Structural analyses and photovoltaic device simulations in two and three dimensions applied to Ag-alloyed Cu(In,Ga)Se2 solar cells

PAPER • OPEN ACCESS Structural analyses and photovoltaic device simulations in two and three dimensions applied to Ag-alloyed Cu(In,Ga)Se2 solar cells To cite this article: Chang-Yun Song et al 2025 J. Phys. Energy 7 035015 View the article online for updates and enhancements. You may also like 2024 roadmap for sustainable batteries Magda Titirici, Patrik Johansson, Maria Crespo Ribadeneyra et al. - Recent status and future prospects of emerging oxygen vacancy-/defect-rich electrode materials: from creation mechanisms to detection/quantification techniques, and their electrochemical performance for rechargeable batteries Sandeep Kumar Sundriyal and Yogesh Sharma - Shape engineering and manufacturing of piezoceramics for energy conversion—a review Guilherme Victor Selicani, Mahmoud Mobin, Vincenzo Esposito et al. - This content was downloaded from IP address 141.48.166.104 on 27/10/2025 at 09:33 J. Phys. Energy 7(2025) 035015 https://doi.org/10.1088/2515-7655/adde84 Journal of Physics: Energy OPEN ACCESS RECEIVED 10 April 2025 REVISED 26 May 2025 ACCEPTED FOR PUBLICATION 29 May 2025 PUBLISHED 9 June 2025 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. PAPER Structural analyses and photovoltaic device simulations in two and three dimensions applied to Ag-alloyed Cu(In,Ga)Se2solar cells Chang-Yun Song1,∗, Zelong Wang2, Matthias Maiberg1, Heiko Kempa1, Julia Horstmann1, Wolfram Witte3, Rico Gutzler3, Dimitrios Hariskos3, Daniel Abou-Ras4, Sinju Thomas4, Roland Scheer1and Ali Gholinia2 1Institute of Physics, Martin Luther University Halle-Wittenberg, Von-Danckelmann-Platz 3, 06120 Halle (Saale), Germany 2Department of Materials and Henry Royce Institute, The University of Manchester, Manchester M13 9PL, United Kingdom 3Zentrum für Sonnenenergieund Wasserstoff-Forschung Baden-Württemberg (ZSW), Meitnerstr. 1, 70563 Stuttgart, Germany 4Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, 14109 Berlin, Germany ∗Author to whom any correspondence should be addressed. E-mail: [email protected] Keywords: 3D EBSD, microstructure analysis, grain boundaries, device simulation, Ag alloying, Cu(In, Ga)Se2solar cells Supplementary material for this article is available online Abstract The present study reports on the structural changes and related photovoltaic properties resulting from the addition of Ag in Cu(In,Ga)Se2(CIGS)-based thin-film solar cells analysed using two-dimensional (2D) and three-dimensional (3D) analytical and modelling techniques. The microstructures of CIGS and Ag-containing CIGS (ACIGS) layers were characterized by means of 2D and 3D electron backscatter diffraction (EBSD). Ag addition significantly increased grain sizes, which is differently observed in the 2D and 3D EBSD analyses due to the different methodology. Moreover, opto-electronic 3D device simulations, which incorporate real 3D structural data obtained from 3D EBSD, confirmed that 2D models tend to underestimate the impact of grain boundaries on the device performance. Device simulations showed that the increased grain size and thus, the decreased grain-boundary density, resulting from Ag addition had a positive effect on the open-circuit voltage (VOC) of the solar cell. The VOC improvement was more pronounced in ACIGS layers of high minority-carrier lifetimes. These findings highlight the necessity of combining 3D EBSD analysis with 3D device simulations to optimize the relationship between microstructural characteristics and photovoltaic performance in solar cells to understand opto-electronic properties more quantitatively. 1. Introduction Thin-film solar cells based on polycrystalline Cu(In,Ga)Se2(CIGS) absorber layers have attracted significant commercial interest as a highly promising renewable energy source owing to their high energy conversion efficiencies and excellent long-term stability [1–3]. Particularly, this technology occupies a crucial position in the field of solar energy due to its high absorption coefficient and exceptional photovoltaic efficiency [4]. However, the performance of CIGS solar cells is often constrained by the polycrystalline nature of their structure, notably at the grain boundaries (GBs), which facilitate charge carrier recombination, thereby reducing the overall conversion efficiencies of the devices [5–7]. To address this issue, recent studies demonstrated that the addition of Ag can influence significantly the micro structure and the average grain size of CIGS thin films [8–11]. Doping with Ag has been shown to enlarge crystal grains and reduce grain boundary densities, potentially decreasing the likelihood of charge carrier recombination. Furthermore, CIGS