Geometry, Electronic Structure, and Bonding in CuMCh2(M = Sb, Bi

Article pubs.acs.org/JPCC

Geometry, Electronic Structure, and Bonding in CuMCh2 (M = Sb, Bi; Ch = S, Se): Alternative Solar Cell Absorber Materials? Douglas J. Temple,† Aoife B. Kehoe,† Jeremy P. Allen,† Graeme W. Watson,*,† and David O. Scanlon*,‡ †

School of Chemistry and CRANN, Trinity College Dublin, Dublin 2, Ireland University College London, Kathleen Lonsdale Materials Chemistry, Department of Chemistry, 20 Gordon Street, London WC1H 0AJ, U.K.

‡

ABSTRACT: Cu-based I−III−VI2 materials have enjoyed much attention as candidate solar cell adsorbers. While the vast majority of studies has centered on materials with group 13 (In, Ga) as the trivalent metal, the scarcity and expense of In has motivated a research drive to discover alternative Cu-based absorber materials. In this study, we use screened hybrid density functional theory (DFT) to investigate the electronic structure and bonding in some novel I−III−VI2 materials, namely, CuMCh2 (M = Sb, Bi; Ch = S, Se). We demonstrate that these materials possess fundamental band gaps that are indirect in nature, which is at variance with previous experimental results. We analyze the crystal structures and rationalize the structural differences between these and typical chalcopyrite materials. The band structure features and bonding of these materials are then discussed in relation to their utility as solar cell absorbers.

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gaps of 1.38 eV (CuSbS2),18 1.52 eV (CuSbS2),19 1.05 eV (CuSbSe2),18 and 1.65 eV (CuBiS2).20 In all cases, the band gap was reported to be direct in nature, which is necessary for high efficiency solar cell absorber materials.4 CuMCh2 (M = Sb, Bi; Ch = S, Se) crystallizes in an orthorhombic, layered structure with the Pnma space group and is composed of MCh5 square pyramids, with nearly regular CuCh4 tetrahedra (Figure 1).21 There are two distinct Ch types: ChA is four-coordinate between two Cu and two M atoms, and ChB is five-coordinate between two Cu and three M atoms. Many I−III−VI2 materials crystallize in the symmetric chalcopyrite structure, but the structure adopted by these materials is assumed to be distorted due to the lone pairs present on the trivalent Sb and Bi sites.22,23 Kyono and Kimata used the Valence Shell Electron Pair Repulsion (VSEPR) theory to rationalize why the M site of Chalcostibite and Emplectite does not possess an octahedral coordination but instead has five M−Ch bonds oriented in a quasi-square-pyramid arrangement, with a vacant site occupied by the lone pair.21 In this article, we study the geometry and electronic structure of CuMCh2 (M = Sb, Bi; Ch = S, Se), using the screened hybrid density functional, HSE06.24 We demonstrate: (i) that the fundamental band gaps of these materials are indirect, meaning that they will not be efficient in optoelectronic devices, (ii) the strength of the lone pair structural distortion is directly related to the cation s and anion p mixing, in agreement with the revised lone pair model,22 and (iii) that the mixing of the lone pair states with the Cu 3d and S 3p states at the valence band maximum (VBM) does not create a material with

INTRODUCTION As the global demand for energy grows inexorably, photovoltaic solar energy production is becoming increasingly important. Solar cells based on single-crystal silicon materials exhibit high efficiencies but have proven to be prohibitively expensive for general and widespread applications.1−3 Solar cells comprising direct band gap, light-absorbing materials hold many advantages over silicon-based technologies. They can be fabricated as thin films which require less energy and material to make, are generally produced in eco-friendly processes, and can be deposited by a wide variety of techniques that allow control over properties such as crystallinity and orientation.4 II−VI CdTe and I−III−VI2 chalcopyrite Cu(In/Ga)Se2 (CIGS) have become the standard thin-film solar cell absorbers and can achieve solar conversion efficiencies of up to 16.5% and 20.3%, respectively.5−10 However, these materials contain cadmium, which is toxic, and the expensive, low-abundance heavy elements, tellurium and indium. To overcome these limitations, there has been huge interest in developing materials that contain abundant, low-cost elements and meet the criteria for solar cell applications: band gaps close to the optimal single-junction value of ∼1.5 eV and high optical absorption of ∼1 × 104 cm−1. Quaternary semiconductors Cu2ZnSnS4 (CZTS) and Cu2ZnSnSe4 (CZTSe) have enjoyed considerable attention as they contain only the abundant and nontoxic elements Cu, Zn, Sn, S, and Se and have displayed band gaps in the range 1.0−1.6 eV.11−16 The efficiencies of these quaternary materials have advanced to nearly 10%,17 although they still lag behind those of CdTe and CIGS. In the past ten years, alternative I−III−VI2 materials have also gained attention as possible solar cell absorbers. CuSbS2 (mineral name Chalcostibite), CuSbSe2, and CuBiS2 (Emplectite) have all been investigated as candidate absorbers, with reported band © 2012 American Chemical Society

