A Strategy to Stabilize Kesterite CZTS for High-Performance Solar

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A Strategy to Stabilize Kesterite CZTS for High Performance Solar Cells Kuang Yu, and Emily A. Carter Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.5b00172 • Publication Date (Web): 03 Apr 2015 Downloaded from http://pubs.acs.org on April 6, 2015

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Chemistry of Materials

A Strategy to Stabilize Kesterite CZTS for High Performance Solar Cells Kuang Yu1 and Emily A. Carter1,2,* 1

Department of Mechanical and Aerospace Engineering and 2Program in Applied and Computational

Mathematics and Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544-5263

ABSTRACT Cu2ZnSnS4-xSex (CZTS) is an important semiconductor with significant potential for applications in the next generation of solar cells. CZTS has an optimal band gap (~1.5 eV) and contains no expensive or toxic elements. However, CZTS-based solar cells suffer from low efficiency due to poor crystal quality, which is partly caused by secondary phase formation during synthesis. We use density functional theory + U calculations to systematically investigate the stabilities of three CZTS phases: kesterite, stannite, and wurtzite. In agreement with previous experiment and theory, we confirm that these three phases have very similar formation energies. This finding is consistent with the known difficulties in synthesizing pure kesterite CZTS, the phase desirable for photovoltaic applications. To overcome this problem, we characterize surfaces and interfaces of CZTS and are able to identify certain “beneficial surfaces” that could be exploited to potentially provide extra stability for the kesterite phase.

* Author to whom correspondence should be addressed. Electronic mail: [email protected].

1

ACS Paragon Plus Environment


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We propose the zinc blende ZnS (001) surface as a substrate to induce formation of these beneficial surfaces and to stabilize the kesterite phase, thereby serving as an effective crystallization template for the fabrication of high performance CZTS solar cells.

Interest in developing clean and sustainable sources of electricity continues to rise, with unprecedented levels of investments in renewable energy technologies. Among these technologies, photovoltaics (PVs) represent a particularly promising and fast growing industry, as the sun provides a near-inexhaustible supply of free, clean, non-CO2-producing energy. To date, multicrystalline silicon (Si) PVs, with ~20% efficiency at best,1 dominate the commercial market, mainly due to the abundance of Si and the mature fabrication techniques provided by the existing electronics industry. Bulk Si features an indirect band gap, which on the one hand prevents electron-hole recombination, while on the other hand reduces light absorption. Therefore, thick Si layers are necessary to enhance sunlight absorption, increasing materials and manufacturing energy costs. In order to overcome this disadvantage, thin-film technologies, which reduce the thickness of the absorption layer to ~micrometers, have been devised based on various semiconductors with direct band gaps, including GaAs, CdTe, CuInxGa1-xSe2 (CIGS), and more recently organic-inorganic hybrid perovskites. Within this category, a quaternary compound Cu2ZnSnS4-xSex (CZTS or CZTSSe) is of particular interest, as it has an almost perfect band gap (1.0~1.5 eV with different Se concentrations) and does not contain any expensive metals (such as Ga in GaAs and In in CIGS), or toxic elements (such as As in GaAs, Cd in CdTe, and Pb in the perovskites).2 Despite their significant economic and environmental advantages, CZTS-based PVs suffer from relatively low efficiencies. Compared to other thin film semiconductors, such as GaAs (~28.8%),3 CdTe 2


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(~20.4 %),1 CIGS (~23.3%),1 or the fast developing hybrid perovskite (~19.3%),4 the efficiency record for CZTS remains at 11% thus far,5 which is similar to organic solar cells3 but about half of the efficiency of state-of-the-art Si modules. Previous photoluminescence (PL) experiments6, 7 indicate that the minority carrier lifetime in CZTS is mainly limited by the nonradiative Shockley-Read-Hall (SRH) recombination process, which is a major bottleneck for performance improvement. In the SRH process, electron-hole pair recombination is mediated by deep mid-gap levels, which are typically associated with defects, impurities, or unsaturated dangling bonds residing at interfaces or phase boundaries. Thus, in order to further improve the performance of CZTS solar cells, it is crucial to develop better strategies to synthesize high quality CZTS single crystals, diminishing the concentration of recombination centers.

