Determining and Controlling the Stoichiometry of Cu2ZnSnS4

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Determining and Controlling the Stoichiometry of Cu2ZnSnS4 Photovoltaics: the Physics and Its Implications Kuang Yu, and Emily A. Carter Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b01612 • Publication Date (Web): 03 Jun 2016 Downloaded from http://pubs.acs.org on June 7, 2016

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Chemistry of Materials

Article Type: Article

Determining and Controlling the Stoichiometry of Cu2ZnSnS4 Photovoltaics: the Physics and Its Implications

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 *

E-mail: [email protected]

ABSTRACT Cu2ZnSnS4 (CZTS) is an environmentally friendly photovoltaic material with promising applications in thin-film solar cells. Although CZTS’s efficiency is currently too low, stoichiometry/defect engineering presents a strategy for further improvement. As-grown CZTS is typically disordered and therefore prone to form secondary phases, making the final product stoichiometry difficult to determine and even harder to control. We use first-principles quantum mechanics in combination with Monte Carlo simulations to determine CZTS stoichiometry under various experimental conditions. We develop an approach to predicting the optimal CZTS stoichiometry, explaining the physical origin of Zn-enrichment observed in experiments. We further propose practical ways to introduce more free carriers into CZTS in order to screen observed local potential fluctuations, increase conductivity, and ultimately improve the efficiency of CZTS.

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1. Introduction The promising thin-film photovoltaic material Cu2ZnSnS4-xSex (CZTS/CZTSSe; see Figure 1 for its crystal structure) features an optimal band gap (1.0-1.5 eV depending on extent of Se addition) and low manufacturing cost.1 CZTS is also an economically and environmentally friendly material compared to CuInxGa(1-x)Se2 (CIGS) and CdTe, as it does not contain any expensive or toxic, heavy metal elements. However, its efficiency record is only 12.6%,2 significantly lower than state-of-the-art, silicon-based solar cells. One important limitation to CZTS’s efficiency is its low open-circuit voltage3 caused by local potential fluctuations originating in the disordered Cu/Zn sublattice.4-6 Empirically, the best performance is achieved by off-stoichiometric CZTS devices fabricated under Cu-poor/Zn-rich conditions ([Zn]/[Sn]=1.2, [Cu]/[Zn+Sn]=0.9, or, equivalently, [Zn]/[Sn]=1.2 and [Cu]/[Sn]=1.98; here, [X] denotes the concentration of species X, with X=Cu, Sn, Zn, and various point defects).7 The Cupoor condition leads to higher concentrations of the copper vacancy (VCu) defect, a very shallow acceptor providing essentially free holes.8 The holes introduced by VCu improve the conductivity of CZTS and give rise to its p-type character. Our previous work9 indicates that free holes effectively screen the potential fluctuations in disordered CZTS and increase the open-circuit voltage. Increasing the hole concentration by increasing hole-introducing defects (e.g., VCu, CuZn, etc.) therefore should improve the performance of CZTS-based solar cells.

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Figure 1. Crystal structure of the kesterite phase (the most stable phase at room temperature) of CZTS. Although it seems straightforward to reduce or increase the [Cu]/([Zn]+[Sn]) ratio to introduce more VCu or CuZn, the stoichiometry control of the CZTS cell is in fact much more delicate. The stable region of CZTS in the phase diagram is very narrow; thus, off-stoichiometric conditions often lead to secondary phases (e.g., Cu2S/CuS, SnS/SnS2, and ZnS).10 It is highly nontrivial to determine and control the real stoichiometry of the final product due to the existence of secondary phases. Furthermore, the secondary phase precipitations inside CZTS are difficult to separate, significantly affecting the efficiency of CZTS devices.11 Consequently, a sophisticated balance exists between introducing defects and preventing formation of secondary phases. Currently, stoichiometry control of CZTS largely relies on human intuition and experience, and thus strategies are needed to optimize experimental procedures in a more systematic way. Here, we use first-principles quantum mechanics together with Monte Carlo simulations to study disordered CZTS, which is the more relevant phase at typical annealing temperatures. We aim to resolve two primary issues in this work: how to 1) predict the actual stoichiometry of CZTS under certain experimental conditions (i.e., annealing temperature, sulfurization condition, and Cu/Zn/Sn ratio), and 2)

