Insights into Intrinsic Defects and the Incorporation of Na and K in the

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Insights into Intrinsic Defects and the Incorporation of Na and K in the CuZnSnSe Thin-Film Solar Cell Material from Hybrid-Functional Calculations 2

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Elaheh Ghorbani, Janos Kiss, Hossein Mirhosseini, Markus Schmidt, Johannes Windeln, Thomas D. Kuehne, and Claudia Felser J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11022 • Publication Date (Web): 06 Jan 2016 Downloaded from http://pubs.acs.org on January 11, 2016

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The Journal of Physical Chemistry

Insights Into Intrinsic Defects and the Incorporation of Na and K in the Cu2ZnSnSe4 Thin-Film Solar Cell Material from Hybrid-Functional Calculations Elaheh Ghorbani,†,‡ Janos Kiss,¶ Hossein Mirhosseini,∗,¶ Markus Schmidt,‡ Johannes Windeln,§ Thomas D. Kühne,k and Claudia Felser¶ †Institute of Inorganic and Analytical Chemistry, Johannes Gutenberg University of Mainz, Staudinger Weg 9, 55122 Mainz, Germany ‡IBM, Hechtsheimer Str. 2, 55131 Mainz, Germany ¶Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, 01187 Dresden, Germany §Wilhelm Büchner Hochschule, Ostendstraße 3, 64319 Pfungstadt, Germany kDepartment of Chemistry and Institute for Lightweight Design with Hybrid systems, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany E-mail: [email protected] Abstract We have performed density functional theory calculations using the HSE06 hybrid functional to investigate the energetics, atomic, and electronic structure of intrinsic defects as well as Na and K impurities in the kesterite structure of the Cu2 ZnSnSe4 (CZTSe) solar cell material. We found that both Na and K atoms prefer to be incorporated into this material as substitutional defects in the Cu sublattice. At this site

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highly stable (Na-Na), (K-K), and (Na-K) dumbbells can form. While Na interstitial defects are stable in CZTSe, the formation of K interstitial defects is unlikely. In general, the calculated formation energies for Na-related defects are always lower compared to their K-related counterparts. Based on thermodynamic charge transition level calculations we can conclude that the external defects are harmless except NaSn and KSn . These defects induce gap states that might be detrimental for the device performance. Keywords: CZTSe, Thin-film solar cell, Group-I dopant

Introduction The global energy demand is constantly on the rise. 17 If renewable-energy resources like solar cells are to make a significant contribution to this growing demand, they should be able to produce energy in the terawatt scale. However, current solar cells with high conversion efficiency such as single-crystal Si cells and thin-film solar cells based on CuIn1−x Gax Se2 (CIGSe) have natural limitations that prevent them reaching the terawatt production scale. Namely, for CIGSe, with the world record efficiency of 21.7%, 13,19 the low attainability and high expense of In and Ga make the large-scale production of CIGSe-based cells unpractical. For the manufacturing of single-crystal Si cells, tremendous amount of energy and natural resources are needed as well. 2 Hence, in recent years there is a constantly growing interest and ongoing scientific discussion to look for alternative photovoltaic materials containing earth-abundant elements. A promising alternative to the CIGSe ternary compound is quaternary CZTSe. Instead of In and Ga, CZTSe contains zinc (Zn) and tin (Sn) that are earth-abundant, inexpensive, and non-toxic elements. Although so far CZTSe-based solar cells are not as efficient as CIGSe-based solar cells, the conversion efficiency of 12.6% for CZTSe-based devices 37 shows a great potential of CZTSe. To further boost the efficiency of CZTSe cells, it is crucial to understand the effects of various defects on this material. By widening our knowledge about the defect physics, we can assess which defects are detrimental for the performance of the 2


