Klaus Jäger, Alvaro Tejada, Sebastian Berwig, Martin Hammerschmidt, Philipp Tockhorn, Steve Albrecht, Christiane Becker
This numerical study investigates, how textures at various locations of all-perovskite tandem solar cells affect their optical performance. For this, hexagonal sinusoidal textures with 750 nm period and aspect ratios (height-to-period) of 27% (moderate) and 54% (pronounced) are considered. The optical simulations are performed with the finite element method and an algorithm to correct for the thick glass superstrate. The complex refractive index data of the wide-bandgap (WBG) and narrow-bandgap (NBG) perovskites with spectroscopic ellipsometry is determined. Texturing between the glass superstrate and the WBG perovskite top cell has an antireflective effect across the whole wavelength region. In contrast, texturing between the WBG perovskite top cell and the NBG perovskite bottom cell has no additional effect for a moderate texture but leads to light trapping in the NBG perovskite for a pronounced texture. Moderate texturing between the NBG perovskite absorber and the metal back contact leads to light trapping in the NBG perovskite but also excites surface plasmons in the copper back contact. Dielectric interlayers between the NBG perovskite and the metal back contact can reduce the plasmonic absorption losses. Texturing potentially allows to increase the current-matched short-circuit current density beyond 17 mA <span data-altimg="/cms/asset/546d7dc4-f86b-4a59-ac23-1b39a0220b53/adts202400724-math-0001.png"></span><mjx-container ctxtmenu_counter="76" ctxtmenu_oldtabindex="1" jax="CHTML" role="application" sre-explorer- style="font-size: 103%; position: relative;" tabindex="0"><mjx-math aria-hidden="true" location="graphic/adts202400724-math-0001.png"><mjx-semantics><mjx-msup data-semantic-children="0,3" data-semantic- data-semantic-role="unknown" data-semantic-speech="c m Superscript negative 2" data-semantic-type="superscript"><mjx-mi data-semantic-font="normal" data-semantic- data-semantic-parent="4" data-semantic-role="unknown" data-semantic-type="identifier"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mrow data-semantic-annotation="clearspeak:simple" data-semantic-children="2" data-semantic-content="1" data-semantic- data-semantic-parent="4" data-semantic-role="negative" data-semantic-type="prefixop" size="s"><mjx-mo data-semantic- data-semantic-operator="prefixop,−" data-semantic-parent="3" data-semantic-role="subtraction" data-semantic-type="operator" rspace="1"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation="clearspeak:simple" data-semantic-font="normal" data-semantic- data-semantic-parent="3" data-semantic-role="integer" data-semantic-type="number"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-semantics></mjx-math><mjx-assistive-mml display="inline" unselectable="on"><math altimg="urn:x-wiley:25130390:media:adts202400724:adts202400724-math-0001" display="inline" location="graphic/adts202400724-math-0001.png" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msu
{"title":"Optical Simulations of Nanotextured All-Perovskite Tandem Solar Cells","authors":"Klaus Jäger, Alvaro Tejada, Sebastian Berwig, Martin Hammerschmidt, Philipp Tockhorn, Steve Albrecht, Christiane Becker","doi":"10.1002/adts.202400724","DOIUrl":"https://doi.org/10.1002/adts.202400724","url":null,"abstract":"This numerical study investigates, how textures at various locations of all-perovskite tandem solar cells affect their optical performance. For this, hexagonal sinusoidal textures with 750 nm period and aspect ratios (height-to-period) of 27% (moderate) and 54% (pronounced) are considered. The optical simulations are performed with the finite element method and an algorithm to correct for the thick glass superstrate. The complex refractive index data of the wide-bandgap (WBG) and narrow-bandgap (NBG) perovskites with spectroscopic ellipsometry is determined. Texturing between the glass superstrate and the WBG perovskite top cell has an antireflective effect across the whole wavelength region. In contrast, texturing between the WBG perovskite top cell and the NBG perovskite bottom cell has no additional effect for a moderate texture but leads to light trapping in the NBG perovskite for a pronounced texture. Moderate texturing between the NBG perovskite absorber and the metal back contact leads to light trapping in the NBG perovskite but also excites surface plasmons in the copper back contact. Dielectric interlayers between the NBG perovskite and the metal back contact can reduce the plasmonic absorption losses. Texturing potentially allows to increase the current-matched short-circuit current density beyond 17 mA <span data-altimg=\"/cms/asset/546d7dc4-f86b-4a59-ac23-1b39a0220b53/adts202400724-math-0001.png\"></span><mjx-container ctxtmenu_counter=\"76\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" role=\"application\" sre-explorer- style=\"font-size: 103%; position: relative;\" tabindex=\"0\"><mjx-math aria-hidden=\"true\" location=\"graphic/adts202400724-math-0001.png\"><mjx-semantics><mjx-msup