Theoretical Investigation of Interaction of CuInSe2 Absorber Material

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C: Energy Conversion and Storage; Energy and Charge Transport 2

Theoretical Investigation of Interaction of CuInSe Absorber Material with Oxygen, Hydrogen, and Water Sudhir Kumar Sahoo, Ramya Kormath Madam Raghupathy, Thomas D. Kuehne, and Hossein Mirhosseini J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06709 • Publication Date (Web): 23 Aug 2018 Downloaded from http://pubs.acs.org on August 24, 2018

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The Journal of Physical Chemistry

Theoretical Investigation of Interaction of CuInSe2 Absorber Material with Oxygen, Hydrogen, and Water Sudhir K. Sahoo, Ramya Kormath Madam Raghupathy, Thomas D. Kühne, and Hossein Mirhosseini∗ Dynamics of Condensed Matter and Center for Sustainable Systems Design, Department of Chemistry, University of Paderborn, Warburger Str. 100, D–33098 Paderborn, Germany E-mail: [email protected] Abstract We performed ab–initio calculations to study oxygen and hydrogen point defects in CuInSe2 (CISe) solar–cell material. We found that H interstitial defects (when one H atom is surrounded by four Se atoms) and HCu (when a H atom is replacing a Cu atom) are the most stable defects. While these H substitutional defects remain neutral, H interstitial defects act as a donor defect and are detrimental for the cell performance. The incorporation of H2 into the CISe lattice, on the other hand, is harmless for the p–type conductivity. Oxygen atoms tend to either substitute Se atoms in the CISe lattice or form interstitial defects, though, the formation of substitutional defects are more favorable. All oxygen point defects have high formation energies, which results in the low concentration of these defects in CISe. However, the presence of oxygen in the system leads to the formation of secondary phases such as In2 O3 and InCuO2 . In addition to the point defects, we studied the adsorption of H2 O molecules on a defect–free surface and a surface with a (2VCu +InCu ) defect using the ab–initio

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thermodynamics technique. Our results indicate that the dissociative water adsorption on the CISe surface is energetically unfavorable. Furthermore, in order to obtain a water–free surface, the surface with defects has to be calcined at a higher temperature compared to the defect–free surface.

Introduction Cu(In, Ga)Se2 (CIGSe) is considered to be the most promising absorber material for thin– film solar cells. 1–3 It is known that the properties of CIGSe films are very sensitive to the nature of defects, growing conditions, and heat treatment. 4–9 Point defects in CIGSe have attracted numerous interests in the scientific community in the hope of understanding the defects nature and improving the efficiency of CIGSe–based devices. Existing studies, so far, focused mainly on the understanding of the role of alkali–metal defects, which are found to alter the electronic properties of CIGSe films significantly. 10–21 A recent study shows that incorporating Rb into the CIGSe absorber improves the conversion efficiency of the cell up to 22.6 %, the world–record efficiency for thin–film solar cells. 22 Alkali atoms, however, are not the only impurities in CIGSe. The CIGSe thin films synthesized by coevaporation techniques in vacuum can be in contact with air after alkali– metal post deposition treatment when CIGSe films are rinsed with water to remove the excess alkali metals and secondary phases from the surface. 20,23–26 Oxygen and hydrogen atoms are also found in the CIGSe lattice after air annealing of the cells that improves the power–conversion efficiency. 7,8,27 Furthermore, oxygen atoms can diffuse from the back contact or the buffer layer (Zn(O, OH) layer for example) into CIGSe. 28 Water vapor can be deliberately introduced into the growth chamber during the growth of CIGS films to increase the hole carrier density and conductivity. 29 The coevaporation technique, usually employed for synthesizing effective CIGSe devices, requires high vacuum, which increases the cost for the thin–film synthesis. The solovothermal technique is one of the alternative non–vacuum methods to synthesize CIGSe. In this method, the annealing of the CIGSe thin 2