Figure 1. CZTS (pure sulfide) crystal structures for: (a) kesterite (space group I 4 ), (b) stannite (space group I 42m ), and (c) wurtzite (space group Pc ) phases. Formation of secondary phases during crystal growth prevents the synthesis of high quality CZTS crystals. These secondary phases are either secondary compounds, such as ZnS, Cu2S, and Cu2SnS3, or multiple phases of CZTS itself, namely kesterite, stannite, or wurtzite (see Figure 1). Similar to CIGS and CdS, the structures of the first two phases (kesterite and stannite) are both based on the cubic zinc blende topology, and the only difference lies in the stacking pattern of the Cu/Zn sub-lattice. The wurtzite phase of CZTS has a lower symmetry unit cell that resembles the wurtzite phase of ZnS. 3



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Neutron diffraction experiments8 and various computational studies that use pure or hybrid density functionals9-11 identify the kesterite phase as most stable. The kesterite phase is also the most desirable structure since both stannite and wurtzite phases have ~100 meV lower band gaps compared to kesterite 12, 13

. Hence, the admixture of multiple phases would lower the final output voltage and be detrimental to

solar cell efficiency. Previous computations9-11 indicate that the energy difference between the kesterite and the stannite phases is less than 3.2 kJ/mol/formula-unit, so stannite is likely to form even though it is slightly less stable than kesterite. Partial disorder of the Cu/Zn sub-lattice was indeed observed in the neutron diffraction and electron energy loss spectroscopy studies.8,

14

This implies that the ordered

Cu/Zn sub-lattice is not stable, which is consistent with the small energy difference between the kesterite and the stannite phases. As part of efforts to improve CZTS crystal quality, new strategies are needed to further stabilize the kesterite phase and minimize secondary wurtzite, stannite or other disordered phases. In this work, we use the two ordered secondary phases (stannite and wurtzite) as a comparison to search for strategies to stabilize both the tetragonal cell and the Cu/Zn stacking pattern of the kesterite phase. Disordered phases are not explicitly considered here as they would require formidably large simulation cells to model realistically. It is known that in very thin films, surface properties play a much more pronounced role than in bulk samples. For example, surface energies play a critical role in the phase ordering of nanostructured zirconia: calculations show that for low-index cleavage planes, the tetragonal phase is energetically favored over the monoclinic phase because of significantly lower surface energies, despite a lower energy of monoclinic ZrO2 in the bulk.15 This finding is in accord with previous experimental work demonstrating that tetragonal rather than monoclinic ZrO2 forms in nanolaminates.16 Similarly, even though bulk FeO is thermodynamically unstable under ambient conditions,17 it has been observed in both nanofilms18 and nanometer-sized islands.19 Small differences in surface energies are also able to reverse the relative stabilities of the rutile and anatase phases of nanocrystalline TiO2.20 And a strong 4


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size-dependence was observed for wurtzite/rock-salt phase transitions in CdSe nanocrystals,21 confirming that this effect is not just limited to oxides. Inspired by these findings, we propose to use a similar strategy for CZTS to attempt to enhance the stability of kesterite. Most previous computational studies of CZTS used density functional theory (DFT) with generalized gradient approximation (GGA) exchange-correlation functionals,9,

22-25

such as Perdew-Wang 91

(PW91)26 or Perdew-Burke-Ernzerhof (PBE),27 which are fast to evaluate but potentially problematic for first-row transition-metal-containing compounds. The approximate exchange in these local functionals tends to poorly describe the interactions between tightly held 3d electrons in these materials. Some other calculations used hybrid functionals (such as Heyd-Scuseria-Ernzerhof 06, HSE0628),10, 29, 30 which are quite accurate for calculating energetics but are also orders of magnitude more expensive and therefore cannot be readily applied to phonon, extended surface, or interface calculations requiring large cells. In this work, we instead use the DFT+U formalism31, 32 with ab initio-derived U parameters,33, 34 which is more accurate than pure DFT-GGA while retaining high computation throughput. With this methodology, we compute the relative stabilities of all three CZTS phases, as well as other possible secondary phases. We calculate cleavage energies of different surfaces of CZTS and thereby identify “beneficial surfaces” that might be exploitable to stabilize the desirable kesterite structure. Finally, we offer evidence that the corresponding ZnS (zinc blende) surface has potential to act as a growth template to synthesize high-quality, single-crystal, kesterite CZTS films.

