Discovery of earth-abundant nitride semiconductors by computational screening and high-pressure synthesis

Nitride semiconductors are attractive because they can be environmentally benign, comprised of abundant elements and possess favourable electronic properties. However, those currently commercialized are mostly limited to gallium nitride and its alloys, despite the rich composition space of nitrides. Here we report the screening of ternary zinc nitride semiconductors using first-principles calculations of electronic structure, stability and dopability. This approach identifies as-yet-unreported CaZn2N2 that has earth-abundant components, smaller carrier effective masses than gallium nitride and a tunable direct bandgap suited for light emission and harvesting. High-pressure synthesis realizes this phase, verifying the predicted crystal structure and band-edge red photoluminescence. In total, we propose 21 promising systems, including Ca2ZnN2, Ba2ZnN2 and Zn2PN3, which have not been reported as semiconductors previously. Given the variety in bandgaps of the identified compounds, the present study expands the potential suitability of nitride semiconductors for a broader range of electronic, optoelectronic and photovoltaic applications.

S emiconductors are increasingly relied upon in modern society. Prototypical elemental semiconductors, Si and Ge, play principal roles in electronics and photovoltaics. Compound semiconductors including GaAs, GaP and GaN have not only enhanced these applications, but also paved the way to optoelectronic devices, such as light-emitting diodes 1 . Current electronics also utilize oxide semiconductors in thin-film transistors 2 , and semiconductor-based photocatalysts and photoelectrochemical cells are being developed, particularly for the electrolysis of water 3,4 . With such a variety of applications, the exploration of novel semiconducting materials has been a fundamentally and technologically important issue. Among the compound semiconductors, nitrides are attractive due to the abundant and environmentally benign nitrogen constituent. Many nitrides possess relatively high chemical stability at high temperature, which is advantageous for applications under severe environments such as power electronics. Moreover, bulk crystal and film growth techniques are well established, especially for group III nitrides. However, the currently commercialized nitride semiconductors are mostly limited to GaN and its based Al x Ga 1 À x N and In x Ga 1 À x N alloys with tuned bandgaps. This situation has stimulated experimental and computational searches of novel nitrides, for instance, spinel-Si 3 N 4 (ref. 5), cubic-Zr 3 N 4 (ref. 6), ZnSnN 2 (ref. 7), CuNbN 2 (ref. 8) and LaWN 3 (ref. 9). In particular, recent developments of highthroughput first-principles screening based on prototype crystal structures and evolutionary algorithm structure searches have enabled the accelerated identification of a variety of previously unreported or uncharacterized semiconductors, including nitrides [8][9][10][11][12][13][14][15][16][17][18][19][20] .
High carrier mobility is desirable or even mandatory, in most applications of semiconductors, and the effective mass is a relevant fundamental physical parameter. Group III nitrides in the wurtzite structure, especially GaN and InN, have small electron effective masses due to spatially diffuse cation s-orbital contributions to their conduction bands. Moderate hole effective masses are also attained in the valence bands with mainly N-2p characteristics. Technological uses for nitride semiconductors could be expanded if alternative materials with similar desirable electronic properties were found. Ideally, such alternatives should be environmentally benign and comprised of earth-abundant constituents. A chemical analogy to GaN and InN suggests that the nitrides composed of Zn, Ge or Sn would be good candidates. In particular, hybridization between closed-shell Zn-3d and N-2p states in the valence band is expected to reduce hole effective masses in Zn nitrides. Indeed, a Zn binary nitride, Zn 3 N 2 , possesses such a band structure 21 , but the fabrication of its high-quality film is still challenging, partly due to its small exothermic formation enthalpy ( À 22.6 kJ mol À 1 or À 47 meV per atom) 22 . In addition, well-known ternary zinc nitride semiconductors are limited to a small number of systems, such as LiZnN (ref. 23), ZnGeN 2 (ref. 24) and ZnSnN 2 (ref. 7).