Received: January 26, 2012 Revised: March 7, 2012 Published: March 8, 2012 7334

dx.doi.org/10.1021/jp300862v | J. Phys. Chem. C 2012, 116, 7334−7340

The Journal of Physical Chemistry C

Article

accurate than those of the local density approximation (LDA), the general gradient approximation (GGA), and meta-GGA.29,31−43 Structural optimizations of bulk CuMCh2 (M = Sb, Bi; Ch = S, Se) were performed at a series of volumes to calculate the equilibrium lattice parameters. In each case, the atomic positions and lattice vectors were allowed to relax, while the total volume was held constant. The resulting energy−volume curves were fitted to the Murnaghan equation of state to obtain the equilibrium bulk cell volume.44 This approach minimizes the problems of Pulay stress and changes in basis set which can accompany volume alteration in plane wave calculations. The Pulay stress affects the stress tensor, which is used only indirectly in obtaining the optimized lattice vectors by equalizing the pressure, and hence this approach is more accurate than utilizing the stress tensor to perform constant-pressure optimization. Convergence with respect to k-point sampling and plane wave energy cutoff was checked, with a k-point sampling of 6 × 6 × 1 and a cutoff of 400 eV determined to be sufficient in all cases. Calculations were deemed to be converged when the forces on each atom were less than 0.01 eVÅ−1. The optical transition matrix elements and the optical absorption spectrum were calculated within the transversal approximation and PAW method.45 With this methodology, the adsorption spectrum is summed over all direct valence band (VB) to conduction band (CB) transitions and therefore ignores indirect and intraband adsorptions.46 In this framework of single particle transitions, the electron−hole correlations are not addressed as they require treatment by higher-order electronic structure methods.47,48 However, this method has been shown previously to provide reasonable optical absorption spectra.35,49,50 Structure and charge density visualization and analysis were performed using VESTA.51 Band Alignment. The VB offset ΔEVA/B between two compounds A and B was calculated with the same procedure used in core-level photoemission measurements.52,53 Initially, the energy level difference between the VBM and the core levels (CL) for A and B was calculated at their equilibrium lattice constants

Figure 1. Unit cell of CuMCh2 (M = Sb, Bi; Ch = S, Se), with Cu, M, and Ch atoms shown as blue, gray, and yellow spheres, respectively. ChA and ChB indicate the four- and five-coordinate chalcogen ions, respectively.

a diffuse VBM and hence would not be expected to show good p-type conductivity. In light of these results, we discuss the utility of these materials as solar cell absorbers.

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THEORETICAL SECTION Structure Minimization. All calculations were performed using the periodic density functional theory (DFT) code VASP,25,26 in which a plane-wave basis set describes the valence electronic states, with the projector-augmented wave27,28 (PAW) method employed to describe the interactions between the core (Cu:[Ar], Sb:[Kr], Bi:[Xe], S:[Ne], and Se:[Ar]) and valence electrons. Calculations were carried out with the screened hybrid density functional proposed by Heyd, Scuseria, and Ernzerhof (HSE06).24,29 This addresses the difficulties in evaluating the Fock exchange in a real space formalism, which are caused by the slow decay of the exchange interaction with distance. In the screened hybrid functional approach, the description of the exchange interaction is separated into long- and short-range (LR and SR) terms with a percentage of exact nonlocal Fock exchange replacing the SR PBE30 functional. HSE06 includes 25% of exact Fock exchange (ExFock,SR) with the DFT exchange (ExPBR,SR and ExPBE,LR) and correlation (EcPBE). A screening of 0.11 bohr−1 is applied to partition the Coulomb potential into LR and SR terms, which gives HSE06 E xc = E xHSE06,SR + E xPBE,LR + EcPBE

1 Fock,SR 3 Ex + E xPBE,SR 4 4

(3)

B B B ΔEVBM,CL = EVBM − ECL

(4)

The core level difference between the two materials was then calculated by forming a superlattice between A and B at the average lattice constants of the two AB AB ΔECLB− CLA = ECL − ECL B A

