Article pubs.acs.org/JPCC
Theoretical Study on the Structure and Energetics of Cd Insertion and Cu Depletion of CuIn5Se8 Janos Kiss,*,† Thomas Gruhn,† Guido Roma,†,‡ and Claudia Felser† †
Institut für Anorganische Chemie und Analytische Chemie, D-55128 Mainz, Germany CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif sur Yvette, France
‡
ABSTRACT: Due to its attractive optical, electrical, and chemical properties, the ternary CuInSe2 (CIS) chalcopyrite-type semiconductor is widely employed as an absorber layer in thin-film photovoltaic devices. Experimental studies have shown that close to the interface of CIS with the CdS buffer layer the former is Cu-depleted, corresponding most probably to an ordered vacancy compound (OVC), and hosts some Cd atoms by diffusion, which originate from the buffer layer. To gain new insights into the insertion of Cd into Cu-depleted CIS phases, we have performed density functional theory calculations, and we have investigated the atomic structure and energetics of neutral Cd impurities in the OVC CuIn5Se8. We found that Cd atoms prefer predominantly to sit on Cu sites or on Cu vacancy sites. Furthermore, our calculations show that the Cu vacancies and Cd atoms have high binding energy at least in some specific configurations. Hence, the insertion of Cd into the CIS materials might enhance the formation of Cu-poor phases.
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INTRODUCTION Solar cells based on CuInSe2 (CIS) and on the structurally similar CuInGaSe2 (CIGS),1,2 which has reached the thin-film record efficiency of 20.3%,3,4 have been especially successful. They have achieved industrial maturity and face now the challenges of reducing production costs. The cell efficiencies are, however, still distinctly below their maximal theoretical performance limits. An important part of the losses in the thinfilm devices is due to doping, vacancies, inhomogeneities, grain boundaries, and other structural defects. First-principles calculations have contributed to the understanding of inhomogeneities,3 but the interplay between structural defects and dopants upon the morphology and macroscopic and electronic properties of CIS/CIGS films is not yet fully understood. Therefore, it is of high relevance to get a deeper insight into the atomic scale in the structure of the absorber in the bulk and near the interfaces, where an important part of the losses is supposed to occur. Regarding the heterojunction between the absorber and the buffer layer, it is of course very important to understand the interdiffusion of the elements, which is strongly connected to the establishment of the stoichiometry in the near-interface regions.5,6 Interdiffusion at the interface can produce Cu impurities in CdS, whose stability has been studied by firstprinciples calculations,7 and Cd impurities in CIGS, especially in the first layers adjacent to the interface, supposed to be Cupoor. Conversely, no first-principles studies of Cd in CIGS have been published. The diffusion coefficient of Cd into CIGS has been recently measured,8 featuring a relatively small activation energy, close to 1 eV; the atom probe tomography analysis shows that it is indeed bulk diffusion, and not grain boundary diffusion, that occurs. The speculations proposing a vacancy mechanism or an interstitial-substitutional mechanism can be © XXXX American Chemical Society
strengthened or invalidated by a better knowledge of the preferred insertion sites based on ab initio total energies. Moreover, the diffusion properties are certainly influenced by the Cu stoichiometry of the first CIGS layers. It is well established that the best efficiency can be achieved by growing the CIS absorber layer under Cu-poor conditions. 9,10 Experimentally, a particularly strong Cu depletion is found close to the interface with the buffer layer.11 The structure and depth of the strongly Cu-poor region in CIS solar cells is still a topic of ongoing debate. However, Cu-poor phases have been created and studied under controlled conditions, and especially the CuIn3Se5 and the CuIn5Se8 are found to form rather easily.12 Recently, the formation conditions for these phases have been studied via combined density functional theory (DFT) calculations and Monte Carlo simulations.13 It is particularly important to understand the microstructure of these Cu-poor photovoltaic materials on the atomic level10,11,14,15 and to control their formation and their longterm stability. It is the goal of this paper to apply first-principles calculations to shed new light on the stability of Cd impurities in such Cudepleted phases. The results from theoretical investigations can have a high potential impact on the optimization of solar cell devices.16 Similar DFT-based theoretical investigations on solar cell materials17−22 were proven to describe rather well the cell parameters and the band structure of these compounds. Also, such theoretical approaches were used to predict the formation energy of various defect sites21,23−30 and the inclusion of impurities in the bulk.31,32 Received: December 18, 2012 Revised: April 23, 2013
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Figure 1. Comparison between the unit cell of CuInSe2 and CuIn5Se8. The conventional unit cell of CuInSe2 containing 16 atoms is shown to the left. Compared to a √2 × √2 × 1 CuInSe2 supercell (middle), the structure of the tetragonal unit cell of the chalcopyrite-like CuIn5Se8 ordered vacancy compound (right) has two In atoms sitting in Cu sites (denoted as InCu), and four Cu atoms are removed (represented as V′Cu). A Se tetrahedron formed by four Se atoms surrounding a V′Cu site is highlighted with red lines. The prime denotes Cu vacancies with respect to CuInSe2. The color scheme of the atoms and the vacancies employed in this figure is used in all subsequent figures throughout this paper.
