Atomistic Modeling of Sulfur Vacancy Diffusion Near Iron Pyrite Surfaces

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Effect of Annealing Conditions on the Healing of Sulfur Vacancies Near the Iron Pyrite Surfaces Yan-Ning Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b08300 • Publication Date (Web): 17 Sep 2015 Downloaded from http://pubs.acs.org on September 19, 2015

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The Journal of Physical Chemistry

Effect of Annealing Conditions on the Healing of Sulfur Vacancies Near the Iron Pyrite Surfaces Y. N. Zhang1,2 1

Chengdu Green Energy and Green Manufacturing Technology R&D Center, Chengdu, Sichuan, 610207 CHINA 2

Beijing Computational Science Research Center, Beijing, 100084, CHINA

Abstract Through density functional calculations, we investigated the segregation of an isolated sulfur vacancy (VS) from interior sites outward to the FeS2(100) and (111) surfaces. The effects of vacancy at different depths on the atomic structure, the vacancy formation energy, and the electronic properties of the iron pyrite crystal are discussed in detail. Significantly, we find that VS tends to migrate toward the either stoichiometric or sulfur-rich surfaces through an “interdimer” exchange mechanism. This indicates that sulfur vacancies in pyrite thin films can be selfhealed in sulfur-rich conditions at a reasonably high temperature, an important concept for the fabrication of high quality solar materials. Keywords: iron pyrite surface, sulfur vacancy, vacancy segregation, first-principles calculations

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1. Introduction How to control vacancies and impurities in solids is a crucial issue for the optimal performance of materials, from semiconductors1,2,3,4,5,6, high-κ materials7,8,9, to steels.10,11 Iron pyrite (FeS2) is a promising material for use in solar photovoltaic and photoelectrochemical cells due to its suitable band gap, excellent optical absorptivity, and essentially infinite abundance of iron and sulfur in the planet’s crust.12 The main hurdle for the development of pyrite solar cells is its unexpectedly low conversion efficiency, 3%, primarily due to the low open circuit voltage, VOC ~200 meV.13,14 Gap states produced by impurities, defects, surface and grain boundaries are typically assigned as the source of the low VOC.15,16 Indeed, ab initio simulations show that some impurities and deficiencies reduce the band gap of pyrite and hence degrade its photovoltaic performance.17,18,19,20,21,22 Fe-vacancies (VFe) and S-vacancies (VS) are the simplest defects in pyrite samples that are fabricated in non-stoichiometric conditions. Despite the high formation energies as predicted by several recent density functional theory (DFT) studies (2.27-2.7 eV under S-poor condition),17,19,20,23,24 high concentration S-vacancies have been detected in pyrite samples, using techniques such as high resolution X-ray diffraction (HRXRD)25, photoemission of adsorbed Xe (PAX)26,27, scanning tunneling microscopy (STM)28, and atomic emission spectroscopy (AES)29,30. Furthermore, the chemical stoichiometry of pyrite samples were found to sensitively changes with temperature or surface conditions.31,32,33,34,35,36 Therefore, it is crucial to optimize the annealing environment for the removal of S-vacancies in pyrite films, starting from understanding the segregation mechanism of a single neutral S-vacancy near the surface region.

According to the calculated surface energies of stoichiometric pyrite surfaces, the preference follows the trend (100) > (111) > (210) > (110).37 Besides (100) surfaces, the (111) facets were also observed in experiments, for example, in the growth of shape-controlled nanocrystal.38,39 In this paper, we report results of density functional theory studies of sulfur vacancy segregation near the two most popular facets in iron pyrite samples, FeS2(100) and FeS2(111), under different surface stoichiometric conditions. Our results show that sulfur vacancies tend to drift toward the surface for all the cases studied here, even though the energy barriers strongly depend on the surface stoichiometry. The availability of energy barriers for the segregation of S-vacancies in


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different conditions and the clear insights allow rational design of optimal fabrication and annealing conditions for the development of iron-pyrite devices.

