I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI - ACS Publications - American

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I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se): Chalcogenides for Thin-Film Photovoltaics Tong Zhu,† William P. Huhn,† Garrett C. Wessler,† Donghyeop Shin,†,‡ Bayrammurad Saparov,§ David B. Mitzi,†,‡ and Volker Blum*,†,‡ †

Department of Mechanical Engineering and Materials Science and ‡Department of Chemistry, Duke University, Durham, North Carolina 27708, United States § Department of Chemistry & Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States S Supporting Information *

ABSTRACT: Recent work has identified a non-zinc-blendetype quaternary semiconductor, Cu2BaSnS4−xSex (CBTSSe), as a promising candidate for thin-film photovoltaics (PVs). CBTSSe circumvents difficulties of competing PV materials regarding (i) toxicity (e.g., CdTe), (ii) scarcity of constituent elements (e.g., Cu(In,Ga)(S,Se)2/CdTe), and (iii) unavoidable antisite disordering that limits further efficiency improvement (e.g., in Cu2ZnSnS4−xSex). In this work, we build on the CBTSSe paradigm by computationally scanning for further improved, earth-abundant and environmentally friendly thinfilm PV materials among the 16 quaternary systems I2−II− IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se). The band structures, band gaps, and optical absorption properties are predicted by hybrid density-functional theory calculations. We find that the Ag-containing compounds (which belong to space groups I222 or I4̅2m) show indirect band gaps. In contrast, the Cu-containing compounds (which belong to space group P31/P32 and Ama2) show direct or nearly direct band gaps. In addition to the previously considered Cu2BaSnS4−xSex system, two compounds not yet considered for PV applications, Cu2BaGeSe4 (P31) and Cu2SrSnSe4 (Ama2), show predicted quasi-direct/ direct band gaps of 1.60 and 1.46 eV, respectively, and are therefore most promising with respect to thin-film PV application (both single- and multijunction). A Cu2BaGeSe4 sample, prepared by solid-state reaction, exhibits the expected P31 structure type. Diffuse reflectance and photoluminescence spectrometry measurements yield an experimental band gap of 1.91(5) eV for Cu2BaGeSe4, a value slightly smaller than that for Cu2BaSnS4.

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12.6%.2 One likely reason is thermodynamically favored antisite disorder in the kesterite structure,3 e.g., Cu on Zn and Zn on Cu. These antisite defects lead to local potential fluctuations and band tailing (as well as prospective deep traps), and thus effectively limit the open circuit voltage, Voc, and device performance.4,5 A possible path forward to reduce the antisite structural disorder is to pursue materials in which the combination of Cu and Zn is replaced by combinations of elements that are chemically less similar but that retain the same valence. Simple examples include the substitution of monovalent Ag on the Cu site6,7 or of divalent Cd,8−14 Hg,9−11 Mn,12,15,16 Fe,12,17 Co,12,15,18−20 or Ni12,15,21 on the Zn site. However, these substitutions are sufficiently chemically similar to not alter the coordination of the cations. In addition, Ag-alloyed CZTSSe shows n-type semiconductor behavior and low carrier densities for higher substitution levels, e.g., >80% substitution, versus ptype and much higher carrier densities for CZTSSe.22 Another

INTRODUCTION Solar energy conversion technologies such as photovoltaic (PV) generation of electricity and photoelectrochemical fuel generation are expected to play increasingly important roles as versatile clean energy sources, deployable in a decentralized fashion as well as by established distribution grids. Commercial thin-film PV cells, e.g., based on metal chalcogenide zincblende-type materials such as CdTe and Cu(In,Ga)(S,Se)2 (CIGSSe), tend to be cheaper to manufacture and offer competitive performance levels relative to traditional crystalline Si-based PVs. Their laboratory-scale cell power conversion efficiencies currently reach ∼22%.1 However, CdTe and CIGSSe rely on elements that are costly or rare in the earth’s crust (In, Te) or even toxic (Cd) and thus are not ideal for terawatt deployment. It is desirable to identify alternative materials for thin-film PVs that employ less toxic and lower cost elements, while maintaining or improving on the advantages of CIGSSe and CdTe with respect to direct band gap tunability, high device performance, and compatibility with low-cost manufacturing. Kesterite Cu2ZnSnS4−xSex (CZTSSe) is one of the best researched alternative candidate materials; however, the best device efficiency achieved to date is currently limited to © 2017 American Chemical Society

Received: June 24, 2017 Revised: August 17, 2017 Published: August 21, 2017 7868

DOI: 10.1021/acs.chemmater.7b02638 Chem. Mater. 2017, 29, 7868−7879

Article

Chemistry of Materials

Figure 1. a) Crystal structures and b) corresponding Brillouin zones and band structure k-space paths for five representative structures of the five different space groups considered for the 16-compound group I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se). The I (Cu/Ag), II (Sr/Ba), IV (Ge/Sn), and VI (S/Se) atoms and their corresponding coordination polyhedra are shown in blue/light blue, brown/orange, light green/green, and light red/red, respectively.

Table 1. Space Groups (SG), Lattice Parameters (in Å), and Band Gaps (in eV) of the 16 Compounds I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se) Investigated in This Worka structure properties

band gaps b

compound

SG

a (Å)

b (Å)

c (Å)

source

Egap (eV)

exp. (eV)

Cu2SrGeS4 Cu2SrGeSe4 Cu2SrSnS4 Cu2SrSnSe4 Cu2BaGeS4 Cu2BaGeSe4 Cu2BaSnS4 Cu2BaSnSe4 Ag2SrGeS4 Ag2SrGeSe4 Ag2SrSnS4 Ag2SrSnSe4 Ag2BaGeS4 Ag2BaGeSe4 Ag2BaSnS4 Ag2BaSnSe4

P32 Ama2 P31 Ama2 P31 P31 P31 Ama2 I222 I222 I222 I222 I4̅2m I222 I222 I222

6.143 10.807 6.290 10.967 6.215 6.490 6.366 11.111 6.820 7.115 6.910 7.193 6.828 7.058 7.127 7.116

b=a 10.735 b=a 10.754 b=a b=a b=a 11.227 6.973 7.389 7.210 7.657 b=a 7.263 8.117 7.499

15.282 6.541 15.578 6.695 15.534 16.355 15.828 6.744 7.690 7.951 7.831 8.034 8.017 8.263 6.854 8.337

exp.37 exp.33 exp.30 exp.36 exp.37 exp.33 exp.25 exp.25 HSE06c HSE06c HSE06c HSE06c exp.40 exp.33 exp.38 exp.39

I/D: 2.49/2.50 I/D: 1.79/1.80 I/D: 1.73/1.75 D: 1.46 I/D: 2.46/2.47 I/D: 1.60/1.61 I/D: 1.74/1.75 D: 1.50 I: 1.33 I: 0.68 I: 1.08 I: 0.66 I: 1.38 I: 0.85 I: 1.26 I: 0.77

