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Strong Interplay between Sodium and Oxygen in Kesterite Absorbers: Complex Formation, Incorporation, and Tailoring Depth Distributions

Sodium and oxygen are prevalent impurities in kesterite solar cells. Both elements are known to strongly impact performance of the kesterite devices and can be connected to efficiency improvements seen after heat treatments. The sodium distribution in the kesterite absorber is commonly reported, whereas the oxygen distribution has received less attention. Here, a direct relationship between sodium and oxygen in kesterite absorbers is established using secondary ion mass spectrometry and explained by defect analyses within the density functional theory. The calculations reveal a binding energy of 0.76 eV between the substitutional defects NaCu and OS in the nearest neighbor configuration, indicating an abundance of NaO complexes in kesterite absorbers at relevant temperatures. Oxygen incorporation is studied by introducing isotopic 18O at different stages of the Cu2ZnSnS4/Mo/soda‐lime glass baseline processing. It is observed that oxygen from the Mo back contact and contaminations during the sulfurization are primary contributors to the oxygen distribution. Indeed, unintentional oxygen incorporation leads to immobilization of sodium. This results in a strong correlation between sodium and oxygen, in excellent agreement with the theoretical calculations. Consequently, oxygen availability should be monitored to optimize postdeposition heat treatments to control impurities in kesterite absorbers and ultimately, the solar cell efficiency.

efficiency (PCE). [1] In recent years, several groups have achieved over 10% efficiency with control over fabrication and doping as key factors. [2][3][4][5][6][7][8] However, control over impurities during processing in kesterite and other chalcogenide technologies is challenging. Although the effects of impurities on solar cell device performance have been discussed extensively, a complete understanding of their behavior and impact is still lacking. For chalcogenide thin film solar cells, Na and O are the prevalent impurities, [6,[9][10][11][12][13] where both are often found to accumulate at grain boundaries (GBs). [14,15] Importantly, moderate amounts of Na present during fabrication are almost exclusively regarded as beneficial for device performance, [9] whereas the effect of O is more ambiguous. For instance, the champion CZTSSe cell from Wang et al. [1] exhibited low C and O concentrations. Early studies on Cu(In,Ga)Se 2 (CIGS), however, implied that an interplay between Na and O affects the PCE because O may passivate Se vacancies at grain boundaries with Na acting as a catalyst. [16][17][18] Indeed, further studies confirmed that Na and O can coexist on the surface and GBs. [19,20] Moreover, for both CIGS and CZTSSe, postdeposition heat treatments were shown to yield improved device performance. [21] For kesterite solar cells, these treatments have been performed in air, inert atmosphere, and vacuum. [10,[22][23][24][25] The heat treatments have been observed to change the photoluminescence intensity and peak position, [22,24] the sodium distribution, [10,24] the bandgap, [22,25] surface properties [22] as well as oxidize the surface and grain boundaries. [14,25] Consequently, impurities such as Na and O can be a critical factor influencing the device performance. On one hand, Na incorporation is achieved by using soda-lime glass substrates (SLG) and suppressing other Na sources. On the other hand, O is not as easily controlled since multiple potential sources may exist. For example, commonly used glass substrates, such as SLG, are composed of oxides. Furthermore, the Mo back contact is polycrystalline and usually contains significant amounts of O. [26] Additionally, the precursors may contain O and all process stages are performed in low-to-medium vacuum conditions, under which O may also be present.