Here we report computational screening of ternary zinc nitrides using a combination of the prototype-based and evolutionary algorithm structure searches. Twenty-one promising semiconductors with small carrier effective masses are identified via systematic first-principles calculations of stability and electronic structure. The proposed nitrides include previously unreported CaZn 2 N 2 with earth-abundant components and a direct bandgap, which is synthesized by high-pressure methods. Alloy calculations indicate a bandgap capable of covering most of the visible light range. Native defect and dopant calculations also predict p-and n-type dopability for CaZn 2 N 2 and the related Ca 2 ZnN 2 .

Results
Theoretical identification of ternary zinc nitride semiconductors. Systems of interest have been selected from 583 existing and hypothetical ternary zinc nitrides, which consist of various polymorphs of 125 chemical formulae. These candidate compounds are constructed using 52 prototype crystal structures, either reported in the Inorganic Crystal Structure Database (ICSD) 25 or previously predicted theoretically 15 (Supplementary Table 1). The considered structures are taken by N 3 À compounds, that is, nitrides, involving two kinds of cations, at least one of that is divalent; those taken by azides, diazenides and pernitrides are excluded. The divalent cation is replaced with Zn(II) and the other is replaced with a cation of the same valence (Supplementary Table 2), which is expected to yield a closed-shell electronic structure and therefore exhibit a quantifiable bandgap. The cation species are not restricted to abundant elements at this stage because the electronic structure of compounds involving any element can provide useful information on the design of novel semiconductors. Subsequently, an evolutionary algorithm 12,26 is used to validate or update the most stable crystal structures. This allows us to overcome the limitations associated with relying on already reported crystal structures in the ICSD.
The screening is performed from various aspects: (i) the electronic structure, that is, bandgaps and effective masses; (ii) dynamic stability against lattice vibration; and (iii) thermodynamic stability against competing phases in the phase diagram.
Here, not only thermodynamically stable phases, but also metastable phases with small positive formation energies (o50 meV per atom) are selected. This tolerance partly accommodates errors associated with the approximations used in first-principles calculations and the omission of temperature effects (Supplementary Method 1). Although metastable phases with higher formation energies may be grown by the use of high pressure, high temperature and/or non-equilibrium conditions, we prioritize the predictions of thermodynamically stable or slightly metastable compounds for the ease of the fabrication. Furthermore, the energetics of relevant native point defects and dopants is assessed to identify the dopability into p type, n type or both for promising compounds. Details of the screening and computational procedures are described in the Methods section and Supplementary Method 1.
Identified from the computational screening are 21 nitrides that are dynamically stable and thermodynamically stable/slightly metastable against competing phases (with formation energies that are o50 meV per atom), possess bandgaps and exhibit small effective masses for holes, electrons or both (smaller than 2m 0 , where m 0 denotes the free-electron rest mass); their crystal structures, phonon densities of states, phase diagrams and electronic band structures are presented in Supplementary  Figs 15 . We note that four of these known nitrides, that is, Ca 2 ZnN 2 , Sr 2 ZnN 2 , Ba 2 ZnN 2 and Zn 2 PN 3 have not, to our knowledge, been considered as semiconductors previously and their appealing band structures are unveiled in the present study. In addition, the majority of the identified nitrides consist solely of abundant elements.
Among the known nitrides, ZnSiN 2 , ZnGeN 2 and ZnSnN 2 are found to favour a wurtzite-derived crystal structure in consistency with previous experiments 7, 24 . ZnTiN 2 is predicted to take this crystal structure among the newly identified Zn-IV-N 2 compounds, whereas ZnZrN 2 and ZnHfN 2 are energetically more favourable with an alternate, P3m1 crystal structure obtained using the evolutionary algorithm. The present results extend the wurtzite derivatives from Zn-IV-N 2 to those involving group V and VI elements. Zn 2 PN 3 can be regarded as a prototype of such kind with a group V element. Our calculations suggest that Zn 2 VN 3 , Zn 2 NbN 3 and Zn 2 TaN 3 are stable in this Zn 2 PN 3 structure. In addition, Zn 3 WN 4 is predicted to take a wurtzite-derived structure as well. In total, 10 unique structure types are observed for the 21 identified nitrides (Supplementary Table 3; Supplementary Fig. 1).
