Diffusion of Alkali Metals in Polycrystalline CuInSe2 and Their Role in

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Alkali Metals Diffusion in Polycrystalline CuInSe and Their Role in the Passivation of Grain Boundaries Manjusha Chugh, Thomas D. Kuehne, and Hossein Mirhosseini ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b02158 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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ACS Applied Materials & Interfaces

Alkali Metals Diffusion in Polycrystalline CuInSe2 and Their Role in the Passivation of Grain Boundaries Manjusha Chugh, Thomas D. Kühne, and Hossein Mirhosseini ∗ Dynamics of Condensed Matter and Center for Sustainable Systems Design, Chair of Theoretical Chemistry, University of Paderborn, Warburger Str. 100, D–33098 Paderborn, Germany E-mail: [email protected]

Abstract

Keywords

The behavior of alkali-atom point defects in polycrystalline CuInSe2 is studied. In this work, three grain boundary models, one coherent twin boundary and two twin boundaries with dislocation cores, are considered. Total energy calculations show that all alkali metals tend to segregate at the grain boundaries. In addition, the segregation of alkali atoms is more pronounced at the grain boundaries with the dislocation cores. The diffusion of alkali metals along and near grain boundaries are studied as well. The results show that the diffusion of alkali atoms along the grain boundary models is faster than within the bulk. In addition, the ion-exchange between Na and Rb atoms at the grain boundaries leads to the Rb enrichment at the grain boundaries and the increase of the Na concentration in the bulk. While the effects of Na and Rb point defects on the electronic structure of the grain boundary with the anion-core dislocation are similar, Rb atoms passivate the grain boundary with the cation-core dislocation more effectively than Na. This can explain the further improvement of the solar cell performance after the RbF-post-deposition treatment.

thin-film solar cells, CuInSe2 absorber, grain boundary passivation, diffusion mechanisms

Introduction Incorporation of alkali metals (AM) into the Cu(In,Ga)Se2 (CIGSe) absorber can improve the solar cell performance by increasing carrier concentration and carrier mobility. 1–5 While the former is related to the effect of alkali atoms on the grain interior (GI) properties, 6–9 the latter has to do with the enhancement of the electronic structure of interfaces and grain boundaries (GBs) in a cell. 10–16 Different mechanisms were proposed to explain how Na atoms increase the carrier concentration in the absorber layer. 5,6,11,17,18 This topic has been discussed for a long time and is still under debate. Heavier AM atoms (K, Rb, and Cs) are found to further improve the efficiency of the solar cell. 19–24 The efficiency of solar cells is increased up to 21.7%, 22.6%, and 22.9% by KF-PDT, RbF-PDT, and CsF-PDT, respectively (PDT stands for postdeposition treatment). 23–25 Along with the conductivity enhancement of the absorber, AM atoms affect the microstructure of CIGSe thin films. Some studies have reported that the grain size of CIGSe increases with the increase of the Na concentration 26

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while some studies do not support this observation. 9 In fact, the increase or decrease in the grain size with respect to the Na concentration depends on the growth conditions of CIGSe and Na doping process. 27 Recently, Ishizuka et al. have reported the decrease in the CIGSe grain size with an improved texture of CIGSe films with the increase in the Na concentration. 27 The grain size does not seem to have a major impact on the efficiency of solar cells. 28 While Na atoms mainly affect the bulk microstructure (the grain size, the surface smoothness of the grains, the Ga/In ratio), other AM atoms like K and Rb mainly affect the surface of CIGSe. 8 The PDT with K and Rb leads to the formation of secondary phases at the surface as well as the diffusion of these atoms into the CIGSe layer, hereby decreasing the concentration of Na. 19,22 Both K and Rb allow a reduction of the CdS buffer layer thickness, hence improving the p-n junction quality. The efficiency of polycrystalline CIGSe solar cells is higher than that of their single crystal counterparts. Apparently, GBs are not detrimental to the carrier mobility in CIGSe. 29 This is in contrast to the Si- and GaAs-based solar cells where GBs act as recombination centers for the light-generated charge carriers. 30,31 Many efforts have been made to understand the electrically benign behavior of the GBs in polycrystalline CIGSe, CuInSe2 (CISe), and CuGaSe2 (CGSe). 12,29,32–38 Ab-initio results showed that the formation of GBs in these materials could be harmful for the carrier mobility because of the dangling, wrong, and extra bonds of atoms at the GBs. 12,39,40 These harmful gap states, however, were removed from the band gap by the presence of intrinsic (selfpassivation) or extrinsic defects at the GBs. 12,40 The ab-initio studies employed mainly semilocal functionals such as GGA or GGA+U to calculate the band structures of the GBs. These functionals underestimate the anion displacement in CISe and poorly describes the semiconducting nature of CISe. 39 We have employed the screened hybrid functional (HSE) 41 to calculate the electronic properties of our GB models. Further, we have considered sufficiently large supercells in order to avoid wrong bonds