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film is carried out in the presence of H2 gas to remove Cu2−x Se2 . 30 It is reported that excess of H2 gas causes etching of Se from the CIGSe surface that in turn can change the surface composition. 31 Oxygen- and hydrogen-based defects, despite their presence in the absorber layer 32,33 and their potential impacts on the cell performance, have not been characterized thoroughly. In this respect, it is necessary to understand the role of O- and H-point defects in CIGSe to prevent the formation of harmful defects which can hinder the further improvement of the cells efficiency. Absorption of water molecules on the CIGSe surface, on the other hand, could affect the post treatment of CIGSe films, CdS layer deposition for example, and should be considered for the optimization of the fabrication process. Hence, in this work we study H and O point defects in the CISe bulk and their effects on the electronic structure of CISe by performing density functional theory (DFT) based calculations. 34 Further, we probed the interactions of H2 O molecules with the CISe surface by employing ab–initio thermodynamics techniques. CIGSe is an alloy of ternary copper indium selenide (CISe) and copper gallium selenide (CGSe). It has been reported that the device efficiency of CIGSe–based solar cells is highest when the Ga/(In+Ga) ratio is nearly 0.30 and the band gap of the system is about 1.1–1.2 eV, which is close to that of CISe. 22,35–37 The atomic and electronic structures of CISe and CGSe are very similar. 38 It is expected that the study of a rather simpler system (CISe) can shed light on the properties of a more complicated system (CIGSe). Therefore, in this work we studied the CISe system. The paper is organized as follows: the computational details and the models employed in this work will be discussed in the next section followed by the results and discussion. A summary of salient results concludes this paper.

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Computational Details H and O Point Defects in CISe In order to model point defects in solids, total energy calculations of supercells with corresponding defects is well suited. 10,39 In these calculations, the size of the supercell is particularly important: it has to be large enough such that spurious interactions between a defect and its periodic images are minimal. 11,40 The bulk CISe was modelled by a supercell (Cu54 In54 Se108 ) of 216 atoms where the defect is created by either substituting or adding/removing an atom. The defect formation energy is computed as ∆Ef =Etot (D, q) − Etot (bulk) ±

X

ni µ0i + ∆µi

i

(1)

q + q EVBM + µe + ∆ν0/b + Ecorr , where Etot (D, q) and Etot (bulk) are the potential energies of the supercells with the defect (D) in the charge state q and the bulk supercell (without defect), respectively. In addition, ni is the number of atoms of species i that are either removed from or added to the system, whereas µ0i is the chemical potential of species i in the native elemental state, and ∆µi is the thermodynamic limit of the chemical potential in order to avoid the formation of secondary phases. The thermodynamic limits to the chemical potentials were computed by determining the stability region for all the competing structures with respect to the reference structure (see Figure 1 and Table 1 in the Supporting Information (SI)). The valence band maximum of the bulk is denoted as EVBM , µe is the Fermi energy position (electron chemical potential), which varies from 0 to the band gap of the system (1.04 eV for CISe), and ∆ν0/b represents the correction term for the electrostatic alignment that is calculated as the difference between the averaged electrostatic potential of the bulk and the host with a defect in the neutral q charge state. Moreover, Ecorr represents the correction term for the total energy when the

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system is charged which also depends on the size of the supercell. 41 All the calculations were performed using the projector augmented plane wave method 42 as implemented in the Vienna Ab initio Simulation Package (VASP). 43,44 A plane wave cutoff of 350 eV was used and all structures were optimized using the conjugate gradient method until the ionic forces were less than 0.01 eV/˚ A. The hybrid exchange correlation functional HSE06 45 was employed to calculate the electronic structures and defect formation energies. 46 In this work, the parameter α, which indicates the percentage of Hartree–Fock exchange to be included, is modified to 0.30 (mod–HSE06 hereafter). It is noted that the mod–HSE06 functional (α = 0.30) predicts the band gap of CISe (1.04 eV) very close to the experimental value. 11 To model the oxygen diffusion in the CISe lattice, we employed the climbing–image nudged elastic band (CI–NEB) method. 47 In this work, five equidistant images were created for each NEB calculation by a linear interpolation technique. The force constant for the string, which connects the images, was set to 5.0 eV/˚ A2 . It is computationally very expensive to carry out such calculations using hybrid functionals, which is why Hubbard–corrected DFT calculations with Hubbard on–site interaction parameter U = 5.0 eV for Cu 3d electrons has been employed here. 48 It is well known that PBE functional 49 underestimates the band gap of solids. By employing PBE+U functional the band gap and bulk structure of CISe improved (see Table 8 in the SI). It is to be noted that our results of the atomic structures, vacancy formation energies, as well as the barriers for diffusion of impurities in CISe are in a reasonable agreement with those calculated using the HSE06 hybrid functional. 50