METHODS AND COMPUTATIONAL DETAILS The VASP 5.3.3 program35-38 was used to perform all-electron projector-augmented-wave (PAW)39 DFT+U calculations within the frozen-core approximation, in order to self-consistently optimize the valence/outer core electron distributions. PAW potentials acted on the 4s/3d electrons of Cu and Zn, the 5s/5p/4d electrons of Sn, the 4s/4p electrons of Se and the 3s/3p electrons of S, while all other (core) 5



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electrons were kept frozen .40 For sulfur, the softer PAW potential with a larger augmentation region was used to accelerate basis set convergence (vide infra). In combination with PBE exchangecorrelation,27 we utilized the U correction developed by Dudarev et al.32 for the 3d electrons in Zn(II), Cu(I), and the 4d electrons in Sn(IV), described further below. We also found that it is critical to include long-range dispersion to obtain reasonable cell parameters for non-bonded layered structures like SnS2. Including dispersion also significantly improves bulk moduli predictions compared to experimental values (vide infra). We therefore applied Grimme’s a posteriori D2 correction41 to account for this interaction and denote our overall computational model then as PAW-PBE+U+D2. The bulk moduli were derived via fitting pressure-volume curves to the Murnaghan equation of state.42 A planewave basis with a 700 eV kinetic energy cutoff was used in all our PAW-PBE+U+D2 calculations, which is sufficient to converge the total energies of all systems examined to within 1 meV/atom. The Γ-point-centered Monkhorst-Pack scheme43 was used to sample the Brillouin zone, with the k-point meshes dense enough to converge all our energies to within 1 meV/atom. The k-point meshes used for each periodic cell model are given in the Supporting Information. The electron occupancy in reciprocal space was determined using the Gaussian smearing method, with a 0.05 eV smearing width. The effective U parameters for Zn(II) and Cu(I) were taken from reference 44 (4.5 eV and 3.6 eV, respectively), and were derived from ab initio unrestricted Hartree-Fock computations on electrostatically embedded metal oxide clusters.33 This method for determining the effective U (actually U-J, where U and J are respectively the effective intra-atomic Coulomb and exchange energies) requires no experimental data as input. The U and J parameters were derived fully ab initio by computing the average onsite Coulomb and exchange interactions between the UHF orbitals. The same method was used here to obtain the U parameter for Sn(IV). All embedded cluster models were constructed from the experimental SnO2 crystal structure,45 and we used the 6-31G(d) basis set for O,46 in conjunction with 6


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the large core Stuttgart-Koel effective core potential (ECP28MDF) and valence double zeta basis set47, 48 for Sn. All clusters were embedded in a point charge array with ~4000 point charge sites to reproduce the Madelung potential of the ionic crystal lattice, with the cluster atoms replacing point charges in the center of the array. The Sn(IV) sites directly bonded to the terminating oxygen ions in the clusters were represented not by point charges but rather by capping Ge4+ ECPs (LANL2DZ ECP49) to approximately account for short range repulsive interactions between the oxygen ions and the Sn(IV) core electrons. A Ge4+ ECP was used since Ge4+ has a similar valence structure and size as Sn (IV), hence reproducing similar interactions with the terminal anions. The U value was converged to within 0.5 eV with respect to cluster size; the resulting U value for Sn(IV) is 4.8 eV. Earlier work has shown that changing U by up to 0.5 eV has little effect on properties predicted by DFT+U.50 Using the above computational setups, the bulk temperature-dependent free energies were computed by adding zero-point energy and thermal corrections to the electronic total energy:

F (T )  Eelec  Fthermal (T ) Fthermal 

1   (q)  kBT q ln(1   (q) / kBT ) 2 q

Here, the thermal correction Fthermal (T ) was evaluated within the harmonic approximation,51 using the q-dependent phonon frequencies (  (q) ). Force constants were calculated utilizing supercells of at least 10 Å length in each dimension, which are large enough to converge the final thermal corrections within 0.1 meV/atom (see Supporting Information for details of supercells used), and the q-dependent phonon frequencies  (q) were obtained using the PHONOPY code suite,52 using the force constants computed by density functional perturbation theory.53 All calculations were carried out at 670 K, which is within the relevant annealing temperature range during synthesis.54

