Tuning the Electronic and Optical Properties of Cu₂ZnSn_1−xGe_xS₄ Alloys for Photovoltaic Applications: A Hybrid Density Functional Theory and Device Simulation Approach

Abstract

In this study, we explore the electronic and optical properties of Cu₂ZnSn_1−xGe_xS₄ using density functional theory combined with hybrid functional calculations. Alloying Cu₂ZnSnS₄ with Ge and the formation of a band gap gradient are investigated as strategies to improve the efficiency of single-junction photovoltaic (PV) devices and as top cells in tandem solar cells. Our findings reveal that increasing Ge concentration leads to a rise in the band gap, with a small bowing constant (b ≈ 0.02 eV) indicating good miscibility of Ge in the host lattice. The electronic properties suggest that lower Ge incorporation may be optimal for PV applications. Additionally, device simulations were conducted to evaluate the impact of Cu₂ZnSn_1−xGe_xS₄ layer thickness on device performance, with and without a back surface field. The integration of first-principles calculations with SCAPS-1D simulations offers a comprehensive framework for predicting the performance of Cu₂ZnSn_1−xGe_xS₄ solar cells, highlighting the potential of Ge alloying for enhancing PV efficiency.

Keywords

band gap engineering / Cu₂ZnSn_1−xGe_xS₄ alloys / density functional theory (DFT) / solar cell efficiency

References

[1] A. Wang, N. L. Chang, K. Sun, et al., “Analysis of Manufacturing Cost and Market Niches for Cu₂ZnSnS₄(CZTS) Solar Cells,” Sustainable Energy & Fuels 5 (2021): 1044-1058.

[2] Y. Hamakawa, “Background and Motivation for Thin-Film Solar-Cell Development,” in Thin-Film Solar Cells Next Generation Photovoltaics and Its Applications, eds. Y. Hamakawa (Springer: Heidelberg, 2004), 1-14.

[3] C. Qian, J. Li, K. Sun, et al., “9.6%-Efficient All-Inorganic Sb₂(S,Se)₃ solar Cells With a MnS Hole-Transporting Layer,” Journal of Materials Chemistry A 10 (2022): 2835-2841.

[4] I. Celik, A. B. Phillips, Z. Song, et al., “Environmental Analysis of Perovskites and Other Relevant Solar Cell Technologies in a Tandem Configuration,” Energy & Environmental Science 10 (2017): 1874-1884.

[5] G. He, C. Yan, J. Li, et al., “11.6% Efficient Pure Sulfide Cu(In,Ga)S₂ Solar Cell Through a Cu-Deficient and KCN-Free Process,” ACS Applied Energy Materials 3 (2020): 11974-11980.

[6] J. Li, J. Huang, F. Ma, et al., “Unveiling Microscopic Carrier Loss Mechanisms in 12% Efficient Cu₂ZnSnSe₄ Solar Cells,” Nature Energy 7, no. 8 (2022): 754-764.

[7] F. Liu, Q. Zeng, J. Li, et al., “Emerging Inorganic Compound Thin Film Photovoltaic Materials: Progress, Challenges and Strategies,” Materials Today 41 (2020): 120-142.

[8] M. He, K. Sun, M. P. Suryawanshi, J. Li, and X. Hao, “Interface Engineering of P-N Heterojunction for Kesterite Photovoltaics: A Progress Review,” Journal of Energy Chemistry 60 (2021): 1-8.

[9] D. Mora-Herrera, R. Silva-González, F. E. Cancino-Gordillo, and M. Pal, “Development of Cu₂ZnSnS₄ Films From a Non-Toxic Molecular Precursor Ink and Theoretical Investigation of Device Performance Using Experimental Outcomes,” Solar Energy 199 (2020): 246-255.

[10] M. Grossberg, J. Krustok, C. J. Hages, et al., “The Electrical and Optical Properties of Kesterites,” Journal of Physics: Energy 1 (2019): 044002.

[11] S. Schorr, “The Crystal Structure of Kesterite Type Compounds: A Neutron and X-Ray Diffraction Study,” Solar Energy Materials and Solar Cells 95, no. 6 (2011): 1482-1488.