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cell, so that the formation of such harmful defects could be prevented during the synthesis. For CIGSe cells it is already well established that the incorporation of a small amount of Na improves the p-type conductivity and conversion efficiency. 32,38 It was commonly accepted that doping with Na is the best choice for improving the performance of CIGSe cells. However, very recently it was found that K impurities also have a benign effect on the CIGSe-device performance. 7,33,34,39 In addition to the diffusion of Na and K from the soda-lime glass substrate into CIGSe, alkaline metals can be incorporated into the absorber layers via the so-called post deposition treatment (PDT). During the PDT a small amount of NaF and/or KF salt is deposited onto the CIGSe layer after its growth has been finished. The PDT unveiled the remarkable role of K in improving the quality of the pn-junction by reducing the electron-hole recombination at the CdS/CIGSe interface. 7,31 Also, the PDT with additional KF shortens the deposition period of CdS, which results in a thinner CdS buffer layer without weakening the cell performance. 7,9,35 Due to the structural similarity between CIGSe and CZTSe (see Fig. 1) one expects that the conclusions obtained from vastly investigated CIGSe devices can also be transferred to CZTSe cells. Considering these regards, one expects that sodium and potassium play a favorable role in solar cells based on CZTSe as well. Therefore, in this work we study the formation energies of Na and K impurities in kesterite CZTSe 5 via hybrid functional calculations. Based on our results, we discuss the structure and energetics of the most likely and unlikely positions in CZTSe for the incorporation of Na and K extrinsic defects. Beside the Na and K point defects, we have also investigated the formation of defect complexes, such as (Na-Na), (Na-K) and (K-K) dumbbells.

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Computational methodology Computational details In the present work, all calculations have been performed within the framework of density functional theory (DFT), using the VASP 22,23 code. We employed the projector augmented wave method 4,24 with a plane-wave cut-off energy of 400 eV. The exchange-correlation potential has been treated with the HSE06 hybrid functional, 16 which provides a rather good description of the formation energies, atomic and electronic structure of semiconductors. There is a recent theoretical work 27 that tackles the issue of Li, Na and K extrinsic defects in CZTSe via GGA (PBE) calculations. 30 It is known that GGA functionals severely underestimate the band gap of CZTSe. The results achieved by PBE, therefore, are affected by the shortcomings of this functional. Regarding the experimental band gap of CZTSe, there are different values published in the literature. The discrepancy between the values are either due to the different methods that have been used to determine the gap or due to the sample preparation, i. e. samples might contain secondary phases like ZnSe and Cu2 SnSe3 . 1 One group of experimental studies reports a direct band gap in the range of 1.4-1.6 eV for CZTSe. 3,20,26,28 Other works report an experimental gap in the order of 0.8-1.0 eV. 1,10,14 In our work, the contribution of the

Cu

In, Ga

Se

Sn

Zn

Figure 1: Comparison between the conventional tetragonal unit cell of CIGSe in the chalcopyrite structure (left panel) and CZTSe in the kesterite structure (right panel). 4


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Hartree-Fock exchange in HSE06 calculations has been set to 27%, so that the calculated band gap of 1.0 eV is in good agreement with the latter experimental findings and previous HSE06 hybrid functional calculations 5 The fully ordered crystal structure of the conventional tetragonal cell of CZTSe is shown in Fig. 1. From experimental works it is established that there is intermixing between Cu and Zn atoms in CZTSe. 8 In our calculations, however, we have used the fully ordered structure, in which this disorder was not taken into account. The CZTSe bulk was represented by employing a large 216-atom supercell built based on the primitive cell. In these supercells a point defect is separated by about 21 Å from its own periodic replica within periodic boundary conditions. The Brillouin zone integration was performed on a Γ-centered 2×2×2 mesh of k-points. To calculate the atomic and electronic structure of various defects, first we have relaxed the atomic positions and equilibrium volume of the defect-free CZTSe bulk. The formation energies of the point defects and impurities have been calculated using the theoretically obtained equilibrium volume for the bulk. In all calculations convergence was assumed when the largest residual force component dropped below 0.1 eV/Å. The calculated a = 5.73 Å, c = 11.42 Å cell parameters, tetragonal elongation η= c/2a= 0.996 and band gap of Eg = 1.0 eV are in good agreement with the experimental results. 11

Formation energy calculation Defect formation energies are calculated via the supercell approach. In this approach defects are surrounded by a large number of CZTSe atoms, and the whole cell is repeated periodically. 36 The intrinsic point defects were created by removing a Cu, Zn, Sn or Se atom. The Na and K substitutional defects were created when an atom on one atomic site was substituted by a Na or a K impurity. The interstitial defects were created by placing one impurity atom on an interstitial site.