H2 O on the CISe Surface The CISe bulk structure was initially optimized using a 1×1×1 supercell (Cu4 In4 Se8 ) where both the atoms and the lattice parameters were relaxed. The (110) surface was created from the optimized structure using the atomic simulation environment (ASE) program. 51 The surface is then translated along the X and Y directions, and a total of eight atomic layers (Cu64 In64 Se128 ) has been constructed. We employed the slab model for the surface where a 5



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vertical vacuum of 14 ˚ A was created along the Z–direction. Hubbard–corrected DFT (PBE+U ) calculations with U = 5.0 eV for 3d electrons of Cu were carried out for all surfaces. The integration of the Brillouin zone was approximated by Γ–point only. All other computational details are the same as mentioned in the previous section. We employed the ab–initio thermodynamics technique 52–54 to investigate the structure of various H2 O/CISe interfaces at finite temperature and pressure. We first computed the surface free energy (γ) in order to find the water adsorption on the surface as

nH2 O(g) + CISe(110) → nH2 O/CISe(110),

(2)

where n, CISe(110), and nH2 O/CISe(110) are the number of H2 O molecules, clean surface (no water molecules on the surface), and surface with water, respectively. Specifically, γ is computed as

γ (T, p) =

1 [G (nH2 O/CISe(110)) − G (CISe(110)) − nH2 O µH2 O ] , A

(3)

where A is the area of the surface, G (nH2 O/CISe(110)) and G (CISe(110)) are the corresponding free energies, and µH2 O is the chemical potential of H2 O. The free energy of water absorption on the surface can be approximated to the potential energy difference of CISe(110) and nH2 O/CISe(110), 54,55 i.e.

γ (T, p) =

1 [E (nH2 O/CISe(110)) − E (CISe(110)) − nH2 O µH2 O ] , A

(4)

where E (nH2 O/CISe(110)) and E (CISe(110)) are the corresponding potential energies. In

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Eq. 4, only µH2 O is dependent on T and p, which is computed as µH2 O (T, p) =E (H2 O) + ∆µ (T, p) =E (H2 O) + ∆H

T, p0H2 O

− T ∆S

T, p0H2 O

+ kB T ln

pH 2 O p0H2 O

,

where E (H2 O) is the potential energy of a single H2 O molecule. Also, ∆H and ∆S are enthalpy and entropy differences which are taken from thermochemical table, 56 where p0H2 O , pH2 O , kB , and T are the standard pressure (1 bar), partial pressure of H2 O, Boltzmann constant, and temperature, respectively.

Results and Discussion H and O Point Defects in CISe The formation energies ∆Ef of various defects in their most stable state computed for point A in the CISe phase diagram (shown in Figure 1 in the SI) are given in Table 1. Point A in the CISe phase diagram 57 corresponds to the growing condition of the high–performance cells, which is Cu–poor and Se–rich. We note in passing that the chemical potentials of Cu, In, and Se for point A (Table 3 of the SI) are in an agreement with those calculated before. 46,58 The formation energies for all charge states are listed in Table 4 of the SI. For calculating the formation energies of O defects, the elemental chemical potential of O is modified to avoid the formation of the competing phases (see Table 2 of the SI). In the case of H defects, the chemical potential of H is taken from the H2 molecule. Our results show that among H substitutional point defects, HCu has the lowest ∆Ef . This is similar to other impurities such as Na and K, where NaCu and KCu substitutional defects were the most favourable defects in Cu–poor CISe. 11,59 The H atom in the HCu position forms only a covalent bond with the nearest Se atom owing to its small size (see Figure 2 in the SI). Similar to HCu , H in the HIn position forms