The hole and electron effective masses of many of the identified nitrides are comparable to or even smaller than those of Zn 3 N 2 and GaN. In particular, much smaller hole effective masses than that of GaN (2.0m 0 ) are recognized for a number of ternary zinc nitrides. This is partly attributed to the hybridization of the Zn-3d orbitals near the VBM and is appealing in view of potential applications utilizing p-type conductivity. Especially, Zn 3 LaN 3 shows a non-degenerate VBM with an exceedingly small hole effective mass of 0.2m 0 ( Fig. 1b; Supplementary Fig. 4). Moreover, some of the identified nitrides have direct bandgaps that are advantageous for light emission and harvesting. Indirect-gap compounds with slightly larger direct gaps can also be good candidates for photoabsorbers in solar cells 13,15 . Identified nitrides having such indirect or direct band structures and exhibiting good matching with the solar spectrum (bandgaps of B0.8 to B1.9 eV) include LiZnN, KZnN, CaZn 2 N 2 , Sr 2 ZnN 2 , Ba 2 ZnN 2 , Zn 3 LaN 3 and ZnSnN 2 (Fig. 1a). In particular, the present study reveals the properties of Ba 2 ZnN 2 with a theoretical indirect gap of 1.3 eV and a high absorption coefficient of 5 Â 10 4 cm À 1 near the absorption threshold at 1.5 eV, which are suited for thin-film photovoltaics ( Supplementary Fig. 5). Compounds with rather wide gaps (44 eV) together with small effective masses are of interest for potential applications in power electronics, where wider gaps allow for higher breakdown voltages. Promising systems in this respect are ZnSiN 2 and Zn 2 PN 3 .
Among the identified nitrides, Ca 2 ZnN 2 and CaZn 2 N 2 are especially attractive due to their earth-abundant constituents, and small hole and electron effective masses. The synthesis of Ca 2 ZnN 2 has been reported 27 , but the electronic properties have not thus far been established experimentally. Electronic density of states from a first-principles calculation has been reported in ref. 30 and our result shown in Fig. 2c is similar in the shape of the valence and conduction bands. Ca 2 ZnN 2 is predicted to have an indirect-type band structure with a minimum bandgap of 1.7 eV (Figs 1a and 2b, left of panel). Ca-3d states mainly constitute electronic states near the conduction band minimum (CBM) (Fig. 2c, left of panel); nevertheless, the electron effective mass is as small as 0.5m 0 for a particular direction (S-G), and a small hole effective mass of 1.0m 0 is also appealing (Fig. 1b). The optical absorption spectrum shows a threshold of B2.0 eV, which is B0.3 eV above the indirect-gap (Fig. 2d, left Supplementary Table 4 for tabulated values and references). (b) Effective masses for holes and electrons normalized by the free-electron rest mass, m 0 . The values for the directions that provide the smallest effective masses are shown (see Supplementary Table 5 for tabulated values). Heavy holes are considered when the valence band maximum is degenerate or nearly degenerate (o0.1 eV differences in band energies). The values for Zn 3 N 2 and GaN are also shown as references. As-yet-unreported nitrides are indicated with a bold purple font.   The other ternary phase, CaZn 2 N 2 , has not been reported previously to the best of our knowledge. Our calculations predict that this phase is stable against the known competing elementary, binary and ternary phases, including Ca 2 ZnN 2 (Fig. 2a). It takes a relatively simple trigonal structure, where the Ca and Zn atoms are coordinated by six and four N atoms, respectively (Fig. 2a). The highest valence states have an N-2p characteristic with sizable contributions of Zn and Ca orbitals (Fig. 2c, right of  panel). The cation s orbitals mainly constitute electronic states near the CBM in stark contrast to the case of Ca 2 ZnN 2 . These bands show large dispersions (Fig. 2b, right of panel) and thereby yield small effective masses of 0.9m 0 and 0.2m 0 for heavy holes and electrons, respectively (Fig. 1b); the heavy hole effective mass is about half the value of GaN and the electron effective mass is comparable to that of GaN. The symmetrically allowed electronic transitions over the direct gap lead to a steep optical absorption threshold and slightly above that, the absorption coefficient reaches as high as 5 Â 10 4 cm À 1 (Fig. 2d, right of panel). The direct bandgap of 1.8 eV (Figs 1a and 2b, right of panel) corresponds to a red region in visible light when light emission is considered. It would also be suitable as a solar cell photoabsorber, given the theoretical photovoltaic energy conversion efficiency at the Shockley-Queisser limit is 27% for this bandgap under the air mass 1.5 G sunlight 31 . The bandgap can be narrowed via alloying towards a higher theoretical efficiency, as discussed later.