[12] S. R. Hall, J. T. Szymanski, and J. M. Stewart, “Kesterite, Cu₂(Zn,Fe)SnS₄, and Stannite, Cu₂(Fe,Zn)SnS₄, Structurally Similar but Distinct Minerals,” Canadian Mineralogist 16 (1978): 131.

[13] N. Kattan, B. Hou, D. J. Fermín, and D. Cherns, “Crystal Structure and Defects Visualization of Cu₂ZnSnS₄ Nanoparticles Employing Transmission Electron Microscopy and Electron Diffraction,” Applied Materials Today 1 (2015): 52-59.

[14] J. J. S. Scragg, L. Choubrac, A. Lafond, T. Ericson, and C. Platzer-Bjorkman, “A Low-Temperature Order-Disorder Transition in Cu₂znsns₄ Thin Films,” Applied Physics Letters 104 (2014): 041911.

[15] F. López-Vergara, A. Galdámez, V. Manríquez, P. Barahona, and O. Peña, “Cu₂Mn_1−xCo_xSnS₄: Novel Kësterite Type Solid Solutions,” Journal of Solid State Chemistry 198 (2013): 386-391.

[16] M. R. Dong, X. H. Chai, H. M. Qing, et al., “A Rapid Microwave-Assisted Method of Synthesizing Wurtzite Cu₂ZnSnS₄ in a Novel Solvent and Its Controlled Phase Evolution,” Ceramics International 48 (2022): 31714-31722.

[17] M. A. Olgar, S. Erkan, and R. Zan, “Dependence of CZTS Thin Film Properties and Photovoltaic Performance on Heating Rate and Sulfurization Time,” Journal of Alloys and Compounds 963 (2023): 171283.

[18] N. Saini, J. K. Larsen, K. Lindgren, A. Fazi, and C. Platzer-Björkman, “Bandgap Engineered Cu₂ZnGe_xSn_1−xS₄ Solar Cells Using an Adhesive TiN Back Contact Layer,” Journal of Alloys and Compounds 880 (2021): 160478.

[19] F. E. Cancino-Gordillo, J. V. Cab, and U. Pal, “Structure and Transport Behavior of Hydrothermally Grown Phase Pure Cu₂ZnSn_1−xGe_xS₄ (X = 0.0, 0.3) Nanoparticles,” Applied Surface Science 571 (2022): 15126120.

[20] N. M. Martin, N. Saini, M. Babucci, T. Törndahl, and C. Platzer-Björkman, “Properties of the Interface Between the Atomic Layer Grown Zinc-Tin-Oxide and Cu₂ZnGeS₄ Relevant for Kesterite Thin-Film Solar Cells,” Physica Status Solidi A: Applications and Materials Science 221 (2024): 2300695.

[21] D. Mora-Herrera, M. Pal, and F. Paraguay-Delgado, “Facile Solvothermal Synthesis of Cu₂ZnSn_1−xGe_xS₄ Nanocrystals: Effect of Ge Content on Optical and Electrical Properties,” Materials Chemistry and Physics 257 (2021): 123764.

[22] G. Chen, W. Wang, S. Chen, et al., “Bandgap Engineering of Cu₂ZnSn_1−xGe_xS(e)₄ by Adjusting Sn-Ge Ratios for Almost Full Solar Spectrum Absorption,” Journal of Alloys and Compounds 718 (2017): 236-245.

[23] S. Bag, O. Gunawan, T. Gokmen, Y. Zhu, and D. B. Mitzi, “Hydrazine-Processed Ge-Substituted Cztse Solar Cells,” Chemistry of Materials 24 (2012): 4588-4593.

[24] D. Mora-Herrera, S. Shaji, and M. Pal, “Ge Incorporation in Kesterite Thin Films by Solution Processing Route: An In-Depth Study of Structural and Optoelectronic Properties,” Journal of Alloys and Compounds 921 (2022): 166184.

[25] Y. Gong, Q. Zhu, B. Li, et al., “Elemental De-Mixing-Induced Epitaxial Kesterite/CDS Interface Enabling 13%-Efficiency Kesterite Solar Cells,” Nature Energy 7 (2022): 966-977, https://doi.org/10.1038/s41560-022-01132-4.