data-semantic-children=\"0,3\" data-semantic- data-semantic-role=\"unknown\" data-semantic-speech=\"c m Superscript negative 2\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c></mjx-c><mjx-c></mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"2\" data-semantic-content=\"1\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"negative\" data-semantic-type=\"prefixop\" size=\"s\"><mjx-mo data-semantic- data-semantic-operator=\"prefixop,−\" data-semantic-parent=\"3\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" rspace=\"1\"><mjx-c></mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c></mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-semantics></mjx-math><mjx-assistive-mml display=\"inline\" unselectable=\"on\"><math altimg=\"urn:x-wiley:25130390:media:adts202400724:adts202400724-math-0001\" display=\"inline\" location=\"graphic/adts202400724-math-0001.png\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><msu","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"1 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wisly Fidel, Guido Perrin, Ikram Anefnaf, Richard K Koech, Dieuseul Prédélus, Nicole Doumit, Jacques Botsoa, Conchi O. Ania, Esidor Ntsoenzok
Despite the numerous efforts to optimize the performance of perovskite solar cells (PSCs), challenges persist. Carbon materials are promising candidates for this purpose, but identifying the most suitable carbon material and understanding its role in the PSC among the wide family of carbons remains a challenging task. In this study, SCAPS‐1D software is employed to optimize the use of carbon materials as interlayers to PSCs. The best configuration of the carbon interlayer and the required physicochemical properties of the carbon materials is identified for improved performance. The simulations show that the insertion of thin carbon interlayers of adequate features in n‐i‐p stacked cells (FTO/TiO2/MAPbI3/HTL/Ni) can increase the efficiency of the resulting PSCs by over 2.3 %, while significantly improving the open‐circuit voltage and the fill factor. These results underline that those carbon materials with optical bandgaps ranging from 3 to 3.5 eV offer the best performance as an interlayer to the hole tranport layer, with negligible impact of the thickness of the interlayer. This contribution offers a novel perspective on the use of carbon materials in PSCs and provides new insights into the understanding of the role of carbon materials as interlayers in PSCs.
{"title":"Numerical Analysis on the Use of Carbon Nanostructures as Interlayers to Perovskite Solar Cells Using SCAPS‐1D","authors":"Wisly Fidel, Guido Perrin, Ikram Anefnaf, Richard K Koech, Dieuseul Prédélus, Nicole Doumit, Jacques Botsoa, Conchi O. Ania, Esidor Ntsoenzok","doi":"10.1002/adts.202400771","DOIUrl":"https://doi.org/10.1002/adts.202400771","url":null,"abstract":"Despite the numerous efforts to optimize the performance of perovskite solar cells (PSCs), challenges persist. Carbon materials are promising candidates for this purpose, but identifying the most suitable carbon material and understanding its role in the PSC among the wide family of carbons remains a challenging task. In this study, SCAPS‐1D software is employed to optimize the use of carbon materials as interlayers to PSCs. The best configuration of the carbon interlayer and the required physicochemical properties of the carbon materials is identified for improved performance. The simulations show that the insertion of thin carbon interlayers of adequate features in n‐i‐p stacked cells (FTO/TiO<jats:sub>2</jats:sub>/MAPbI<jats:sub>3</jats:sub>/HTL/Ni) can increase the efficiency of the resulting PSCs by over 2.3 %, while significantly improving the open‐circuit voltage and the fill factor. These results underline that those carbon materials with optical bandgaps ranging from 3 to 3.5 eV offer the best performance as an interlayer to the hole tranport layer, with negligible impact of the thickness of the interlayer. This contribution offers a novel perspective on the use of carbon materials in PSCs and provides new insights into the understanding of the role of carbon materials as interlayers in PSCs.","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"64 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142236175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study presents a simple analytical model to investigate wave propagation in 2D carbon nano‐onions (CNOs) and nitrogen‐doped carbon nano‐onions (N‐CNOs) lattices. Furthermore, the dispersion relationships of the waves and bandgaps in these lattices are derived based on Bloch's theorem. The CNOs and N‐CNOs lattices are modeled as infinite 2D mass‐in‐mass structures accurately assembled using linear springs. The Lennard–Jones potential energy is employed to obtain equivalent spring constants. A key finding of this research is the identification of bandgaps within all lattice structures, signifying regions where wave propagation is prohibited. The existence of these bandgaps offers potential for the advancement of adjustable nano‐scale metamaterials.