2.7735 2.0535

1.91b 2.0225 1.7225

In the “Source” column, “exp.” indicates the compounds for which experimental lattice parameters are known. For the four compounds based on Sr and Ag, either no experimental structure determination exists or previous experimental synthesis attempts led to a structure/composition that is unrelated to the compounds/space groups considered in this work. In these cases (labeled “HSE06” in the “source” column), the reported space group, lattice parameters, and atomic positions correspond to the minimum-energy structure from among the five main space groups/structure types considered in this work (Ama2, P31, P32, I222, I4̅2m). The HSE06-predicted band gaps for these geometries are summarized in the column labeled “Egap”. The label “I” stands for indirect band gap type, and the label “D” stands for direct band gap type. The label “I/D” stands for a quasi-direct band gap. In those cases, both the indirect and the direct band gap values are given. The experimental band gaps reported in the literature for some compounds are also included in the table. bExperiment/this work. cHSE06/this work. a

they do offer promising band gaps in the range of 1.5−2.0 eV and distinct cation environments that may lead to suppressed intrinsic defect formation (lower likelihood of antisite

option is to replace Zn with much larger alkaline-earth (AE) metals, such as Ba and Sr. The resulting Cu2AESn(S,Se)4 compounds are not based on a zinc-blende-type lattice, but 7869



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disorder).3,23−28 Cu2BaSnS425,29 (CBTS) and Cu2SrSnS430 adopt a trigonal structure type with space group P31 (shown in Figure 1). The electronic structure of both compounds, as well as their Se analogues, have been reported,23 albeit using only the P31 structural motif (in experiment, the Se analogues adopt space group, Ama2; see below). We recently reported the first prototype solar cell based on trigonal CBTS, with a power conversion efficiency (PCE) of 1.6%25 for the pure sulfur compound. Pure CBTS, however, has an optical gap (from absorption data) of 2.02 eV,25 slightly too high for PVs based on the AM 1.5G solar spectrum. In an effort to reduce the band gap of the trigonal compounds, S/Se-mixed Cu2BaSn(S4−xSex) (CBTSSe) bulk samples and films were prepared,25,31,32 with optical gap values of as low as 1.55 eV for x ≈ 3. Devices for the x ≈ 3 material have now been demonstrated with PCE exceeding 5%.32 The pure selenide, Cu2BaSnSe4 (CBTSe), adopts a different crystal structure, the orthorhombic Cu2SrGeSe4-type33 structure with space group Ama2. It exhibits a direct band gap of 1.72 eV (from diffuse reflectance data) and a slightly smaller carrier effective mass than CBTS. 25 A prototype solar cell based on this orthorhombic Cu2BaSn(SexS1−x)4 structure has also been reported recently, with a PCE of 1.57%.34 These examples show that there is still significant promise for identifying new PV materials in the space of multinary inorganic compounds, inspired by existing compounds but not restricted to materials of just one given, e.g., zinc-blende-type, lattice arrangement. In this work, we expand on the CBTSSe paradigm by exploring 16 related compounds, denoted I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se), for their possible utility as thin-film PV absorbers. For 12 of these compounds, experimental structure determinations exist,25,30,33,35−40 as summarized in Table 1. Their experimental structures are drawn from five different space groups: Ama2, P31, P32, I222, and I4̅2m. Prototypes for each structure are shown in Figure 1. A common thread among these structure types is that the coordination environments of the I and IV cations are simple (tetrahedral for Cu, Ge, and Sn; distorted-tetrahedral for Ag), whereas the larger II cations (Sr, Ba) have a very different, 8fold coordination environment. Previous experimental studies25,30,33,35−40 focus predominantly on the crystal structures, but a comprehensive assessment of the electronic band properties and other key suitability indicators of the 16 compounds considered in this work for PV or other optoelectronics-related purposes is still missing. The present work fills this gap by providing a systematic, high-level electronic structure theory-based approach to the structural, electronic, and optical properties of the 16 I2−II−IV−VI4 compounds. This comparative analysis employs the correct space group and experimentally confirmed crystal structure (when available) and rests exclusively on HSE0641,42 hybrid density-functional theory (DFT) for all of its electronicstructure-related conclusions, providing a sound basis for materials selection in future experimental and computational research. Among the 16 compounds, four particularly promising candidates for PV emerge, based on their predicted direct or nearly direct band gaps, with values ranging from ∼1.46 to 1.8 eV, and small effective masses near the band edges: Cu2BaSnS4, Cu2BaSnSe4 (both already known), Cu2SrSnSe4 and Cu2BaGeSe4 (new possibilities). For these four compounds, optical properties and (for Cu2BaGeSe4) experimental validation are also discussed.

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METHODS

All calculations were performed using the FHI-aims43−45 all-electron code, a high accuracy46,47 implementation of electronic structure theory based on numeric atom-centered orbital basis sets. FHI-aims includes a linear-scaling approach to evaluate hybrid density functionals.48,49 We employed the numerical settings referred to as “tight” in FHI-aims (these settings specify accurate basis sets, integration grids, and multipole expansion order for the electrostatic potential). The basis sets used for all elements are also given in Table S1 in the Supporting Information (SI). Unless otherwise noted, all calculations presented use the short-range screened hybrid exchangecorrelation functional HSE0641,42 with a fixed screening parameter (ω = 0.2 Å−1) and a fixed exchange mixing parameter (α = 0.25), which we refer to as the “standard HSE06 functional” in this work. The kpoint grids used to sample the Brillouin zone in all total-energy calculations are different for each space group type: Γ-point centered 8 × 8 × 8 for I222 and I42̅ m, Γ-point centered 8 × 8 × 4 for P31, P32, and Ama2. In Figure 1, the corresponding crystal structures, Brillouin zones, and the selected k-space paths for band structure calculations in this work are shown for five representative compounds: Cu2BaSnSe4 (Ama2), Cu2BaSnS4 (P31), Cu2SrGeS4 (P32), Ag2BaGeSe4 (I222), and Ag2BaGeS4 (I4̅2m). Spin−orbit coupling (SOC) was included in all calculated band structures, densities of states (DOS) and optical properties using a second-variational approach50 recently implemented in FHI-aims. Carrier effective masses, m*, were estimated from calculated band structures by numerical fitting to expressions of the form E(k) = E0 + ℏ2/(2m*) · (k − k0)2 at selected maxima (minima) k0 of the valence (conduction) bands, as described in Figures S3−S8. Spin−orbit coupling has been shown to induce indirect band gaps by way of Rashba splittings in semiconductors containing very heavy elements (e.g., Pb-containing compounds), potentially reducing the propensity for carrier recombination in PV after relaxation of the electrons/holes to their respective conduction/valence band extrema.51−54 To illustrate the (much weaker) SOC effect in the compounds studied here, we include comparisons of HSE06-predicted band structures calculated with versus without SOC for the five compounds Cu2BaGeSe4, Cu2BaSnSe4, Cu2SrGeSe4, Cu2SrSnSe4, and Ag2BaSnSe4 in the SI (Figures S12−S16 and associated text). SOC effects are visible as quantitative corrections but do not induce qualitative band structure changes. The largest impact on the band gap occurs for systems that have SOC-split valence band maxima at the Γ point, e.g., changing the predicted band gap of for Cu2BaSnSe4 by 0.07 eV. Actual Rashba splittings can be seen in the VBM band structure close-ups in Figures S7 and S8 but amount to only a few meV at most. We note, however, that the determination of effective masses by way of second derivatives at specific points in the band structure (see below) can be affected by SOC and requires consideration of these splittings. Normal-incidence absorption coefficients α(ω) were calculated according to the following expression55 ⎤1/2 ⎡ Re ε(ω)2 + Im ε(ω)2 − Re ε(ω) ⎥ ⎢ α(ω) = (4πω /hc) ⎥⎦ ⎢⎣ 2 (1) Here, ω is the photon energy, and ε(ω) denotes elements of the diagonal but nonisotropic complex dielectric tensor, calculated at the level of the HSE06 functional including spin−orbit coupling (SOC), using dense Γ-point centered 12 × 12 × 6 k-point grids. The frequency-dependent imaginary component Im ε(ω) was calculated at the level of the random phase approximation (RPA) using the Lindhard formula,56 which is dominated by the momentum matrix elements of the valence and conduction wave functions.55 A Lorentzian broadening with an imaginary frequency component of 0.1 eV was used to ensure smooth integrated ε(ω) components based on the employed k-point integration grid. The real part Re ε(ω) was obtained directly from the integration of the complex dielectric function.57 7870