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improve the current synthesis procedure to increase the free hole concentration while minimizing formation of secondary phases. 2. Methodologies In this work, we only consider disorder on the Cu/Zn sublattice, while assuming a perfect Sn/S sublattice in our energy model. This assumption was validated by previous calculations on ordered CZTS, which indicate that the defects with the lowest formation free energies are all associated with the Cu/Zn sublattice.12-16 We first perform density functional theory (DFT) + U calculations – shown previously to be an appropriate level of quantum mechanics theory17 – on 642 2×2×1 64-atom supercells (with random Cu/Zn sublattices and stoichiometries), and use the results to develop a cluster expansion model18, 19 for disordered CZTS. This model is then applied to larger 6×6×3 1728-atom supercells to avoid the finite-size effects of the smaller supercells. Utilizing test particle deletion (TPD)20 and an umbrella-sampling-like technique that we have developed (see Supporting Information (SI) for details), we obtain the chemical potentials for all three relevant elements in CZTS (µ(Cu, CZTS), µ(Zn, CZTS), and µ(Sn, CZTS)) at various stoichiometries around the stoichiometric point. Via comparing these chemical potentials in CZTS with various secondary phases (CuS, Cu2S, SnS2, SnS, ZnS), we are able to determine the accessible stable region of CZTS at a particular temperature and sulfurization condition. In contrast to previous work,12, 14 which used the chemical potentials as variables, our approach directly elucidates the stability of the CZTS sample with different elemental ratios, which is a quantity much easier to control in experiment. More importantly, this approach allows us to incorporate the Cu/Zn configurational entropy effect into the defect and the secondary phase studies, which was usually neglected in previous investigations. The technical details of the computational methods can be found in the SI. 3. Results and Discussion 4


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In this section, we first mainly focus on the Cu-poor region of the CZTS phase diagram ([Cu]/[Sn] < 1), as experiments already have shown that the best performing CZTS devices are fabricated under Cupoor conditions.7 It therefore is more important to understand the phase boundaries of CZTS in the Cupoor half of the CZTS phase diagram. We briefly discuss the Cu-rich region thereafter, elucidating one of the possible reasons that Cu-rich CZTS is not as effective as Cu-poor CZTS. Cu-Poor Region In Figure 2, 3, and 4, we show contour maps of the chemical potentials of Cu, Zn, and Sn in the Cupoor region computed at 750 K. In these compositional phase diagrams, the stoichiometric point ([Cu]/[Sn]=2 and [Zn]/[Sn]=1) is labeled with the letter “S.” Since interstitial defects are not included in this study, we do not consider systems that contain more Cu/Zn atoms than the total number of sites in the Cu/Zn sublattice. The grey region above the blue dotted line “C-S” (([Cu]+[Zn])/[Sn] = 3) therefore will not be investigated. Furthermore, we note that any phase points below the blue dotted line “A-S” ([Zn]/[Sn]=1) correspond to a Zn-poor stoichiometry and formation of VZn. This VZn region (filled in blue) should be avoided during synthesis, as previous calculations indicate that VZn introduces local hole traps.13 In the region encompassed by the triangle ∆ACS, the system is dominated by two types of defects: VCu and excess ZnCu, which serve as hole and electron donors, respectively. (Note that the Cu/Zn sublattice is highly disordered; thus, we have extremely high concentrations of both ZnCu and CuZn antisites that compensate each other in charge. The carrier concentration is eventually determined by [VCu] and [ZnCu]-[CuZn], which is defined as the excess [ZnCu] in this paper. From here on, we simply denote the excess [ZnCu] using the notation [ZnCu].) The ∆ACS region can be further partitioned into two parts by the blue dashed line “B-S,” which represents the equation [VCu]-[ZnCu]=0 (or, equivalently, the hole concentration [h+]=0). Above line “B-S” (region ∆BCS, filled in orange), there exist more excess ZnCu than VCu defects and the entire system is thus converted into an n-type semiconductor, while in 5