films with added Ag maintain high performance even at low growth temperatures, enhancing the flexibility of the manufacturing process and reducing production costs [3,12,13]. Furthermore, Ag affects not only the fabrication process and grain structure but also the electrical © 2025 The Author(s). Published by IOP Publishing Ltd J. Phys. Energy 7(2025) 035015 C-Y Song et al properties. Depending on the Ag content, the bandgap can be tuned from 1.0 eV to 1.8 eV, providing a wider bandgap range than that achievable with conventional Ag-free CIGS [14–20]. Additionally, Ag incorporation can shift the band edges, allowing for control of band alignments and band offsets with adjacent layers, which is crucial for optimizing charge transport and minimizing recombination losses [21]. Moreover, at low Ag substitution levels, the addition of Ag increases carrier lifetime and mobility while decreasing the doping density [22,23]. So far, most studies on CIGS and other types of solar cells have relied on two-dimensional (2D) analytical techniques, which are limited in their ability to capture fully the complex three-dimensional (3D) structures within the devices [24,25]. In this paper we present advanced 3D analytical techniques which we employed to precisely analyse the grain structure of Ag-added CIGS thin films and to compare these findings with traditional 2D analysis results. We employed 3D electron backscatter diffraction (EBSD) analysis and device simulations to show how Ag-induced changes in microstructure affect the photovoltaic properties. By means of this integrated approach, we provide new insights into optimizing the design and performance of next-generation thin-film solar cells, including tandem solar cells [12,26–28]. 2. Sample preparation and analytical approach 2.1. Sample preparation CIGS and silver-alloyed CIGS (ACIGS) thin films were prepared on molybdenum-coated alkali-containing glass substrates using a three-stage co-evaporation process [29,30] or an in-line multi-stage co evaporation process [10]. The CIGS absorber layer had a thickness of approximately 2.8 µm, and the [Ga]/([Ga]+[In]) ratio (GGI) was kept 0.35. To further optimize the absorber properties, CsF post-deposition treatment (PDT) was performed under a selenium atmosphere [31]. For the ACIGS absorber layer, Ag was incorporated directly during deposition without the use of precursors resulting in an [Ag]/([Ag]+[Cu]) ratio (AAC) of 0.07. The absorber thickness was approximately 2.1 µm, and the GGI was 0.28, and in-situ RbF-PDT was applied at the end of the in-line process under selenium atmosphere [10]. For both CIGS and ACIGS a solution-grown CdS buffer layer was deposited on the absorbers. Transparent conductive layers were then added by sputtering. ZnMgO and ZnO:Al layers were used for CIGS devices, while ZnO and ZnO:Al layers were used for ACIGS devices. A Ni/Al/Ni grid was added to both device types to ensure reliable electrical contacts. The cells had a total area of 0.5 cm2and contained no anti-reflective coating. 2.2. Analytical approach Microstructural and crystallographic properties, including grain size, orientation, and grain boundary density, were analysed using 2D and 3D EBSD techniques. 2D analyses were conducted on in-plane and on cross-sectional planes, while 3D analysis utilized focused ion beam (FIB) serial sectioning for reconstructing grain structures. Measurements were performed with the Helios™ 5 Laser PFIB system (Thermo Scientific) [32,33]. The 3D EBSD datasets consisted of each 80 individual EBSD maps. Between each 2D EBSD measurement, a slice with a thickness of about 50 nm was sectioned using a Xe plasma ion beam (30 kV, 15 nA). The EBSD mapping was conducted at 20 kV and 1.6 nA beam current. For the CIGS sample, a 200 pixel ×200 pixel area was covered at a step size of 50 nm. For the ACIGS sample, the same slicing and mapping conditions were applied, but the mapping area was extended to 400 pixel ×400 pixels to account for the larger average grain size. Both samples achieved an indexing success rate of over 70%, and the data were processed using AZtec and AZtecCrystal software (Oxford Instruments). The EBSD data were used to reconstruct 3D grain structures and evaluate grain size, shape, and local crystal orientation. 