(5)

with the VB offset given by B A ΔEVA/B = ΔEVBM,CL − ΔEVBM,CL + ΔECLB− CLA (6)

(1)

In the case of CuMCh2 (M = Sb, Bi; Ch = S, Se), we constructed 1 × 1 × 6 supercells in the [001] direction, comprising three unit cells of each compound. As HSE06 calculations are computationally very expensive, we have used the GGA+U approach to calculate the alignments, in which the + U of Dudarev et al.54 effectively acts as a penalty to delocalization of electron density. A U value of 5.2 eV was applied to the Cu d states, which has been shown to reproduce the VB features of a number of CuI-based materials.55−58 The Cu (1s) levels were chosen as the representative core levels, as they are the deepest

where E xHSE06,SR =

A A A ΔEVBM,CL = EVBM − ECL

(2)

The Fock and PBE exchange are therefore mixed only in the SR part, while LR exchange interactions are represented solely by those of the PBE functional.24 The HSE06 functional has been shown to produce structural and band gap data that are more 7335



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levels in all the materials. It should be noted that no consideration of deformation potentials was included in this method.59,60 Once the relative energy of each VBM had been established, the band gap calculated with HSE06 (ΔEgA/B) was added to the VBM to determine the energy of the conduction band minimum (CBM) and the CB offsets (ΔECA/B)

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ΔECA/B = ΔEVA/B + ΔEgA/B

(7)

RESULTS Results. The lattice parameters calculated by HSE06 are shown in Table 1, with comparison to experimentally Table 1. Lattice Vectors and Bond Lengths in the HSE06Calculated Structures of CuMCh2a CuSbS2 a b c M−ChA M−ChB Cu−ChA|| Cu−ChA⊥ Cu−ChB

6.06 3.80 14.56 2.57 2.43 2.32 2.32 2.34

(0.70) (0.11) (0.45) (0.12) (0.08) (1.00) (0.17) (0.39)

CuSbSe2 6.38 4.00 15.11 2.71 2.58 2.42 2.46 2.43

(1.29) (0.67) (0.70) (0.74) (1.82) (1.17) (2.63) (0.12)

CuBiS2 6.21 3.94 14.53 2.66 2.55 2.31 2.33 2.37

(1.24) (0.74) (−0.12) (1.14) (3.36) (−0.82) (0.22) (−0.34)

CuBiSe2 6.53 4.11 15.08 2.80 2.68 2.43 2.46 2.46

a

All data are written with percentage differences to experiment in parentheses. Note: no experimental structural data were available for CuBiSe2. All distances are quoted in Å. Two bond lengths were seen for Cu−ChA, depending on whether the bonds were parallel or perpendicular to the layers, designated by the superscript || and ⊥, respectively.

Figure 2. Electronic density of states (DOS) of (a) CuSbS2, (b) CuSbSe2, (c) CuBiS2, and (d) CuBiSe2, as calculated with HSE06. The top of each VB is aligned to 0 eV.

determined results also given. Since no experimental structural data were found for CuBiSe2, the initial structure was modeled on the other three materials in the space group of Pnma. As expected, the HSE06 results show good agreement with those obtained experimentally, with a difference of less than 1% achieved in the majority of cases. This small discrepancy can be attributed to the van der Waals forces responsible for binding the layers of these materials together, which have previously been shown to be poorly described in standard or hybrid DFT functionals HSE06.61−65 However, the lattice parameters were also obtained with PBE + U with a U of 5.2 eV applied to the Cu d states. These had an average deviation of 2% from experiment, with the highest overestimation being 4.58% for the c vector of CuBiS2 indicating that HSE06 yields better lattice constants than standard DFT functionals. The density of states (DOS) of all the compounds have been computed by HSE06, the results of which are shown in Figure 2. The overall shape of the states is similar between the four systems. The main contribution from the valence cation s states is shown by a peak at around −10 eV for the Sb systems and −11 eV for those containing Bi. Mixing of these cation s states with the anion p states is in evidence. The VB is predominantly made up of Cu d states, cation p states, and anion p states, with a small amount of Sb/Bi s states also present. The CB consists primarily of p states, from both the chalcogens and the group 15 metals. The contribution of the Sb and Bi s states to the VB can be accounted for by the lone pairs on these elements. Like many of the heavier metals in groups 13−16, the stability of the n s electrons compared with that of the n p electrons can result in a stable oxidation state two lower than the group valency.