3d9.54s1, [Kr] 4d9.55s25p1, and [Kr] 4d9.55s25p0 configurations as reference states for Cu, In, and Cd. In the case of Se, we have taken the neutral [Ar + 3d10]4s24p4 configuration as a reference state. The all-electron reference wave functions were computed by using the scalar-relativistic wave equation, and nonlinear core corrections were also included in the potentials. The bulk CuIn5Se8 was represented by employing a large periodically repeated tetragonal supercell containing 504 atoms built up from 3 × 3 × 2 tetragonal unit cells (see Figure 1). Due to the large size of the system, the Brillouin zone sampling could be restricted to the Γ-point. For the determination of the equilibrium bulk lattice parameters of perfect chalcopyrite phases, we have performed variable cell dynamics calculations, where the forces were minimized both on the atoms and on the stress tensors, under the constraint that the crystal system remained tetragonal. The calculations for the respective systems were stopped, and convergence was assumed when the largest component of the residual forces on the atoms dropped below 0.01 eV/Å and the diagonal components of the stress tensors were lower than 0.02 GPa. Calculations of defected supercells were mostly performed at the CuIn5Se8 equilibrium structure, unless otherwise specified. By using the mentioned large system size, we are able to describe Cd concentrations as low as 0.2 atomic %, allowing us to get rid of spurious image interactions induced by the use of periodic boundary conditions. For the sake of comparison, for smaller supercells (56 atoms) and for the unit cells we performed also some calculations with the PBE functional and with the HSE0636,37 hybrid functional using the code VASP.38 The formation energies for supercells containing NCd cadmium atoms and NVCu copper vacancies (i.e., 36-NVCu copper atoms) are calculated as
In this article, we consider the insertion of Cd atoms into the CuIn5Se8 structure as a model of the Cu-poor CIS phases occurring in the vicinity of the interface between the absorber and the CdS buffer layer. We study the structure and energetics of Cd as a neutral impurity into the chalcopyrite-based polytype of CuIn5Se8. We are aware that dealing only with neutral impurities is a limitation; however, our focus was on the variety of configurations assumed by Cd at different concentrations, and in this perspective, a thorough study with methods able to accurately describe the relative stability of various charge states would not be applicable. By studying the interaction of Cd with CuIn5Se8 we gain new fundamental details on the atomic scale concerning the possible binding sites of Cd in the Cu-poor absorber material. Furthermore, we investigate the interplay of Cd impurities and Cu vacancies and how this can lead to even Cu-poorer phases as the CuIn5Se8.
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COMPUTATIONAL DETAILS All calculations were carried out with the PWscf33 program package, which is a suite of computer codes based on density functional theory (DFT), plane waves, and pseudopotentials. For the approximate treatment of electron exchange and correlation in our DFT calculations, we employed the generalized gradient approximation (GGA) via the functional proposed by Perdew, Burke, and Ernzerhof (PBE)34 together with Vanderbilt-type ultrasoft pseudopotentials.35 The wave functions and densities were expanded in a plane-wave basis set up to a cutoff energy of 25 and 100 Ry, respectively. For all systems with an odd number of electrons, spin polarization was employed. To improve the transferability of the pseudopotentials, the respective semicore 3d, 4d, 4s, and 4d states of Cu, In, Se, and Cd were treated as valence states. To construct pseudopotentials which are well suited for the description of pure and Cddoped CuIn5Se8, we have used the slightly ionized [Ar] B
dx.doi.org/10.1021/jp312467f | J. Phys. Chem. C XXXX, XXX, XXX−XXX
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chalcopyrite-like CuIn5Se8 consists thus of 2 Cu, 10 In, and 16 Se atoms, i.e., 28 atoms altogether. In CuInSe2, all atoms are tetrahedrally coordinated, where each Cu and In cation is surrounded by four Se anions and each Se has two Cu and two In atoms as nearest neighbors. Cu, In, and Se have one, three, and six valence electrons, respectively. To fulfill the octet rule, two Cu atoms donate 0.25 + 0.25 electrons to each neighboring Se atom, and two In atoms donate 0.75 + 0.75 electrons. Hence, in the case of CuInSe2, the number of valence electrons on each Se atom is k = 8 (see Figure 2, left).