In this work, a correlation between Na and O distribution in kesterite absorbers is identified using secondary ion mass spectrometry (SIMS) and explained by defect analyses within the density functional theory (DFT), where a model with complex formation and subsequent trapping of Na is proposed. The model is experimentally explored by introducing the less abundant 18 O isotope into different stages of the CZTS baseline process. Further, the 18 Figure 1 shows SIMS depth profiles for two CZTSSe absorbers chosen from our previous study of high-performance devices. [27] The lines represent Na (red) and O (black) distribution in the absorbers which yielded PCEs of 8.5% (solid lines) and 7.2% (dashed lines), respectively. SIMS depth profiles of the constituent elements are shown in Figure S1 (Supporting Information). For both samples, the Na and O profiles are correlated, which is a trend previously observed for CZTSSe and CIGS. [28][29][30] Interestingly, the correlation persists regardless of the shape of the profile. This is exemplified in Figure 1 for the 7.2% PCE device where an abnormal accumulation for both Na and O is observed at about 500 nm into the sample. The fact that the accumulation is in the middle of the absorber cannot be easily explained by the SIMS intensity only representing GB density. [31] Indeed, none of our scanning electron microscopy cross-section images showed an increase of GB density in this region. To understand the correlation between Na and O in kesterite absorbers at the atomic level, first-principles DFT was employed to study the point defects formed by these impurities in CZTS. The sole defects and possible complexes can be formed in the grain interior, but it is also known that both sodium and oxygen often accumulate at GBs of both CZTS [14,32] and CIGS. [15,33,34] In recent studies, alkali impurities were even shown to segregate at specific GBs, [35] marking a new stage in understanding the impact of Na on polycrystalline Cu-based solar cells.

Interplay between Na and O Impurities in Kesterite Absorbers
In this work, we analyze defect physics in bulk CZTS, and thus, we do not try to describe more complex situations for GBs. [36][37][38][39][40][41][42] For bulk CZTS, Na-related defects are already relatively well investigated in the literature. It is known that Na prefers to occupy Cu site in CZTS to form Na Cu , [43][44][45] although formation of interstitial Na i is possible during diffusion. [46,47] The substitutional Na Cu is an isovalent defect, and since the ionic radius of Na is about 0.4 Å larger than that of Cu, it does not yield any local reconstruction of the crystal. [48] These results were confirmed by our calculations. On the other hand, the O impurities have only been addressed by a few first-principles studies, [36,49] which hypothesized the dominant role played by substitutional O S defect. Conversely, we found that O S induces a substantial local lattice distortion due to significant differences in both size and electronegativity between the O 2− and S 2− ions.
While the calculated CuS, ZnS, and SnS bond lengths in CZTS are 2.32, 2.37, and 2.47 Å, the Cu(2a)O, Cu(2c)O, ZnO, and SnO distances for the O S defect are 3.23, 2.18, 1.99, and 2.02 Å, respectively. This change in the coordination for O S can be interpreted as breaking the Cu(2a)O and shortening the remaining bonds by 0.14-0.45 Å, in accordance with a general tendency for stabilizing shorter bonds between atoms with smaller ionic radii. [48] These optimized configurations for substitutional defects were further used as reference systems to compute binding energy between Na Cu and O S .
Apart from the isolated defects, Na and O impurities in CZTS may interact through formation of defect complexes. Now, consider that the NaO complex is formed by Na Cu and O S . The binding energy for such defect complex can be computed as where E tot (Na), E tot (O), E tot (Na + O), and E tot (pristine) are the total energies of CZTS supercells containing isolated Na Cu , isolated O S , both Na Cu and O S , and pristine supercell, respectively. Similar expressions can also be written for the larger NaO complexes using the supercell with NaO complex as a reference system, hence, the binding energy computed in such a way defines strength of the subsequent NaO bonds. It was found that NaO binding energy of the NaO complex strongly depends on distance between the defects, as shown in Figure 2a.
The highest computed binding energy of 0.76 eV corresponds to the NaO complex where Na Cu and O S are nearest neighbors. This binding energy is remarkably high considering that both Na Cu and O S are isovalent substitutional defects. In case of the Na 2 O complex, binding energy for the second Na Cu with the existing NaO complex is 0.56 eV (i.e., total binding energy of 0.76 + 0.56 = 1.32 eV), which is comparable to that for the NaO complex. Further, since Na diffusion in CZTS can be mediated by the interstitial defects, [46] binding energy was also computed for interstitial Na i and substitutional O S , demonstrating qualitatively similar results. In fact, the most stable complex formed by neutral Na i and O S has binding energy of 1.19 eV, which is even higher than that for Na Cu and O S . More Adv. Energy Mater. 2019, 9,1900740  detailed analysis of the defect interaction in the Na 2 O complex and for Na i with O S is given in the Supporting Information. This strong tendency for binding suggests that Na atoms introduced into O-containing CZTS grains can be kinetically trapped by forming the nearest neighbor complexes.