Classical lone pair theory attributes the resulting structural distortions to the energetically favorable hybridization of metal s states close to the Fermi level and higher energy unoccupied p states, which only occurs at metal centers that do not possess inversion symmetry. However, a number of computational studies have reported that the metal s states are predominantly found at the bottom of the VB, too far in energy from the p states for such hybridization to occur.62,66−69 Instead, the mixing of the metal s states with anion p states results in a filled antibonding state at the top of the VB. This facilitates the indirect coupling of Sb/Bi s and p states and produces the asymmetric electron density responsible for the irregular structures, as confirmed by high-resolution X-ray photoemission and soft X-ray emission spectroscopies.70 Another Bi ternary system which displays lone pairs is BiVO4, in which the Bi s states and O p states interact, resulting in the predominantly O 2p VB increasing in energy relative to its position in pure vanadium oxide, while the V 3d states mix with Bi 6p and O 2p states so that the CB is lowered. Overall, the band gap between pure O 2p and the V 3d states of 2.78 eV is narrowed to 2.16 eV when mixing with the Bi states occurs.50 This lone pair effect is strongest for oxides and is lessened down to the chalcogen group as a result of increasing energy of the anion p states, reducing interaction with the cation s states and weakening the lone pairs.22,69 Lone pairs are also weaker in systems with 6s states due to a reduction in energy of the Bi s states by relativistic effects.22 Consequently, the cation s states are most influential in the CuSbS2 system and have the least contribution in CuBiSe2. It is important to note that the coupling of the antibonding interaction of the Sb/Bi s states 7336



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Table 2. Computational Values for the Direct (Egd) and Indirect (Egi) Band Gaps of CuMCh2 (M = Sb, Bi; Ch = S, Se)a

and the anion p states with the Sb/Bi p states produces the lone pair effect and that the required mixing with the anion states shows that the lone pair is not chemically inert.23 Evidence of the lone pairs can also be seen from the VB charge density plots in Figure 3. These clearly show that while

CuSbS2 CuSbSe2 CuBiS2 CuBiSe2

Egd(HSE06)

Egi (HSE06)

Ego(HSE06)

Egexptl

1.73 1.32 1.60 1.28

1.68 1.27 1.42 1.12

1.88 1.46 1.77 1.43

1.38,18 1.5219 1.0518 1.6520 −

a

Calculations were performed with HSE06. Optical band gaps (Ego) were determined by linear regression (as shown by dotted lines) from Figure 5. Experimental values, where found, are also listed.

although very good agreement is achieved in the case of CuBiS2, with a calculated direct band gap of 1.60 eV comparing favorably to that reported of 1.65 eV.20 The magnitude of this band gap in particular is close to that considered ideal for solar cell absorbers, ≈1.5 eV.4 The band structures show some dispersion of the VB around the VBM, suggesting that these materials may exhibit p-type behavior. The nature and extent of the semiconductor behavior was examined by performing effective mass calculations around the VBM and CBM, the results of which are given in Table 3. Table 3. Effective Masses of the Carriers in the VBM and CBM of CuMCh2 (M = Sb, Bi; Ch = S, Se), Obtained with HSE06 Figure 3. Charge density of the VB of (a) CuSbCh2 and (b) CuBiCh2 (Ch = S, Se), with Cu, Sb, Bi, and Ch atoms shown in blue, gray, purple, and yellow, respectively. The contours are shown at 0.45 eV Å−3.

valence band (m*) CuSbS_2 CuSbSe_2 CuBiS_2 CuBiSe_2

there is minimal charge density surrounding the Sb and Bi atoms there is a small anisotropic density on one side of these spheres. The lone pair effect is more prominent in the Sb systems than in those of Bi as expected. The majority of the charge density in the VB originates from the chalcogen and copper states, corroborating the DOS (Figure 2). The band structures of all four systems are shown in Figure 4. Notably, all of the compounds are indirect band gap materials, a result which is contrary to experiment18,18,19 and makes them less efficient for applications in optoelectronic devices.4 The VBM in all cases is in the Γ−Z region, while the CBM lies on the line from Γ to Y. The values of the indirect and direct band gaps for each system are listed in Table 2. HSE06 overestimates the band gaps of both Sb materials relative to experiment,18,19

conduction band (m*)

