8 GPa12. Thus, when pressure is below 9 GPa, B4 phases are considered and above 9 GPa B1-ZnO is considered for the lowest energy. Similarly in the case of CaO, B1 phases below 58 GPa and above 58 GPa, B2 phases are considered. The relative energetics of CaO-ZnO alloys from 10 to 60 GPa are summarized in the convex hull plots shown in Fig. 1. The formation enthalpies were evaluated as the difference in the enthalpy of the predicted CaO-ZnO alloys with respect to CaO and ZnO at the selected pressures. Structures lying on the convex hull are either thermodynamically stable or metastable and can be synthesized in principle. Figure 1 reveals that CaZn6O7 is the first stable alloy below 10 GPa, which has the most negative enthalpy of formation. In Fig. 2 we show the calculated enthalpy difference of CaZn6O7 as a function of pressure, calculated against the decomposition into the constituent oxides (B1-CaO, B1-ZnO, or B4-ZnO). As shown in Fig. 2, the structure of CaZn6O7 becomes stable above 8.7 GPa. The space group of this high-pressure phase is R-3. In the case of B4-ZnO and B1-CaO, the formation enthalpies of all CaxZn1–xO alloys are positive before 8.7 GPa, indicating the tendency for the segregation into ZnO and CaO.

Figure 1
figure 1

Convex hull diagram for CaO-ZnO alloys.

The formation enthalpies (ΔH, with respect to ZnO and CaO of their most stable phases at selected pressures) of CaxZn1−xO. The abscissa x is the fraction of CaO in the structures. Circles on the solid lines represent stable ground-state compounds under the corresponding pressure.

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Figure 2
figure 2

Enthalpy curves for R−3_CaZn6O7.

(relative to ZnO and CaO in their most stable phases at selected pressures).

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At above 8.7 GPa, more stable CaxZn1–xO structures appear. As depicted in Supplementary Fig. S1, enthalpy calculations reveal that CaZn3O4 alloys exist above 12 GPa. At higher pressure, CaZnO2 and CaZn5O6 become stable at 32.6 GPa and 36.8 GPa, respectively. The thermodynamic results show that the formation enthalpy of CaZn5O6 is always slight in the pressure range of 36.8–65 GPa. The CaZn5O6 structure will become unstable completely when pressure reaches 65 GPa, with a tendency to segregate into CaZn6O7 and CaZn3O4. All of the expected stable alloys of CaZn6O7 (R–3), CaZn5O6 (C2/M), CaZn3O4 (P2/C) and CaZnO2 (R–3M) are depicted in Fig. 3. More alloy structures with higher Ca-concentration appear with further increase in pressure. However, the structures can only be stable when the Ca-concentration is no more than 50%, even if pressure is increased over 60 GPa.

Figure 3
figure 3

Pressure-composition phase diagram of the CaxZn1−xO alloys.

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These detailed calculations for stable structures allow us to construct a P-x phase diagram of CaO-ZnO alloys, as shown in Fig. 3. There is a tendency for the number of CaxZn1–xO alloys to increase with pressure, similar to MgxZn1–xO alloys12. However, with pressure increasing, more Mg-rich structures appeared in the MgO-ZnO case, but more Zn-rich structures appear in our study. CaO, ZnO and MgO all exhibit cubic structures under pressure; and the ionic radii of Ca, Zn and Mg is 1, 0.74 and 0.72 Å, respectively33. In this case, the element with the smaller ionic radius trend to turn into higher component in the alloys.

For all the predicted structures shown in Fig. 4, the corresponding structural information is listed in Table 1. We calculated the phonon dispersions under pressure and found them to be dynamically stable (Supplementary Fig. S2). We also calculated the phonon dispersions and elastic constants of the four predicted structures under 0 GPa, as shown in Supplementary Fig. S3 and Table S1, which show the structures are mechanically and dynamically stable at 0 GPa. So we think our predicted alloys can be synthesized at high pressure and reserved at ambient conditions.

Table 1 Lattice constants, formation enthalpy, atomic coordinates and pressure for CaO-ZnO alloys.
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Figure 4
figure 4

Crystal structures of the predicted CaxZn1−xO at the selected pressures.