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at the periodic boundary planes which was not considered in earlier studies. 12,39 To improve the efficiency of the solar cells, a deep insight into the underlying physics of the GB passivation mechanisms is needed. In the present study, we have systematically investigated the effects of AM atoms (Li, Na, K, and Rb) point defects on the electronic properties of the GBs in CISe. This comprehensive study provides an understanding of the effect of chemical nature and size of AM atoms on the formation of AM point defects at the GBs as well as on the electronic properties of the GBs. In addition, we have extensively studied the diffusion mechanisms of AM atoms along and near the GBs. Our results can explain the ionexchange mechanism at the GBs, where heavier alkali atoms replace the lighter ones. The change in the electronic structure of GBs in the presence of heavy alkali metals explains the further enhancement of the solar cell efficiency after the PDT.

Methodology Grain Boundary Models Various types of GBs exist in a polycrystalline CISe layer. 14,42 A GB can be categorized according to the misorientation between the two adjoining grains and the relative orientation of the boundary plane with respect to the grains orientation. 43–45 In this work, three GB models have been considered. The first model is a twin boundary (TB) made up of a cation-containing (112) plane facing an anion-containing (112) plane. We label this GB model as Σ3(112) throughout our work. The structure of this GB has been determined experimentally using high-resolution scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS). 46 The atomic structure of the Σ3(112) GB is very similar to the bulk CISe except for the wrong cation-anion bonds at the GB. These GBs do not have any dangling bonds and are charge neutral. 36,42,46 The other two GB models considered here are made up of the interface between the {114}


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˚. Brilon each atom was less than 0.05 eV/A louin zone integrations were performed using a Monkhorst-Pack set of k-points. 55 K-point meshes of 10×6×1 and 5×1×1 were used for the supercell containing the Σ3(112) GB and Σ3(114) GB, respectively. Since semilocal functionals tend to underestimate the band gap of CISe, the screened hybrid functional (HSE) 41 was used to calculate the electronic properties of the GBs. A dense k-point mesh was employed for the band structures and density of states (DOS) calculations. In this work, formation energy of a point defect is calculated as X bulk α − − Etot ni (µi + ∆µi ) (1) Ef = Etot

planes. Such GBs have dislocation cores at the interface of the two grains. We refer to these GB models as Σ3(114)-I, which contains anioncore dislocation with mainly anions dangling bonds and Σ3(114)-II, which contains cationcore dislocation with mainly cations dangling bonds. Compared to Σ3(112) GBs, Σ3(114) GBs have a lower symmetry and are expected to accommodate point defects owing to the presence of voids and dislocation cores. 14,42 These models have been used to study the GBs properties in CISe, CGSe, and Cu2 ZnSnSe4 . 12,35,39,47 It should be mentioned that Σ3(114) GB models are adopted from the GB structures in CdTe, which has a similar atomic structure as CISe. 35,40,48,49 It is to be noted that in cubic systems, Σ3(112) and Σ3(114) TBs are referred to as coherent and incoherent TBs, having {111} and {112} interface planes (Σ3(111) and Σ3(112) TBs), respectively. 43–45 The supercells used in our calculations contain 16, 25, and 24 atomic layers to model our Σ3(112), Σ3(114)-I and Σ3(114)-II GBs, respectively. The atomic positions of the outer 4 atomic layers were kept fixed at their bulk positions to mimic the bulk material. All other atoms were allowed to relax during the geometry optimization. The dangling bonds at the surface of the slabs were passivated by pseudohydrogens of fractional charges to avoid any charge transfer in the slabs. 50 The model structures of the Σ3(112), Σ3(114)-I and Σ3(114)-II GBs are shown in Fig. 1.