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region ∆ABS (filled in cyan), VCu dominates and thus p-type character is expected. One of our goals in this work is to maximize [h+], which is equivalent to maximizing the quantity [VCu]-[ZnCu]. This can be treated as a simple, two-dimensional linear programming problem, in which the slope of the optimization target ([VCu]-[ZnCu]) is indicated by the line “B-S.” More specifically, we can consider all possible stoichiometries that correspond to a certain hole concentration ([h+]), which form a straight line (represented by equation [VCu]-[ZnCu] = [h+]) parallel to “B-S” in the phase diagram. The intercept of this line on the vertical axis is controlled by the constant [h+]: for higher [h+], the intercept should be lower. Maximizing [h+] therefore is equivalent to finding the lowest experimentally accessible line parallel to “B-S.” The accessibility of a particular stoichiometry can be obtained by considering the constraints enforced by the Cu/Zn/Sn chemical potentials in the secondary phases (vide infra), as well as the requirement to avoid the blue VZn region. Once we define the accessible region in the phase diagram, we can consider lowest line parallel to “B-S” with at least one contact point with the accessible region, which corresponds to the stoichiometry with the highest carrier concentration. Below, we discuss the constraints originating from all secondary phases enforced by the chemical potentials of Cu/Zn/Sn in the corresponding states (µ(Cu, CuS), µ(Cu, Cu2S), µ(Zn, ZnS), µ(Sn, SnS2), and µ(Sn, SnS)). We first perform first-principles calculations at the DFT+U level of theory to obtain the chemical potentials of all secondary phases (µ(CuS), µ(Cu2S), µ(ZnS), µ(SnS2) and µ(SnS)). The sulfur chemical potentials (µ(S)) are then calculated using the gas phase S8 molecule at a pressure of 1 bar and temperature of 750 K as a reference. The Cu/Zn/Sn chemical potentials in secondary phases can be easily extracted from these calculations (see SI for details) and compared with µ(Cu/Zn/Sn, CZTS) as plotted in Figure 2, 3, and 4.

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Figure 2. Chemical potential of Cu in the disordered 1728-atom CZTS supercell (µ(Cu, CZTS), eV) at a temperature of 750 K and 1 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase diagram.

For Cu, we obtain µ(Cu, CuS) = -3.523 eV and µ(Cu, Cu2S) = -3.445 eV, both of which are higher than all µ(Cu, CZTS) values plotted in Figure 2. This indicates that in the Cu-poor region we investigate, no CuS and Cu2S precipitates should form, at least from a thermodynamic point of view. This conclusion is more or less trivial since the Cu-poor condition is presumed, although computational reproduction of this conclusion does serve as a sanity check for our method.

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Figure 3. Chemical potential of Zn in the disordered 1728-atom CZTS supercell (µ(Zn, CZTS), eV) at a temperature of 750 K and 1 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase diagram. The red isoline represents the stoichiometries with µ(Zn, CZTS) = µ(Zn, ZnS).

For Zn, we obtain µ(Zn, ZnS) = -2.944 eV, corresponding to the red isoline plotted in Figure 3. Above this red isoline is the forbidden region enforced by ZnS, in which we have µ(Zn, ZnS) < µ(Zn, CZTS). In this region, the CZTS will then decompose into ZnS and a more Zn-poor product. It is particularly interesting that the point “S” is inside the forbidden region, and thus the perfectly stoichiometric CZTS sample is not stable. Our cluster expansion model predicts a positive formation energy for VZn (~0.843 eV) in ordered CZTS, which is in agreement with all previous studies.12-16 Yet, we find that the formation of VZn is spontaneous once the disordered Cu/Zn sublattice is utilized in our simulation. This finding highlights that the previous defect stability predictions for the ordered phase can be misleading, and it therefore is important to account for disorder and the corresponding configuration entropy. For any stoichiometries below the red isoline, we have µ(Zn, ZnS) > µ(Zn, CZTS). In this case, the CZTS sample is stable without ZnS precipitation, but it may react with the ZnS to form a more Zn-rich 8