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Slab models of surfaces were constructed by inserting a 15 Å vacuum gap into the supercell. Cleavage energies were computed by simply taking the difference between the energy of slab with the vacuum gap present and the energy of the corresponding supercell without vacuum. The cleavage energy is the sum of the surface energies of the two newly formed, fully relaxed surfaces (which may or may not be the same) and can be considered a metric for the stability of the surfaces created. Dipole energy corrections (all with magnitudes less than 5 meV/atom) were applied for polar surfaces and all cleavage energies were converged to within 0.01 J/m2 with respect to the slab thickness. Se addition effects on cleavage energies were investigated for kesterite and stannite phases containing 50% Se. First, a 16-atom unit cell containing four Se and four S sites was constructed utilizing the special quasirandom structures (SQS) method, which approximately reproduces correlations of the Se positions in a random solid solution55,

56

(the pair correlation function of the SQS cell matches the

random alloy within 5 Å). Then supercells and slabs were built based on the SQS unit cell analogous to the pure sulfide case, and the cleavage energies were then computed. The CZTS/ZnS interface models were constructed by adding the CZTS slab on top of the ZnS(001) slab, followed by insertion of a 15 Å vacuum gap. Since we mean to simulate a CZTS thin film growing on a ZnS substrate, we scaled the CZTS slab structure to adopt the ZnS cell parameter, inducing 0.2% lateral strain. All interface structures were fully relaxed using the same level of theory and numerical parameters introduced above. A 0.01 eV/Å convergence threshold was used for all forces on atoms during geometry optimizations. The relative energies ( E ) of CZTS slabs deposited on ZnS (001) were calculated using the bare ZnS substrate and ground state bulk CZTS (i.e., the kesterite phase) as common reference states. This relative energy metric is given by:

E  ( Einter  Esub  ekesterite nczts ) / nczts 8


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Here, Einter is the energy of the entire structurally relaxed CZTS (kesterite or stannite)/ZnS interface slab, E sub is the energy of the structurally relaxed, isolated ZnS substrate slab maintaining the same lattice vectors as the interface slab, ekesterite is the ground-state equilibrium bulk CZTS (kesterite phase) energy per formula unit, and nczts is the number of formula units in the CZTS layer. Essentially, this relative energy metric contains two contributions: the cleavage energy to create a kesterite slab or a stannite slab; and the adhesion energy between CZTS slab and the ZnS substrate. Both terms will contribute to the relative stability of the interface structures and should be included in the metric. In this equation, it is important to note that we always adopt a bare ZnS substrate surface and bulk kesterite CZTS as our reference states, regardless of which phase of CZTS we are studying in the interfaces. By using consistent reference states, the relative energies of different interface structures containing different phases of CZTS are directly comparable. Using this definition, we are able to directly quantify the relative stability of a CZTS layer (for different phases) coated on a ZnS substrate. To gain deeper insight into the contributions of the cleavage energy and the adhesion energy to the interface energy, we also compute the adhesion energy between the two slabs:

Ead  ( Einter  Esub  Eczts  slab ) / S Here, Eczts  slab is the energy of the optimized free-standing CZTS slab with bulk CZTS lattice constants and S is the surface area. Note that for different interfaces, the reference free-standing CZTS slab is different, so the Ead metric does not directly reflect the relative stability of a particular interface system. In principle, this metric only represents the adhesion contributions to the relative energy, but does not include the cleavage energy contribution.

RESULTS AND DISCUSSION 9



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Crystal Structures In this work, we aim to explore the phase stabilities of CZTS, so we will benchmark our methodology using mainly ground state calculations, such as crystal parameters and thermodynamic properties; we will not study excited states properties such as the optical band gap, which requires a higher level of theory (such as GW). To verify the validity of the Sn(IV) U parameter and our methodology, we first compare the lattice parameters and bulk moduli of SnO2 and kesterite CZTS computed using PBE+U(+D2) and the pure PBE functional with experimental data (see Table 1). Table 1. SnO2 and pure sulfide CZTS lattice parameters (a and c) and bulk modulus (B).