To explain the origin of the remarkably strong binding, we analyze in detail the most stable configuration of the NaO complex between Na Cu and O S (see Figure 2d). First, it is notable that the NaO bond of 2.19 Å is very close to the corresponding CuO bond for the isolated O S defect (2.18 Å), suggesting relatively small contribution of the lattice relaxation. Indeed, we found that binding energy of NaO complex where both Na Cu and O S occupy the ideal lattice sites (without atomic relaxation) is 0.67 eV. Second, effective (Bader) charges were calculated for Na and O with respect to the distance between them, as shown in Figure 2b,c. Evidently, the charges transferred to Na and O correlate with the binding energy, that is, charge transfers are significant in the nearest neighbor configurations only. This behavior suggests that binding in the complexes is determined by ionicity of the NaO bond and justifies why the binding energy causing formation of the second NaO bond in Na 2 O complex (0.56 eV) is almost as high as that for NaO (0.76 eV). Third, the binding energies for five other isovalent XO (X = Ag, Li, K, Rb, Cs) defect complexes were also computed. As can be observed in Figure 2e, the binding energy correlates with electronegativity of the X atom, affirming that bonding between Na and O in bulk CZTS is indeed determined by the ionic bond, and thus, qualitatively similar interaction between the defects at the GBs can be expected. Fourth, the binding energies were calculated for the complexes formed by O S and interstitial X i defect (X = Ag, Li, Na, K, Rb, and Cs), as shown in Figure S3 (Supporting Information), further evincing that the interaction between the alkali elements and oxygen is driven by the ionic bonding. These results corroborate the conclusion that Na and O concentrations in CZTS are indeed correlated, as seen in the SIMS depth profiles in Figure 1, and that the origin of this correlation is indeed NaO defect complexes.
Although the calculations show a clear tendency for binding between Na Cu and O S in CZTS, the binding energy alone does not guarantee the formation of the complexes at the processing and/or operating temperatures. The concentration of AB complexes at temperature T can be estimated from the law of mass action as where C A and C B are concentrations of isolated A and B defects, respectively; GF is a factor accounting for both the lattice symmetry and the complex geometry. [50] The law of mass action can be applied to all other complexes as well and should be collectively satisfied for all defects in equilibrium. Equation (2) is strictly valid in the dilute limit, but for this study it would be a reasonable approximation for the defect concentrations below 1 at% because the NaO interaction is very short-ranged and the change in entropy is insufficient to outcompete the strong NaO bond. In our CZTS samples, the total concentrations of Na and O impurities were estimated using elastic recoil detection analysis (ERDA) to be 0.8 and 0.5 at%, respectively. Based on this stoichiometry, one could expect NaO and Na 2 O to be dominant. Assuming no influx of the impurities upon heating, their total concentrations are constrained as Hence, by solving the system of equations with E b = 0.76 eV and GF = 8 representing the NaO complex and E b = 0.56 eV and GF = 4 for the Na 2 O complex in CZTS, the temperature dependence for the defect concentrations can be obtained, as shown in Figure 3a (solid lines). As one can see, these high binding energies ensure the formation of both complexes at all temperatures of CZTS baseline processing (below 600 °C). In a wider range of compositions, however, the dominant type of complexes depends on the ratio of the defects introduced, as shown in Figure 3b. Thus, when concentration of O is closer to that of Na, formation of NaO would be dominant (e.g. dotted lines in Figure 3a)  O impurities primarily coexist in the form of defect complexes throughout the typical temperature interval adopted in CZTS processing. At the same time, they do not exclude the possibility of clustering between the NaO complexes forming even larger complexes. Most importantly, however, the tendency for binding between Na and O in CZTS ensures that these impurities do interplay and cluster owing to the strong ionic NaO bonding, and therefore, must be considered together for developing high-performance CZTS solar cells.