158 ΔE(NCd , NVCu) = Etot(NCd , NVCu) − Etot − NCdμCd
+ NVCuμCu
(1)
where Etot(NCd,NVCu) is the total energy of the supercell containing Cd (and possibly other defects); E158 tot is the total energy of the supercell containing 36 formula units of CuIn5Se8 (shortened as 158) and no defects; and μi are the chemical potentials of the elements i. The latter are taken as the metallic ground states, unless specified otherwise. Many calculated configurations involve only Cd insertion, without Cu removal (i.e., NVCu = 0). The reliability of elemental reference states calculated with DFT-GGA has been recently scrutinized,39 and corrections have been suggested, based on fitting of a number of compounds. In our specific case, however, we prefer to stick to the coherence of our DFT calculations and not to add any corrections, essentially for two reasons. First, the results of ref 39 imply the use of a rather high on-site Coulomb repulsion U for Cu (which we do not use here). Second, we have checked a number of calculated formation enthalpies of relevant compounds, and we find, as shown in Table 1, that they are
Figure 2. Bond lengths around the Se anions in CuInSe2 (left) and in CuIn5Se8 (middle and right), where the number of valence electrons is represented with k. The selenium atoms in the middle and right tetrahedra are labeled A and B in the text.
Table 1. Comparison of Calculated and Experimental Formation Enthalpies (in eV/atom) of a Few Binary Compoundsa
a
compound
ΔHPBE [eV] f
ΔHEXP [eV] f
CdSe CdS Cu2Se InSe In2Se3
−0.81 −0.99 −0.25 −0.53 −0.54
−0.75 −0.78 −0.21 −0.62 −0.67
In contrast to CuInSe2, in the crystal structure of CuIn5Se8 the Se atoms are undercoordinated because they have only three nearest neighbors. During the relaxation of the structures, we found that the Se atoms move closer to the neighboring In, InCu, and Cu atoms, so the bond lengths are somewhat shorter compared to CuInSe2 (see Figure 2). Half of the Se atoms are bound to a Cu atom and to two InCu atoms, so these Se atoms have k = 7.75 valence electrons. The other half is bound to two InCu atoms and an In atom; i.e., they have k = 8.25 valence electrons, which gives rise to two types of inequivalent Se atomswe call them SeA and SeBschematized in Figure 2 (middle and right). To keep the system charge-neutral and to ensure that the structure is stabilized via the Coulomb attraction between Se atoms, the number of the two different kinds of Se atoms is equal in the bulk solid CuIn5Se8. Furthermore, the two types of Se atoms, SeA and SeB, are close to each other, being distributed in an alternating ordered pattern. In the case of the chalcopyrite polytype of CuIn5Se8, this means that there are Se tetrahedrons formed surrounding a vacancy, where there are two SeA and two SeB located in the four vertices. One of such Se tetrahedrons is outlined with red color in Figure 1; the yellow sphere is a vacancy for the CIS structure but could be simply seen as an interstitial site for CuIn5Se8: we call it a pristine vacancy, V′Cu, to distinguish it from genuine vacancies, VCu, created by removal of Cu atoms in the CuIn5Se8 structure. All Cu atoms are 4-fold coordinated by four equivalent Se atoms, so all Cu−Se bonds have the same length. Both the In and InCu atoms are surrounded by four nearest-neighbor Se atoms. The InCu atoms are sitting in the center of the regular tetrahedrons formed by four equivalent Se atoms, similar to the Cu atoms. Thus, all four InCu−Se bonds have the same length of 2.64 Å. Although the In atoms are also 4-fold coordinated by Se, in their case two In−Se bonds are shorter (2.61 Å), and the other two In−Se bonds are longer (2.69 Å) compared to the InCu−Se bond distances (see Figure 2.) Through full structural relaxations we have obtained for CIS the cell parameters a = 5.86 Å and c = 11.76 Å corresponding to a tetragonal elongation of η = c/2a = 1.003. The Cu−Se and
Experimental values are taken from ref 39.