3. Result and discussion 3.1. Microstructure analysis of CIGS and ACIGS thin films using EBSD To investigate the grain morphology and grain size of CIGS and ACIGS samples, EBSD measurements were performed as shown in figure 1, classifying grains based on their crystallographic orientations. In order to obtain microstructural insights in 3D, 2D EBSD maps were acquired in plan-view configuration at various depths (alternatingly measuring EBSD maps and removing material using a FIB) to generate a stack of 2D EBSD maps, which was subsequently reconstructed into a 3D EBSD data cube (a multi-dimensional data structure storing crystallographic features in 3D space) [33,34]. Figures 1(a) and (b) show 2D EBSD maps acquired in plan-view on CIGS and ACIGS layers, both at a depth of about 1 µm. It is apparent that the ACIGS layer (figure 1(b)) reveals larger grain sizes at the same depth. EBSD maps measured on cross-sections of these thin films (figures 1(c) and (d)) corroborate this finding. In figure 1(c), the CIGS layer 2 J. Phys. Energy 7(2025) 035015 C-Y Song et al Figure 1. EBSD analysis and 3D reconstructed models of CIGS and ACIGS samples (note the different scale bars). (a) and (b) show the EBSD in-plane images of CIGS and ACIGS, respectively, measured at a depth of 1 µm, with ACIGS exhibiting larger grain sizes. (c) and (d) are EBSD cross-sectional images, illustrating the effect of Ag addition along the z-axis. (e) and (f) represent 3D reconstructed grain models, depicting the grain structures of CIGS and ACIGS, respectively. exhibits a gradient in grain size perpendicular to the substrate, with smaller grains near the back contact and larger grains toward the surface. This variation is strongly influenced by the Ga/In chemical composition ratio perpendicular to the substrate (figure S1). CuInSe2tends to form larger grains compared with CuGaSe2 owing to its lower (absolute) formation energy, leaving more residual energy for grain growth that is, energy that can promote grain boundary migration and coalescence [35–37]. Additionally, the tetragonal crystal structure of CuInSe2exhibits a lattice-constant ratio c/athat deviates less from the pseudocubic value (c a −1=2), leading to reduced microstrain compared with the crystal structure of CuGaSe2[38–41]. Due to the significant difference in bond lengths between In–Se and Cu–Se, In atoms tend to segregate towards the surface during film growth [42,43]. This surface enrichment leads to a higher local concentration of CuInSe2 near the top of the absorber, where grain growth is more favourable, thereby contributing to the observed grain size gradient. In contrast, figure 1(d) shows that the ACIGS layer exhibits significantly larger and more contiguous grain structures across the entire thickness of the film. Unlike CIGS, which features a noticeable grain size gradient, the ACIGS sample maintains consistently large grains throughout the entire film thickness, despite having a similar Ga gradient (figure S1). This effect is attributed to Ag incorporation. The formation energy of AgInSe2is smaller than that of CuInSe2(in absolute terms), leading to enhanced grain growth (at same deposition temperatures) and promoting grain coalescence by modifying the bonding environment and reducing microstrain in the ACIGS film, provided that the Ag content is not excessively high [9,37,44,45]. Figures 1(e) and (f) show the 3D EBSD data cubes of CIGS and ACIGS reconstructed from the 2D EBSD stacks. For further details on the reconstruction process, the reader is referred to [41]. These 3D reconstructions incorporate the information visible in both the plan-view and cross-sectional analyses, while providing additional insights that cannot be obtained from 2D analysis alone, such as grain volume, surface area, and morphology [24,46,47]. To quantitatively the analyse grain size distributions in each layer, histograms of grain sizes obtained by corresponding 2D and 3D analyses were calculated (figure 2). In the 2D data, grain size was measured based on the equivalent circle diameter, while the 3D data used the equivalent sphere diameter. Due to grain size variations caused by Ga/In gradients through the film thickness, cross-sectional EBSD analysis is a commonly used approach. Figures 2(a) and (d) give the grain size distributions as obtained from one EBSD cross section view. These grain size distributions of the Ag-free (a) and Ag-doped (d) samples illustrate the significant increase in median grain size due to Ag addition, from 0.29 µm in CIGS to 0.71 µm in ACIGS, representing approximately a 2.5 times increase. Subsequently, EBSD measurements were conducted on all 3 J. Phys. Energy 7(2025) 035015 C-Y Song et al Figure 2. Histograms of grain size distributions for CIGS and ACIGS samples were analysed using 2D cross sectional view, 2D in-plane-view, and 3D methods. (a)–(c) Show results for CIGS, and (d)–(f) show results for ACIGS. (a) And (d) are 2D cross section-view data, (b) and (e) are 2D in-plane data, and (c) and (f) are 3D data. The median grain size (Med) is displayed in each histogram. ACIGS samples exhibit significantly larger grain sizes compared to CIGS across all methods. The 3D data provides more accurate grain size estimations, highlighting