2. Computational methodology As sketched in Fig. 1(a), the pyrite FeS2 structure adopts a NaCl-like structure, with a facecentered cubic sublattice of diamagnetic Fe2+ ions and ⟨111⟩-oriented S-S dimers occupying the anion positions.19 Each Fe ion has an octahedral coordination to six S ions, and each S ion has three Fe neighbors and one S neighbor. The cleavage of pyrite FeS2 typically leads to complex morphology and surface stoichiometry. For example, cleavage of only Fe-S bonds perpendicular to a (100) plane creates the stoichiometric (100) surface, whereas mixed cleavage of S-S and FeS bonds creates various nonstoichiometric surfaces.40 Here, we use three different stoichiometric conditions to mimic different environments for the segregation of S-vacancy at the FeS2(100) surfaces, as shown in Fig. 1(b). Our previous DFT studies have shown that these three surfaces are thermodynamically stable in SO2, H2S and S-rich conditions, respectively.40 We used a periodic slab model that consists of eleven FeS2 atomic layers and a vacuum of 17 Å thick for mimic these FeS2(100) surfaces. The slabs were constructed with two identical surfaces in order to avoid artificial electric fields in the vacuum for studies of polar surfaces. A (2×2) supercell in the lateral plane was adopted, and one sulfur ion was removed from different sulfur layers to simulate the motion of a sulfur vacancy. For discussions below, we denote a sulfur atom in the nth (n=1~6) layer as S_n and a sulfur vacancy in this layer as VS_n, as depicted in Fig. 1(c). The FeS2(111) surface is more complex, with five different surface terminations. One of them is Fe-terminated and the others contain 1~4 layers of S atoms (denoted by (111)-Fe, (111)-S, (111)2S, (111)-3S, and (111)-4S, respectively, cf. Fig. 5 in Ref.37). Here, we performed our calculations for the stoichiometric (111)-2S, and S-rich (111)-3S and -4S surfaces. A period hexagonal slab model with nine FeS2 atomic layers and a vacuum of 18 Å thick was used. To get a similar vacancy concentration as for the FeS2(100) surfaces, we adopted a (2×1) supercell in the lateral plane, so the entire slab model contains more than 230 atoms, as depicted in Fig. 1(d)).

Spin-polarized density functional calculations were performed using the Vienna Ab initio Simulation Package (VASP)41 along with the projector augmented wave (PAW) method.42 The



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generalized-gradient approximation (GGA)43 was adopted to describe the exchange-correlation interaction among electrons, and a Hubbard U of 2 eV was added for Fe 3d orbitals40,44,45. We used an energy cutoff of 350 eV for the plane-wave basis expansion. The convergence of our results against the number of k-points in the Brillouin zone was carefully monitored for all the cases. The lattice size of unit cell in the lateral plane was set according to the optimized lattice constant of bulk pyrite, a = 5.422 Å. The Fe and S atoms in the central layer were fixed at their bulk positions, whereas all other atoms were fully relaxed until forces on them became smaller than 0.01 eV/Å.

(b)

(a)

(d) FeS2(111)-4S top view

intra-dimer inter-dimer

VS_4 VS_5

Surf(-1) VS_1

(c) surface VS_1 VS_2 VS_3 VS_4 VS_5 VS_6

bulk-like

S1 S2 S3 S4 S5 S6

Surf(0)

VS_2 VS_3

side view

VS_1 VS_2 VS_3

VS_4 VS_5

Surf(+1)

Fig. 1 (Color online) (a) The bulk unit cell of pyrite FeS2 and the sketch of ‘intra-’ and ‘inter-’ dimer exchanges during vacancy segregation. Yellow (light gray) and blue (medium gray) spheres represent S and Fe atoms, respectively. (b) Relaxed structures of the three FeS2(100) surfaces explored in this study. The large orange (dark gray) spheres represent the additional sulfur atoms added to the stoichiometric surface, Surf(0). (c) Schematic diagram of one sulfur vacancy, the green sphere, in the nth layers in Surf(0), VS_n. This shows a (010) projection of the (100) surface. (d) The top- and side- views of FeS2(111)-4S surface. VS_1-VS_5 are the various positions of sulfur vacancy near the surface. The pink arrow shows the hopping of neighboring


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sulfur atom to VS_4.