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Chemistry of Materials Accurately capturing the geometry of each phase studied (lattice vectors and cell-internal atomic positions) is essential for the resulting predicted electronic properties. For example, for the Cu2ZnSnS4 (CZTS) system, Botti et al.58 showed that the electronic properties are exceptionally sensitive to both the exact unit cell vectors and to the cell-internal Cu−S and Sn−S bond lengths. Botti et al.58 and Paier et al.59 also showed that atomic coordinates derived from the HSE06 functional41,42 are substantially improved compared to, e.g., the popular semilocal PBE60 functional. In our previous study25 of the CBTS/CBTSe compounds, we reached similar conclusions. We thus pursue the following strategy to construct the geometries used to predict the electronic properties of each compound structure in this work: 1) For structures for which experimental lattice parameters were reported previously (see Table 1), we fix the unit cell vectors to the experimentally obtained room-temperature values and only adjust the (usually unknown) cell-internal atomic positions to their HSE06optimized positions. 2) For four of the 16 compounds studied in this work (I = Ag, II = Sr), experimental structure determinations do not exist. For these structures, we therefore resort to HSE06-predicted structural parameters, including the lattice parameters, for all our predictions. Specifically, for each of the four unknown compounds, we consider the five main experimentally known prototype structures that occur among the remaining 12 compounds (Ama2, P31, P32, I222, and I4̅2m in Figure 1). For each of the four compounds, we then select the lowestenergy structure for computational predictions as reported in the remainder of this paper. We note that it is possible that some or all of the (I = Ag, II = Sr) compounds occur in different space groups (a global structure search beyond the space groups shown in Figure 1 was not performed in the current work) or that they do not form at all in the stated stoichiometry.61 3) Fully HSE06-optimized unit cell parameters and cell-internal coordinates were used for the CZTS compound, which was considered for comparison of optical properties and for which no experimental structure determination of a fully ordered stoichiometric compound exists to our knowledge. Cell-internal atomic positions and/or lattice vectors were adjusted until the residual total energy gradients did not exceed 5 × 10−3 eV/Å for atomic positions and 5 × 10−3 eV/Å3 for stress tensor-based unit cell relaxation.62 For CBTS, the fully-HSE06-optimized geometry and band structure calculated using the standard HSE06 functional and spin-orbit coupling (second strategy above) predicted a band gap within 0.03 eV of the gap as calculated when using the experimentally determined unit cell vectors instead (first strategy above).25 The overall value is within 0.3 eV of the experimentally determined band gap of the actual material. For related materials, e.g. for III−V semiconductors,63 past work also confirms the qualitative accuracy of the standard HSE06 functional. The level of theory used here is thus appropriate for a series comparison among compounds, providing a satisfactory starting point for further, more targeted experimental assessments. Experimental details regarding the Cu2BaGeSe4 samples synthesized and characterized are provided in the “Experimental Validation of Cu2BaGeSe4” section below, as well as in the SI.

that does not appear in CZTS. The four experimentally known Ag compounds (all with II = Ba) adopt a tetragonal I4̅2m crystal structure (Ag2BaGeS4) or an orthorhombic crystal structure corresponding to one of the subgroups of I4̅2m, i.e., I222 (Ag2BaGeSe4, Ag2BaSnS4, Ag2BaSnSe4). Again, the II cations are 8-fold coordinated. Compared to the Cu-based compounds, the distorted-tetrahedral coordination of the Ag ions here marks an additional structural difference to CZTS. As mentioned in the Computational Methods section, for the four Ag2-Sr-IV−VI4 compounds for which no experimental crystal structure is known, full structure optimizations at the HSE06 level of theory were performed, considering each of the five structure types occurring among the 12 known compounds: Ama2, P31, P32, I222, and I42̅ m. Within this limited set of structure types, the most stable structure for the unknown compounds based on their HSE06-calculated formation energies is, in all cases, the orthorhombic I222 crystal structure; however, for Ag2SrSnSe4, the Ama2 structure is negligibly close in energy (see Figure S1). The corresponding lattice parameters, space group types, and band gaps calculated using the HSE06 functional are listed in Table 1. However, we also note that the overall stability of these four compounds with respect to competing compounds of different stoichiometry is not certain. For instance, Tampier61 reports the successful synthesis of Sr3Ag2Ge2Se8 in his Ph.D. thesis, while SrAg2GeSe4 could not be synthesized. The structure synthesized is described as related to Ag2BaGeSe4, but Ag is found to exhibit a coordination somewhere between 2-fold (linear) and 4-fold (tetrahedral) and with inequivalent, fractionally occupied Ag positions in the lattice. While we cannot comment on this or other potential alternative structures with certainty within the scope of the present work, we still report the theoretically calculated I222 Ag−Sr compounds since they would form the limiting case of Sr-alloyed variants of the four Ag−Ba compounds, the alloying range for which still remains to be determined. For Cu2SrSnSe4, a recent computational assessment23 using a hypothetical, trigonal P31 structure type found no range of thermodynamic stability when compared to a range of likely competing secondary compounds. This compound was synthesized in a recent experimental study;36 however, powder X-ray diffraction (PXRD) points to an Ama2 structure type rather than the P31 variant. We therefore assessed the thermodynamic stability of Cu2SrSnSe4 in the Ama2 structure, using the HSE06 functional and fully relaxed (minimum energy) unit cell parameters and cell-internal atomic coordinates for all structures. The experimentally determined structure36 and the computationally predicted structure of Cu2SrSnSe4 are close to one another (see Table S2). Interestingly, the HSE06-predicted energy difference between Cu2SrSnSe4 (Ama2) and a phase mixture of SrSe and Cu2SnSe3 is still positive (+0.01 eV/atom). This value would also indicate the phase mixture to be more stable than single-phase Cu2SrSnSe4; however, the predicted energy difference is well within the expected uncertainty of the HSE06 functional. The very small energy difference could mean that the stability range of Cu2SrSnSe4 is narrow. Further experimental work would be desirable to more precisely delineate the true stability range of Cu2SrSnSe4 (versus metastability or only marginal stability). Electronic Properties. Based on the geometries given in Table 1 and in the SI, the calculated standard HSE06 band structures for the 16 compounds I2−II−IV−VI4 are shown in Figure 2. All HSE06-predicted fundamental gap values are also