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product if excess ZnS exists. In the typical Zn-rich synthesis condition (e.g., [Zn]/[Sn] = 1.2), the system is essentially bound to the one-dimensional red isoline in equilibrium with the Zn reservoir in the environment. The stoichiometry of the CZTS product is then solely controlled by the [Cu]/[Sn] ratio on the abscissa of Figure 3. The stoichiometry with the highest [h+] is determined by the linear programming procedure we described above and is the point at which the red isoline and the line “A-S” intersect, which is labeled in Figure 3 as point “O1”. Further decreasing the [Cu]/[Sn] ratio pushes the system into the Cu-poor and Zn-rich end of the red isoline. In this case, we introduce a large amount of Zn substitutions (ZnCu antisites) instead of VCu, which is detrimental to the photovoltaic performance. This n-type defect introduces electrons compensating the holes, decreasing the concentration of free carriers. Moreover, the positively charged ZnCu+ antisites create more local potential fluctuations, lowering the open-circuit voltage. This result is in agreement with the experimental observation of Znrich domains inside CZTS,4 the formation of which is an apparent sign of a local Cu-deficiency. Based on the location of point “O1,” we can conclude that a [Zn]/[Sn] ratio slightly higher than 1 is optimal in an ideal Cu-poor situation, while an even higher [Zn]/[Sn] ratio only leads to the ZnS secondary phase. We note that the empirically optimal [Zn]/[Sn] ratio is over 1.2, which is probably due to kinetic reasons: an absolute excess amount of Zn is necessary to ensure the Zn-rich environment over the entire crystal.

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Figure 4. Chemical potential of Sn in the disordered 1728-atom CZTS supercell (µ(Sn, CZTS), eV) at a temperature of 750 K and 1 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase diagram. The blue isoline represents the stoichiometries with µ(Sn, CZTS) = µ(Sn, SnS2). The red isoline represents the stoichiometries with µ(Zn, CZTS) = µ(Zn, ZnS).

If we choose a close-to-unity [Zn]/[Sn] ratio and do not use excess amount of Zn in the synthesis, the region below the red isoline is stable by itself. In this situation, the red isoline serves as the upper bound of the accessible region, while the lower bound is enforced by the formation of SnSx phases. For Sn, we obtain µ(Sn, SnS) = -5.809 eV and µ(Sn, SnS2) = -6.106 eV for both relevant secondary phases. Since µ(Sn, SnS2) < µ(Sn, SnS) in this condition, we will simply use SnS2 to set the lower bound for CZTS, as plotted using the blue isoline in Figure 4. The upper bound enforced by ZnS is also plotted in Figure 4 as reference, and the accessible region is between the blue and red isolines. CZTS with stoichiometries below the blue line will decompose into SnS2 and new CZTS products with higher [Cu]/[Sn] and [Zn]/[Sn] ratios. The highest [h+] while avoiding VZn is obtained at the stoichiometry labeled as “O2” in Figure 4 (the intersection point of the blue isoline and the line “A-S”). The [VCu] is tunable in between 10


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~0.5% (point “O1”) to ~1.5% (point “O2”) based on the aforementioned thermodynamic analysis, depending on different [Cu]/[Sn] ratios, which introduces the corresponding concentration of holes. We note that these results are only semi-quantitative considering the ~0.1 eV accuracy of the underlying DFT+U method. Nevertheless, from a thermodynamic perspective, this study provides a clear, physical picture to explain the existence of an optimal stoichiometry and an effective model to predict its position. The entire analysis above is subject to a particular µ(S), which is tunable via changing the sulfurization conditions in the experimental procedure. For example, decreasing the partial pressure of S8 by half (0.5 bar) at a temperature of 750 K decreases µ(S) by 0.045 eV, correspondingly changing µ(Sn, CZTS), µ(Sn, SnS2), and µ(Zn, ZnS). The results in this condition are plotted in Figure 5 with the accessible region moved towards the Cu-rich direction as compared to Figure 4, generating less VCu and less holes. This demonstrates a higher [VCu] can be achieved at higher µ(S), corresponding to a more reactive sulfurization environment. The upper bound of µ(S) is, of course, constrained by the chemical potential of the most stable sulfur allotrope at the particular temperature and pressure.