Experimental verification of Ca 2 ZnN 2 and CaZn 2 N 2 . The theoretical phase diagram of the Ca-Zn-N ternary system indicates that the stable region of the newly identified CaZn 2 N 2 phase is limited to high nitrogen chemical potential conditions. The corresponding nitrogen partial pressure is much higher than 0.1 MPa at, for instance, 800 K and above ( Fig. 2a; Supplementary Figs 6 and 7; Supplementary Note 1). Therefore, we have utilized high-pressure synthesis that can allow access to such conditions. Conventional synthesis without applying external pressure successfully forms the previously reported Ca 2 ZnN 2 (Fig. 3a) and predominantly yields this phase even with the starting composition corresponding to CaZn 2 N 2 ( Supplementary Fig. 8). Using high pressure, trigonal CaZn 2 N 2 is obtained as the primary component with a minority presence of Zn metal ( Fig. 3b; Supplementary Fig. 9; Supplementary Tables 6 and 7); the origin of Zn metal segregation is a chemical reaction between the Ca component and BN in the high-pressure cell. This result demonstrates that high-pressure synthesis is effective to realize complex nitrides that are stable only under high nitrogen partial pressure conditions. The experimentally determined lattice parameters of CaZn 2 N 2 are a ¼ 3.46380(11) Å and c ¼ 6.00969(30) Å. These values are close to theoretically predicted lattice parameters of a ¼ 3.454 Å and c ¼ 5.990 Å, with 0.3% differences between experiment and theory for both a and c. The Ca to Zn ratio measured for a CaZn 2 N 2 region using the electron probe micro-analyzer is 1.00(1):1.97(3), which is almost exactly the target composition.
As mentioned above, our calculations predict that the previously reported Ca 2 ZnN 2 is an indirect-type semiconductor, whereas the newly identified CaZn 2 N 2 is direct-type. Corresponding to such differences in theoretical band structures and absorption spectra between the two phases (Fig. 2b,d), CaZn 2 N 2 exhibits a steeper absorption threshold, with an energy of B1.9 eV at 300 K (Fig. 3c). Furthermore, red photoluminescence originating from a band-to-band transition is observed (Fig. 3d). The band-edge luminescence peak is located at 1.98 eV at 10 K and gradually shifts to lower energies with increasing temperature, down to 1.92 eV at 300 K. It should be noted that the red luminescence is visible even at room temperature ( Supplementary Fig. 10) and no deep-level emissions are observed despite the polycrystalline nature. Therefore, this nitride is a promising candidate not only for a photoabsorber, but also a red light emitter. The diffuse reflectance and photoluminescence results indicate that the direct bandgap of CaZn 2 N 2 is B1.9 eV at room temperature. This value is close to the theoretically predicted direct gap of 1.83 eV. The bandgap of the Ca 2 ZnN 2 phase has not been reported either, and we estimate its indirect and direct gaps to be B1.6 and B1.9 eV from the diffuse reflectance, respectively, again in good agreement with the corresponding theoretical values of 1.65 and 1.92 eV. The theoretically proposed earth-abundant nitride, CaZn 2 N 2 , is thus verified experimentally, as well as Ca 2 ZnN 2 whose fundamental properties have not been well established previously.