(a) R-3_CaZn6O7 at 40 GPa, (b) C2/m_CaZn5O6 at 60 GPa, (c) P2/c_CaZn3O4 at 40 GPa and (d) R-3 m_CaZnO2 at 40 GPa. The large purple, medium-sized gray and small red spheres represent Ca, Zn and O atoms, respectively. More structural details are listed in Table 1.

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Previous studies suggest that the symmetry of component structures is important in alloys of ZnO with other group-II metal oxides6,18,26,27,34. Most of these structures were created using the substitution method, where Zn was replaced with Ca in the wurtzite supercell or Ca was replaced with Zn in the rocksalt supercell. However, our current study shows that the stable CaO-ZnO alloys undergo a transition from hexagonal to monoclinic and back to hexagonal structure, with the increase in the Ca concentration. At 8.7 to 9 GPa, the CaZn6O7 alloy made from the nonisostructural components (wurtzite + rocksalt) is stable through both dynamics and thermodynamic analysis. At above 9 GPa, more structure became stable, however, none of the alloys have the rocksalt structure, without even the cubic symmetry adopted, although they were made from the isostructural components (rocksalt + rocksalt). In our previous study, we found similar results in the MgO-ZnO alloys12, where the alloys have a hexagonal structure with a high Mg-concentration, while both ZnO and MgO have a similar cubic structure under pressure. In BeO-ZnO alloys, the solubility of BexZn1–xO in the Zn-rich region is low, although ZnO and BeO have the same wurtzite structure18. In addition, no BeO-ZnO alloy structures with thermodynamic stability were found using our USPEX calculations. In contrast to previous views, the symmetry of component structure shows little impacts on the alloy structure here.

Band gap (Eg), which denotes the required energy of an electron from valence band maximum (VBM) to conduction band minimum (CBM), is an important parameter to determine the optoelectronic properties of semiconductors. The band gap of ZnO increases with pressure and that of CaO decreases with pressure, as shown in Supplementary Fig. S3. Therefore, it is interesting to observe the pressure effects on band gaps of CaO-ZnO alloys. These band gaps are graphed in Fig 5(b) as a function of Ca composition for ground-state CaxZn1–xO structures under high pressure. The band gap increases with pressure and also increases in an almost linear fashion with Ca concentration, when the pressure increases from 10 to 60 GPa. The more CaO mixing with ZnO, the wider band gap of alloy will be formed. In our previous theoretical study12, we also found the band gap linearly increases with Mg content in the MgxZn1–xO alloys, which is consistent with the experimental results35.

Figure 5
figure 5

The electronic band structures of CaO-ZnO alloys.

(a) Depicts the electronic band structures of CaZn6O7, CaZn5O6, CaZn3O4, CaZnO2 at 60 GPa. (b) Depicts the band gaps as the function of pressure at selected pressures.

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As shown in Fig. 5(b), band gaps of all alloys increase with pressure except CaZnO2, whose band gaps have different variation rules for pressure. Calculated electronic band structures are graphed in Fig. 5(a) at selected pressures. The CBMs of CaZn6O7, CaZn5O6 and CaZn3O4 are all located at the Γ point (0,0,0) and the CBM of CaZnO2 is located at the M point (0,1/2,0). The CBM transforms from the Γ point to the M point as the Ca concentration increases.

We further analyze whether the different concentrations of alloys lead to a variation in the electronic band structures. Firstly, when Ca concentration is less than 0.5, the band gap increases with pressure and the CBM is always located at the Γ point. Band gaps are plotted as a function of pressure in Supplementary Fig. S4. However, CaZnO2 displays some extraordinary properties. The band gap of CaZnO2 first increases and then decreases with pressure, as shown in Fig. 6. The CBM of CaZnO2 under 40 GPa is located at the Γ point (0, 0, 0) and the band gap at Γ point increases with pressure, similar to the behavior in B1-ZnO. Meanwhile, the CBM of CaZnO2 from 40 to 60 GPa is located at the M point (0, 1/2, 0) and the gap at the M point reduces slowly with pressure, same to CaO at the X point (1/2, 0, 1/2). Using qualitative analysis, we keep the lattice constants unchanged, remove Ca or Zn atoms, respectively and analyze the band structures of the broken crystal. The CBM of CaZnO2 without Ca atoms located at the Γ point and without Zn locates at the M point, which reveals that the conduction band at the Γ point basically comes from ZnO and at the M point comes from CaO. Thus, with the increase in pressure, the CaO band-gap is more significant than the ZnO one.