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Table 1: The formation energies ∆Ef for various O- and H-point defects (in Cu–poor condition) in CISe in their most stable state. The two interstitial sites between four anions (Se atoms) and four cations (2Cu+2In) are denoted as int1 and int2, respectively. Defects HCu HIn HSe Hint1 Hint2 (H2 )Cu (H2 )int2 OCu OIn OSe Oint1 Oint2

q 0 0 1+ 1+ 1+ 10 0 0 0 0 0

∆Ef (eV) 0.34 2.08 2.02 0.29 0.80 2.08 0.85 3.34 4.29 1.74 1.89 2.85

a covalent bond with one of the Se atoms. But this defect has a larger ∆Ef compared to that of HCu . It is evident from Figure 1 that the HCu point defects remain charge neutral for almost all values of µe , i.e. they have no effect on carrier concentration. The H atom can also occupy the interstitial position and forms a bridging bond along the Cu–Se bond owing to its low value of ∆Ef . Moreover, the Hint1 defect is stable with 1+ charge (donor), which makes this defect detrimental for hole conductivity in CISe. HCu and Hint1 defects can form rather easily in CISe owing to their low formation energies. Therefore, one can expect that H atoms quench the VCu present in the top few layers of the CISe surface or form a H–Se bond at the surface. It is to be noted that our results are in a qualitatively agreement with those of Kilic and Zunger 59 that indicated H–related defects are either detrimental for the p–type conductivity or can neutralize the p typeness of CISe. We also considered the incorporation of H2 molecules into the CISe lattice. In particular, H2 in the Cu sublattice and H2 in the interstitial position (Figure 3 in the SI), where the H2 molecule remains intact. It is interesting to see that the nature of HCu and (H2 )Cu defects are very different from each other: (a) the defect formation energy is larger in the later

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case and (b) (H2 )Cu enhances the hole concentration, while HCu is a neutral defect. It has been reported that VCu is stable in its 1− state 58,60 and this might be the reason for the enhanced p–type conductivity in Cu–poor CISe. Interestingly, when a H2 molecule occupies the Cu vacancy site, it remains negatively charged for all values of µe . This is to say that the occupation of Cu vacancies with H2 molecules does not decrease the hole concentration. In addition, when the H2 molecule occupies the interstitial position in the CISe lattice ((H2 )int2 ) as found in our calculations (see Table 1), it is stable in its charge neutral state. Based on our results, we can conclude that the incorporation of H2 molecules into the CISe lattice does not affect the p–type conductivity of CISe. In contrast, the presence of H atoms are detrimental either by the formation of the positively charged interstitial defects or by

2.5 2

∆Ef (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.5 1

0 HCu Hint1 OSe Oint1 (H2)Cu (H2)int2

0

1-

1-

0

0

1+

0.5

0 1-

0 0

0.2

0.4

0.6

0.8

1

µe (eV) Figure 1: Formation energies ∆Ef for various H and O point defects in CISe as a function of electron chemical potential (µe ). Point defects with low formation energies are shown here.

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reducing the concentration of Cu vacancies. Regarding oxygen impurities, the most stable point defect forms when a Se atom is replaced by an O atom, as can be seen in Table 1. Similar to Se atoms in the CISe lattice, OSe forms four bonds with two Cu and two In atoms, though, the O–In bond length is smaller than that of Se–In (Figure 4 in the SI). Both O and Se belong to the same group in the periodic table, even though, O has a larger electronegativity. Therefore, OSe remains charge neutral and becomes negatively charged for µe larger than 0.85 eV. Considering interstitial defects, the O atoms occupy the bridging position along the In–Se bond. Oxygen interstitial defects remain charge neutral for the whole range of µe (see Figure 1). This means that Oint1 defects do not alter the carrier concentration in CISe. Considering the rather high values of ∆Ef of the oxygen defects, it can be concluded that these defects do not play a major role in the defect physics of CISe. The most striking effect of the presence of oxygen in the system is the formation of secondary phases: In2 O3 and InCuO2 are the most stable compounds that can coexist with CISe. 61 The band gap of In2 O3 is much larger than that of CISe 62 and the formation of this secondary phase could affect the efficiency of CIGSe–based devices. Various secondary phases that can form when O is present in the system are listed in Table 2 of the SI. Ishizuka et al. 29 have reported that the addition of water vapor during the thin–film deposition improves the crystal structure of CIGSe and the performance of the solar cell. In CuGaSe2 (CGSe), VSe defects act as donor defects 46 and are detrimental for the performance of the CGSe–based cell. The effects of VSe defects in CGSe can be compensated by the formation of OSe . 29 In CISe, however, the VSe defects are charge neutral. 46,60 Our results show that OSe is also charge neutral for p–type CISe. This means that in contrast to CGSe, the incorporation of O into the CISe lattice and formation of OSe cannot improve the p– conductivity. This is in agreement with experimental findings suggesting that the treatment of CIGSe with only O2 gas does not improve the cell performance. 29,63 We showed that hydrogen point defects are either detrimental or benign in CISe. Given these facts, we