Predictions on the bandgap engineering of CaZn 2 N 2 . The applications of semiconductors often require tuning of bandgaps, typically via alloying. This is explored for CaZn 2 N 2 theoretically. CaMg 2 N 2 (ref. 32), which is a known phase isostructural to CaZn 2 N 2 , is found to be a good alloying agent (Fig. 4a). As expected from a relatively small lattice mismatch ( þ 2.1 and þ 1.0% against CaZn 2 N 2 for lattice parameters a and c, respectively), our cluster expansion and grand canonical Monte Carlo simulations predict alloy formation for the whole composition range of CaMg 2x Zn 2(1 À x) N 2 (0rxr1) even at room temperature ( Supplementary Fig. 11). The bandgap of the CaMg 2x Zn 2(1 À x) N 2 alloy increases almost linearly with the Mg composition from 1.8 eV to the bandgap of CaMg 2 N 2 , 3.3 eV, preserving the direct-type band structure (Fig. 4b). This covers most of the visible light range. The hole and electron effective masses of CaMg 2 N 2 are 1.8m 0 and 0.2m 0 , respectively (Supplementary Table 5). These values, coupled with the similarity in valence and conduction band structures between CaZn 2 N 2 and CaMg 2 N 2 (Fig. 2b, right of panel; Supplementary Fig. 4v), imply that the electron effective mass does not change significantly by alloying, whereas the hole effective mass increases up to 1.8m 0. We note that this value is still comparable to the hole effective mass of GaN (2.0m 0 ).
The bandgap of CaZn 2 N 2 can also be narrowed towards the near-infrared range. Isostructural SrZn 2 N 2 , which is previously unreported and found to be metastable with respect to decomposition into competing phases ( Supplementary Fig. 3f), shows a theoretical bandgap of 1.6 eV (Fig. 4a) and the substitution of Sr for Ca reduces the bandgap of CaZn 2 N 2 (Fig. 4b). Given the similarity in band structures and carrier effective masses between CaZn 2 N 2 and SrZn 2 N 2 (Fig. 2b, right of panel; Supplementary Fig. 4x; Supplementary Table 5), the changes in the effective masses by alloying are expected to be small. The predicted mutual solubility of CaZn 2 N 2 and SrZn 2 N 2 is limited at low temperature, compared with the CaZn 2 N 2 -CaMg 2 N 2 system ( Supplementary Fig. 12). Still, quenching from a moderate temperature (B1,000 K or above) or non-equilibrium growth would allow for bandgap tuning via alloying in a wide composition range. Isostructural BaZn 2 N 2 was also considered as an alloying agent, but is found to be unstable against lattice vibration ( Supplementary Fig. 2y). Another option for bandgap narrowing is the substitution of Cd for Zn. This is expected to reduce the bandgap of CaZn 2 N 2 substantially, given the theoretical bandgap of 0.4 eV for CaCd 2 N 2 ; however, replacing too much Zn with Cd is likely to result in an excessive relaxation that leads to the breakdown of the CaZn 2 N 2 structure (Supplementary Method 2). In addition, the use of Cd would ideally be avoided in view of the toxicity of many of Cd compounds. The bandgap of CaZn 2 N 2 is thus most readily tuned via alloying with CaMg 2 N 2 towards higher energies. We note that the lattice mismatch in the CaZn 2 N 2 -CaMg 2 N 2 system (B2%) is much smaller than that of the GaN-InN system (B10%), as shown in Fig. 4a. This, in turn, allows for the stable alloy formation as discussed above.