SnO2

CZTS (kesterite)

a

a (Å)

c (Å)

B (GPa)

Expa

4.737

3.185

212.3

PBE

4.827

3.243

168.7

PBE+U

4.698

3.137

183.7

PBE+U+D2

4.662

3.13

205.8

Expb

5.426-5.435

10.81-10.848

-

PBE

5.475

10.938

69.7

PBE+U

5.444

10.866

66.5

PBE+U+D2

5.348

10.681

78.6

References 45, 57; b Reference 58

Simple DFT-PBE overestimates the cell parameters for both materials and greatly underestimates the bulk modulus of SnO2, while the predictions of PBE+U are superior to PBE for both materials. The D2 correction slightly overcorrects the cell parameters compared to the PBE+U method, but greatly improves the bulk modulus of SnO2. We note that due to the large nuclear charge of Sn(IV), the d-orbitals of Sn(IV) are more contracted, leading to stronger intraatomic (on-site) Coulomb and exchange interactions and larger Ueff compared to 10


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Cu(I) and Zn(II).44 So the U correction leads to much larger effects (2.7-3.3%) on the lattice constants of SnO2 compared to Cu2O (0.4%) and ZnO (1.3-1.4%). The lattice constants of CZTS are mainly determined by the sizes of the largest ions in the lattice, which are Cu and S. Therefore, the CZTS lattice constants only change by 0.7%, similar to the Cu2O case. We found that methods missing dispersion lead to completely incorrect geometries for layered materials, such as SnS2, since the interactions between layers are dominated by dispersion. Hence, it is critical to include the D2 correction so that all compounds considered can be treated on the same footing. Therefore, all subsequent calculations that follow here use the PBE+U+D2 method. Phase Stability To investigate the thermodynamics of CZTS synthesis, we calculated the free energies of the three phases (kesterite, stannite, and wurtzite) of bulk CZTS, as well as various relevant secondary compounds, namely, ZnS, CuS, Cu2S, SnS, SnS2, and Cu2SnS3. All results are listed in Table 2. Table 2. Thermally corrected free energies (kJ/mol/formula-unit) of CZTS and relevant secondary phases. All values are computed at T = 670 K. Compound

Phase

Eelec

Fthermal

F

SnS2

Berndtite

-1410

-45

-1454

SnS

Herzenbergite

-945

-44

-989

CuS

Covellite

-737

-33

-770

Cu2S

Low-chalcocitea

-1025

-64

-1089

ZnS

Zinc blende

-684

-30

-714

ZnS

Wurtzite

-684

-31

-716

Cu2SnS3

Monoclinic

-2474

-106

-2581

Cu2ZnSnS4

Kesterite

-3171

-135

-3306

Cu2ZnSnS4

Stannite

-3169

-135

-3303

11



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Cu2ZnSnS4

Wurtzite

-3166

-135

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-3301

a

We used the low-temperature phase because high-chalcocite has partially occupied sites, leading to a more complicated unit cell which is too large to model. First, we confirm that the most stable CZTS phase is the kesterite phase. However, the free energy differences are only ~3 and ~5 kJ/mol/formula-unit compared to the stannite and wurtzite phases, respectively. Hence, it is not surprising that it is a challenge to obtain pure kesterite in experiments as the other phases are almost as energetically favorable to form. The data listed in Table 2 allow us to also evaluate the thermodynamics of different CZTS formation reactions, all of which are predicted to be exoergic at 670 K: the F of the reaction of

is -47 kJ/mol, the F

is -61 kJ/mol, and the F of

is -9

kJ/mol. We used wurtzite ZnS data in these calculations since wurtzite ZnS is predicted to be the ground state in our calculations. The experimental ground state for ZnS is the zinc blende phase, contrary to the calculations. However, the predicted energy difference between the two phases of ZnS is only ~2 kJ/mol, smaller than the typical error of DFT approximations. Therefore all the thermodynamic predictions will lead to essentially the same result no matter which phase of ZnS we use. Thus there is a strong thermodynamic driving force for CZTS formation, which should aid its synthesis. Previous computations23 reported that thermal corrections Fthermal (T ) significantly affect defect formation energies. However, we find that the thermal corrections for all three phases of CZTS are identical (see Table 2), so thermal effects are not essential to our analysis here and thus are neglected in the rest of this study for simplicity. Similar data have been reported by several other groups,22, 25 computed using either the PW91 or PBE GGA exchange-correlation functionals without any thermal corrections. While roughly generating the similar trends, the pure GGA functionals yield qualitatively incorrect predictions of the thermodynamics of certain reactions. For example, according to the data reported in reference 25, the reaction free energy for