VBM → Γ

VBM → Z

CBM → Γ

CBM → Y

3.93 1.18 3.87 0.89

3.76 2.05 2.35 2.67

0.56 0.71 0.25 0.18

1.13 0.87 0.46 0.42

A typical value for a hole effective mass in an efficient p-type material such as CuBO2 is 0.45 eV,71 while in the n-type material In2O3, the VBM and CBM effective masses are 16 and 0.24 eV, respectively.72 The values for the VBM in all directions are significantly higher than those for the CBM, which is not conducive to high hole mobility and instead indicative of higher electron mobility in these materials, although the hole mobilities of the selenides are generally higher than those of the sulfides. The Bi systems have higher electron mobilities than those containing Sb which, given the weaker lone pair effect in

Figure 4. HSE06 band structure calculations for (a) CuSbS2, (b) CuSbSe2, (c) CuBiS2, and (d) CuBiSe2, with the VBM aligned to 0 eV. 7337



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The CBM of all the materials is predominantly made up of antibonding Sb/Bi p and anion p states. Due to the shorter M−Ch bond length in sulfides than selenides, there is increased mixing and hence greater repulsion in the S compounds, resulting in a higher CBM, as previously reported for CZTS and CZTSe.73 As a consequence of the greater ionic radius of Bi(III) compared to Sb(III), Bi states experience smaller overlap with the chalcogen states than Sb, lowering the CBM relative to the Sb complexes.

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DISCUSSION Of much interest are the effects of lone pairs on the electronic structure of materials. For example, in SnO, PbO, and BiVO4, the lone pair states on Sn, Pb, and Bi, respectively, mix with anion p states to make the VB more diffuse, reducing the effective mass and promoting hole mobility.22,50 In the case of the systems studied here, the lone pairs actually cause structural distortion in comparison to the symmetric chalcopyrite structures, which possess similar bonding but no elements that experience a lone pair effect. In the chalcopyrite structure, the M ions are tetrahedrally coordinated, while here, they are in a square pyramidal arrangement based on an octahedron but with a lone pair at the sixth vertex meaning that the lattice contains layers bonded together by van der Waals forces. In agreement with the revised lone pair model,22 the greatest density of the metal s states is not at the top of the VB but is 10 eV lower in energy. It is only through mixing of these states with the anion p states that any Sb/Bi s density is present near the Fermi level, where it can mix with the Sb/Bi p states in the CB. The strength of the lone pairs across the range of materials is also in line with previous studies,69 with the gap between anion p states and Sb/Bi s states responsible for the magnitude of the interaction which promotes s electron density to the antibonding state at the top of the VB. As expected, S containing compounds undergo mixing of the anion p states and Sb/Bi s states to a larger extent than those that include Se, due to the lower p states of the former, leading to a greater lone pair effect. Sb is further seen to have stronger lone pairs than Bi, as has been previously rationalized.22 All of the systems are predicted to have indirect band gaps, at variance with previous experimental studies which have reported direct band gaps.18−20 This discrepancy probably arises because all of the previous band gap measurements have been carried out using only optical absorption to analyze the nature of the band gap. To truly understand the nature of a band gap, more sophisticated measurements are necessary, such as photoluminescence or two-photon absorption spectroscopies. It is clear from our results that the nature of the band gap of this class of materials warrants experimental reinvestigation. Indirect band gap materials have a lower theoretical efficiency in optoelectronic devices than those with a direct band gap. This is because in an indirect band gap material, for electron− hole pair annihilation to occur, emission or absorption of a phonon is required in addition to that of a photon. In direct band gap materials, such vibrations are not necessary, leading to higher efficiency that makes them more suited for optoelectronic applications than their indirect counterparts. For solar cell absorber materials, however, the optical absorption is the key factor, as the smaller the direct band gap, the thinner the layer of absorber necessary. Crystalline Si, with its indirect band gap of 1.1 eV and direct band gap of ∼3.2 eV, necessitates thicknesses an order of magnitude bigger than direct band gap absorbers.2 The materials calculated here, while being indirect,

Figure 5. Plot of (αhν)2 vs hν for CuMCh2 (M = Sb, Bi; Ch = S, Se), with the dotted lines denoting linear regression to determine the optical band gaps.

these materials, could suggest that the presence of lone pairs reduces electron mobility. To explain the observed trend in band gap size, the relative energies of the VB and CB for the series of systems were obtained by means of a VB alignment, the results of which are shown in Figure 6. The larger band gaps of the sulfides over

Figure 6. Band alignments of CuMCh2 (M = Sb, Bi; Ch = S, Se). The VBM offsets are calculated with GGA + U, and the positions of the CBMs are determined using the HSE06 band gaps. The values shown (in eV) are relative to the lowest VBM, that of CuBiS2, which is set to 0 eV.