Predictions on the dopability of Ca 2 ZnN 2 and CaZn 2 N 2 . We now discuss the dopability of Ca 2 ZnN 2 and CaZn 2 N 2 into p and/or n type, including the effect of alloying of CaZn 2 N 2 with CaMg 2 N 2 , based on the defect chemistry, that is, whether carrier compensation by native defects can be sufficiently suppressed and whether dopants that act as shallow accepters or donors exist. The  theoretical defect energetics indicates that dominant donor-type native defects are N vacancies (V N ) in both Ca 2 ZnN 2 and CaZn 2 N 2 (Fig. 5a,b). They form shallow donor levels, which are associated with host CBM states perturbed by the N vacancies. The formation energies of the N vacancies are relatively low under N-poor conditions, such as condition II for Ca 2 ZnN 2 and IV for CaZn 2 N 2 . In particular, the N vacancy shows quite low formation energy in Ca 2 ZnN 2 even with the Fermi level near the CBM, implying its native n-type characteristic when prepared under N-poor conditions. Turning to N-rich conditions, as represented by condition I, allows for the suppression of the N vacancy formation. In connection with this relatively large chemical potential dependence, our Ca 2 ZnN 2 sample exhibits a semiconducting behaviour with an activation energy of B20 meV ( Supplementary Fig. 15), whereas a previous study obtained an insulating sample 27 . Among acceptor-type defects, the Ca and Zn vacancies (V Ca and V Zn ) are dominant in both nitrides. Interstitial defects (Ca i , Zn i and N i ) generally show high formation energies. Cation antisites are often major defects in ternary compounds, while the formation energies of Ca-on-Zn and Zn-on-Ca antisites (Ca Zn and Zn Ca ) are not significantly low (41.2 eV) in both Ca 2 ZnN 2 and CaZn 2 N 2 . This is presumably because of a relatively large-size mismatch between Ca(II) and Zn(II) ions. More importantly, the isovalence of Ca and Zn results in neutral and, therefore, electrically inactive antisite defects. This leads to a design principle of ternary compound semiconductors: a large-size mismatch and/or the isovalence of two types of cations are desirable to suppress the charge compensation by antisite defects.
The controllable range of the Fermi level is restricted by the spontaneous formation of charged native defects that compensate carriers, that is, their negative formation energies 33 . All defects show positive formation energies in Ca 2 ZnN 2 under N-rich conditions as represented by condition I, irrespective of the Fermi level position. Similarly in CaZn 2 N 2 , positive formation energies are recognized for almost whole range of the Fermi level under both N-rich (III) and N-poor (IV) conditions. Therefore, electron and hole densities are not significantly limited in terms of native defect compensation, when the Fermi level is controlled towards the VBM or CBM via doping. In other words, both n-and p-type doping is feasible in both Ca 2 ZnN 2 and CaZn 2 N 2 . The defect energetics in CaMg 2 N 2 (Fig. 5c), in contrast, indicates that electron carrier density is limited by the compensation by cation vacancies in CaMg 2x Zn 2(1 À x) N 2 alloys with a high Mg content.
The above assessment of the dopability assumes the availability of dopants that act as shallow acceptors or donors. Our calculations indeed found such dopants having small size mismatches with host ions: Na and K at the Ca site as shallow acceptors and Ga at the Zn site as a shallow donor in Ca 2 ZnN 2 , where Al at the Zn site acts as a deep donor; and Na and K at the Ca site as shallow acceptors, and Al and Ga at the Zn or Mg site as shallow donors in CaZn 2 N 2 and CaMg 2 N 2 . Another assumption made is a thermodynamic equilibrium. The use of non-equilibrium growth and/or doping conditions can allow for the Fermi level control over the aforementioned limits.

Discussion
Our high-throughput first-principles screening has identified 10 previously reported and 11 unreported nitrides as promising semiconductors. The latter class of materials includes CaZn 2 N 2 , which has a tunable direct bandgap and small effective masses, is comprised of only abundant elements, and is obtainable via high-pressure synthesis. Other predicted rare-element-free nitrides include newly identified Mg 2 ZnN 2 , ZnTiN 2 and ZnZrN 2 , as well as Ca 2 ZnN 2 , Sr 2 ZnN 2 , Ba 2 ZnN 2 and Zn 2 PN 3 , for which synthesis has been reported previously, but the applications as semiconductors have not been suggested to the best of our knowledge. The variety in bandgaps of the identified nitrides, coupled with small effective masses, widens the choice of nitride semiconductors that can be used in electronics, optoelectronics and photovoltaics. The present study demonstrates accelerated materials discovery via computational screening followed by targeted experiments, particularly showing high-pressure synthesis to be effective in the realization of as-yet-unreported nitrides.