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The defect formation energies are calculated as q Ef [dq ] = E[dq ] − E[p] + Ecorr

(1)

− Σi ni µi + q[EVBM + µe + ∆v0/b ], where dq stands for a defect in charge state q. E[dq ] denotes the total energy of the supercell containing the impurity or defect d and E[p] is the total energy of the pure defect-free charge neutral bulk CZTSe. ni represents the number of atoms of type i (host atoms or impurity atoms) that have been added to (ni > 0) (like Na and K) or removed from (ni < 0) (like Cu, Zn, Sn and Se) the supercell when a defect or an impurity was created, and µi is the equivalent chemical potential of the elements in their native elemental state. EVBM is the valence band maximum (VBM) of the defect-free bulk and µe represents the position of the Fermi energy relative to EVBM . The thermodynamic charge transition levels ǫd (q/q′) were computed as the Fermi energy in Eq. 1 at which the charge state of defect d transforms from q to q′. Due to the finite-size of the supercells the formation energies are corrected by two terms: q q∆v0/b and Ecorr , where ∆v0/b is the difference between the average electrostatic potential of q the bulk and the supercell containing the associated neutral defect. 21 Ecorr accounts for the

interaction of a charged defect with its periodic replicas. In the current work we used the q approach proposed by Lany and Zunger 25 to calculate Ecorr .

RESULTS and DISCUSSION Intrinsic defects in CZTSe The removal of a Cu, Zn, Sn or Se atom from the CZTSe lattice creates intrinsic point defects. The formation of such defects in CZTSe and the isostructural sulfide compound (Cu2 ZnSnS4 ) have been studied. 6,15 In agreement with the aforementioned work, 6 our results show that

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among intrinsic point defects in CZTSe the copper vacancy VCu has the lowest formation energy for the whole range of the chemical potential of the electrons, i. e. under both p- and n-type conditions (see Fig. 2). By computing the thermodynamic charge transition levels, we found that the only stable charge state for VCu is -1, i. e. this vacancy does not induce any defect level within the band gap and is not detrimental for the carrier transport in CZTSe. In contrast to VCu , the tin vacancy VSn creates three levels: ǫ(-2/-) at EVBM +0.08 eV, ǫ(-3/-2) at EVBM +0.27 eV, and ǫ(-4/-3) at EVBM +0.7 eV. As it is shown in Fig. 2, the formation energy of VSn falls rapidly by increasing µe , i. e. when CZTSe becomes n-type. Considering that VSn has the highest formation energy among native vacancies (4.21 eV for charge state -1 at the VBM), such defects should have a negligible concentration in a p-type CZTSe material. Although the creation of the ǫ(-4/-3) and ǫ(-3/-2) level of VSn could have negative impact on the efficiency of CZTSe thin-film solar cells, this detrimental effect is controlled by the conditions of the CZTSe deposition process, where films are grown p-type and the probability of the formation of Sn vacancies is low. The Zn vacancy VZn , similar to VCu , does not induce transition levels within the band gap. The formation energy of VZn is rather high compared to VCu but decreases by increasing µe (see Fig. 2). For the anion vacancy VSe we have calculated the formation energy of 1.91 eV for charge state +1 at the VBM. The presence of VSe in the material induces a charge transition level ǫ(0/+) which is located at EVBM +0.05 eV and is not detrimental for the carrier transport.

Formation energy of Na and K defects After investigating the intrinsic defects, now we turn our attention toward the discussion on the incorporation of Na and K impurities into CZTSe. To assess the relative stability of Na- and K-related defects, we have computed the formation energies of various defects in different charge states using Eq. 1. Interstitial and substitutional defects are formed by inserting Na and K into the CZTSe bulk and substituting the constituent atoms with Na 7



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and K, respectively. Our results are summarized in Fig. 3 that shows the formation energies as a function of the chemical potential of the electrons µe . Na and K atoms can occupy two different interstitial positions with different chemical environments: a Na or K impurity in an interstitial position is either octahedrally coordinated (oc) by three Cu, two Sn, and one Zn cations (see the left panel in Fig. 4), or tetrahedrally coordinated (tc) by two Cu, one Sn, and one Zn atom (as shown in the right panel of Fig. 4). Our results reveal that for both Na and K impurities, it is energetically more preferable to be located in the tc position rather than in the oc site. For Na impurities in CuInSe2 similar results have been found. 12,29 Both Na and K interstitials have the charge state +1 over the whole range of µe . In p-type CZTSe the respective formation energy for Na+ oc and Na+ tc are -1.14 eV and -1.41 eV, so they are both likely to form. Conversely, due to the larger + size of the K impurity, K+ oc and Ktc interstitials have considerably high formation energies

of 1.08 eV and 0.57 eV, respectively. This suggests that in contrast to Na, K interstitials are highly unlikely to be formed in CZTSe. Next, we have studied the formation of Na and K substitutional defects. On the basis of our results we can state that both Na and K prefer to be incorporated into CZTSe in the

Figure 2: The calculated formation energies of native vacancies in Cu2 ZnSnSe4 as a function of the chemical potential of the electrons µe , where the left (µe =0) and right side (µe =1.0 eV) of the figure corresponds to p-type and n-type conditions, respectively. The positive and negative numbers next to the lines indicate the charge state.