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might conclude that the cell performance improvement in the presence of water vapor in the fabrication chamber could be due to the enhanment of alkali metal effects. 29,63 In order to understand the diffusion of oxygen defects in the CISe lattice, we calculated the diffusion barriers for two specific paths: (a) diffusion of an O atom from one Se position to the nearest VSe site and (b) diffusion of an O atom from the most stable interstitial position to an equivalent interstitial position. We considered these two paths based on the corresponding low formation energies of these two point defects (see Table 1). The diffusion barriers obtained from CI–NEB calculations are given in Figures. 5 and 6 of the SI. The barrier for diffusion of an O atom from one Se lattice to the nearest VSe site is found to be 0.84 eV, whereas the barrier of migration of O atom from one interstitial site to another is found to be 1.15 eV. Considering the fact that ∆Ef and the diffusion barrier of OSe are smaller than those of Oint1 , we can conclude that OSe defects are more favorable than Oint1 and they can move in the CISe lattice by jumping from one VSe site to another.

H2 O on CISe Surface Surface Relaxation It has been reported that the (112) surface of CISe is the most exposed surface, however, this surface is a polar surface. 64,65 Among all non–polar surfaces, the (110) surface is the most stable one. 66 Interestingly, all atoms in the top layer of the (110) surface are tri–coordinated which is similar to the coordination number of atoms in the (112) surface. 66 Therefore, we believe that the chemical properties of these two surfaces are not much different. The atomic structure of the (110) surface before and after relaxation are shown in Figure 2. It can be seen that Cu and In atoms are moving downwards, while Se atoms are moving upwards during relaxation. The surface energy is calculated as

∆Esurf =

1 (Esurf − n × Ebulk ) , A 11


(5)


(a)

(b)

Figure 2: Structure of the CISe (110) surface before (a) and after (b) relaxation. Atoms color: Cu–cyan, In–pink and Se–yellow.

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where A is the area of the surface and n is the number of CuInSe2 units present in the surface. Therein, Esurf and Ebulk are the potential energies of the relaxed surface and the bulk (of CuInSe2 unit), respectively. The values of ∆Esurf with respect to the number of layers that are relaxed indicate that mainly the top 3 layers of the (110) surface contribute to ∆Esurf (see Table 5 in SI). Therefore, in all following surface calculations only the top 4 layers are relaxed while all others are kept fixed. It is known that the topmost layers of the CISe surface are Cu poor. 67,68 It has been suggested that Cu–poor top layers of the CISe surface could be an ordered defect compound (ODC). 69,70 It has been also observed from theoretical studies that the introduction of (2VCu +InCu ) defect in CISe leads to the formation of ODC. 71 Hence, a (2VCu +InCu ) defect is created in the top layer of the (110) surface to represent the Cu–poor condition.