i α where Etot is the total energy of a supercell bulk containing a defect α, Etot is the total energy of the corresponding defect-free supercell, ni is the number of atoms of type i which are added to/removed from the perfect supercell. µi is the chemical potential of the element of type i in its native elemental phase, and ∆µi is the thermodynamic limit of the chemical potential. The defect formation energies were calculated taking two limits on the chemical potential of the elements into account. That is, when the elements are in their elemental phase (µi ) and when the chemical potentials are thermodynamically limited (µi + ∆µi ) to avoid the formation of the secondary phases. In the former case, the formation energy denotes the energy needed for accommodating a defect in the lattice. In the latter case, the thermodynamic limits of the chemical potentials were computed by determining the stability region for all competing structures with respect to the reference structure. It should be mentioned that in this limit, equilibrium conditions are assumed which are barely achieved during the growth and the PDT processes. The saddle points for migration paths were identified by performing climbing image nudged elastic band (CI-NEB) calculations 56 The migration barrier Em indicates the energy difference between the initial (final) configuration and the saddle point. For some paths, the ini-

Computational Details All calculations were performed within the framework of density functional theory (DFT) using the Vienna Ab-initio Simulation Package (VASP). 51 The Projector augmented wave (PAW) method was used to describe electronion interactions. 52,53 The plane-wave cutoff energy was set to 350 eV. For the geometry optimization and formation energy calculations, Hubbard-corrected DFT calculations with a Hubbard on-site interaction parameter of U = 5.0 eV (applied to the Cu 3d orbitals) were performed. 54 The atomic structures were considered to be optimized when the residual force


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Figure 1: Atomic structures of the Σ3(112), Σ3(114)-I, and Σ3(114)-II GBs. Cu- and Insubsitutional sites considered as defect sites for alkali metals are labeled. Interstitial defect sites are shown as dashed circles. Cu, In, and Se atoms are shown as cyan, brown, and yellow colored spheres, respectively. tial atomic configuration relaxed to the final atomic configuration. For these diffusion paths the migration barriers were estimated by the energy difference between the initial and final atomic configurations.

next to this GB. These results are in line with the results of Saniz et al. for Na atom point defects at the Σ3(112) GB. 13 There is a relatively large difference beTable 1: Calculated formation energies for AM point defects in the bulk∗ and at the GBs under Cu-poor and AM-rich conditions. The formation energies are calculated at the valence band maximum.

Results and Discussion Formation of Alkali Atoms Point Defects

Defect

Three types of point defects, namely, Cusubstitutional, In-substitutional, and interstitial defects are considered. The defect sites for the Σ3(112) and Σ3(114) GBs are shown in Fig. 1. The formation energies of interstitial and the most stable substitutional defects under Cu-poor and AM-rich conditions are tabulated in Table 1 (see also Table S1 in the Supporting Information (SI)). Few interpretations can be made from the calculated formation energies. Similar to the bulk, the most stable substitutional defect at the Σ3(112) GB is the Cu-substitutional (AMCu ) defect. In addition, the formation energy of all point defects at this GB increases by increasing the size of alkali atoms. Although the atomic structure of this GB is very similar to the CISe bulk, there is a tendency for AMs to segregate

LiCu LiIn Lii NaCu NaIn Nai KCu KIn Ki RbCu RbIn Rbi ∗

Formation energy (eV) (114)-I (114)-II (112) Bulk∗ -2.28 -2.25 -2.31 -2.28 -3.02 -2.04 -1.61 -1.38 -1.42 -1.43 -0.58 -0.35 -2.17 -1.89 -1.70 -1.61 -2.71 -1.86 -1.12 -0.85 -1.25 -1.57 -0.21 0.32 -2.43 -1.65 -0.98 -0.80 -1.87 -∗∗ -0.58 -0.26 -1.41 -2.01 0.66 -∗∗ -2.28 -1.58 -0.60 -0.40 ∗∗ -1.63 -0.68 -0.30 -1.14 -1.82 1.22 -∗∗

A supercell formed by (112) planes is considered as the bulk reference. ∗∗ No stable atomic configuration was found.