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copper sublattice as Na0Cu and K0Cu substitutional defect. The defects are charge neutral, since both Na and K are monovalent, and they are substituting a monovalent Cu atom. For Na0Cu and K0Cu , our computed formation energies are -1.56 eV and -0.23 eV, respectively. The negative formation energies of these defects indicate that at low concentrations it is energetically favorable to incorporate Na and K impurities into VCu defects. Moreover, since the formation energy of Na0Cu is more than 1.3 eV lower than K0Cu , if a Cu site is already occupied by Na, then K most likely cannot kick out Na to take its place. For the CuInSe2 light absorber we have obtained qualitatively similar results. 12 Given the high formation energy of 1.58 eV for K− Zn , the formation of a K substitutional defect in a Zn position is not likely. In contrast to K, the formation energy of 0.34 eV computed for Na− Zn suggests that such substitutional defects might form. The Sn-related

Figure 3: The calculated formation energies of Na- and K-related defects in Cu2 ZnSnSe4 as a function of the chemical potential of the electrons µe . 9



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Figure 4: Atomic structure showing the local coordination of octahedrally coordinated interstitial (left panel) and tetrahedrally coordinated interstitial (right panel). The Na or K interstitial atom is represented by a red sphere, and for the rest of the atoms the same color scheme has been used as in Fig. 1. For clarity, only half of the conventional tetragonal cell is shown. defects can have a wide range of stable charge states and their formation energy drops rapidly as µe increases. Since the light absorber layers are grown under p-type conditions, the role of NaSn and KSn should be negligible in the films used for actual solar cells. Regarding the Se site, our data shows that Na and K-related substitutional defects at the Se site in CZTSe have similar formation energies computed for substitutional defects in the CuInSe2 thin film solar cell material. 12,29 The qualitatively and quantitatively similar results clearly show that Se-related substitutional defects are energetically rather unfavorable both in CZTSe and CuInSe2 . In addition to the point defects, we have also looked into the formation of three types of dumbbells in CZTSe, namely (Na-Na), (Na-K) and (K-K) dumbbells in a copper site. + + Our data presented in Fig. 3 show that the formation of (Na-Na)+ Cu , (Na-K)Cu , and (K-K)Cu

dumbbells with the respective formation energies of -3.18 eV, -1.95 eV and -0.66 eV is highly probable in CZTSe, similar to CuInSe2 . 12,29 The (Na-Na) dumbbells are the most stable defects over the whole range of the chemical potential of the electrons µe . For (Na-K) and (K-K) as the system becomes more n-type, the Na0Cu and K0Cu substitutional defects will become more stable. Comparing the formation energies of a (Na-Na)+ Cu dumbbell (-3.18 eV) with two Na in two distinct and spatially well-separated copper positions (-2.84 eV) unveils that for the p-type system it is more favorable to cluster two Na atoms together, probably to lower the strain in the material. A comparison between the formation energy of a (K-K)+ Cu dumbbell and two 10


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KCu point defects reveals that K atoms behave in the same way as Na: K impurities also have the preference to form dumbbells instead of occupying two distinct substitutional Cu positions. Concerning the charge state of the Na- and K-related defects, as one would expect, 3− acceptor defects such as Na− Zn and NaSn form more easily in a n-type material, where µe is

at the CBM. Conversely, donor defects such as Na+ tc form more easily in a p-type material where µe is at the VBM. We note in passing, that regarding the most stable charge state of dumbbells, we found a qualitative difference between CuInSe2 and CZTSe. Namely, while in the former compound dumbbells with the charge state +2 are stable 12 at the VBM, in CZTSe the +1 charged dumbbells are stable for the whole range of µe .