Methods
Calculations of fundamental properties and stability. The first-principles calculations were conducted using the projector augmented-wave method 34 and either the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) functional 35 or the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional 36,37 , as implemented in the Vienna Ab initio Simulation Package (VASP) 38,39 . The PBE-GGA was used for screening in terms of thermodynamic and lattice dynamic stability. The HSE06 hybrid functional was employed for evaluating the bandgaps, carrier effective masses, electronic band structures, electronic densities of states, absorption spectra and point-defect energetics of the identified compounds. Thermodynamic stability was also investigated using HSE06 and such results for the Ca-Zn-N and Ca-Mg-N ternary systems are shown in Fig. 2a and Supplementary Fig. 13 for consistency with point-defect calculations. The phase diagrams were drawn using the CHESTA code 40 Supplementary Tables 4 and 8 for tabulated values and references). (b) Theoretical bandgaps of CaMg 2x Zn 2(1 À x) N 2 and Sr x Ca 1 À x Zn 2 N 2 (0rxr1) alloys. The curves are quadratic fittings to E g ¼ ð1 À xÞE A g þ xE B g À bxð1 À xÞ, where E g , E A g and E B g are the bandgaps of the alloy and alloy components A and B, respectively. Band bowing parameters b are 0.24 and 0.17 eV for CaMg 2x Zn 2(1 À x) N 2 and Sr x Ca 1 À x Zn 2 N 2 , respectively. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11962 ARTICLE phases that are reported to be stable in the Materials Project database 41 are considered. Plane-wave cutoff energies of 550 and 400 eV were used for the geometry optimization of perfect crystals and for the calculations of fundamental and defect properties, respectively. Even k-point meshes were used in geometry optimization, which were determined on the basis of the convergence of PBE-GGA total energies: the criterion of the total energy change was set at o0.005 meV per atom per the number of incremental k points. For instance, this results in an 8 Â 8 Â 4 mesh for the wurtzite GaN unit cell. Three times finer meshes were used in the calculations of electronic densities of states and absorption spectra. The bandgaps obtained using the HSE06 hybrid functional are generally close to available experimental values for relevant systems as shown in Supplementary  Table 4, alongside comparison with theoretical values from the GW approximation 42 to many-body perturbation theory (see also a discussion in Supplementary Note 2). Effective masses were estimated by quadratic fittings of the bands that constitute the VBM and CBM, using fine sampling of k points around the VBM and CBM. The absorption spectra were obtained via the calculations of dielectric functions within the independent particle approximation, where excitonic effects and phonon-assisted absorption were not considered. Details of the screening procedure based on these calculations are described in Supplementary Method 1.
Crystal structure prediction. The crystal structure search was performed using an evolutionary algorithm as implemented in the USPEX code 12,26 , in conjunction with first-principles calculations using the PBE-GGA as described above. The chemical formula for each system was fixed, but allowed to vary in multiples of between 1 and 4. The calculations were considered converged when no lower energy structure could be found after 20 generations; with each generation containing 20 individual structures.