is 13.5 kJ/mol, which is endothermic. The 12


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experimental standard reaction enthalpy is exothermic, -26.3 kJ/mol. Notably, our calculation predicts a qualitatively correct value of -16.1 kJ/mol; the error of about 10 kJ/mol is to be expected considering the typical accuracy of density functional approximations. The same reaction energy calculated using the hybrid HSE06 functional is -25.1 kJ/mol,30 in excellent agreement with the experimental value, albeit with a two orders of magnitude higher computational expense. Both the HF terms in HSE06 and the U correction terms we adopt here alleviate the self-interaction error and achieve better accuracy. Thus this reaction enthalpy comparison highlights the importance of self-interaction error corrections for first-row transition metal sulfides and validates our choice of methodology. To summarize this section, we computed thermally corrected free energies of different bulk CZTS phases and various secondary compounds. Calculated relative stabilities agree with previous studies, showing that the kesterite phase is the most stable, even though it is only favored by a few kilojoules per mole. This result indicates that even though the formation of CZTS is exothermic, we need special strategies to further stabilize the kesterite phase such that crystals of better quality can be obtained. CZTS Cleavage Energies As stated in the introduction, we aim to exploit surface properties to help stabilize the kesterite phase in nanoscale structures. In order to find surfaces that may facilitate formation of kesterite CZTS, we evaluated the cleavage energies of all symmetry-unique, low-index surfaces for all three phases of CZTS. The structures of all calculated surfaces can be found in Figure 2 and all cleavage energies are listed in Table 3 and Table 4. Table 3. Cleavage energies for kesterite and stannite phases of CZTS, in J/m2. Pure sulfide

50% Se

Surface

Kesterite

Stannite

Kesterite

Stannite

(001)-aa

1.22

1.49

0.92

1.28

13



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(001)-b

1.61

1.29

1.27

1.15

(100)

1.22

1.39

1.07

1.16

(110)

0.78

0.79

0.66

0.65

(112)

0.78

0.77

0.70

0.69

(102)

0.77

0.68

0.69

0.65

a

Two different cleavage planes exist in this particular surface normal direction, denoted by letters (a) and (b), respectively (see Figure 2).

Table 4. Cleavage energies for the wurtzite phase of pure sulfide CZTS, in J/m2. Surface

Pure Sulfide Wurtzite

(001)

0.78

(010)-aa

0.36

(010)-b

0.95

(100)

0.78

(210)

0.68

a

Two different cleavage planes exist in this particular surface normal direction, denoted by letters (a) and (b), respectively (see Figure 2).

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Figure 2. Structures for: (a) surfaces for the kesterite and stannite phases, (b) surfaces for the wurtzite phase and (c) optimized structure of the interface between the metal-terminated ZnS (001) substrate and the four bilayers of the kesterite (001)-a slab model. Red lines indicate cleavage planes identified with Miller indices in black. By comparing Table 3 and Table 4, we observe that the wurtzite phase of CZTS tends to have lower cleavage energies. Especially the (010)-a surface of wurtzite CZTS is much more stable than all lowindex surfaces of kesterite and stannite. Thus, when the crystal particle is small enough that the surface energy dominates the energetics, CZTS will favor formation of the wurtzite phase. This result agrees with the fact that most wurtzite CZTS samples that have been made are predominantly nanocrystalline.59-68 To suppress formation of wurtzite will require some means of bypassing formation of nanocrystals or to convert them once formed. We consider the former in what follows. For both kesterite and stannite, the (110), (112), and (102) surfaces have significantly lower cleavage energies than the (100) and (001) surfaces. Indeed, in a typical powder X-ray diffraction spectrum of CZTS,69, 70 the peaks corresponding to the interplanar distances of (110), (112), and (102) are much 15