Band structure and thermodynamic charge transition levels In this section we discuss the effect of defects upon the electronic structure of CZTSe. Since the band structure calculations with hybrid functionals are computationally extremely demanding, these calculations have been performed for a smaller 64-atom supercell employing the same methodology as described in the computational details. Fig. 5 shows the band structure of the defect-free CZTSe bulk and native defects. While the Sn vacancy creates a gap state, other intrinsic defects induce no gap state. The charge transition level calculations for the large 216-atom supercell show that Se and Sn vacancies create gap states but Cu and Zn vacancies do not induce gap states. We note in passing that the discrepancy between band structure calculations and charge transition levels can have several origins. One reason is the difference between the supercell sizes. Band structure calculations are performed for 64-atom supercells, where there is a considerable interaction between a defect and its periodic replica. For comparison, the charge transition levels are calculated for supercells with 216 atoms. The other reason has to do with the position of the orbitals that might be placed wrong by DFT. 18 3− 3− − Fig. 6 depicts the band structures calculated for the Na0Cu , K0Cu , Na− Zn , KZn , NaSn , KSn ,

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2 1 0 -1 -2 Z

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XZ

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Γ

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Γ

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Figure 5: Band structure for the bulk CZTSe and native defects in CZTSe. The occupied bands are drawn in black and the unoccupied band are shown in blue. The red dashed line represents the defect level. The dotted lines indicate the position of the Γ point in the Brillouin zone. 0

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Figure 6: Band structure for Na- and K-related defects in CZTSe. + + − Na− Se , KSe , Natc and Ktc defects. The band structures show that NaSe and KSe together with

NaSn and KSn are responsible for introducing a defect level within the band gap. However, we have to mention that due to the high formation energy of such defects, we expect that Na and K impurities in Se and Sn substitutional positions play a negligible role in the efficiency of solar cells based on CZTSe. The charge transition levels calculated for the large 216-atom supercell reveal that only Sn-related defects have transition level located close to the middle of the band gap. Therefore, they could act as a trap for carriers in CZTSe and become detrimental for the device performance. NaSn exhibit three transition levels: the ǫ(0/-) level around EVBM +0.17 eV, the (-/-2) 12


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level close to EVBM +0.55 eV that is a deep level, and the (-2/-3) level near EVBM +0.87 eV. KSn also shows three transition levels within the band gap: (0/-), (-/-2) and (-2/-3) which are located at EVBM +0.39 eV, EVBM +0.45 eV and EVBM +0.9 eV, respectively. Other Na- and K-related defects do not show any charge transition levels and therefore they do not act as carrier traps.

SUMMARY AND CONCLUSIONS We have carried out hybrid functional computations on native point defects as well as Na and K extrinsic defects in several substitutional and interstitial positions in CZTSe. According to our results the most favourable way to incorporate Na and K impurities is to form substitutional defects in the copper sublattice, similar to the CuInSe2 . The incorporation of Na in a tetrahedrally coordinated interstitial site is also highly probable, whereas the formation of K interstitials is not very likely, which can be understood due to the large size of the K impurity. Comparing the formation energies of two Na in two separate Cu sites with a (Na-Na) dumbbell in a Cu site reveals that Na atoms prefer to assemble as dumbbells in this site. The formation energy of (Na-Na) dumbbell in a Cu site is -3.18 eV, so such dumbbells are highly stable. Similarly, K atoms prefer to assemble as (K-K) dumbbells in Cu sites with a formation energy of -0.66 eV. If CZTSe is exposed to both Na and K simultaneously, then under p-type conditions (Na-K) mixed dumbbells can be formed as well. As a general remark, the formation energy of Na-related defects is always lower than their respective K-related counterparts in all studied substitutional and interstitial sites. Therefore, it is unlikely that K atoms replace Na from those sites that are already occupied by Na. Also, one has to keep in mind that most of the time Na diffuses out from the sodalime glass into CZTSe and K is incorporated into CZTSe via the PDT after the growth of the absorber. From the thermodynamic charge transition level calculations we can conclude that all Sn

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and Se vacancies create charge transition levels. While The gap state induced by Se vacancies is harmless for the carrier transport, the gap states created by Sn vacancies might be detrimental. The NaSn and KSn defects introduce transition levels within the band gap that might be detrimental for the device performance. Other extrinsic defects do not introduce gap levels.

Acknowledgment Financial support is gratefully acknowledged from the German Bundesministerium für Wirtschaft und Energie (BMWi) for the comCIGS II project (0325448C). E.Gh. would like to acknowledge IBM for the work proposal and for the provided computing resources.

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Insights into Intrinsic Defects and the Incorporation of Na and K in the

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