[26] R. Scaffidi, G. Birant, G. Brammertz, J. de Wild, D. Flandre, and B. Vermang, “Ge-Alloyed Kesterite Thin-Film Solar Cells: Previous Investigations and Current Status - A Comprehensive Review,” Journal of Materials Chemistry A 11 (2023): 13174-13194.

[27] A. Wang, J. Huang, J. Cong, et al., “Cd-Free Pure Sulfide Kesterite Cu₂ZnSnS₄ Solar Cell With Over 800 mV Open-Circuit Voltage Enabled by Phase Evolution Intervention,” Advanced Materials 36 (2024): 2307733.

[28] T. Amrillah, “Enhancing the Value of Environment-Friendly CZTS Compound for Next Generation Photovoltaic Device: A Review,” Solar Energy 263 (2023): 111982.

[29] T. Ratz, J.-Y. Raty, G. Brammertz, et al., “Opto-electronic Eroperties and Solar Cell Efficiency Modelling of Cu₂ZnXS₄ (X = Sn, Ge, Si) Kesterites,” Journal of Physics: Energy 2 (2020): 035004.

[30] M. I. Ziane, M. Hadjab, M. Tablaoui, H. Bennacer, M. B. Kanoun, and S. Goumri-Said, “Investigating Solid Solutions: Geometric Transformations Triggered by Germanium Incorporation in Cu₂ZnGe_xSn_1−xS₄,” Materials Today Communications 38 (2024): 107967.

[31] S. Smidstrup, T. Markussen, P. Vancraeyveld, et al., “Quantum ATK: An Integrated Platform of Electronic and Atomic-Scale Modelling Tools,” Journal of Physics: Condensed Matter 32 (2020): 015901.

[32] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters 77 (1996): 3865-3868.

[33] M. J. van Setten, M. Giantomassi, E. Bousquet, et al., “The PSEUDODOJO: Training and Grading a 85 Element Optimized Norm-Conserving Pseudopotential Table,” Computer Physics Communications 226 (2018): 39-54.

[34] M. Burgelman, P. Nollet, and S. Degrave, “Modelling Polycrystalline Semiconductor Solar Cells,” Thin Solid Films 361-362, no. 1-2 (2000): 527-532.

[35] L. Rakocevic, R. Gehlhaar, T. Merckx, et al., “Interconnection Optimization for Highly Efficient Perovskite Modules,” IEEE Journal of Photovoltaics 7 (2017): 404-408.

[36] M. Stuckelberger, T. Nietzold, G. N. Hall, et al., “Charge Collection in Hybrid Perovskite Solar Cells: Relation to the Nanoscale Elemental Distribution,” IEEE Journal of Photovoltaics 7, no. 2 (2017): 590-597.

[37] S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (New York: John Wiley & Sons, 2006).

[38] D. B. Khadka and J. Kim, “Band Gap Engineering of Alloyed Cu₂ZnGe_xSn_1-xQ₄ (Q = S, Se) Films for Solar Cell,” Journal of Physical Chemistry C 119 (2015): 1706-1713.

[39] K. Doverspike, K. Dwight, and A. Wold, “Preparation and Characterization of Copper Zinc Germanium Sulfide Selenide (Cu₂ZnGeS_4−ySe_y),” Chemistry of Materials 2, no. 2 (1990): 194-197.

[40] M. Gusain, P. Rawat, and R. Nagarajan, “Solvent Mediated Rapid Synthesis of Orthorhombic Cu₂ZnSnS₄ (CZTS),” Materials Letters 133 (2014): 220-223.

[41] R. I. Biega, M. R. Filip, L. Leppert, and J. B. Neaton, “Chemically Localized Resonant Excitons in Silver-Pnictogen Halide Double Perovskites,” Journal of Physical Chemistry Letters 12, no. 8 (2021): 2057-2063.

[42] V. Batir and V. Zalamai, “Optical Properties of Cu₂ZnSnS₄ and Cu₂CdSnS₄ Quaternary Compounds,” Romanian Reports in Physics 76 (2024): 506.

[43] F. Wooten, Optical Properties of Solids (New York: Academic Press, 1972).

[44] S. Goumri-Said and M. B. Kanoun, “DFT+U Study of the Oxide-Ion Conductor Pentalanthanum Hexamolybdenum Henicosaoxide,” Journal of Solid State Chemistry 197 (2013): 304-311.