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RESULTS AND DISCUSSION Structural Properties. Based on earlier experimental studies, the following four compounds studied in this work adopt the trigonal P31 crystal structure (Figure 1/Table 1): Cu2SrSnS4, Cu2BaSnS4, Cu2BaGeS4 and Cu2BaGeSe4. The orthorhombic Ama2 crystal structure is adopted by Cu2SrGeSe4, Cu2SrSnSe4, and Cu2BaSnSe4. The remaining Cu-based compound, Cu2SrGeS4, adopts a trigonal P32 crystal structure (P31 and P32 are enantiomorphic pairs). All of these compounds share similar structural motifs to those seen in CZTS, that is, tetrahedrally coordinated I and IV cations, whereas the II cations (Ba or Sr) show an 8-fold coordination 7871


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Figure 2. Calculated band structures (HSE06 functional with spin−orbit coupling) for 16 I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se) compounds. Full HSE06 relaxation was used for four compounds Ag2−Sr−IV−VI4 (IV = Ge, Sn; VI = S, Se), and fixed experimental lattice parameters with internal atomic positions optimized using the HSE06 functional were employed for the remaining 12 compounds. The elemental components of this 4 × 4 compound matrix appear along the left and top panels. The background color for each band structure represents the corresponding space group of the structure typei.e., light yellow, light orange, light green, light blue, and salmon for I222, I4̅2m, P31, P32, and Ama2, respectively. The positions of valence band maximum (VBM) and conduction band minimum (CBM) are marked with blue and red arrows, respectively. The band structure character (direct or indirect) is indicated along the right-hand side of the figure.

belonging to the P31/P32 space groups are all predicted to have quasi-direct band gaps, and they include the highest predicted band gap values found in this work. The Ama2-based compounds, on the other hand, include Cu2SrSnSe4 and Cu2BaSnSe4, with lower predicted direct band gaps (1.46 and 1.50 eV, respectively). The third Ama2 compound, Cu2SrGeSe4, offers a higher and quasi-direct band gap according to the calculated band structure. As a tendency, replacing Ge with Sn appears to decrease the fundamental gap, with changes of ∼0.2−0.7 eV depending on the compound. The S-based compounds in the same column of Figure 2 show systematically larger band gaps than their Se-based counterparts, by 0.25−0.9 eV. Replacing Ba with Sr appears to have little effect on the band gap. In contrast to the Cu-based compounds, all Ag-based compounds (i.e., Ag2−II−IV−VI4) show band gaps that are clearly indirect. Ag2SrSnSe4 in the I222 structure has the lowest band gap (0.66 eV), as the general compositional trends described above all tend to reduce this value. We note that, for Ag2SrSnSe4, the energy-degenerate Ama2 structure may yield a substantially higher band gap in the range of interest for PV;

included in Table 1, as well as the type of the band gap: direct (D), indirect (I), or “quasi-direct” (I/D). By quasi-direct, we denote compounds in which the fundamental gap is technically indirect, but for which the smallest direct gap is within ∼0.02 eV (≈kBT at ambient temperature) of the indirect gap value. In addition, Table 1 includes the experimentally determined band gaps for five of the I2−II−IV−VI4 compounds. In line with expectations from the literature,25 these experimental values agree to within 0.3 eV of the calculated band gaps from the standard HSE06 density functional (HSE06 consistently underestimates the band gap values by this amount). The band structure comparison (Figure 2 and Table 1) reveals several interesting trends. As a tendency, the band gap values found in the Cu-based compounds are higher (1.46− 2.50 eV), whereas the Ag-based compound band gaps span a range of significantly lower values (0.66−1.38 eV). The eight Cu-based compounds (i.e., Cu2−II−IV−VI4) show direct or quasi-direct band gaps, which would be beneficial for thin-film PVs, and their CBMs and smallest direct band gaps are found at the Γ point. For the Cu-based compounds, further meaningful trends arise based on the detailed structure. The compounds 7872


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Chemistry of Materials however, due to the energetic ambiguity of the competing structures for this compound, we did not pursue this question further in this work. At least four of the Ag2−II−IV−Se4 (II = Ba, Sr; IV = Ge, Sn) compounds show quite interesting multivalley semiconductor properties. While their indirect band gaps do not seem to recommend them for PV, this multivalley physics may well lead to other interesting application opportunities in the future. Based on the overall comparison of band structures of the 16 pure (unalloyed) I2−II−IV−VI4 compounds, four compounds emerge as particularly promising candidates for potential thinfilm PV application: 1) Cu2BaSnS4, which has a quasi-direct band gap (I/D: 1.74/1.75 eV), 2) Cu2BaGeSe4, also with a quasi-direct band gap (I/D: 1.60/1.61 eV), 3) Cu2BaSnSe4, with a direct band gap (D: 1.50 eV), and 4) Cu2SrSnSe4, with a direct band gap (D: 1.46 eV). Cu2BaSnS4 (P31) and Cu2BaSnSe4 (Ama2) have already emerged as promising candidates in recent studies,25−28,31,32,34 including demonstration of prototype devices. While the experimental band gap of Cu2BaSnS4 itself is relatively large (2.02 eV), the value can be significantly reduced by alloying with up to 75% Se (i.e., corresponding to Egap = 1.55 eV), even below the experimental value for the pure selenide Cu2BaSnSe4 (1.72 eV) in the Ama2 space group.25 Cu2SrSnSe4, which has not been explored for PV before, may lead to a further slight band gap reduction; however, based on previously mentioned compositional trends, we would expect the band gap to be similar to that for Cu2BaSnSe4. Finally, Cu2BaGeSe4 shows substantial promise for PV applications and was therefore selected for experimental synthesis and determination of its band gap (see below). The observed band gap trends as a function of substitution are also reflected in the total and element-resolved projected densities of states (DOS) near the band edges of all compounds investigated in this work. Figure 3 shows the DOS profiles for all 16 compounds, extending from 2.0 eV below the VBM to 2.0 eV above the CBM. A close-up view of the DOS distributions and decompositions near the band edges appears in Figure 4, within 0.3 eV of either side of the VBM and CBM, respectively. In view of potential PV applications, it is particularly interesting to examine these results in the context of the known kesterite PV candidate material CZTS. Analysis of the nature and origin of valence/conduction band edges for CZTS59,64−66 suggests the VBM to be composed primarily of Cu- and S-derived states, while the CBM is part of a distinct DOS peak ascribed to antibonding Sn-5s and S-3p states. A similar analysis appears to hold for kesterite Ag2ZnSn(S,Se)4 (AZTSSe).67 A key feature of these band structures is the dominant role of the group I and group IV metals in the formation of the CBM and VBM. The states from the II element contribute little to the near band edge character of these systems. Paier et al.59 also link the transitions between group I and group IV metal-based states quantitatively to the absorption coefficient of CZTS in the PV-relevant energy range. Similar to the case of CZTS, the broader-scale view of the DOS profiles of the 16 compounds in Figure 3 each reveals a distinct, high-DOS energy band near the CBM that shows dominant anionic contributions from VI elements (S/Se), as well as from I (Cu/Ag) and IV (Ge/Sn) elements. In addition, these bands also contain significant contributions from II elements (Sr/Ba), which are clearly absent from the VBM. Instead, the cationic contribution in the VBM range shown in Figure 3 originates almost exclusively from the group I