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Figure 5. Chemical potential of Sn in the disordered 1728-atom CZTS supercell (µ(Sn, CZTS), eV) at 750 K and 0.5 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase diagram. The blue isoline represents the stoichiometries with µ(Sn, CZTS) = µ(Sn, SnS2). The red isoline represents the stoichiometries with µ(Zn, CZTS) = µ(Zn, ZnS).

Figure 6. Chemical potential of Sn in the disordered 1728-atom CZTS supercell (µ(Sn, CZTS), eV) at a temperature of 600 K and 1 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase 12


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diagram. The blue isoline represents the stoichiometries with µ(Sn, CZTS) = µ(Sn, SnS2). The red isoline represents the stoichiometries with µ(Zn, CZTS) = µ(Zn, ZnS).

We also performed the same analysis at a lower temperature of 600 K to investigate the temperature dependence of these predictions; the corresponding results are shown in Figure 6. Similar to Figure 4, the blue and red isolines represent the boundaries enforced by SnS2 and ZnS, respectively. We observe two features from the lower temperature simulation: first, the accessible region becomes much narrower (note the blue and the red isolines almost overlap each other in Figure 6), indicating that the system is much more prone to secondary phase formation; and second, the stoichiometric point “S” becomes stable and the allowed maximum [VCu] is much lower than the high temperature case. We therefore conclude that a higher temperature is needed to increase the VCu and hole concentration. In contrast, our previous work9 indicated that a lower temperature was beneficial for restoring the order of the Cu/Zn sublattice and opening the band gap. These two competing factors specify that there may be an annealing temperature range within which the optimal balance can be reached. Below 600 K, the Cu/Zn sublattice still has significant disorder (the order-disorder transition occurs ~530 K), and no VCu can be introduced to remedy the voltage loss. Beyond 750 K, the lattice disorder causes more than 0.4 V voltage loss, which cannot be compensated for even with 10% Cu vacancies. Therefore, we estimate the optimal annealing temperature is between 600-750 K; a more quantitative estimation of this temperature range is difficult and must be the subject of future research. Cu-Rich Region In this section, we briefly discuss the Cu-rich region. As noted earlier, the best-performing CZTS devices are usually fabricated under Cu-poor conditions; thus, the phase boundaries in the Cu-rich region are not as important from a practical perspective. According to our previous study,9 the free holes introduced by VCu effectively screen the local potential fluctuations and open up the band gap, which is 13



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a likely reason for the necessity of Cu-poor synthesis conditions. In the Cu-rich region, the excess CuZn antisites also introduce holes and thus are expected to have band gap opening effects similar to VCu. However, the hole introduced by CuZn is more localized around the defect site compared to VCu, so these holes should be less effective in screening electrostatic potential fluctuations. To verify this hypothesis, we repeat our band gap calculations in reference 9 by taking ten random 1728-atom CZTS structures sampled at a temperature of 750 K, manually introducing equal concentrations (5%) of either VCu or ZnCu. The resulting band gaps of the defective disordered structures are compared with the stoichiometric disordered structures in Figure 7.

Figure 7. Band gaps of the disordered CZTS supercells with defects in comparison with the band gaps of stoichiometric supercells. The line is meant merely as a visual guide, corresponding to the hypothetical case in which the band gaps of the stoichiometric and defective cells were identical for a given disordered structure.

It is clear that both VCu and CuZn open the band gap, with the band gaps of the VCu-containing structures tending to be higher than the CuZn-containing structures. This finding confirms our previous interpretation, providing one possible explanation as to why the Cu-poor condition is favored over the Cu-rich condition in CZTS-based photovoltaics. 14


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Figure 8. Chemical potential of Cu in the Cu-rich 1728-atom CZTS supercell (µ(Sn, CZTS), eV) at a temperature of 750 K and 1 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase diagram.