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tween the formation energies of Cu-, and Insubstitutional defects in the bulk and at the Σ3(114) GBs. The difference between the formation energies of the interstitial defects in the bulk and at the Σ3(114) GBs is even more pronounced. These results indicate that, independent of the GB models and the size of the AM atoms, all AM atoms tend to segregate at the GBs in CISe. The preferential segregation of the AM atoms at GBs has been observed experimentally using atom probe tomography (APT) technique and by secondary ion mass spectrometry (SIMS) profiles. 19,57–60 From Table 1, one can see that the point defects are more pronounced at the Σ3(114) GBs than at the Σ3(112) GB. That means that the AM atoms segregate more at the GBs with intrinsic structural defects like voids and dislocation cores (see also Table S4 of the SI for segregation energy of AM point defects). The segregation of alkali metals near low-symmetric GBs like the Σ3(114) GBs could be due to the fact that these GBs are charged and thus can attract charged AM point defects. 14,36,37,42,46 Our results show that Rb atoms have a high tendency to segregate next to the GBs. The RbCu defect is more stable than the NaCu defect at the Σ3(114)-I GB and Rbi is more stable than the Nai defect at the Σ3(114)-II GB. More importantly, the difference between the formation energies of Rb point defects in the bulk and at the Σ3(114) GBs is larger than the corresponding energy difference for Na point defects. This trend was also observed experimentally using APT measurements and SIMS profiles. 18,60 Recently, Clemente et al. 60 observed that after the RbF-PDT of the samples grown on sodalime glass (SLG) substrates, the concentration of Rb atoms at the GBs is higher than that of Na, whereas the concentration of Rb in the grain is below the detection limit. K was found to have almost the same effect as Rb on the solar cell performance except that the short-circuit current is lower for KF-PDT treated samples as compared to those treated with the RbF-PDT. 22,24 K and Rb both were found to form Cu-poor secondary phases at the CIGSe surface and improve the p-n junction quality of the CdS/CIGSe interface. From

our formation energy calculations (Table 1), we can see that the formation energies of K and Rb defects at the Σ3(114) GBs are comparable. Hence, K is as prone to segregate at these GBs as Rb. However, the formation energies of K and Rb defects in the bulk are different. 61 Therefore, K can also be found in the GI of CISe, while the concentration of Rb in the GI is very small. 60 The effect of Li atoms on the solar cell performance is less studied as compared to those of Na, K, and Rb atoms. 62 Our calculations show that LiIn and Lii defects have low formation energies at the GBs as compared to the bulk, whereas the LiCu defect has a comparable formation energy at the GBs and in the bulk.

Diffusion of Alkali Atoms Along and Near GBs The diffusion of the AM atoms in the CISe bulk has been extensively studied. 11,61,63–65 In the CISe bulk, Cu-vacancy-mediated and interstitial diffusion mechanisms were suggested to be responsible for the AM atoms mass transport. In this work, we also considered these two mechanisms to study the diffusion of AM atoms. Further, we have divided our diffusion studies into two parts: the diffusion of AM atoms along GBs and the diffusion of AM atoms near GBs. The diffusion paths for the migration of alkali atoms along and near the Σ3(112) and Σ3(114)I GBs are shown in Figs. 2(a) and (b), respectively. The corresponding migration barriers for Na and Rb atoms are tabulated in Table 2 and Table 3. We note in passing that the diffusion barriers of AM atoms along the Σ3(114)II GB are similar to those along the Σ3(114)I. For convenience, the diffusion barriers of an atom jumping forward and backward from one site to another are labeled as the forward barrier (FB) and the reverse barrier (RB). For the diffusion near the GBs, the forward diffusion mechanism means the diffusion of an AM from the GB into the GI, whereas the reverse diffusion mechanism indicates the diffusion of an AM atom from the GI towards the GB. Our results show that the migration barriers for diffusion of Na atoms along the GBs are