To control the formation of NaO complexes, however, the origins of Na and O incorporation in kesterite processing must be identified. While Na is incorporated from Na 2 O present in SLG, [51] concurrent diffusion of O from the substrate is also possible, even though the diffusivities of alkali elements are much higher in SLG compared to that of O. [52] Additionally and different to Na, O in kesterite absorbers has several additional potential sources: outdiffusion from the Mo back contact, from the precursors as well as from the air during and after processing.

Evaluation of Sources of O in Kesterite Processing by Isotopic 18 O Diffusion
To further study the relationship between Na and O in kesterite absorbers, controlled O incorporation during processing is needed. To evaluate possible sources of O, isotope 18 O was introduced at different stages of the CZTS baseline processing by heat treatments in an 18 18 O anneal). The heat treatments were performed (①) on the SLG substrate, (②) after the Mo sputtering, (③) after the CZTS precursor sputtering, and (④) after the sulfurization, as shown in Figure 4. The SLG was only heat treated at 400 °C since no significant diffusion was expected at lower temperatures. [ Figure 5. The cation ratios, processing steps, and annealing conditions are summarized in Table 1.
In Figure 5a, the depth profile for "SLG 400 °C" (①, brown dashed line) has increased isotopic ratio in the Mo back contact. The increased 18 O concentration demonstrates that O can diffuse from the SLG into the Mo layer during the CZTS processing. However, since the isotopic ratio in the treated and untreated CZTS layers are at the same level, SLG can be excluded from the list of potential sources of O in CZTS for baseline processing conditions. Additionally, Figure 5a shows that 18 O diffuses into the Mo back contact during the 18    isotopic ratio increases with annealing temperature up to 20% for "Mo 400 °C". During the precursor deposition and sulfurization, 18 O from the Mo back contact diffuses into the CZTS layer (dashed lines), indicating that O from the Mo back contact inevitably ends up in the CZTS layer. The isotopic ratio is higher near the Mo back contact, suggesting that O diffusion in the CZTS layer is not fast enough to uniformly distribute O throughout its thickness. From 100 nm to about 600 nm from the surface, the isotopic ratio is nearly constant, while the isotopic ratio approaches the background natural abundance level, C bg = 0.2%, near the surface. Surprisingly, a small increase in the isotopic ratio above the background level is found in all profiles, including that for the untreated sample. This feature can be attributed to a minor 18 O exchange effect caused by keeping all the samples in the same graphite box during the sulfurization. Indeed, a follow-up control experiment for an untreated sample in a separate box (not shown) revealed only the natural abundance of 18 O, confirming the exchange mechanism causing the abnormality in the isotopic profiles.
After the 18 O anneal (②) of "Mo 400 °C", the Mo layer turned from metallic to dark red and X-ray diffraction data unveiled the presence of MoO 2 ( Figure S5, Supporting Information). The formation of oxide phase should not affect the isotopic ratio, even though it causes an increase in SIMS intensity for both 16 O and 18 O due to higher ionization yield in MoO 2 compared to that of Mo. Here, it should be noted that high SIMS intensities require a faraday cup detector to be used to protect the normal electron multiplier, which yields an uncertainty in the isotopic ratio. This effect may explain the higher ratio measured after the precursor deposition and sulfurization for "Mo 400 °C" (Figure 5a, purple dashed line).
In this work, the CZTS baseline processing employs CuS, ZnS, and SnS sputtering targets with 99.99% purity in chamber with an Ar (99.9995% purity) background pressure of 666 Pa. Despite the high purities, noticeable O concentrations are detected by SIMS in the samples prior to sulfurization (not shown). Hence, 18 O anneals were performed before the sulfurization to study whether the O from the precursors eventually ends up in the CZTS absorber.