3. Results and discussions To fill a sulfur vacancy within the crystal bulk, surface sulfur atoms may directly penetrate into the interior region by migrating between tetrahedral interstitial sites in FCC Fe lattice. However, our calculations indicate that the energy barrier for such direct penetration mechanism is extremely high. For example, a sulfur atom at Surf(+1) moving from the topmost layer to VS_6 needs to overcome energy barriers as high as 4.1 eV. Considering the typical annealing temperatures46, it is very unlikely to have interior vacancies healed via this direct way. Therefore, the most probable path for fill VS is through layer-by-layer hopping, i.e., by stepwise exchange between VS_n and VS_(n-1) species. To see if this vacancy hopping mechanism is feasible, we calculated the position dependence of the formation enthalpy of VS according to: ∆Hf = Evac - Eperf + µS

(1)

Here, Evac and Eperf are the energies of surface slabs with and without vacancies, respectively. The chemical potential of one S atom, µS, is a parameter to simulate the change of environment from oxidizing conditions to S-rich conditions (e.g., µS=-6.32 eV in SO2 and µS = 0 for an isolated sulfur atom). Using µS = -3.77 eV, which corresponds to a S-poor condition, the calculated vacancy formation energies at three FeS2(100) surfaces are shown in Fig. 2 as a function of depth of VS. Clearly, ∆Hf decreases as the vacancy moves from the interior region to the surface, indicating that interior vacancies have a natural tendency to diffuse towards the surfaces. This is understandable since it is easier for neighboring surface atoms to adjust their positions and charge states to compensate the removal of the sulfur atom. The only exception is for Surf(-1) where the calculated ∆Hf of VS_2 is higher than that of VS_3 by 0.4 eV. The vacancy is likely to be trapped in the subsurface layer, VS_3, instead of moving to the topmost S_2 layer that is already S-poor. The calculated ∆Hf is only 0.42 eV for VS_1 in Surf(0), a value that is much lower than the ∆Hf of 2.36 eV in bulk pyrite under the same S-poor condition. Accordingly, the vacancy density at the surface should be rather high, particularly under the weakly oxidizing growth or annealing conditions. The calculated equilibrium vacancy concentration, [Vs], which is determined by [VS] = [VS]maxexp(-∆Hf/kT) with [VS]max = 5×1022 cm-3, changes from 107 cm-3



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for VS_6 to 1019 cm-3 for VS_1 at Surf(0) at room temperature. Note that under this condition, the ∆Hf for VS_0 in Surf(+1) even lowers to a negative value of -0.62 eV, as shown by the red circles in Fig. 2, indicating an automatic presence of VS_0 at Surf(+1). This is consistent with results of our previous studies, that Surf(+0.875) has a lower surface energy than Surf(+1) at µS = -3.77 eV.40 It has been known that along the (100) orientation Surf(0) is the most stable surface in the range of −3.85 eV < µS < −3.17 eV; and Surf(+1) is stable in a large range of µS under the S-rich condition, with a lower surface energy than Surf(+1)+Vs surface. Therefore, we perceive that the continuous segregation of Vs to surface won’t affect the surface stoichiometry in a sulfur reservoir with a fixed µS. While the segregation of VS towards the surface is energetically favorable, the energy barriers along the pathways govern the efficiency of this process. To address this issue, we calculated the energy barriers in each VS hopping step at Surf(0) and the results are also given in Fig. 2 in open black squares along with the ∆Hf line for Surf(0). We displaced sulfur vacancy in small steps along the surface normal (0.3 Å) and the lateral positions of all atoms were relaxed until forces on them became smaller than 0.01 eV/Å. For the process that S_5 exchanges with VS_6, the energy barrier is only 0.23 eV. This is understandable since these two sites are at the ends of a SS dimer in pyrite. Actually, the S_5 atom already moves toward the VS_6 site by about 0.16 Å along their joint line, even though no obvious shift is found for the Fe atoms around. The Bader charge analyses show that while the charge state of Fe atoms remain unchanged (+0.88e), the Bader charge the S_5 atom near VS_6 becomes -0.80e, almost doubled from that of a S atom in the perfect bulk pyrite. This is akin to what occurs nears Vs in bulk pyrite. Overall, the “intradimer” exchange as depicted in Fig. 1(a) appears to be very easy even at room temperature.