a threefold increase in ACIGS grain size relative to CIGS. 50 in-plane sections across the film thickness, which gives a larger number of grain counts for analysis (figures 2(b) and (e)). Certainly, by this procedure identical grains would be counted repeatedly. Unlike the cross-sectional results in (a) and (d), the median grain size measured in-plane exhibited a more substantial increase, from 0.26 µm (CIGS) to 0.91 µm (ACIGS), approximately 3.5 times. This observation implies that grain growth induced by Ag addition is anisotropic, resulting in a greater expansion in-plane compared to the thickness direction. Lastly, figures 2(c) and (f) present grain size histograms from the reconstructed 3D grain structures as determined from the equivalent sphere diameters. Here, the median grain size of ACIGS was observed to be approximately 2.3 times larger compared to CIGS. When comparing the grain sizes obtained from 2D in-plane and 3D analyses, the difference was more pronounced in ACIGS than in CIGS. For ACIGS, the in-plane grain size was approximately 1.6 times larger than the 3D value while for CIGS this factor is close to 1. Moreover, the grain size distributions derived from the 3D reconstructions appeared narrower than those from both 2D analyses. Assuming a lognormal distribution, this narrower histogram shape implies a smaller variance [48,49]. This occurs because in thin films containing grains of varying sizes, larger grains are frequently observed multiple times in 2D analyses (if the same grains are sectioned repeatedly), whereas in 3D analyses, they are uniquely identified as individual grains. Even in the simplified case of isotropic spherical grains with uniform size, 2D cross-sectional analyses typically underestimate the actual grain size by a factor of approximately πR/4 (figure S2 (a)). For anisotropic structures and samples comprising various grain sizes, these differences can be even larger, emphasizing the difficulty in accurately determining grain sizes from simple 2D measurements (figure S2 (b)). While the grain statistics in figure 2were based on equivalent circle or sphere data, the specific grain shape information is not included. This limitation is particularly critical in analysing complex microstructures, such as those found in the CIGS sample, which contains approximately 500 grains. Due to the large number of grains, visualizing each grain individually in three dimensions is impractical. Moreover, selecting only few, specific grains for the analysis may not appropriately represent all grains in a layer. To address this issue, a virtual average grain was generated. Because of different grain position and size, averaging is easier to be performed in k-space than in real-space. Using all grain data, each grain was transformed into frequency-domain data through Fourier transformation: Fn(kx,ky,kz)=ˆˆˆfn(x,y,z)exp(−2πi(kxx+kyy+kzz))dxdydz.(1) Here, fn(x,y,z) is an indicator function that equals 1 inside the nth grain and 0 otherwise. Subsequently, the transformed signal data Fnwas summed up and averaged according to equation (2). During this process, 4 J. Phys. Energy 7(2025) 035015 C-Y Song et al Figure 3. FFT signals and reconstructed grain shapes for CIGS (a) and ACIGS (b). The left graph shows the top 1% magnitude of the averaged FFT signals from all grains measured in each film. The right image presents the reconstructed grain obtained via inverse FFT (i-FFT). The flatter shape observed in ACIGS indicates enhanced growth along the xand y-axes due to z-axis constraints imposed by the thin-film thickness. all grains were normalized to the same maximum diameter of each grain (maximum distance between with indicator function value of 1 within one grain) to eliminate the influence of grain size, retaining only the morphological information. The result of this procedure is the function ¯ F(kx,ky,kz) ¯ F(kx,ky,kz)=1 N N ∑ n=1 Fn(kx,ky,kz).(2) The left panels in figure 3visualize the average spectrum obtained after the 3D Fourier transformation. More precise, these panels represent the magnitude (intensity) of the k-space spectrum, converted into a logarithmic scale using log(√(Re(¯ F)2+Im(¯ F)2)+1). In order to visualize, we display only the top 1% of the spectrum intensity (see colour code). We see that for ACIGS, the signals in the 1% topmost magnitude range are more elongated along the kz-direction than in the kxand kydirection. This is in distinct difference to the CIGS sample which shows less clear zelongation. Next, based on the averaged signal an inverse fast Fourier transform (i-FFT) was performed using the following equation f′(x,y,z) = ˆˆˆ¯ F(kx,ky,kz)exp(2πi(kxx+kyy+kzz))dkxdkydkz.