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sion of Rb atoms along the Σ3(112) GB are smaller than those in the bulk (see values of M1 and M2 in Table 2). These results are in line with the findings of Wuerz et al. who observed that Rb atoms diffuse faster at the GBs (Em = 0.29 eV) as compared to the bulk (Em = 0.44 eV). 66 The diffusion of Rb atoms in the bulk is dependent on the availability of Cu vacancies 67 We explored the migration of Rb atoms in the Cu-depleted region close to the Σ3(114) GBs (see M8 in Fig. 2(b) and in Table 3) and the Σ3(112) GB. These migration paths have almost the same energy barriers as the diffusion of Rb atoms in the bulk. This suggests that the Rb diffusion can also happen in the Cu-poor regions close to the GBs where the presence of Cu vacancies facilitate the vacancy-mediated diffusion of the Rb atoms. 58 We note in passing that there can exist some other low-barrier migration mechanisms that cannot be modeled in our GBs since our GB models do not represent all kinds of GBs in the system. From the formation energy calculations (Table 1), we see that both Na and Rb can segregate at the GBs. Regarding the diffusion mechanisms near the GBs, our results show that the forward mechanisms (the diffusion from the GBs towards the GI) for Na have comparable energy barriers to the reverse mechanisms (diffusion from the GI into the GBs). Furthermore, the forward mechanisms for Rb atoms have larger energy barriers compared to the reverse mechanisms (see M3 in Table 2, and M5– M7 in Table 3). This indicates that Na atoms can jump back and forth between the lattice sites in the GI and at the GBs, whereas Rb can not easily diffuse from the GBs into the GI. The low formation energy and the high forward diffusion barriers (from GBs towards GI) of the Rb point defects make Rb atoms more prone to segregate at the GBs. Previously, the ion-exchange mechanism was proposed to explain the replacement of lighter AM atoms by the heavier ones in CIGSe after the PDT. 19,60,61 The Na-Rb ion-exchange mechanism is shown schematically in Fig. 3 and can be explained by our results as follows. In the GI, the formation energies of Rb point defects

Figure 2: Diffusion paths (Mi ) for AM atoms along the (a) Σ3(112) GB and (b) Σ3(114)-I GB. The paths (Mi ) are listed in Tables 2 and 3. Notice that the demarcation of the GB and GI is an approximate. smaller than the migration barriers for diffusion of Na in the bulk (the calculated migration barriers for Na in the bulk are 0.42 and 0.54 eV, respectively, for Cu-vacancy-mediated and interstitial diffusion mechanism) except for the interstitial diffusion (M1) along the Σ3(112) GB. That indicates that the diffusion of Na atoms along our GB models are faster than the diffusion of Na atoms in the bulk. Our findings are consistent with the experimental findings of Laemmle et al. who distinguished between the diffusion of Na along GBs and in the GI. 64 They observed that the Na diffusion along the GBs with the diffusion barrier of 0.21 eV is faster than the Na diffusion in the bulk with the diffusion barrier of 0.36 eV. The migration barriers for the diffusion of Rb atoms along the Σ3(114) GBs are larger than the migration barrier of the Cu-vacancymediated diffusion of Rb in the bulk (0.30 eV). Interestingly, the energy barriers for the diffu-


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Table 2: Calculated migration barriers (in eV) for Na and Rb along and near the Σ3(112) GB. The diffusion paths are shown in Fig. 2(a). Diffusion mechanism along and near Σ3(112) M1 : AMi → AMi M2 : AMCu1 → AMCu2 M3 : AMCu2 → AMCu3 M4 : AMCu3 → AMCu4

Na FB RB 0.90 0.85 0.16 0.27 0.45 0.33 0.35 0.35

Rb FB RB 0.33 0.10 0.13 0.15 0.54 0.27 0.38 0.65

Figure 3: Schematic diagram of the replacement of Na atoms by Rb atoms. (a) Na atoms are mostly segregated at the GBs. (b) After the RbF-PDT, Rb atoms replace Na atoms at the GBs, and push them into the GI.

Table 3: Calculated migration barriers (in eV) for Na and Rb along and near the Σ3(114)-I GB. The diffusion paths are shown in Fig. 2(b). Diffusion mechanism along Σ3(114)-I M1 : AMCu1 → AMCu3 M2 : AMCu1 → AMi M3 : AMi → AMCu3 Diffusion mechanism near Σ3(114)-I M4 : AMCu1 → AMCu M5 : AMCu2 → AMCu M6 : AMCu3 → AMCu M7 : AMCu → AMCu M8 : AMCu → AMCu