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more distinctive than the (100)/(001) surfaces, suggesting a possible preference for growth along those directions. Subsequent experimental studies71-80 confirmed that the most preferable growth direction for the CZTS films is always [112] on either Mo or glass substrates, in qualitative agreement with our calculated cleavage energies. For these three low-energy surfaces, we find no essential difference in stability between the kesterite and stannite phases. On the other hand, the kesterite (001)-a and (100) cleavage energies are up to 0.27 J/m2 lower than the same surfaces of stannite. However, these two surfaces have higher energies compared to the other low-index surfaces and therefore are disfavored during growth. Therefore, to exploit surface thermodynamics to stabilize pure CZTS in the kesterite phase, we need to find a way to stabilize the “beneficial (001) and (100) surfaces” that favor kesterite over stannite, while disfavoring wurtzite nanocrystal formation. In other words, we need to find the means to encourage crystal growth - of thin films rather than nanocrystals - along the [001] and [100] directions via providing proper crystallization templates. We return to this point momentarily. We next investigated the effects of Se additions on the cleavage energies of kesterite and stannite CZTS to see if adding Se might be a way to stabilize kesterite; the results are shown in Table 3. Se alloying is predicted to stabilize all surfaces of both phases, while the effect is most prominent for the (001) and (100) surfaces. With 50% Se, the energies for the (001) and (100) surfaces are lowered by ~0.2-0.3 J/m2 whereas for the other three directions only a ~0.1 J/m2 decrease is predicted. Se additions therefore could be effective at stabilizing the “beneficial surfaces”, although this effect is not strong enough to alter the trend of the most stable surfaces being (110)/(102)/(112) rather than (100)/(001). Based on these results, we instead explore whether the stability of (100) and (001) kesterite CZTS surfaces can be enhanced at interfaces with appropriate substrates that might be used as growth templates in the synthesis process. CZTS/ZnS(001) Interfaces 16


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We consider zinc blende ZnS, which topologically is a parent compound for both the kesterite and stannite CZTS structures. The computed cell parameter for ZnS is 5.34 Å, which is very close to the kesterite cell parameter of 5.35 Å. ZnS has the same stacking pattern as kesterite/stannite CZTS and very minor lattice mismatch, making its (001) surface a perfect crystallization template for CZTS (001) and (100) surfaces. We consider here only the two tetragonal phases and not the wurtzite phase for two reasons: 1) wurtzite CZTS has highest bulk free energy and 2) the hexagonal lattice of wurtzite CZTS does not match well the cubic lattice of the zinc blende ZnS (001) substrate. Thus it is highly unlikely that wurtzite will be a competitive phase on this particular substrate. Which phase is more stable on the substrate, kesterite or stannite? If the kesterite phase is more stable, is there any extra stability provided by the substrate and the thin film geometry, compared to the bulk situation? To answer these questions, we calculated the relative energy of CZTS overlayers deposited on the ZnS (001) surface. The ZnS substrate was built with four ion bilayers, with each of the bilayers composed of one layer of cations and one layer of anions. We tested two models of the CZTS overlayer with different thicknesses, containing two (corresponding to half a unit cell in the (001) direction) or four bilayers (corresponding to one unit cell in the (001) direction) respectively, representing different stages of crystal growth. Both models maintained the correct stoichiometry of the bulk CZTS. The interfaces can be further divided into two different types: sulfur-terminated (S-term) CZTS in contact with metal-terminated (M-term) substrate, or M-term CZTS with S-term substrate. The relative energies computed for all these systems are summarized in Table 5. Table 5. Interface relative energies (in kJ/mol/formula-unit). Overlayer phase and orientation

Kesterite (001)-a

S-terminated substrate

Zn-terminated substrate

2-bilayer

4-bilayer

2-bilayer

4-bilayer

48.96

43.12

-129.76

-49.20

17



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Kesterite (001)-b

79.28

39.44

-0.40

17.04

Stannite (001)-a

118.48

83.68

-98.48

13.44

Stannite (001)-b

69.76

35.92

-79.52

22.40

Kesterite (100)

52.00

24.00

-77.76

-40.88

Stannite (100)