Figure 3. Total densities of states (DOS) and element-decomposed DOS, based on the HSE06 functional with spin−orbit coupling for the 16 systems I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se). To aid in side-by-side comparison of the band edge compositional makeup, the VBMs and CBMs are set to zero energy separately in each plot, while the actual band gap is omitted. Band gap values are noted in each subplot. The outermost line of the DOS shape indicates the total DOS. The fraction of the element-resolved DOS is shown by different colors as defined by the element panels on the left and at the top: dark/light blue represent elements I (Ag/Cu), brown/ red represent elements II (Ba/Sr), dark/light purple represent elements IV (Sn/Ge), and dark/light green represent elements VI (Se/S), respectively. Ωunit cell denotes the unit cell volume of each compound.

Figure 4. Total densities of states (DOS) and element-decomposed DOS, based on the HSE06 functional with spin−orbit coupling for the 16 systems I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se) in a close-up view. For details, see the caption of Figure 3.

elements (Cu/Ag), again similar to the case of the CZTS/ AZTSSe VBM. For (quasi)direct transitions, the VBM and CBM states are also expected to be involved in the onset of absorption. Here, it is worth noting that the narrow, tall band close to the CBM in all 16 compounds in Figure 3 is not always directly associated with the actual CBM. The close-up view of the band edges in Figure 4 reveals that the sharp onset of this 7873


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Table 2. Relative Fraction (in %) of the Partial DOS for Each Element Pair near the Valence and Conduction Band Edges (within 0.3 eV of Either Side of the VBM and CBM, Respectively), Averaged within the Different Structure Types (I42̅ m (Ag2BaGeS4), I222 (Ag2−II−IV−VI4 Compounds except Ag2BaGeS4), P31 (Cu2BaGeS4, Cu2SrSnS4, Cu2BaSnS4, Cu2BaGeSe4), P32 (Cu2SrGeS4), Ama2 (Cu2SrGeSe4, Cu2SrSnSe4, Cu2BaSnSe4)), with Further Details Shown in Table S3 valence band (VB) edge

conduction band (CB) edge

elements

I4̅2m

I222

P31

P32

Ama2

I4̅2m

I222

P31

P32

Ama2

II(=Sr/Ba) I(=Cu/Ag) IV(=Ge/Sn) VI(=S/Se)

0% 29% 1% 70%

0% 28% 2% 70%

1% 38% 3% 58%

1% 40% 3% 56%

2% 32% 3% 63%

14% 63% 10% 13%

21% 40% 16% 23%

18% 21% 24% 37%

14% 13% 20% 53%

17% 16% 24% 43%

It should be noted that, from a PV point of view, a primary motivation to inspect the DOS is its relationship to absorption. However, similarity of trends observed for individual bands, e.g., for the conduction bands on their own, does not guarantee similarity of absorption properties. In particular, the direct transitions at a given k-point may be higher in energy than the fundamental gap, as is seen, for example, near the K (X) points of the P31/P32 (Ama2) compounds. Additionally, the relevant matrix elements must be nonzero, i.e., the transitions must not be forbidden. Still, based on the DOS themselves, the qualitative similarity of the DOS found for the 16 compounds in this work to CZTS, particularly for the four promising Cucontaining compounds already identified based on their band gaps, bodes well for the electronic properties of thin-film PVs. The effective mass tensors of the 16 compounds may be systematically compared on equal footing by considering the point group symmetries of the crystal structures. For the orthorhombic (I222 and Ama2) crystal structures, the effective mass tensor can be expressed as

band coincides with the CBM only for three compounds, i.e., Cu2SrGeS4, Cu2BaGeS4, and Cu2SrGeSe4. In all other compounds, the first sharp onset of the DOS near the CBM is preceded by a smaller tail or peak. A qualitative inspection of the band structures shown in Figure 2 reveals that this smaller peak with its relatively low DOS corresponds to the parabolic lowest-energy conduction band at the Γ point, where the CBM is located in all cases, and where the lowest-energy (quasi)direct transitions might appear. In contrast, the sharp onset of the tall band dominating the low-lying conduction bands in Figure 3 appears to be associated with off-Γ conduction bands, such as those found at the K and X points in the band structures for P31/P32 and Ama2, respectively. Similar trends can be observed for the Ag-based compounds. For CZTS, the published HSE06 band structure and DOS by Paier et al.59 also suggest that the steep onset of the antibonding Sn-5s/S-3p band occurs at a higher energy than the actual CBM at the Γ point. In Table 2, the integrated contribution of each element to the band edges of the 16 compounds is quantified, averaged by structure type, for the precise energy ranges shown in Figure 4 (0−0.3 eV from the VBM/CBM, respectively). The averaging procedure is detailed in the caption of Table S3 which also lists the corresponding integrated elemental DOS fractions for each individual compound. For the VBM, the trends across all 16 compounds are broadly similar, namely showing the band edges to be derived almost exclusively from elements VI (S/Se) and I (Ag/Cu). However, the quantitative comparison of the CBM onset in Tables 2 and S3 reveals an important difference between the Ag- vs Cu-based compounds. While the dominant contribution in the Cu-based compounds is element VI (S/Se), followed by similar fractions of the cationic elements I, II, and IV, in the Ag-based compounds the dominant contribution of the small density of states at the CBM (related to the Γ point) is derived predominantly from element I (Ag), with much smaller contributions from all other elements. Thus, the electronic properties of the Ag-based compounds may be somewhat different than those of the Cu-based compounds, as already indicated by the overall different dispersion relations of their conduction bands in Figure 2. Finally, inspection of Table S3 reveals that the fraction of element VI (S/Se) in the conduction bands is highest for the three compounds Cu2SrGeS4, Cu2BaGeS4, and Cu2SrGeSe4, i.e., those with a sharp immediate onset of the conduction bands (51%−57% S/ Se DOS fraction near the CBM). The corresponding DOS fraction is only 29%−38% S/Se in the other Cu-based compounds. Again, the large contribution of S/Se to the overall conduction band is consistent with kesterite CZTS. As for the cationic elements (I, II, IV), all of them appear to be represented somewhat evenly in the conduction band DOS range probed by Figure 4 and Tables 2 and S3.