Na FB 0.12 0.26 0.00

RB 0.42 0.36 0.26∗ Na FB RB 0.16 0.58 0.31 0.36 0.20 0.06 0.26 0.39 0.33 0.33

Rb FB 0.00∗ 0.03 0.00

RB 1.33∗ 0.81 0.32∗ Rb FB RB 0.54 0.82 0.68 0.10 0.82 0.21 0.74 0.40 0.34 0.41

Table S2 and Table S3 of the SI, respectively. The bulk migration barriers for Li (K) atoms are 0.63 (0.18) eV and 0.64 (0.61) eV for the Cu-vacancy-mediated and the interstitial diffusion mechanisms, respectively. 61 Similar to Na, the diffusion of Li along the GBs is found to be faster than that in the bulk, whereas the behavior of K atoms is similar to Rb atoms. When a CIGSe layer is subjected to the RbFPDT, Rb atoms accumulate at the GBs, at the p-n junction, as well as at the interface between CIGSe and the Mo substrate. 68 This indicates the large mobility of Rb atoms diffusing from the surface of the absorber towards the Mo substrate. Similarly, Na atoms diffuse from the SLG substrate to the CIGSe surface. 57 Our calculations show that Na and Rb diffuse differently in the CISe layer. We observed Harrison type C diffusion 69 for Rb, meaning that Rb mainly diffuses along the GBs with very little diffusion of Rb from the GBs towards the GI. For Na, Harrison type B diffusion 69 is confirmed. That is, Na diffuse mainly along the GBs with the additional diffusion into the GI from the GBs.

∗

Estimated from the energy difference between the initial and final configurations.

are higher than Na point defects. Hence, the concentration of Rb defects is much less than Na defects. 60 At the GBs, on the other hand, the formation energies of Na and Rb defects are comparable and some Rb point defects are more stable than Na point defects (see Table 1). That means that Rb atoms can replace the Na at the GBs. The low energy barrier of Na atoms to migrate from GBs towards the GI makes it feasible that the Na atoms replaced by Rb atoms diffuse into the GI. Hence the concentration of Na in the GI is enhanced after the RbF-PDT. 60 The overall decrease in the Na concentration in the RbF-PDT treated CIGSe sample is probably the out-diffusion of Na either through the GI (bulk) or via the GBs towards the CIGSe surface. The diffusion barriers of Li and K atoms along the Σ3(112) and Σ3(114)-I GBs are tabulated in

Effect of Alkali Atoms on the Electronic Structure of the Grain Boundaries The highly symmetrical Σ3(112) GB does not affect the cathodoluminescence (CL) intensity


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considerably (hence lower recombination activity) and charged defects do not segregate at this GB. 14,29,42 We have shown previously that the formation of the Σ3(112) GB merely modifies the band alignment between the bulk and the GB. 39 Thus, this GB is not expected to affect the CIGSe solar cell performance considerably. 14,46 On the other hand, the Σ3(114) GBs create gap states and modify the band alignment between the bulk and the GBs. 39 Here we have performed HSE calculations for Σ3(114) GBs to study the electronic structures of these GB models in the presence of alkali atoms. The calculated partial/atom projected DOS for the AM-free Σ3(114)-I and Σ3(114)-II GBs are shown in Figs. 4(a) and (b). Considering the AM-free Σ3(114)-I GB, the Se1-Se10 wrong bond (dSe1−Se10 =2.57 ˚ A) gives rise to deep gap states, as it is shown in Fig. 4(a). These gap states act as recombination centers and are detrimental to the conductivity of CISe. Se2 and Se20 dangling bonds and Cu3-In1 wrong bond (dCu3−In1 =2.61 ˚ A) give rise to states which are spanned 0.5 eV above the valence band maximum (VBM). Our results indicate that in this GB model, anionanion wrong bonds, cation-cation wrong bonds, and dangling bonds create gap states that can be detrimental to the carrier mobility. Our results for the Σ3(114)-I GB qualitatively match with those of reference 15. Likewise, it has been shown that gap states arise due to the formation of a similar GB in polycrystalline CdTe. 40,70 We now examine the changes in the electronic structure of the Σ3(114)-I GB in the presence of AM atoms. Since the Cu3 site at the Σ3(114)-I GB is the most favorable site for AM atoms, we have calculated the DOS for all AM atoms at this site. By substituting Cu3 by AM atom the bond between the AM atom and In1 weakens. As an example, the distance between KCu3 and In1 is 3.90 ˚ A while the Cu3-In1 bond length was 2.61 ˚ A. Weakening of this bond shifts the gap states towards the VBM which is beneficial for the carrier mobility since the gap states become shallower (see Fig. 5(a)). In this GB model, In sites can be occupied by lighter alkali atoms. By substituting In1 by Na, the states arising from the Cu3-In1 wrong