Adv. Energy Mater. 2019, 9,1900740 Figure 5b illustrates that the isotopic ratio in the samples after the 18 O anneals (③) is roughly constant throughout the precursor layer followed by a decrease in the Mo layer (solid lines). Additionally, the isotopic ratio increases with annealing temperature. After the sulfurization, the isotopic ratio in the CZTS layer for "Precursor 300 °C" and "Precursor 200 °C" drop significantly. The reductions are from about 4 to 1% for "Precursor 300 °C" and from about 1.4 to 0.3% for "Precursor 200 °C". Interestingly, these depth profiles in the CZTS layer resemble those after 18 O was introduced in the Mo layer ( Figure 5a). Consequently, the isotopic profiles are likely to be formed by 18 O diffusing through the CZTS precursor and into the Mo during the 18 O anneal (solid lines in the Mo region).
Conversely, for "Precursor 400 °C", the majority of the 18 O remains in the CZTS layer. The total O concentration is also higher for this sample (not shown), which indicates that the precursor oxidizes to an extent such that outdiffusion during the sulfurization process is prevented. An effort was made to fabricate devices from the precursor-annealed samples. However, most of them flaked off during the chemical bath deposition. Interestingly though, "Precursor untreated" and "Precursor 400 °C" flaked off the least. Some small subcells were fabricated from these films, but their PCE was low presumably due to nonideal cation stoichiometry and no difference in PCE was observed between the untreated and heat-treated samples. For close to ideal stoichiometric cation ratios, one could expect that air anneal of the precursors at 400 °C increases the O concentration in the CZTS layer and may affect the solar cell performance. Ultimately, apart from "Precursor 400 °C", the O from the precursor accounts for only a miniscule part of the O concentration found in the CZTS absorber.
To investigate how likely O is to be introduced into crystallized absorbers, 18 O anneals were also performed after the sulfurization (④). SIMS depth profiles in Figure 5c show that after 18 O anneals above 100 °C, 18 O diffused into the CZTS layer and the Mo back contact. In the CZTS layer, the isotopic ratio is nearly constant for the "Absorber 200 °C", while for higher temperatures the isotopic ratio starts to decline toward the Mo layer at a depth of about 650 nm.
Interestingly, the 18 O anneals starting from 200 °C for the absorbers (④) and from 100 °C for the precursors (③) yielded a depth profile with distinct regions of constant isotopic ratio. These constant profiles define regions where shapes of the 16 [53] the isotopic ratio can be corrected for the C bg and for the 18 O isotopic ratio in the 18 O-rich atmosphere, C g . This parameter is defined here as O O bg g b g 18 18 From the flat regions in the depth profiles in Figure 5b,c, the C′18 O can be calculated and plotted with respect to the annealing temperature, as shown in Figure 5d. As one can see, the 18 O isotopic ratio follows an Arrhenius behavior for both the precursor and the absorber. The activation energy for O incorporation into the precursor is half of that into the absorber. Indeed, the Arrhenius behavior indicates a negligible (<0.01%) increase in C′18 O during the 100 °C anneal of the absorber, which is less than the natural abundance and is not detectable with SIMS. Consequently, it can be concluded that prolonged room-temperature air exposure, such as storage, does not incorporate significant amounts of O into the CZTS absorbers. Nonetheless, the O partial pressure in air is about ten times higher compared to the O partial pressure in the 18 O anneals and hence the activation energies in Figure 5d could be underestimated as for ambient storage. Since O within few hundred nanometers from the surface cannot originate from the precursor, the Mo back contact, the SLG, or air exposure at less than 100 °C, the remaining possibility is that it arises from contaminations during the sulfurization or postsulfurization treatments. For example, during the sulfurization, a drop in sulfur partial pressure in the furnace has been previously observed, [54] indicating possible air leakage causing O contamination. Additionally, possible exchange between the SLG, which is close to temperatures where the glass starts to soften, and the atmosphere cannot be ruled out. These possible contamination sources are aggregated as the "Sulfurization step". Figure 6 shows a Adv. Energy Mater. 2019, 9,1900740  proposed assignment of the contributions to a typical O depth profile from a baseline processed CZTS absorber derived from the results given in Figure 5. The gray thick line represents the O depth profile for a baseline processed absorber ("Absorber untreated"), while the dashed lines illustrate a qualitative overview over which regions each oxygen source contributes mainly to. Based on the conducted analysis, we conclude that the sulfurization step and Mo layer account for the majority of O in the CZTS absorber. In addition, trace amounts of oxygen from the precursor may persist in the absorber as well. Conversely, O from the SLG does not diffuse sufficiently far to enter the CZTS layer during baseline processing. These results as such outline the strategies to tailor the O concentration in the kesterite absorbers.