9.12

6.16

-73.44

-38.08

For the S-terminated substrate, the most stable configuration is the stannite (100) surface in both 2bilayer and 4-bilayer cases, which is not desirable. However, for the M-terminated substrate, kesterite (001)-a becomes the most stable geometry and is energetically favored by ~30 kJ/mol/formula-unit (in the 2-bilayer case) and ~11 kJ/mol/formula-unit (in the 4-bilayer case) compared to the most stable stannite configuration. Considering the bulk energy difference between the two phases is only 3 kJ/mol/formula unit, we can conclude that the zinc-terminated ZnS (001) substrate provides significant extra stability for the kesterite phase, especially in the early stage of crystallization (the 2-bilayer case). Furthermore, the adhesion energies between the kesterite(001)-a slab and the Zn-terminated ZnS slab are very attractive (-3.09 J/m2 for the 2-bilayer case and -3.02 J/m2 for the 4-bilayer case), showing that the two slabs adhere well to each other and formation of the interface is naturally favored. We thus predict that use of a zinc-terminated ZnS (001) substrate may aid in synthesis of pure kesterite CZTS crystals. It is interesting to further compare the adhesion energies of the ZnS/kesterite(001)-a interface with the ZnS/stannite(001)-a system. For the 2-bilayer case, we obtained ΔEad = -3.09 J/m2 for kesterite(001)-a and -3.44 J/m2 for stannite(001)-a. Apparently the stannite phase should be favored over the kesterite phase from the perspective of adhesion energies, in contrast with the trend observed in the total relative energy metric. Therefore, the extra stability of the kesterite(001)-a interface is controlled by the lower cleavage energies of the kesterite(001) slab (see Table 3). The only advantage of the ZnS(001) substrate is to provide an appropriate template for the beneficial orientations, and we do not have to rely on any 18


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special chemical affinities between the ZnS substrate and the kesterite film. Hence, in later stages of growth, we expect the extra stability of the kesterite phase to remain as long as the orientation of the film surface is unchanged. We can consider the entire growth process to be a combination of many elementary thin-layer deposition steps. Within each elementary step, the formation of a new kesterite layer is always strongly favored over a new stannite layer. Therefore, the lower cleavage energy of the kesterite(001) surface provides an advantage for the kesterite phase during the entire deposition process. CONCLUSIONS In this study, we investigated the bulk, surface, and interface stabilities of three phases of CZTS (kesterite, stannite, and wurtzite) using PBE+U+D2 level of theory. The results show that the formation of CZTS is thermodynamically favored and that the different phases of CZTS are very close in energy, in accordance with previous studies. This near-degeneracy is likely responsible for secondary phase formation in CZTS films, introducing SRH recombination centers, lowering the band gap and the open circuit voltage, ultimately decreasing PV cell efficiency. The stannite phase is particularly problematic for the desired kesterite phase, as these two phases share the same lattice topology. Partial Cu/Zn disorder has been observed experimentally, indicating the instability of the ordered Cu/Zn sub-lattice, which is consistent with the quasi-degeneracy of the kesterite and stannite phases. Via computer simulations, we explored the feasibility of a strategy that exploits the surface and interface properties of CZTS to enhance kesterite’s relative stability. Our calculations indicate that the wurtzite phase of CZTS generally has the lowest cleavage energies and thus will be the most favored phase in nanocrystals where surface energetics dominates, consistent with recent measurements. No essential difference in stability was found between kesterite and stannite for all low energy surfaces that naturally emerge in current synthesis procedures. However, two surfaces ((001) and (100)) with slightly higher energies may provide extra stability for kesterite and thus might be exploitable as “beneficial surfaces”. Se additions could lower the formation energies of these “beneficial surfaces” but not very 19



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significantly. Instead, we assessed whether a zinc blende ZnS (001) surface could serve as a successful template to induce selective growth of kesterite CZTS (001)/(100) surfaces. This substrate has two important features: 1) its lattice parameters are almost identical to the corresponding surfaces of kesterite/stannite CZTS and formation of wurtzite CZTS will be inhibited due to significant lattice mismatch and 2) we predict that the kesterite/ZnS(001) interface indeed has significantly higher stability than the stannite/ZnS(001) interface, provided the ZnS(001) substrate is zinc-terminated. Compared to the bulk, the energy difference between the two phases is significantly enhanced in the interface structure, especially in the initial stage of crystallization when surface properties play a more important role. We therefore propose that zinc-terminated zinc blende ZnS (001) or other similar substrates that stabilize “beneficial surfaces” during synthesis should be explored to see if indeed better quality CZTS crystals are formed.

Supporting Information Available Table S1 contains the sizes and k-point setups of the simulation cells we used for all secondary phases, surfaces and interfaces.

ACKNOWLEDGMENTS E.A.C. thanks the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0002120 for funding this project.

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A Strategy to Stabilize Kesterite CZTS for High-Performance Solar

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