Now let us see how difficult the “inter-dimer” exchange process is, i.e., the position change between a vacancy and a S atom across two adjacent S-S dimers, as sketched in Fig. 1(a). Taking the process of VS_5 ↔ S_4 as an example, we found that the calculated energy barrier in Fig. 2 is as large as 1.5 eV, indicating the low mobility and the need of high annealing temperature. This value is already smaller than the calculated energy barrier for the same process in bulk pyrite, 1.95 eV, as shown in Fig. 2 with the crossed squares. Interestingly, we found that the energy barrier for a positively charged sulfur vacancy in a (2×2×2) bulk pyrite drops to 1.91 eV, and is


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even lower if in a larger (3×3×3) supercell. So we can expect a lower energy barrier than 1.5 eV in experimental samples that may include various charged vacancies. From the structure of the transition state illustrated by the inset in Fig. 2, the S atom (highlighted by the orange sphere) that moves away from the red tetrahedron toward the vacancy becomes coplanar with the three Fe atoms (highlighted by the blue shade). Note that the high barrier for S-segregation is not due to the strain, since the triangle of Fe is large enough for the sulfur atom to pass through. The average distance between the S4 atom and its neighboring Fe atoms of 2.30 Å is comparable with the Fe-S bond length of 2.27 Å in bulk pyrite. The main cause for the high activation energy is the cleavage of S-S dimer, since the S-S bond length in the transition state expands by 20% to larger than 2.58 Å. Obviously, “inter-dimer” exchanges determine the rate of vacancy diffusion towards the surface.

Fig. 2 (Color online) (a) The vacancy formation energy, ∆Hf, as a function of vacancy depth for FeS2(100) surfaces with three different stoichiometries. The black squares show the energy barriers in each hopping step at Surf(0), along with the energy barrier of the “inter-dimer” motion in bulk pyrite marked with dark cyan crossed squares. The inset is the atomic structure in the saddle point of VS_5 VS_4, respectively. The yellow (light gray) and blue (medium gray) spheres denote S and Fe atoms, as highlighted by the green arrow. The green and orange spheres represent the vacancy and migration sulfur atom, respectively. (b) The energy barriers of the



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vacancy hopping from the subsurface layer to the topmost layer for three FeS2(100) surfaces and one FeS2(111)-4S surface. Strikingly, the energy barrier for either intra- or inter-dimer hopping gradually decreases near the surface because of the flexibility of surface atoms. In particular, the energy barriers at the final step, VS_2 VS_1 (or the initial step for S atoms to enter the surface), are only 0.8 eV, which can be easily overcome in a typical annealing condition. It is also worthwhile to point out that the energy barriers are strongly biased for the outward segregation processes near the surface due to the monotonic decrease of ∆Hf near the surface. For example, the inward hopping, VS_2 VS_3, has an energy barrier of 1.6 eV, much higher than 0.8 eV for the opposite process. Such biases effectively frustrate the formation of new Vs in the deep layers. To explore the effects of surface conditions, we also calculated energy barriers for Vs segregating from the subsurface layer to the topmost layer at two other FeS2(100) surfaces, Surf(-1) and Surf(+1). As shown in Fig. 2(b), the energy barrier at the last step at Surf(+1) is only 0.25 eV. Therefore, the excess sulfur atoms can easily diffuse into the subsurface. In contrast, the barrier for VS_3 VS_2 is about 1.1 eV at Surf(-1) with opposite bias against that for VS_2 VS_3, 0.7 eV. Therefore, we expect a high Vs density in the subsurface layer of Surf(-1) and segregation of S is essentially blocked. Accordingly, a S-rich condition on the FeS2(100) surfaces should be beneficial for the removal of Vs.

To see if the same outward segregation tendency of Vs is applicable for other facets, we also performed calculations for three FeS2(111) surfaces and the stoichiometric (110) and (210) surfaces. We first identified the most probable surface morphologies by calculating their surface energies at temperature T and pressure p according to the equation:

γ (T, p) =

1 [G(T,p,N Fe ,N S )- N Fe µFe (T ,p) - N S µS (T ,p)] 2A

(2)

Here, A is the surface area, G(T, p, NFe, NS) is the Gibbs free energy of the slab, and NFe and NS are the numbers of Fe and S atoms. We applied a constraint that requires the chemical potentials of Fe (µFe) and S (µS) to obey µFe + 2 µS = µFeS2 , where µFeS2 is the chemical potential of one FeS2 formula unit in bulk pyrite. Under ambient conditions, G can be approximately replaced by the total energy without contributions from configurational or vibrational entropy.