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bonds are completely removed from the band gap. The distance between Cu3 and NaIn1 is 4.13 ˚ A. This indicates that by replacing one of the cations having wrong bonds by an AM atom (wrong-bond breaking), the gap states move toward the VBM or merge with the bulk continuum. It should be noted that the anionoriginated gap states are not affected by the Cu- and In-subsitutional defects (Fig. 5(a)). The AM atoms at the interstitial site have no beneficial effects on the electronic structure of the Σ3(114)-I GB (see Figs. S1(e), and S1(f) in the SI). Although the presence of AM increases the distance between Se1 and Se10 atoms (thus reducing the charge density between these Se atoms), these states remain in the gap. The probable reason for the presence of the Se-4p states in the band gap is the weak hybridization between AM-s orbitals and Se-4p orbitals. As a test, we calculated the DOS for the Cu interstitial defect at this GB model (not shown here). Because of the significant hybridization between Cu-3d and Se-4p orbitals, the gap states originated from the anion-anion (Se1Se10 ) wrong bond are completely removed from the band gap. Similarly, the gap states arising from wrong Te-Te bonds in the Σ3(112) GBs in CdTe are removed when Cd interstitial defects form at this GB. 70 It was shown by Yin et al. 12 that other intrinsic defects like CuIn can also passivate this GB model (self passivation). Let us now examine the electronic structure of the Σ3(114)-II GB. The calculated DOS for the AM-free Σ3(114)-II GB is shown in Fig. 4(b). Although In1-In10 dimers (dIn1−In10 =2.70 ˚ A) are present at this GB, these do not give rise to any state in the band gap. These states are in the bulk continuum near to the VBM. The Cu2 and Cu20 atoms at this GB undergo a large relaxation during the geometry optimization (their hybridization changes from sp3 to sp2 as shown by Li et al. 47 ) and their states are also in the bulk continuum. Apparently, there is no gap state in the band gap of this GB model originated from the cations wrong and dangling bonds. On the other hand, the dangling bonds of Se atoms at the center of this GB (labeled as Sec in Fig. 4(b)) give rise to the deep gap states. A careful analysis shows that these gap


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like Rb. Heavier alkali atoms are not stable at the In sites of this GB model. For NaIn2 , we have calculated the DOS (see Fig. S2(b) in the SI) and found that this defect is not effective in passivating the Σ3(114)-II GB. The formation of NaIn2 , however, makes the deep gap states shallower (closer to the conduction band minimum (CBM)). The interstitial site at the Σ3(114)-II GB is the most favorable one for heavier AM atoms (see Table 1). All AMi defects compensate the dangling bonds of Sec atoms and make this GB electrically benign (see Figs. S2(c) to S2(f) in the SI). Interestingly, Rb at this interstitial position is more stable than Na. We also calculated the DOS for InCu3 and Cui intrinsic defects (not shown here) at the Σ3(114)-II GB. We found that the gap states are completely removed from the band gap. It can be concluded that the Σ3(114) GBs can be effectively passivated by AM defects and intrinsic defects like Cui and CuIn . In the presence of AM atoms, one has to compare the formation energies of intrinsic defects and AMrelated defects. 10 Our results show that AM defects are preferably formed at the Σ3(114) GBs as compared to intrinsic defects. Yuan et al. argued that the out-diffusion of alkali atoms from the CIGSe layer during the cooling/water rinsing process can lead to the enhancement of hole concentration. 18 Our results suggest that the ion-exchange between Na and Rb atoms can take place at the GBs. The Na atoms replaced by Rb atoms can diffuse into the GI and occupy Cu vacancies or replace Cu atoms in the CISe lattice. 67 When RbF treated samples are cooled down, the out-diffusion of Na-substituting defects from the bulk leads to the increase of Cu vacancies. Due to the stability of Rb point defects at the GB and relatively slow diffusion of Rb atoms along the GBs (compared to Na atoms) Rb atoms remain at the GBs. As we have shown, Rb is more effective in passivating some GBs than Na. The combined effects of lighter AM atoms (in increasing hole concentration), and heavier AM atoms (in passivating the GBs) make CISe-based solar cells more efficient.