(3) This results for each sample in a virtual average grain that represent the average grain shape in real space. The virtual average grain images presented in figures 3(a) and (b) demonstrate a tendency for the grains to become flatter upon the addition of Ag. This explains why the discrepancy in grain size between the 2D in-plane and 3D analysis is more pronounced in ACIGS compared to CIGS. The ACIGS grains are larger in xand y-direction than in z-direction having a disk size. Therefore, the grain size if evaluated by multiple EBSD in-plane sections is becomes overestimated. This morphology of the ACIGS sample is attributed to the limitation in sample thickness, which suppresses growth along the z-axis while promoting more significant expansion in the xand ydirections, even though grain growth in principle would be possible in all directions due to Ag addition. This trend is expected to persist in thin films with a thickness of approximately 3 µm. 5 J. Phys. Energy 7(2025) 035015 C-Y Song et al Table 1. Comparison of grain boundary characteristics between CIGS and ACIGS. The table includes grain boundary densities from 3D evaluation, NGBD: nearest grain boundary distances (average) for 2D and 3D, and twin boundary ratios, which represent the proportion of twin boundaries relative to the total grain boundaries (3D). CIGS ACIGS Grain boundary density from 3D (µm2/µm3) 1.04 0.51 Average NGBD 2D (µm) 0.15 0.55 Average NGBD 3D (µm) 0.12 0.40 Twin boundary ratio 3D (%) 16 19 3.2. Grain boundary analysis The shape and size of grains also affect their boundaries. Since grain size measurements can vary depending on the used method, the information related to GBs may also differ. We note that only 3D EBSD data cubes are able to provide the grain-boundary orientations throughout the analysed thin film (from 2D EBSD maps, only the trace of a grain boundary can be estimated, and not any information can be obtained on the curvature or connectivity, such as the overall 3D geometry of the grain boundary plane). To gain a deeper understanding of the differences arising from 2D and 3D measurement methods, this study analysed the GBs of CIGS and ACIGS samples using both approaches (table 1). For a fair comparison, the 3D structures were constructed by stacking individual 2D slices without connecting the GBs along the z-axis, thus, preserving the one-dimensional representation of GBs as in 2D (figure S3). Although in a real 3D microstructure, GBs form continuous surfaces, our approach treats them as lines, resulting in open boundaries at the top and at the bottom of the layer. The CIGS and ACIGS thin films were then analysed separately. According to the results in table 1, the ACIGS sample with Ag addition exhibited a lower grain-boundary density 3D as compared with CIGS. This is simply because of the larger median grain size of ACIGS. On the other hand, we found that the fraction of twin boundaries (with respect to the total density of GBs) in the ACIGS layer is larger than in the CIGS layer. This trend was also found in ACIGS and CIGS layers with different GGI (table S1). This result can be explained by different mechanisms for the reduction of microstrain in the thin films. For layers with large grains reduction of microstrain is realized preferentially via twinning [50]. For layers with small grains (and correspondingly high densities of GBs) microstrain is reduced via relaxation along GBs. Additionally, to gain a more intuitive understanding of the impact of decreased grain boundary density on charge-carrier recombination, the average, nearest grain-boundary distance (NGBD) was calculated. Because the 3D grain structure data contains a large number of points, calculating all pairwise distances would be computationally inefficient. Therefore, a k–d tree algorithm [51] was implemented to identify the nearest grain boundary for each point. This approach enabled a more than 200-fold improvement in computational speed compared to a brute-force method, allowing for fast and accurate NGBD estimation even in large 3D datasets. Once the nearest grain boundary was identified using the k–d tree, the Euclidean distance from each evaluated point to the closest grain boundary was calculated as ||q−x||2=√(∑d i=1(qi−xi)2).