the selenides is due to both a higher CBM and a lower VBM. As already determined from the DOS, there is a filled antibonding state at the top of the VB consisting mainly of anion p states, Sb/Bi s states, and Sb/Bi p states, with some Cu d state contribution. The p levels of S are lower in energy than those of Se, giving rise to a VBM in CuSbS2 that is 0.20 eV lower in energy than in CuSbSe2 and 0.21 eV lower in CuBiS2 than CuBiSe2. In a competing effect, the Cu−S bond is shorter and therefore more conducive to mixing than the Cu−Se bond. This contributes to a greater antibonding split, giving rise to an elevated antibonding level in the sulfides relative to the selenides and narrowing the difference between the VBMs. The VBM offset is therefore less than the 0.5 eV difference between the atomic p orbital energies of S and Se.22 The VBM of CuSbSe2 is the highest of the four systems, rendering it the most likely to be effectively hole-doped, although as our effective mass calculations have shown none of these materials are expected to be possess high hole mobility. 7338


The Journal of Physical Chemistry C would still be able to be deposited relatively thinly, as their optical absorptions compare well with CdTe and CIGS. The band gaps calculated with HSE06 are slightly overestimated with respect to experimental values in the cases of CuSbS2 and CuSbSe2 and underestimated for CuBiS2, while no experimental band gap for CuBiSe2 has been reported. However, data on the electronic properties of all of these systems are rather limited, and those which do exist are inconsistent, a fact attributed to varying grain size of samples.18 The major limitations to the use of these materials as solar cell absorbers is likely to be the high effective mass of the VBM, which means that hole mobility in this material will be quite low. Adjustment of the Cu/M ratio could create more charge carriers in the system but is unlikely to affect the mobility greatly. The layered nature of this material also plays a significant role in mobility, as conductivity in these materials will be highly anisotropic, being mostly in the layers and not across layers. Replacement of some of the S/Se with Te should raise the VBM of this material and possibly alter the curvature of the VBM, but this will come at the cost of a lowering of the optical band gap. Alloying Cu(Bi/Sb)Ch2 (Ch = S, Se) with Cu(Bi/Sb)Te2 would be a worthwhile exercise in the future. Taking into consideration the indirect nature of these materials’ band gaps, their highly anisotropic conductivity resulting from the van der Waals bonded layered structure, and their large carrier effective masses, they are unlikely to fulfill the current criteria for ideal photovoltaic absorbers. In a recent study of another lone pair material, SnS, as a potential solar cell absorber, the authors similarly reported an indirect band gap and high carrier effective masses arising from the layered structure, citing these as disadvantages to such an application despite promising defect chemistry.74 However, there are a number of alternative materials under investigation that warrant further research, including Zn3P2, which is a highly cost-effective material with great potential in solar cells,75 and the copper chalcogenides Cu3MCh3 (M = Sb, Bi; Ch = S, Se) and Cu3MCh4 (M = V, Nb, Ta; Ch = S, Se, Te), both of which are not layered materials. Although it is improbable that the systems studied here will provide the solution, the search for cost-effective, naturally abundant, high-efficiency solar cell absorbers continues.

ACKNOWLEDGMENTS

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REFERENCES

This work was supported by SFI through the PI programme (PI Grant numbers 06/IN.1/I92 and 06/IN.1/I92/EC07). Calculations were performed on the IITAC and Lonsdale cluster as maintained by TCHPC and the Stokes cluster as maintained by ICHEC. D.O.S. is grateful to the Ramsay Memorial Trust and University College London for the provision of a Ramsay Fellowship. A.B.K. would like to thank the IRCSET EMBARK initiative for a postgraduate scholarship.

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CONCLUSION The geometric and electronic structures of CuMCh2 (M = Sb, Bi; Ch = S, Se) have been studied with the screened hybrid functional HSE06. It has been found that these systems are indirect band gap materials, which is at variance with previous experimental measurements. The origin and relative strength of the lone pairs of Sb and Bi have been examined, as well as their distorting effect on the crystal structure. In addition, effective mass calculations have indicated that the mixing of these Sb/Bi s states with S/Se p states and Sb/Bi p states in the VB results in low p-type ability. In conclusion, despite promising band gap magnitudes, the nature of the band gaps combined with the poor hole mobility suggests that these materials are unlikely to be well suited to applications as solar cell absorbers.

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Geometry, Electronic Structure, and Bonding in CuMCh2(M = Sb, Bi

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