{"title":"Elastic Wave Propagation in 2D Carbon Nano‐Onion Lattices","authors":"Reza Lashani, Esmaeal Ghavanloo","doi":"10.1002/adts.202400444","DOIUrl":"https://doi.org/10.1002/adts.202400444","url":null,"abstract":"This study presents a simple analytical model to investigate wave propagation in 2D carbon nano‐onions (CNOs) and nitrogen‐doped carbon nano‐onions (N‐CNOs) lattices. Furthermore, the dispersion relationships of the waves and bandgaps in these lattices are derived based on Bloch's theorem. The CNOs and N‐CNOs lattices are modeled as infinite 2D mass‐in‐mass structures accurately assembled using linear springs. The Lennard–Jones potential energy is employed to obtain equivalent spring constants. A key finding of this research is the identification of bandgaps within all lattice structures, signifying regions where wave propagation is prohibited. The existence of these bandgaps offers potential for the advancement of adjustable nano‐scale metamaterials.","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"30 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142236176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rida Fatima, Nabeel Shahzad, Tahreem Fatima, Sonia Perveen, Ashraf M. M. Abdelbacki, Kai Wang, Javed Iqbal
This quantum mechanical approach recommends push–pull molecular engineering to fabricate hole‐transporting materials (HTMs) for photovoltaic cells. It integrates acceptor moieties via thiophene to fluorene core, resulting in five novel HTMs (SFD‐1 to SFD‐5). The results exhibit that derivative HTMs show excellent coherence in excitation, dispersion, and transportation of charge carriers, ensuring robust hole mobility. The anchor moieties functionalized HTMs unveil excellent band alignment with perovskite with fitting HOMO energy levels (−4.93–−5.35 eV), less optical absorption in visible portion ( < 520). This acceptor integration has improved the hole mobility in derivatives, accredited to the smaller hole reorganization energy (0.14–0.68 eV), and greater hole transfer integral (0.22–0.33 eV). The transition density matrix analysis exhibited robust electronic coupling, subtler charge carrier overlapping and greater charge transfer length (7.48–13.73 Å). This resulted in an excellent upsurge in intrinsic charge transference (70.75–92.70%) and smaller exciton binding energy, leading to easier exciton dissociation, and fewer recombination fatalities. However, an adequate variation in dipole moment (4.04 D to 16.34 D) and Gibbs solvation‐free energy (−18.06 to −21.89 kcal mol−1) ensures facile film formation and processability. In conclusion, this approach recommends these flourene‐based HTMs are highly desireable for forthcoming solar cell technology.
{"title":"Tailoring Diversified Peripheral Anchor Groups in Spirofluorene‐Dithiolane‐Based Hole Transporting Materials for Efficient Organic and Perovskite Solar Cells from First‐Principle","authors":"Rida Fatima, Nabeel Shahzad, Tahreem Fatima, Sonia Perveen, Ashraf M. M. Abdelbacki, Kai Wang, Javed Iqbal","doi":"10.1002/adts.202400773","DOIUrl":"https://doi.org/10.1002/adts.202400773","url":null,"abstract":"This quantum mechanical approach recommends push–pull molecular engineering to fabricate hole‐transporting materials (HTMs) for photovoltaic cells. It integrates acceptor moieties via thiophene to fluorene core, resulting in five novel HTMs (SFD‐1 to SFD‐5). The results exhibit that derivative HTMs show excellent coherence in excitation, dispersion, and transportation of charge carriers, ensuring robust hole mobility. The anchor moieties functionalized HTMs unveil excellent band alignment with perovskite with fitting HOMO energy levels (−4.93–−5.35 eV), less optical absorption in visible portion ( < 520). This acceptor integration has improved the hole mobility in derivatives, accredited to the smaller hole reorganization energy (0.14–0.68 eV), and greater hole transfer integral (0.22–0.33 eV). The transition density matrix analysis exhibited robust electronic coupling, subtler charge carrier overlapping and greater charge transfer length (7.48–13.73 Å). This resulted in an excellent upsurge in intrinsic charge transference (70.75–92.70%) and smaller exciton binding energy, leading to easier exciton dissociation, and fewer recombination fatalities. However, an adequate variation in dipole moment (4.04 D to 16.34 D) and Gibbs solvation‐free energy (−18.06 to −21.89 kcal mol<jats:sup>−1</jats:sup>) ensures facile film formation and processability. In conclusion, this approach recommends these flourene‐based HTMs are highly desireable for forthcoming solar cell technology.","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"9 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142236630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Amir Bazrafshan, Farhad Khoeini, Catherine Stampfl
Aiming at an efficient method to determine the transport properties of a physical system, an effective and accurate band‐counting algorithm is presented to extract the transmission spectrum of a low‐dimensional system, directly from the band structure. This approach is more efficient than Hamiltonian‐dependent formalisms such as the standard Green's function (GF) or the transfer matrix methods. The only constraint of the approach is that the bands should not be mixed, i.e., for each band in the k‐path, there should be a set of eigenvalues. The efficiency of the approach is comparable to that of Green's function method, and it is applicable to any computational approach whose output is a band structure, whether for particles or quasiparticles such as electrons and phonons. Since the transport coefficient is calculated separately for each band, the occurrence of eigenvalues at the same k‐point can be captured by the algorithm. The proposed algorithm will be useful for studying transmission coefficient‐dependent quantities, such as thermoelectric‐related quantities, and also the electric current within the Landauer–Büttiker formalism.