(4) Here, qrepresents the reference coordinate, and xdenotes the target coordinate being measured. The results calculated using this method indicate that the average NGBD in ACIGS samples increased by approximately threefold compared to CIGS due to Ag addition. This suggests that the probability of electrons as minority carriers reaching a grain boundary decreases, thereby reducing electron-hole recombination at GBs. These findings serve as a critical indicator for quantitatively explaining the impact of structural changes on the electrical performance of solar cells, based on the correlation between changes in grain size and grain boundary density. As shown in section 3.1, the grain boundary density and average NGBD also exhibited different results between the 2D and 3D analyses. To ensure a fair comparison between the 2D and 3D data, connections between layers were excluded in the 3D analysis, and the uppermost and lowermost horizontal GBs, which are not detectable in 2D analysis, were also excluded. However, in real thin films, such connections and boundaries do exist, suggesting that the differences between 2D and 3D analyses reported in the present study may be smaller than the actual difference. This issue highlights the inability of 2D analysis to fully capture complex structural characteristics of polycrystalline materials, emphasizing the necessity of 3D modelling for accurate analysis. 6 J. Phys. Energy 7(2025) 035015 C-Y Song et al Figure 4. (a) Simplified 2D model with uniform grain boundaries. (b) Realistic 2D model, reconstructed using EBSD data from nine cross-sectional slices. (c) Realistic 3D model, reconstructed using 3D EBSD data, capturing the experimentally determined grain structure. (d) Simulated J–V curves for different models (Simple 2D, one selected Real 2D, and Real 3D) under grain boundary recombination velocities of 103and 106cm s−1. (e) VOC as a function of Sgb for each model, showing that 3D models better capture the effects of structural complexity, particularly at high recombination velocities. 3.3. Device simulation results To evaluate the impact of different spatial dimensions of the analysis methods applied on CIGS and ACIGS absorbers on the simulated photovoltaic performance of corresponding solar cells, the present study constructed an optoelectronic solar-cell model consisting of the absorber layer with two contacts. For the absorber layer model, three configurations were used. The first was a simplified 2D model with GBs running perpendicular to the substrate at 0.48 µm intervals, matching the nearest grain boundary distance of the 3D model (see figure 4(a)). The second was a 2D model based on a grain-boundary grid extracted from a cross-sectional slice of the 3D structure, taking into account grain-size distributions determined at nine different positions (figure 4(b)). The third was a full 3D model incorporating the actual grain structure measured by 3D EBSD (figure 4(c)). The reconstruction process of the real 3D model follows methodologies established in a previous study [41]. Before conducting the 2D and 3D simulations, several electronic material parameters were determined by fitting multiple experimental datasets—such as J–V, TRPL, EQE, and CV—using a 1D solar-cell model [52]. Iterative fitting of the experimental data was performed simultaneously using the Nelder–Mead and Levenberg–Marquardt–Gauss algorithms. Subsequently, key parameters such as doping density, effective carrier lifetime, mobility, and conduction band offset derived from the 1D fitting were applied equally to simulate both the 2D and the 3D models (figure S4 and table S2). Using the Sentaurus TCAD software, the Poisson and continuity equations for each model were numerically solved, and J–Vcurves were simulated under standard AM1.5 G conditions. From these simulations, the photovoltaic parameters VOC,JSC, FF, and PCE were derived by analysing the calculated J–Vcurves based on a given recombination velocity at the GBs. Under a short-circuit condition, for which no voltage is applied, the space-charge region (SCR) is rather extended, leading to rather small impact of structural changes at the grain boundary and in the bulk on the charge-carrier collection. In contrast, under an open-circuit condition, the quasi-neutral region becomes wider, while the SCR becomes narrower, making structural changes at the grain boundary and in the bulk more relevant. Indeed, we find clear differences in the simulated VOC values between the models (figure 4(e)), as will be discussed further below. In case of high grain boundary recombination velocities (e.g. 106cm s−1), the extent of VOC reduction varied significantly among the models. In the simplified 2D model, the decrease was less significant, while in 7 J. Phys. Energy 7(2025) 035015 C-Y Song et al Table 2. Photovoltaic performance parameters of CIGS and ACIGS solar cells, including VOC, JSC, fill factor (FF) and power conversion efficiency (PCE), as determined from experimental J–Vcurves. The PCE and VOC of ACIGS are lower despite its superior grain structure. CIGS ACIGS VOC (mV) 733 702 JSC (mA cm−2) 33.0 32.2 FF (%) 79.0 77.8 PCE (%) 19.1 17.6 the realistic 2D model reflecting actual structures, the decrease was more pronounced. The largest VOC decrease was found when using the 3D model. These results indicate that