Alloy property calculations. The phase diagrams of the CaZn 2 N 2 -CaMg 2 N 2 and CaZn 2 N 2 -SrZn 2 N 2 pseudobinary systems were constructed using the PBE-GGA and the cluster expansion technique 43,44 in conjunction with grand canonical Monte Carlo simulations, using the CLUPAN code 45 . Quasi-random structures 46 were employed for predicting band bowing using the HSE06 hybrid functional.   Fig. 2a and Supplementary Fig. 13. The range of the Fermi level is given by the valence band maximum, which is set to zero, and the conduction band minimum. V in defect species denotes vacancies. The subscripts designate defect sites, where i means interstitial sites. The results for two interstitial sites in Ca 2 ZnN 2 are shown with solid and broken lines ( Supplementary Fig. 14). The charge states of defects, which correspond to the gradients as defined by equation (1) Fig. 14). Atomic positions were relaxed with the cell parameters fixed at the perfect crystal values. Spin polarization was considered for odd-numbered electron systems. Defect formation energies were evaluated as 47 where E d is the total energy of a supercell containing a defect in charge state q, E p is that of the perfect crystal supercell and Dn i is the difference in the number of constituent atom i between these supercells. m i and e F are the chemical potential of atom i and the Fermi level, respectively. E d and E p are evaluated using the HSE06 hybrid functional. The finite-size effects of supercells associated with electrostatic interactions between charged defects, their periodic images and the charge compensating background were corrected using the scheme reported in refs 48,49. Our implementation accounts for the anisotropic screening of defect charges using dielectric tensors. In addition, atomic-site local potential is used as a potential marker, which has been shown to be effective for relaxed atomic configurations 49 . To obtain high-purity Ca 2 ZnN 2 , the precursor powders were mixed in the glove box at the molar ratio of Ca 3 N 2 :Zn 3 N 2 ¼ 2.0:1.0 and then the mixture was uniaxially pressed into a disk (6 mm in diameter and ca. 10 mm in height), which was covered by a BN crucible and sealed in an Ar-filled stainless tube as shown in Fig. 3a. The BN crucible prevents chemical reaction between the pressed disk and the stainless tube. The stainless tube was heated at 680°C (temperature as used in ref. 27) for 40 h. For the synthesis of CaZn 2 N 2 , we employed a belt-type high-pressure apparatus developed by Fukunaga et al. 50 . The precursor powders were mixed in the glove box at the molar ratio of Ca 3 N 2 :Zn 3 N 2 ¼ 1.0:2.0. The mixture was set up in a high-pressure cell composed of NaCl (10 wt% ZrO 2 ) and BN with a carbon heater as shown in Fig. 3b. Pressure was increased to 5.0 GPa for ca. 20 min at room temperature. Temperature was then elevated to 1,200°C in 30 min and retained for 1 h. After the high-pressure/temperature treatment, the high-pressure cell was water-cooled to room temperature and then returned to ambient pressure. We slightly polished the sample pellet by a file to obtain an unreacted and fresh bulk region of CaZn 2 N 2 because the top surface of the pellet chemically reacted with a BN surface. The final size of the pellet was 5.5 mm in diameter and ca. 3 mm in height. CaZn 2 N 2 is air-stable: any decomposed and impurity phases are not observed by X-ray diffraction, when the sample is exposed at room temperature in air for 1 week. It is stable up to at least 300°C in air and 500°C in Ar atmosphere; oxidization occurs at 400°C in air, and CaZn 2 N 2 decomposes into Ca 2 ZnN 2 at 600°C in Ar atmosphere. On the other hand, Ca 2 ZnN 2 rapidly decomposes into some oxides and hydroxides, such as ZnO and Ca(OH) 2 in air.
Characterization. Crystalline phases were determined by X-ray diffraction using a Cu Ka 1 þ Ka 2 source radiated from a rotary anode (45 kV Â 360 mA, to detect a small amount of impurity phases) and a y-coupled 2y scan with Bragg-Brentano geometry. We used an Ar-filled O-ring-sealed sample holder in the X-ray diffraction measurements for exact assessment of formed crystalline phases. Lattice parameters were determined using the Pawley method. Structure refinement was performed using the Rietveld method. These analyses were made using TOPAS Version 4.2 (Karlsruhe, Germany: Bruker AXS). X-ray diffraction profile simulations were conducted using the RIETAN-FP code 51 . Chemical composition, that is, atomic ratio of Ca to Zn, was evaluated with an electron probe micro-analyzer employing a wavelength-dispersive spectroscopy mode.
Diffuse reflectance (R) spectra of the polycrystalline samples were measured in the visible-near-infrared wavelength region using a conventional spectrophotometer. To estimate the optical bandgaps, the observed diffuse reflectance spectra were converted by the Kubelka-Munk equation (1-R) 2 /(2R) ¼ a/S, where a and S denote an absorption coefficient and a scattering factor, respectively. Photoluminescence spectra were measured using excitation by third harmonic generation of Nd:YAG pulsed laser (wavelength: 355 nm) with an energy density of B7 mJ cm À 2 .
Data availability. The authors declare that the data supporting the findings of this study are available within the article and its Supplementary Information file.