globally satisfactory. Moreover, the corrections suggested in ref 39, although certainly very useful in the specific setup, are still somewhat dependent on the choice of the pseudopotential. As an example, for CdS (standard PBE calculations without U), our formation enthalpy (0.99 eV) is in fair agreement with experiment (−0.78 and −0.84 eV, cited in refs 39 and 7, respectively) without adding either the rather large correction (+0.35 eV) proposed in ref 39 for elemental Cd or the small one for S (+0.06 eV), which would both, anyway, worsen the results. In conclusion, although an error of 0.1−0.2 eV may be expected on chemical potentials, the general trends that we discuss in the following are not affected.
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RESULTS AND DISCUSSION Crystal Structure. In the literature, theoretical and experimental studies have shown that CuIn5Se8 is an ordered vacancy compound.12,21,40 The arrangement of atoms in the tetragonal unit cell of the chalcopyrite-like polytype is shown in Figure 1, which was proposed to be the ground state21,40 of bulk CuIn5Se8. The structure is best understood by starting from a conventional tetragonal CIS unit cell consisting of 16 atoms and expanding it to a √2 × √2 × 1 CIS supercell containing 32 atoms. The chalcopyrite-based CuIn5Se8 is formed via the removal of four Cu atoms from the original CIS supercell (V′Cu in Figure 1) and via the substitution of two Cu atoms with In, which will then be sitting on Cu sites forming InCu anti-sites. The tetragonal unit cell of the C
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In−Se bond distances RCu−Se and RIn−Se are 2.53 and 2.76 Å, respectively. All these parameters are in good agreement with the theoretical data presented in the literature.17−20,22,41 The experimentally42 determined cell parameters a = 5.78 Å and c = 11.61 Å are somewhat shorter compared to our computed values. On the basis of the energies of the native elemental phases i. e., solid metallic Cu (face-centered cubic), solid In (bodycentered tetragonal), and Se (hexagonal phase with helical chains)we have computed a formation enthalpy ΔHf(CuInSe2) of 1.75 eV (0.44 eV/atom) for the solid chalcopyrite-type CIS. This is in reasonable agreement compared to the 1.97 eV reported by refs 21 and 40, and it is in perfect agreement with the 1.74 eV calculated in ref 13 with different pseudopotentials. For CuIn5Se8 the computed equilibrium cell parameters were a = 5.85 Å, c = 11.73 Å, and η = 1.002, respectively. These values are in good agreement with the experimental results43 of a = 5.71 Å and c = 11.62 Å, which show that in the case of CuIn5Se8 the cell shrinks a bit along a compared to CIS. Furthermore, in experimental studies it was found that η is slightly larger than 1.000; i.e., c is longer than 2a both for CIS and CuIn5Se8, and the value of η is quite similar for both compounds (see refs 12, 43, and 44 and references therein). For CuIn5Se8 we have computed a formation enthalpy of 7.20 eV (0.51 eV/atom), with respect to the mentioned elemental phases. As a last point, concerning structural features, we discuss the so-called anion displacement parameter u, defined as u = 0.25 − ((R2In−Se − R2Cu−Se)/a2), which describes the departure of Secentered tetrahedra from the regular tetrahedra of the zincblende structure. For the optimized CuInSe2 with the PBE functional we find a value of 0.219 (0.217 with VASP), which is somewhat smaller than the reported experimental values, between 0.22 and 0.235.45 This underestimation was previously shown45 to be correlated to the failure of the GGA to correctly describe the electronic properties of the material. Hybrid functionals predict values that are closer to experiment for CuInSe2.45,46 In agreement with those predictions, we find u = 0.226 with the HSE06 functional. In the case of CuIn5Se8 the situation is slightly more complex; we can calculate u only for tetrahedra centered on SeA atoms, having one Cu and two In neighbors. A bimodal distribution of u values appears, due to reduced symmetry, where the splitting of peaks is very small (