⎛a 0 0⎞ 1 1⎜ ⎟ = 2 ⎜0 b 0⎟ ⎟ m* ℏ ⎜ ⎝0 0 c ⎠

in a coordinate system that diagonalizes the tensor, with three independent componentsi.e., in the directions parallel to the reciprocal a, b, and c axes in the conventional cell, here denoted as ∥a, ∥b, and ∥c, respectively. For tetragonal (I42̅ m) and trigonal (P31/P32) crystal structures, the effective mass values along the ∥b direction (parallel to the reciprocal b axis in the conventional cell) are identical to the values along the ∥a direction, according to the point group symmetry. We calculate the carrier effective mass tensor m* by numerical parabolic fits to the HSE06+SOC-calculated band structures. A detailed discussion of the fitting procedure used may be found in Figures S3−S8. The values for the independent tensor components are graphed in Figure 5, and the corresponding numerical values of the hole and electron effective masses, as well as the k-space directions to which they correspond, are tabulated in Figure S2. Low values are predicted for the electron effective masses me of all 16 compounds (0.12−0.42 m0). Although other structural factors may play a role, the low effective electron masses may be taken as a tentative indicator that good electron transport properties are possible in these materials. The hole effective masses, mh, are uniformly larger than the electron effective masses but also reveal clear trends. For all Ag-based compounds, the hole effective masses are large but not excessive, spanning a range of 0.25−1.01 m0. The predicted indirect nature of the band gaps of all Ag-based compounds will likely not make for good thin-film PV candidates; however, the 7874


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∥a, 1.04 m0 along ∥c), which is close to the hole effective masses of kesterite Cu2ZnSnS4 (0.22 m0 along ∥a, 0.74 m0 along ∥c).68 The fourth promising candidate based on its predicted band gap, Cu2SrSnSe4, shows a rather high hole effective mass of 3.51 m0 along the ∥c direction, implying a potentially significant anisotropy of its hole mobilities. In contrast, the mh values along the other two directions are well below 0.5 m0. For these four compounds, we next comment on predicted absorption properties and (for Cu2BaGeSe4) on experimental validation of the compound and its band gap. Optical Properties. We finally examine the predicted optical properties of the four candidate materials Cu2BaSnS4 (P3 1 ), Cu 2 BaGeSe 4 (P3 1 ), Cu 2 BaSnSe 4 (Ama2), and Cu2SrSnSe4 (Ama2). Specifically, their dielectric functions (Figure S9) and absorption coefficients (Figure 6) have been Figure 5. Effective mass tensor values for electrons (me: downward triangles) and holes (mh: upward triangles) determined by parabolic fits to the calculated band structures at valence band maximum (mh) and conduction band minimum (me) in high-symmetry directions (∥a, parallel to the reciprocal a axis in conventional cell, ∥b parallel to the reciprocal b axis in conventional cell, ∥c parallel to the reciprocal c axis in conventional cell) for all 16 compounds studied in this work. All values are presented in units of the free electron mass, m0. The numerical effective mass values are reported in Figure S2 in the SI. The effective mass tensor values are colored according to direction (∥a (red), ∥b (blue), ∥c (green)), respectively. For the compound Cu2SrGeSe4, the hole effective mass in the ∥a direction lies well below the figure threshold, and it is denoted by a single red upward triangle below the main figure.

effective mass range indicates that other interesting semiconductor applications may well be possible for these materials. Some of the Cu-based compounds, on the other hand, show significantly higher hole effective masses than the Ag-based compounds in individual k-space directions. While a correspondingly lower hole mobility might result from semiclassical considerations, the lower band curvature also means a higher density of states at the VBM. The resulting higher joint density of states of valence and conduction bands could translate into a steeper increase of the absorption coefficient above the band gap energy and thus improved PV efficiency based on the absorption. Additionally, the impact of the hole mobility also depends on the majority carrier nature of each material. If the material were p-type, then the minority carrier (electron) mobility would be acceptably high, enabling good collection of photogenerated carriers. Majority (hole) mobility would play a larger role in the case of high light intensity (high photogenerated carrier density)i.e., would become more important under concentrated illuminationand might also impact the device series resistance for systems with thick absorber layers. Cu2BaSn(S,Se)4 is found to be p-type in character.23,32 However, for the other members of this 16 compound family, a more detailed experimental and computational examination will be required to firmly establish the dominant carrier type in each system, which in turn will have a critical influence over the choice of corresponding prospective device design. Interestingly, three of the four Cu-based compounds identified as most promising for thin-film PVs based on their band structures show relatively small hole effective mass values. This includes the recently discovered thin-film PV candidate compounds Cu2BaSnS4 (0.43 m0 along ∥a, 1.40 m0 along ∥c) and Cu2BaSnSe4 (0.32−1.44 m0). The lowest hole effective mass range of the Cu-based compounds is found for the newly predicted thin-film PV candidate Cu2BaGeSe4 (0.26 m0 along

Figure 6. Calculated absorption coefficients as a function of energy (1.2−3.3 eV) in different directions (E∥a parallel to reciprocal a axis, E∥c parallel to reciprocal c axis) for the four candidate compounds, Cu 2BaGeSe 4 (CBGSe: green), Cu 2SrSnSe 4 (CSTSe: purple), Cu2BaSnS4 (CBTS: red), and Cu2BaSnSe4 (CBTSe: blue), as well as kesterite Cu2ZnSnSe4 (CZTS: black), generated from the calculated dielectric functions of Figure S9 and eq 1. A Lorentz broadening function with a broadening value of 0.1 eV was used to produce smoothly integrated curves based on the finite Brillouin zone integration grid used in the calculations. The broadening function leads to small but finite tails of the absorption coefficients below the calculated fundamental band gaps (dashed arrows), which are not shown since they do not reflect physical absorption processes in the actual materials.

calculated using the random-phase approximation (i.e., exciton effects are not included), based on the predicted energy band structures deduced using the HSE06 functional including spin− orbit coupling effects. As a reference, we also include the calculated dielectric functions and absorption coefficients for the kesterite Cu2ZnSnS4, using a fully ordered structural model with lattice parameters and internal atomic coordinates relaxed at the level of the HSE06 functional. The HSE06-predicted band gap for CZTS with this geometry is 1.38 eV. This value is at the low end of the experimentally reported band gap range summarized by Botti et al.58 and slightly lower than the HSE06 band gap reported there. However, as mentioned earlier, the calculated gap is known to depend sensitively on the cellinternal coordinates, particularly the anion displacements ux and uy as documented in Figure 2 of ref 58. While Botti et al.58 report band gaps under the constraint ux = uy, for our HSE06relaxed geometry, we find different values ux = 0.2416 and uy = 0.2445. Although the precise ux and uy values for our structure are thus not directly comparable with the restricted geometries 7875