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The calculated surface energies of several FeS2(111), (110) and (210) surfaces are shown in Fig. 3, along with their configurations on the right side. Here, values of µS range from the energy of a sulfur atom in H2S (-3.77 eV) to that of a sulfur atom in S2 (-2.63 eV) to simulate environments from S-poor to S-rich conditions. We see that the stoichiometric FeS2(100) surface has the lowest surface energy in S-poor condition, whereas the S-rich FeS2(111)-3S and 4S surfaces are more stable than others in the S-rich side. This is in consistent with our experimental observations and previous DFT studies.37,47 Obviously, it is necessary to study the segregation of S-vacancies near the FeS2(111) surfaces. Similar to what we discussed above, the vacancy formation energies at the (111)-4S surface increase from VS_1 to VS_5 for the reason that atoms near the surfaces can relax more easily. Since ∆Hf is small, e.g. 0.53 eV for VS_4 at the (111)-4S surface under the condition µS = 3.77 eV, we expect that the population of VS in FeS2(111) facets is also high in as grown samples. Nevertheless, the calculated energy barrier of the exchange of VS_4 and its neighboring sulfur atom, as highlighted by the arrow in Fig. 1(d) and the green diamonds in Fig. 2(b), is only 0.33 eV, shallow sulfur vacancies on (111) facets should be easily healed under S-rich conditions as well.

Fig. 3 Calculated surface energies of different FeS2(111), (110) and (210) surfaces versus the sulfur chemical potential, µS, in the left panel and the corresponding optimized structures in the right panel. The yellow (light gray) and blue (medium gray) spheres represent S and Fe atoms, respectively.



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One important number that can be directly measured in experiments is the diffusion coefficient of sulfur vacancy in bulk pyrite. It can be represented as D = gΓd2, where Γ is the hopping rate from a filled to a vacancy site, d is the hopping distance, and g is the geometric factor. According to the Vineyard-Rate theory Γ is given by the Arrhenius-type expression: Γ = νexp(-Ea/kBT), where ν is the attempt frequency, Ea is the migration barrier along the diffusion pathway, kB is Boltzmann’s constant, and T is the temperature. Therefore, the sulfur diffusion coefficient can be written more explicitly as D = gνd2exp(∆Ea/kBT). In general g is of the order of 1, and d is approximately 3.1 Å in pyrite between two neighboring octahedral sites of sulfur, i.e., the distance between the orange and green spheres in the inset in Fig. 2(a). The attempt frequency, ν, is determined by calculating the vibrational frequency of the migration atom through the linear response approach. The values of ν are about 1013 s-1 for the sulfur atoms oscillating around their equilibrium sites. With these parameters, the diffusion coefficient of sulfur as a dependence of temperature is displayed in Fig. 4. Clearly, we see that D is exceptionally low, ~2.0×10-36 cm2s-1 at 300K for deep Vs but it can be increased by many orders of magnitude near the surface or at higher temperature. It appears to be necessary to anneal pyrite samples at high temperature for the reduction of deep sulfur vacancies under the (100) facets but it is relatively easier to do so under the (111) facets. It is desired to have any experimental versification for our important predictions.

Fig. 4 The diffusion coefficient of sulfur in bulk pyrite as a dependence of temperature.


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In summary, we performed systematic density functional calculations for studies of segregation of sulfur vacancy in different pyrite surfaces. The formation energy calculations reveal that the shallow sulfur vacancies tend to move outward the surface through the “intra-dimer” and “interdimer” exchange mechanism and the latter determines the rate of vacancy diffusion towards the surface. For the removal of deep sulfur vacancies, the growth and annealing conditions need to have elevated temperature. A S-rich condition should be helpful for the removal of S-vacancies on FeS2(100) and (111) surfaces. Our studies shed some light for the understanding of vacancy formation and diffusion in iron pyrite, a promising low-cost and earth abundant solar material.

Acknowledgement Work was supported by startup fund of China Thousand Young Talents. The calculations were supported by Tianhe2-JK in Beijing Computational Science Research Center and supercomputer in National Supercomputing Center in Shenzhen.

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