Figure 6
figure 6

The electronic band structures of CaZnO2.

At pressure of (a) 45 GPa, (b) 65 GPa, respectively. And (c) the band gap at the Γ and M points as the function of pressure are depicted by black and red lines, respectively.

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Furthermore, other than the above-mentioned four stable structures, we find a metastable structure when Ca concentration is 0.75, as shown in Fig. 7(a). There is no imaginary frequency in Fig. 7(c), so the Ca3ZnO4 structure is dynamically stable. Although the formation enthalpy (with respect to ZnO and CaO) is negative as shown in Fig. 1 above 40 GPa, the enthalpy respect to CaZnO2 and CaO is always positive, which indicates a tendency to segregate into CaZnO2 and CaO. From the calculated electronic band structures in Fig. 7(b), the CBM of Ca3ZnO4 alloy is located at M the point. The band gap of this metastable structure is represented by the purple dotted line in Supplementary Fig. S4. The band gap of those large Ca-concentration structure decreases with pressure, while the low Ca-concentration structure exhibit the opposite behavior. In view of the band structure of all of these alloys and considering the effects of pressure on band gap, the effect of Ca-concentration is also significant. In summary, the band gap of CaO-ZnO alloy depends on a fine interplay between concentration and pressure.

Figure 7
figure 7

The metastable phase of Ca3ZnO4.

(a) the crystal structure, (b) the electronic band structures and (c) the phonon dispersion curve.

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Conclusion

We investigate the composition and structure of the CaO-ZnO alloys at high pressure using USPEX codes. In a range of 0–60 GPa, four stable alloy structures with different Ca concentrations have been found. With increasing pressure, more alloys with higher Ca concentrations appear. However, the structure can only be stable when the Ca-concentration is no more than 50%, with pressure up to 60 GPa. When the Ca concentration increases, the stable structures of CaZn6O7, CaZn5O6, CaZn3O4 and CaZnO2 undergo a hexagonal to monoclinic transition and then transforms back to a hexagonal phase. We find that ground-state structures of the alloys do not share the cubic nature of ZnO and CaO, indicating the symmetry of component structures has little impact on the alloy structure. Through detailed analysis of band structure, we note an almost linear increase in band gap as a function of Ca-concentration at the selected pressure. When the concentration is below 50% the band gap increases with pressure. The band gap of CaZnO2 first increases with pressure up to 40 GPa and then starts to decrease with pressure.

Methods

To search for the stable and low-enthalpy structures of CaO-ZnO alloy, an ab initio evolutionary algorithm (EA), which has been designed to find the most stable structure for a given chemical composition range at given external conditions as implemented in the USPEX code, is employed36,37,38. In this work, evolutionary crystal structure prediction calculations were performed at 0, 20, 40 and 60 GPa for (CaO)m–(ZnO)n system (m + n ≤ 20), all at zero temperature. We performed ab initio calculations with the Local Density Approximation (LDA)39 as implemented in the Vienna ab initio simulation package (VASP) code40, which is based on density functional theory. The electron-ion interaction was described by the projector augmented wave (PAW) scheme41. The electron configurations 10d2p, 6p2s and 4p2s were treated as valence for Zn, Ca and O, respectively. During structural relaxation, a tested energy cut off of 550 eV was used for the plane wave basis sets and a k-point resolution of 0.03 Å–1 in the reciprocal space was used for all structures to minimize error from the k-point meshes. The atomic positions, lattice parameters and cell volume were fully relaxed until the force on each atom was less than 1 meV/Å. Phonons were calculated with the supercell method implemented in the PHONOPY program.

Additional Information

How to cite this article: Sha, X. et al. Ab initio investigation of CaO-ZnO alloys under high pressure. Sci. Rep. 5, 11003; doi: 10.1038/srep11003 (2015).