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Chemistry of Materials for which Botti et al.58 report HSE06 band gap values, our predicted band gap is qualitatively consistent with the curve shown by Botti et al.58 For all four candidate compounds, the real and imaginary components of the dielectric function are somewhat anisotropic between the ∥a and ∥c directions, as is clearly evident from the visually different curve shapes for both directions in Figure S9. Since suitability for PV represents the primary motivation for inspecting these properties, a more detailed analysis of the calculated absorption coefficients in the visible light region (1.65−3.26 eV; shown in Figure 6) is in order. The absorption coefficients of the established zinc-blende-type PV compound CZTS serve as the reference. For CZTS, the absorption coefficient is largely isotropic, showing only minor variations between the ∥a and ∥c directions. As expected from its relatively large band gap, the absorption coefficient of Cu2BaSnS4 falls significantly lower than that of CZTS in the energy range up to approximately 3 eV (the atmospheric solar spectrum, relevant for PVs, peaks around 500 nm wavelength or 2.5 eV). Overall, its absorption coefficient appears to be essentially isotropic in this range. Computational analysis for Cu2BaGeSe4 yields a significantly higher absorption coefficient than Cu2BaSnS4, reaching similar values as CZTS in the energy range at and above ∼2.5 eV, although still with significantly lower predicted absorption than CZTS in the energy range below 2.5 eV. The low-energy Cu2BaGeSe4 absorption coefficient in the ∥a direction is also slightly higher than in the ∥c direction, potentially indicating a small but nonnegligible performance dependence on film orientation for thin-film PVs. Finally, the predicted low-band gap Ama2 materials Cu2BaSnSe4 and Cu2SrSnSe4 show very similar and high absorption coefficients in the spectral range up to 2.5 eV, with noticeably higher absorption coefficients in the ∥a than in the ∥c direction. For the ∥a direction, both materials are predicted to significantly exceed CZTS regarding the absolute magnitude of their absorption, again indicating some possible influence of film orientation for thin-film PVs based on these materials. Experimental Validation of Cu2BaGeSe4. A bulk powder sample of Cu2BaGeSe4 was prepared using a process described in the SI. A typical PXRD pattern of the dark brown Cu2BaGeSe4 powder appears in Figure S10. Pawley profilefitting of the pattern confirms that Cu2BaGeSe4 adopts a trigonal crystal structure in space group P31, with refined lattice constants of a = b = 6.504(4) Å and c = 16.31(2) Å. These values agree (i.e., to within several standard deviations) with previous published results from ref 33 (see Table 1) and are analogous to our previous work on trigonal Cu2BaSnS4 material with space group P31.25,32 To validate our earlier band gap prediction, we recomputed the minimum-energy internal atomic coordinates for these new (fixed) lattice parameters using the HSE06 functional and recomputed the band structure, finding the same predicted indirect/direct band gap values of 1.60/1.61 eV as reported in Table 1 (i.e., no change in band gap arises based on use of the literature or our own lattice constants). These band gaps can be compared to experimental values based on diffuse reflectance measurements for the Cu2BaGeSe4 powder (Figure 7)i.e., the Kubelka−Munk model direct band gap fit yields a 1.91(5) eV value. Similar to the case for Cu2BaSnSe4 and Cu2BaSnS4 (Table 1), HSE06 consistently underestimates the band gap by ∼0.25−0.3 eV. As the Kubelka−Munk theory strictly depends on having highly reflective samples, we tried diluting the Cu2BaGeSe4 sample

Figure 7. Diffuse reflectance measurement on a Cu2BaGeSe4 sample plotted using the direct band gap Kubelka−Munk model. The red line is a linear fit of the absorption edge corresponding to a 1.91(5) eV band gap. F(R) is the Kubelka−Munk function and is proportional to the absorption coefficient, α.

using BaSO4 in various concentrations69 to determine whether this would impact the extracted band gap value. However, dilution of the sample did not significantly change the outcome of the diffuse reflectance analysis, yielding a band gap of 1.86(5) eV for the diluted samples (Figure S11), as compared to 1.91(5) eV for the undiluted sample. Photoluminescence measurements show a weak emission peak at 1.98(1) eV, a value that is (within experimental uncertainty) consistent with the band gap extracted from diffuse reflectance. While larger than ideal for a single junction PV in AM1.5 radiation, this experimental Cu2BaGeSe4 band gap is of great interest for solar energy conversion applications, such as multijunction photovoltaics or photoelectrochemical cells. Future experiments and calculations will focus on reduction in the band gap of Cu2BaGeSe4 materials. A feasible mechanism for band gap engineering of trigonal I2−II−IV−Se4 material systems involves cation substitutions such as I = Ag for Cu and IV = Sn for Ge.

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CONCLUSIONS In summary, this work presents an HSE06 hybrid densityfunctional theory study including spin−orbit coupling to investigate the space of 16 compounds, I2−II−IV−VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se), expanding the CBTSSe paradigm. Two key electronic characteristics were examined for screening of PV suitability: (i) band structures including band gap values and band gap types and (ii) carrier effective mass tensors fitted to the VBMs and CBMs of each compound. All Cu-containing compounds show direct or quasidirect band gaps (i.e., the direct gap falls within 0.02 eV ≈ kBT of the HSE06+SOC-predicted indirect value) with band gap values spanning 1.46−2.50 eV. In contrast, the Ag-containing compounds show indirect band gaps with a lower range of values (0.66−1.38 eV). Based on these predictions, four compounds emerge as particularly promising prospective thin-film PV candidate materialsi.e., Cu 2 BaSnS 4 , Cu2BaSnSe4, Cu2BaGeSe4, and Cu2SrSnSe4. These four compounds also show relatively small hole and electron effective mass values. The newly predicted thin-film PV candidate Cu2BaGeSe4 shows the lowest carrier effective mass among these four compounds, competitive with kesterite Cu2ZnSnS4.68 To further assess the suitability of these four candidates for thin-film PV applications, optical properties were computationally assessed. The absorption coefficients of Cu2BaSnSe4 and Cu2SrSnSe4 exceed that of the established 7876


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06OR23100. The authors gratefully acknowledge computational resources provided by the Argonne Leadership Computing Facility and by the Barcelona Supercomputing Center.

material Cu2ZnSnS4 in much of the PV relevant spectral range. Cu2BaGeSe4 shows a similar or slightly lower absorption coefficient than Cu2ZnSnS4, while Cu2BaSnS4 has a generally lower absorption coefficient in the energy range covered by the AM1.5G solar spectrum. Finally, we experimentally characterized a powder sample of Cu2BaGeSe4, corroborating the crystal structure predicted by DFT analysis and determining a slightly higher experimental band gap (1.91 eV) than the theoretical estimate (1.6 eV). These experimental/theoretical values are slightly smaller than for the analogous Cu2BaSnS4 system, for which PV devices have already been demonstrated.25 Cu2BaGeSe4 is thus a promising target to initiate further study of its performance in thin-film PVs and photoelectrochemical (PEC) devices. Future work on the I2− II−IV−VI4 materials investigated here should include consideration of defect properties (formation energies and defect levels) and solid solutions among these different compositions/ structures.