Implications of O Incorporation and Trapping of Na
Based on the results presented in Sections 2.1 and 2.2, a deeper understanding of the mechanisms behind the correlation and the overall shape of the depth profiles for Na and O in Figure 1 can be deduced. The computed binding energy of 0.76 eV for NaO complexes and the distinct ionic bonding nature evince that Na and O impurities in CZTS inevitably cluster together, whether it be in the bulk, surface, or grain boundary of the absorber. Na is known to be a fast diffuser in CIGS [15,55] and evidently CZTS, [10] where it promotes crystallization of the absorber layer. [56,57] Consequently, the correlation between Na and O profiles observed in the kesterite absorbers can be explained by relatively slow O diffusion from the Mo back contact and the atmosphere during the sulfurization, as shown in Figure 6, and subsequently immobilizing the fast-diffusing Na via extensive formation of NaO defect complexes. Hence, provided Na and O concentrations are of the same order, their depth profiles would appear correlated, as seen in Figure 1. Indeed, for "Precursor 400 °C", where the majority of the 18 O remained after the sulfurization, the depth profile exhibits an unusual but gradual increase in the total O concentration from the nearsurface to the in-depth region of the sample ( Figure S6, Supporting Information). Accordingly, for this sample, the Na and O profiles are also correlated throughout the sample, except for the CZTS/Mo interface region yields increased Na intensity.
Further, the proposed mechanism of O incorporation and interplay with Na can provide new insight into the Na redistribution occurring during postdeposition heat treatments. The Na distribution near the surface is likely to depend on the O 2 partial pressure in the atmosphere. Indeed in previous studies where postdeposition heat treatments were performed in N 2 atmosphere, the PCE was observed to reach a minimum between 100 and 200 °C and a maximum between 145 and 400 °C, with the optimum temperature depending on the N 2 pressure. [10,24,58] These temperatures are sufficient to cause extensive O incorporation in kesterite absorbers, as evident from our results shown in Figure 5c. Therefore, the change in PCE may also be influenced by in-diffusion of trace O from the atmosphere, in addition to the purely thermal effects emphasized in the original studies. As such, extensive care must be taken to tightly control O incorporation during the kesterite processing.

Conclusions
A general tendency for correlation and clustering between Na and O in kesterite absorbers formed by cosputtering was established by SIMS measurements. The atomistic mechanism behind the correlation was further explained using defect analy ses within the DFT. A strong tendency for binding between Na and O impurities mediated by the strong ionic bonding was demonstrated. The computed total binding energies of 0.76 eV for NaO and 1.32 eV for Na 2 O were proven to trigger formation of the nearest neighbor complexes of Na Cu and O S at all temperatures of baseline kesterite processing. The contributions from various O sources were evaluated by incorporation of the less abundant isotope 18 O at different stages of the CZTS baseline process. Based on these results, a model was proposed where the sulfurization step and the Mo layer are the main contributors of O in CZTS. Hence, the correlation between Na and O distributions can be explained by O immobilizing Na. Consequently, the redistribution of Na during postdeposition heat treatments of kesterites is strongly dependent on the availability of O. The observed interplay between Na and O in kesterite absorbers provides a foundation for more accurate impurity control needed for fabricating high-performance solar cell devices.