Single Water Molecule on the (110) Surface In order to find the structures of the H2 O/CISe interface, we first studied adsorption of a single water molecule on the CISe (110) surface. On this surface there are two types of unsaturated cations, Cu and In, where a water molecule could be adsorbed. It is to note that there is also a possibility of dissociative water adsorption on the surface, where a OH group and a H atom of the H2 O molecule can bind to one of the cations (either Cu or In) and Se atoms, respectively. The adsorption energy is calculated as

∆Eads = E (nH2 O/CISe(110)) − E (CISe(110)) − nH2 O E (H2 O) ,

(6)

where E (nH2 O/CISe(110)), E (CISe(110)), and E (H2 O) are the potential energies of nH2 O molecules adsorbed on the CISe (110) surface, the CISe (110) surface, and the H2 O molecule, respectively. The negative values of ∆Eads indicate that the adsorption of a H2 O molecule on the surface is thermodynamically favorable. Interestingly, from our calculations of ∆Eads , we found that the H2 O molecule is adsorbed

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on the In atom instead of the Cu atom, as can be seen from Table 2 and Figure 7 of the SI. The In–O distance (2.39 ˚ A) is slightly larger than that of Cu–O (2.33 ˚ A). On the surface with the (2VCu +InCu ) defect, the water molecule is adsorbed on the InCu site (see Figure 3) and the corresponding ∆Eads value is found to be very large (−125.8 kJ mol−1 ). Moreover, ∆Eads of the H2 O molecule on the In atom close to the InCu site is larger than ∆Eads of the H2 O molecule on the In atom of the defect–free surface. This indicates that the presence of this defect changes the nature of water adsorption on the CISe surface. We also studied the dissociative water adsorption on both surfaces, defect–free and with defect. Interestingly, we found that ∆Eads is positive for both the surfaces (see Tables 2 and 3), which indicates that the dissociative water adsorption is energetically not . Recently, Senftle and Carter reported a study on band edge alignments at the CuInS2 (112) surface/water interface. 72 Interestingly, on the CuInS2 (112) surface the water molecule is adsorbed on In atoms rather than on Cu atoms. Moreover, dissociatively water adsorption is energetically not favorable. This indicates that our results on the CISe (110) surface are in the same line with the CuInS2 (112) surface. 72 Table 2: Adsorption energy ∆Eads for a water molecule on the defect–free (110) surface, where OIn and OCu represent the water molecule adsorbed on In and Cu atoms, respectively. Structure H2 OIn /CISe H2 OCu /CISe H2 Odiss In /CISe

∆Eads (kJ mol−1 ) −73.5 −32.5 17.3

Table 3: Adsorption energy ∆Eads for a water molecule on the (110) surface with (2VCu +InCu ) defect, where OInCu and OIn0 represent the water molecule adsorbed on InCu and the In atom close to InCu , respectively. Structure H2 OInCu /CISe H2 OIn0 /CISe H2 Odiss InCu /CISe

∆Eads (kJ mol−1 ) −125.8 −81.1 16.6

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In

Cu

(a)

(b)

(c) Figure 3: Structure of H2 O molecule adsorbed on the InCu site (a), In atom close to InCu site (b) and dissociatively adsorbed over InCu site (c) on the CISe surface with a (2VCu +InCu ) defect. 15 ACS Paragon Plus Environment


Structure of H2 O on the (110) Surface In order to determine the structure of the H2 O/CISe interface, we optimized the structures where more than one water molecule was adsorbed on the surface. In the case of the defect– free surface, the second water molecule (when two water molecules are there) is also adsorbed on the In atom rather than the Cu atom. Similarly, other water molecules are adsorbed on In atoms only (Figure 8 in the SI). The computed adsorption energies per water molecule does not change much with respect to the number of H2 O molecules, which indicates that the water molecules on the surface are non interacting (Table 6 in the SI). In the case of a surface with defects, the second water molecule is adsorbed on the In atom close to InCu . The effect of temperature T and pressure pH2 O on the structure of CISe/H2 O interface is investigated using ab–initio thermodynamics, as explained in the previous section. We increased the number of water molecules one by one to the total number of In atoms on the surface (8 for the defect–free surface and 9 for the surface with defects). The computed free energies (γ) as a function of T (at pH2 O = 1 bar) are given in Figures 4 and 5 for the defect–free and the surface with defects, respectively. The negative and positive values of γ indicate adsorption and desorption of water on/from the surface, respectively. Our results show that at low temperatures, water molecules bind to the surface, while at higher temperatures water molecules tend to remain in the gas phase. We ascribe this trend to the fact that ∆Eads is more dominant at lower temperature, while at higher temperature the entropy of water is more dominant. In the case of the defect–free surface, the clean surface is obtained at 430 K and when the temperature is less than 418 K all In atoms are occupied with water molecules. For the surface with defects, the clean surface is obtained at a higher temperature (T > 682 K) and when the temperature is below 382 K all In atoms are occupied with water molecules. We find that this is due to the larger adsorption energy of the H2 O molecule on the surface with defects compared to the defect– free surface. It is evident from Figure 5 that there are many cross–overs in the diagram of the surface with a defect as compared to that of the defect–free surface. We ascribe this is 16