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(1) Green, M. A.; Emery, K.; Hishikawa, Y.; Warta, W.; Dunlop, E. D. Solar Cell Efficiency Tables (Version 44). Prog. Photovoltaics 2014, 22, 701−710. (2) Wang, W.; Winkler, M. T.; Gunawan, O.; Gokmen, T.; Todorov, T. K.; Zhu, Y.; Mitzi, D. B. Device Characteristics of CZTSSe ThinFilm Solar Cells with 12.6% Efficiency. Adv. Energy Mater. 2014, 4, 1301465. (3) Shin, D.; Saparov, B.; Mitzi, D. B. Defect Engineering in Multinary Earth-Abundant Chalcogenide Photovoltaic Materials. Adv. Energy Mater. 2017, 7, 1602366. (4) Gokmen, T.; Gunawan, O.; Todorov, T. K.; Mitzi, D. B. Band Tailing and Efficiency Limitation in Kesterite Solar Cells. Appl. Phys. Lett. 2013, 103, 103506. (5) Gokmen, T.; Gunawan, O.; Mitzi, D. B. Semi-Empirical Device Model for Cu2ZnSn(S,Se)4 Solar Cells. Appl. Phys. Lett. 2014, 105, 033903. (6) Gershon, T.; Sardashti, K.; Gunawan, O.; Mankad, R.; Singh, S.; Lee, Y. S.; Ott, J. A.; Kummel, A.; Haight, R. Photovoltaic Device with over 5% Efficiency Based on an N-Type Ag2ZnSnSe4 Absorber. Adv. Energy Mater. 2016, 6, 1601182. (7) Chagarov, E.; Sardashti, K.; Kummel, A. C.; Lee, Y. S.; Haight, R.; Gershon, T. S. Ag2ZnSn(S,Se)4: A Highly Promising Absorber for Thin Film Photovoltaics. J. Chem. Phys. 2016, 144, 104704. (8) Fu, J.; Tian, Q.; Zhou, Z.; Kou, D.; Meng, Y.; Zhou, W.; Wu, S. Improving the Performance of Solution-Processed Cu2ZnSn(S,Se)4 Photovoltaic Materials by Cd2+ Substitution. Chem. Mater. 2016, 28, 5821−5828. (9) Adachi, S. Earth-Abundant Materials for Solar Cells; John Wiley & Sons, Ltd.: 2015. (10) Schäfer, W.; Nitsche, R. Zur Sytematik Tetraedrischer Verbindungen Vom Typ Cu2MeIIMeIVMeVI4 (Stannite Und Wurtzstannite). Z. Kristallogr. 1997, 145, 356−370. (11) Olekseyuk, I. D.; Gulay, L. D.; Dydchak, I. V.; Piskach, L. V.; Parasyuk, O. V.; Marchuk, O. V. Single Crystal Preparation and Crystal Structure of the Cu2Zn/Cd,Hg/SnSe4 Compounds. J. Alloys Compd. 2002, 340, 141−145. (12) Cui, Y.; Deng, R.; Wang, G.; Pan, D. A General Strategy for Synthesis of Quaternary Semiconductor Cu2MSnS4 (M = Co2+, Fe2+, Ni2+, Mn2+) Nanocrystals. J. Mater. Chem. 2012, 22, 23136−23140. (13) Zou, Y.; Su, X.; Jiang, J. Phase-Controlled Synthesis of Cu2ZnSnS4 Nanocrystals: The Role of Reactivity between Zn and S. J. Am. Chem. Soc. 2013, 135, 18377−18384. (14) Cao, M.; Li, L.; Fan, W. Z.; Liu, X. Y.; Sun, Y.; Shen, Y. Quaternary Cu2CdSnS4 Nanoparticles Synthesized by a Simple Solvothermal Method. Chem. Phys. Lett. 2012, 534, 34−37. (15) Thompson, M. J.; Blakeney, K. J.; Cady, S. D.; Reichert, M. D.; Pilar-Albaladejo, J. D.; White, S. T.; Vela, J. Cu2ZnSnS4 Nanorods Doped with Tetrahedral, High Spin Transition Metal Ions: Mn2+, Co2+, and Ni2+. Chem. Mater. 2016, 28, 1668−1677. (16) Liang, X.; Guo, P.; Wang, G.; Deng, R.; Pan, D.; Wei, X. Dilute Magnetic Semiconductor Cu2MnSnS4 Nanocrystals with a Novel Zincblende and Wurtzite Structure. RSC Adv. 2012, 2, 5044−5046. (17) Evstigneeva, T. L.; Kabalov, Y. K. Crystal Structure of the Cubic Modification of Cu2FeSnS4. Crystallogr. Rep. 2001, 46, 368−372. (18) Gillorin, A.; Balocchi, A.; Marie, X.; Dufour, P.; Chane-Ching, J. Y. Synthesis and Optical Properties of Cu2CoSnS4 Colloidal Quantum Dots. J. Mater. Chem. 2011, 21, 5615−5619. (19) Murali, B.; Krupanidhi, S. B. Facile Synthesis of Cu2CoSnS4 Nanoparticles Exhibiting Red-Edge-Effect: Application in Hybrid Photonic Devices. J. Appl. Phys. 2013, 114, 144312.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b02638. Detailed input settings for the electronic structure calculations; a comparison of atomic coordinates from previous experiment and present theory for Cu2SrSnSe4; relative fractions of elemental contribution to DOS near VBM and CBM; computed energy differences for 5 space groups considered for Ag−Sr based compounds; calculated effective masses and details of the fitting procedure used to determine effective masses from band structures; calculated dielectric functions; measured XRD pattern of Cu2BaGeSe4 sample; diffuse reflectance and photoluminescence measurements for Cu 2BaGeSe4 samples; supplemental experimental procedure and analysis of Cu2BaGeSe4; complete geometry information for all compounds considered in electronic structure calculations in this work (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

David B. Mitzi: 0000-0001-5189-4612 Volker Blum: 0000-0001-8660-7230 Notes

All opinions expressed in this paper are the authors’ and do not necessarily reflect the policies and views of NSF, DOE, ORAU, or ORISE. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. 1511737. One of the authors (B.S.) acknowledges support from a Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy (EERE) Postdoctoral Research Award administered by the Oak Ridge Institute for Science and Education (ORISE) for the DOE. ORISE is managed by Oak Ridge Associated Universities (ORAU) under DOE contract number DE-AC057877


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I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI - ACS Publications - American

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