the effect of GBs tends to be underestimated as the structural complexity of the model is reduced. Therefore, it was confirmed that simulations incorporating 3D structures are valuable for accurately evaluating the structural changes caused by Ag addition and their impact on photovoltaic performance. In the previous section, it was confirmed that the addition of Ag significantly increases the grain size of CIGS and that these structural changes can affect the electrical properties of solar cells. However, despite the superior grain structure of the actual ACIGS sample used in this study, its efficiency and VOC were lower than those of CIGS, as shown in table 2. Table S3 as well as Figures S4 and S5 give the result of fitting of several electrical and optoelectronic experiments using one-dimensional modelling. The extracted material properties showed distinct differences between the CIGS and ACIGS layers, in particular higher carrier lifetimes of the CIGS cell (table S3). Thus, the two layers exhibit variations not only in the microstructure but also in optoelectronic properties. At this point, we ascribe these variations to differences in the fabrication process rather than to the inherent effect of Ag addition. Other works have shown that Ag incorporation can improve carrier lifetime and reduce recombination by passivizing defects [22,23]. However, these effects strongly depend on Ag concentration and process conditions, which may account for differing trends reported in the literature. Therefore, to disentangle the structural effects from other varying factors, a controlled simulation approach was required. To isolate the effect of Ag-induced structural changes on solar cell efficiency while minimizing the influence of other factors, J–V simulations were conducted using the two distinct 3D models (CIGS model and ACIGS model) but one identical electronic parameter set, here the one of CIGS. Since fabricating samples that differ only in the Ag content is practically challenging, this approach ensured that the impact of Ag-induced structural modifications was analysed independently, without interference from variations in carrier properties, band-gap energy, or net-doping concentration. Figure 5(a) shows the J–V simulation results using such CIGS and ACIGS device models. In case of a high recombination velocity at the grain boundary (106cm s−1), the VOC of the CIGS solar cell was found to be smaller than for the ACIGS device. In contrast, the JSC was similar for both solar cells. Again, this result can be attributed to the collection in the SCR being influenced only slightly by changes in the grain boundary properties. Figure 5(b) illustrates the difference in VOC between CIGS and ACIGS as the grain boundary recombination velocity increases. As expected, the VOC increase due to structural changes induced by Ag addition was more pronounced with higher grain boundary recombination velocity Sgb. However, this result was derived using carrier lifetime values obtained from one-dimensional fitting, which does not distinguish between bulk and grain boundary effects. Therefore, when considering the actual intra-grain lifetime separately, the resulting minority carrier lifetime is likely higher than the initially set value. As shown by the red symbols in figure 5(b), at a grain boundary recombination velocity of 103cm s−1, which has been reported in [40]., an increase in the intra-grain carrier lifetime by a factor of 2 or even 4 results in a larger VOC gain due to Ag induced structural changes. While figures 5(a) and (b) present simulation results without considering grain boundary band bending, it has been reported that CIGS GBs exhibit a mixture of upward and downward band bending [6,40]. Downward band bending acts as hole barrier [53]. In contrast, upward band bending has a relatively minor impact on efficiency compared with downward band bending [5,54,55], because it primarily affects minority carriers (electrons), whereas downward band bending impedes the majority carriers (holes) that are crucial for current flow. To simplify the analysis, the present study employed a model assuming only downward band bending at the GBs to calculate the normalized VOC (Sgb)/VOC (Sgb =10 cm s−1) (figure 5(c)). A band bending value of 30 meV was used [40], and the results were compared with the reference case (effective lifetime from fit and without band bending). The comparison shows that as the recombination velocity at the grain boundary increases, the VOC decreases more gradually. Specifically, when the minority carrier lifetime is high and band bending occurs, the recombination rate at the grain boundary increases, leading to a more pronounced impact on the Voc. These results suggest that in absorbers with high 8