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3 1H2O/CISe

2

-1

-2

γ (kJ mol Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

2H2O/CISe 3H2O/CISe 4H2O/CISe 5H2O/CISe 6H2O/CISe 7H2O/CISe 8H2O/CISe

0 -1 -2 0

200

400

T (K)

600

800

1000

Figure 4: Surface free energy as a function of temperature for the defect–free CISe (110) surface.

17



3 1H2O/CISe

2

-1

-2

γ (kJ mol Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 0

2H2O/CISe 3H2O/CISe 4H2O/CISe 5H2O/CISe 6H2O/CISe 7H2O/CISe 8H2O/CISe 9H2O/CISe

-1 -2 0

200

400

T (K)

600

800

1000

Figure 5: Surface free energy as a function of temperature for the CISe (110) surface with a (2VCu +InCu ) defect.

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due to different adsorption energies of water molecules on different In atoms in this surface. From our calculations, we could confirm that at ambient conditions (room temperature and 1 bar pressure) CISe surfaces are hydrated. Our results also suggest that in the presence of defects, it is required to calcine the CISe surface at a higher temperature in order to remove water molecules from the surface.

Conclusions We have studied the atomic and electronic structures of H- and O-point defects in CISe using DFT–based calculations. From the defect formation energies, it is evident that the H atom could form substitutional (HCu ) as well as interstitial (Hint1 ) defects. The incorporation of H atoms into CISe has detrimental effects on the performance of solar cell because (a) HCu could quench the excess hole generated by VCu , and (b) H interstitial defects act as a donor defect which could reduce the hole concentration. Interestingly, when H2 molecules are incorporated into the CISe lattice they have a benign effect on the carrier concentration, albeit, the formation energy is larger in comparison to H point defects. When oxygen is incorporated into CISe, the substitutional defect (OSe ) is more likely to form compared to the interstitial defect. All oxygen point defects remains charge neutral which means these defects do not alter the carrier concentration. The relatively low diffusion barriers of oxygen suggests that O atom could migrate from one Se site to another. We have also studied the structure of the H2 O/CISe interface using the ab–initio thermodynamics approach. We observe that water molecules tend to be adsorbed molecularly rather than dissociatively. On the defect–free surface, water molecules tend to absorb on top of the In atoms instead of the Cu atoms. In addition, on the surface with defects, water molecules tend to adsorb on the InCu site or on the In atoms next to these defects. The surface free energy calculations suggest that at higher temperature, the water molecule desorbs from the surface, while at lower temperature the surfaces are hydrated. Our results indicate

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that to obtain a clean (water free) surface, the surface with defects has to be calcined at a higher temperature compared to the defect–free surface.

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 gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gausscentre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at the Leibniz Supercomputing Centre (www.lrz.de). The authors also acknowledge the Paderborn Center for Parallel Computing (PC2 ) (https://pc2.uni-paderborn.de/hpcservices/available-systems/oculus/) supercomputing time on OCuLUS where a part of the calculations were carried out.

Supporting Information The contents of the material supplied as Supporting Information: 1. Stability diagram for CISe 2. Calculated formation energies for different possible phases 3. Formation energies for various oxygen and hydrogen defects in CISe 4. Diffusion paths for O point defects in CISe 5. Structure of H2 O on the (110) surface 6. Comparison between the experimentally measured and theoretically calculated lattice parameters

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Figure 6: TOC

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Theoretical Investigation of Interaction of CuInSe2 Absorber Material

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