[45] C. Yan, J. Huang, K. Sun, et al., “Cu₂ZnSnS₄ Solar Cells With over 10% Power Conversion Efficiency Enabled by Heterojunction Heat Treatment,” Nature Energy 3 (2018): 764-772.

[46] A. Bag, R. Radhakrishnan, R. Nekovei, and R. Jeyakumar, “Effect of Absorber Layer, Hole Transport Layer Thicknesses, and Its Doping Density on the Performance of Perovskite Solar Cells by Device Simulation,” Solar Energy 196 (2020): 177-182, https://doi.org/10.1016/j.solener.2019.12.014.

[47] Y. Dong, Z. Liu, Y. Wang, and Y. Zhang, “Boosting VOC of Antimony Chalcogenide Solar Cells: A Review on Interfaces and Defects,” Nano Select 2 (2021): 1818-1848, https://doi.org/10.1002/nano.202000288.

[48] A. Haddout, M. Fahoume, A. Qachaou, A. Raidou, and M. Lharch, “Understanding Effects of Defects in Bulk Cu₂ZnSnS₄ Absorber Layer of Kesterite Solar Cells,” Solar Energy 211 (2020): 301-311, https://doi.org/10.1016/j.solener.2020.09.067.

[49] M. S. Rana, M. M. Islam, and M. Julkarnain, “Enhancement in Efficiency of CZTS Solar Cell by Using CZTSe BSF Layer,” Solar Energy 226 (2021): 272-287, https://doi.org/10.1016/j.solener.2021.08.035.

[50] K.-J. Yang, S. Kim, J.-H. Sim, et al., “The Alterations of Carrier Separation in Kesterite Solar Cells,” Nano Energy 52 (2018): 38-53, https://doi.org/10.1016/j.nanoen.2018.07.039.

[51] T. AlZoubi, A. Moghrabi, M. Moustafa, and S. Yasin, “Efficiency Boost of CZTS Solar Cells Based on Double-Absorber Architecture: Device Modeling and Analysis,” Solar Energy 225 (2021): 44-52, https://doi.org/10.1016/j.solener.2021.07.012.

[52] M. F. Rahman, M. Chowdhury, L. Marasamy, et al., “Improving the Efficiency of a CIGS Solar Cell to Above 31% With Sb₂S₃ as a New BSF: A Numerical Simulation Approach by Scaps-1D,” RSC Advances 14 (2024): 1924-1938, https://doi.org/10.1039/D3RA07893K.

[53] P. Chauhan, S. Agarwal, V. Srivastava, et al., “Kesterite CZTS-Based Thin Film Solar Cell: Generation, Recombination, and Performance Analysis,” Journal of Physics and Chemistry of Solids 183 (2023): 111631, https://doi.org/10.1016/j.jpcs.2023.111631.

[54] M. F. Rahman, A. Lubaba, L. B. Farhat, S. Ezzine, M. H. Rahman, and M. Harun-Or-Rashid, “Efficiency Enhancement Above 31% of Sb₂Se₃ Solar Cells With Optimizing Various BSF Layer,” Materials Science and Engineering: B 307 (2024): 117527, https://doi.org/10.1016/j.mseb.2024.117527.

[55] A. Benyoucef, M. Belarbi, O. Zeggai, et al., “Numerical Investigation of Octakis (4-Methoxyphenyl) Spiro [Fluorene-9, 9′ Xanthene]−2, 2′, 7, 7′-Tetraamine) (X60) as Hole Transport Layer in Solid-State Dye-Sensitized Solar Cell,” Physica Scripta 98, no. 9 (2023): 095009, https://doi.org/10.1088/1402-4896/aceb37.

[56] M. Belarbi, O. Zeggai, S. Khettaf, and S. Louhibi-Fasla, “Efficiency Enhancement of Triple Absorber Layer Perovskite Solar Cells With the Best Materials for Electron and Hole Transport Layers: Numerical Study,” Semiconductor Science and Technology 37, no. 9 (2022): 095016, https://doi.org/10.1088/1361-6641/ac83e4.

RIGHTS & PERMISSIONS

2024 The Author(s). Battery Energy published by Xijing University and John Wiley & Sons Australia, Ltd.