Figure 9. Chemical potential of Sn in the Cu-rich CZTS supercell (µ(Sn, CZTS), eV) at a temperature of 750 K and 1 bar of S8, plotted in the [Zn]/[Sn] versus [Cu]/[Sn] compositional phase diagram. The blue isoline represents the stoichiometries with µ(Sn, CZTS) = µ(Sn, SnS2). The red isoline represents the stoichiometries with µ(Zn, CZTS) = µ(Zn, ZnS). 15



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Although the Cu-rich situation is apparently less important, we nevertheless computed the chemical potential maps in this part of the phase diagram (Figure 8 and 9) to explore the boundary of the accessible region. Surprisingly, µ(Cu, CZTS) is always lower than µ(Cu, CuS) (-3.523 eV) in all of the stoichiometries we have investigated so no CuS precipitation is expected, similar to the Cu-poor situation. Therefore, the accessible region in the Cu-rich condition is still a striped area defined by µ(Zn, ZnS) and µ(Sn, SnS2), as shown in Figure 9. We predict that this region stretches to highly Cu-rich and Zn-poor stoichiometries, while there are no constraints to define its boundary at that end. Calculations indicate that µ (Cu 2SnS3 ,CZTS) = 2 µ (Cu) + µ (Sn) + 3µ (S) increases towards the Cu-rich/Zn-poor end of the accessible region, indicating that a boundary exists (although beyond the region investigated) enforced by the formation of the Cu2SnS3 secondary phase. However, we will not explore the phase diagram further, as our cluster expansion model was only validated around the stoichiometric point. Nevertheless, our calculation indicates a high tolerance of CZTS to Cu substitution, while further studies are needed to examine electronic structure properties of extremely Cu-rich CZTS. 4. Summary and Conclusions In this study, we computed maps of Cu and Zn chemical potentials for disordered CZTS with varying compositions using first principles quantum mechanics combined with Monte Carlo simulations. By comparing these maps with Cu and Zn chemical potentials in secondary phases, we directly predicted the stoichiometry of the final CZTS product at specified experimental conditions of [Cu]/[Sn] and [Zn]/[Sn] ratios, temperatures, and sulfurization conditions. We also offered a physical reason for the Zn-enriched domains observed in experiments, as being due to a too-low [Cu]/[Sn] ratio in the corresponding local region. By comparing the Cu/Zn chemical potentials in CZTS and the corresponding secondary phases, we also predicted the optimal [Cu]/[Sn] ratio that avoids detrimental 16


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Zn-enrichment. Furthermore, to address our objective of suggesting improvements in synthesis methods, we proposed two ways to increase the [VCu] (or equivalently [h+]) under Cu-poor conditions. The first approach is to increase the synthesis temperature, which leads to higher concentrations of free holes, but also increases the Cu/Zn disorder that lowers the band gap. The two competing effects found in our studies implied the existence of an optimal annealing temperature range, the estimation of which requires further research. The second perhaps superior approach is to use a more reactive sulfurization condition, which should allow access to stoichiometries with higher [VCu] to improve CZTS performance. Possible practical solutions to increasing the sulfur chemical potential include, but are not limited to: applying higher pressure to the sulfur atmosphere, continuously removing H2 from the system if H2S is used as a sulfur source, or using a more reactive form of sulfur. We also investigated the Curich region of the phase diagram and predict a high tolerance of CZTS to Cu substitution. Further studies are needed to clarify the impact of a high concentration of Cu substitution on the disordered phase of CZTS. Lastly, we note that while all previous studies have tried to deduce defect concentrations from formation energies of isolated defects in ordered supercells, here we directly simulated disordered samples with different stoichiometries for the first time. We believe that both the specific results of this study, as well as the modeling approach, can help guide experimentalists synthesizing new inorganic materials.

Supporting Information Computational details for all ab initio and Monte Carlo calculations.

Acknowledgments 17



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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. We also thank Dr. John Mark Martirez for helping to revise the manuscript.

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Determining and Controlling the Stoichiometry of Cu2ZnSnS4

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