(a) Se1 Se1’

In2

Se2’

Se2

Cu1

In2’

Cu1’

In1 Cu3

Cu1’

Cu1 Se c

(b)

In3’

In3 In1

In1’

Cu2’

Cu2 In2 Cu3

Figure 4: The calculated total and partial (atom-wise) DOS of the (a) AM-free Σ3(114)-I GB and (b) AM-free Σ3(114)-II GB. Vertical dashed lines show the VBM and CBM of the system. The energy is referred with respect to the Fermi level. Part of the GBs with atom labels are shown in the inset. Yellow, brown, and green colored spheres represent Se, In, and Cu atoms, respectively. states are mainly originated from the Sec atom bonded to the In2 atom. There is a small contribution from In3 (In30 ) and Cu1 (Cu10 ) atoms despite having complete bonds. We have calculated the DOS for AM atoms at the Cu3 site which is the most stable substitutional defect site at this GB model. The states originated from the Sec dangling bonds persist when Cu3 is replaced by Na (Fig. 5(b)) but are removed from the band gap when Cu3 is replaced by Rb (Fig. 5(c). Being bigger in size and more electropositive, Rb atom compensates Sec dangling bonds more effectively than Na. The distance between RbCu3 and Sec atom is 3.43 ˚ A, whereas the distance between NaCu3 and Sec atom is 4.67 ˚ A. K substitutional defect (KCu3 ) (Fig. S2(a) in SI) has a similar effect


9


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Figure 5: The calculated partial DOS of (a) the Σ3(114)-I GB with NaCu defect, and (b), and (c) the Σ3(114)-II GB with NaCu , and RbCu defect, respectively. Yellow, brown, green, and blue colored spheres represent Se, In, Cu, and Na atoms, respectively.

Conclusions

device efficiency. Interestingly, in the Σ3(114)II GB, Rb point defects passivate the GB more efficiently than Na point defects. The Na-Rb ion-exchange and more efficient passivation of GBs by Rb point defects can explain the further improvement of the solar cell performance containing heavy AM atoms.

The segregation of Li, Na, K, and Rb atoms next to different GB models are investigated. Our total energy calculations show that, in contrast to the CISe bulk, the formation energies of light and heavy AM point defects at the GBs with dislocation cores are comparable. The large difference between the formation energy of heavier alkali atom point defects in the bulk and at the GBs makes these atoms prone to segregate more profoundly next to GBs. The associated energy difference for lighter alkali atoms is smaller. That means that lighter AM atoms like Na can be found in the bulk as well as at the GBs. The diffusion mechanisms of Na and Rb between GBs and the GI are different. While Na atoms can diffuse easily from the GB regions into the bulk, the diffusion of Rb atoms towards the GI has large energy barrier and is limited to the Cu-poor regions close to the GBs. The ion-exchange between Na and Rb atoms at the GBs can take place owing to the low formation energy of Rb point defects and easy diffusion of Na from GBs towards GI. The enhanced concentration of Na in the GI after the RbF-PDT is due to the migration of Na atoms replaced by Rb atoms at the GBs. All alkali atoms can to some extent passivate the GB models considered in this work. In fact, intrinsic and extrinsic defects together can completely passivate our GB models. Thus, the beneficial effects of AM atoms in passivating the GBs lead to the lower recombination activity at the GBs and in turn contribute in improving the

Acknowledgment The authors would like to acknowledge financial support from the German Bundesministerium f¨ ur Wirtschaft und Energie (BMWi) for the speedCIGS project (0324095C). The authors would like to acknowledge the Paderborn Center for Parallel Computing (PC2 ) for computing time on OCuLUS and FPGA-based supercomputer NOCTUA. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at the Leibniz Supercomputing Centre (www.lrz.de).

Supporting Information Formation energies for AM point defects without considering thermodynamic limits on the chemical potentials of the elements Calculated migration barriers for Li and K Calculated partial DOS for substitutional and interstitial defects


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Calculated energies of segregation of AM point defects at the GBs.

at Different Temperatures. Thin Solid Films 2005, 480-481, 55 – 60, EMRS 2004.

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TOC

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Diffusion of Alkali Metals in Polycrystalline CuInSe2 and Their Role in

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