为了采用高效方法确定物理系统的传输特性,本文提出了一种有效而精确的带计数算法,可直接从带结构中提取低维系统的传输谱。这种方法比依赖哈密顿形式的方法(如标准格林函数 (GF) 或传递矩阵方法)更有效。该方法的唯一限制条件是带不应该混杂,即 k 路径中的每个带都应该有一组特征值。该方法的效率与格林函数法不相上下,适用于任何输出为带状结构的计算方法,无论是粒子还是准粒子(如电子和声子)。由于每个能带的输运系数都是单独计算的,因此该算法可以捕捉到同一 k 点出现的特征值。所提出的算法将有助于研究依赖于传输系数的量,如热电相关量,以及兰道尔-比提克形式主义中的电流。
{"title":"Efficient Algorithm for Extracting Transmission Spectrum From Band Structure in Low‐Dimensional Systems","authors":"M. Amir Bazrafshan, Farhad Khoeini, Catherine Stampfl","doi":"10.1002/adts.202400801","DOIUrl":"https://doi.org/10.1002/adts.202400801","url":null,"abstract":"Aiming at an efficient method to determine the transport properties of a physical system, an effective and accurate band‐counting algorithm is presented to extract the transmission spectrum of a low‐dimensional system, directly from the band structure. This approach is more efficient than Hamiltonian‐dependent formalisms such as the standard Green's function (GF) or the transfer matrix methods. The only constraint of the approach is that the bands should not be mixed, i.e., for each band in the <jats:italic>k</jats:italic>‐path, there should be a set of eigenvalues. The efficiency of the approach is comparable to that of Green's function method, and it is applicable to any computational approach whose output is a band structure, whether for particles or quasiparticles such as electrons and phonons. Since the transport coefficient is calculated separately for each band, the occurrence of eigenvalues at the same <jats:italic>k</jats:italic>‐point can be captured by the algorithm. The proposed algorithm will be useful for studying transmission coefficient‐dependent quantities, such as thermoelectric‐related quantities, and also the electric current within the Landauer–Büttiker formalism.","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"15 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142236178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mobina Abbaspour, Mahmoud Nikoufard, Alireza Malek Mohammad
This study proposes a novel plasmonic optical modulator integrating the phase-change material germanium-antimony-tellurium (GST) with a silicon carbide (SiC) waveguide for telecom applications. The design utilizes a 10 nm GST cladding layer and a 290 nm thick, 100 nm wide SiC ridge waveguide, with gold electrodes enabling electrothermal switching of GST between amorphous and crystalline states. Comprehensive simulations spanning optical, electrical-thermal, and opto-thermal domains investigated the modulator's performance. Optical simulations examine the effects of wavelength, ridge width, and GST thickness on effective refractive index, confinement factor, and effective area. Electrical-thermal simulations determines voltage pulse parameters for phase transitions and analyzed temperature distributions. Opto-thermal simulations explored temperature's influence on the effective refractive index during phase transitions. Results demonstrate the modulator's potential, achieving 160 Mb s−1 at 1.55 µm. The SiC-GST integration offers high thermal conductivity, low thermo-optic coefficient, and significant refractive index contrast between GST phases, enabling efficient light modulation for high-performance, compact, energy-efficient optical modulators advancing integrated photonics.
{"title":"Electro-Thermo-Optical Simulations of Phase-Change GST-SiC Plasmonic Optical Modulator for Telecom Applications","authors":"Mobina Abbaspour, Mahmoud Nikoufard, Alireza Malek Mohammad","doi":"10.1002/adts.202400546","DOIUrl":"https://doi.org/10.1002/adts.202400546","url":null,"abstract":"This study proposes a novel plasmonic optical modulator integrating the phase-change material germanium-antimony-tellurium (GST) with a silicon carbide (SiC) waveguide for telecom applications. The design utilizes a 10 nm GST cladding layer and a 290 nm thick, 100 nm wide SiC ridge waveguide, with gold electrodes enabling electrothermal switching of GST between amorphous and crystalline states. Comprehensive simulations spanning optical, electrical-thermal, and opto-thermal domains investigated the modulator's performance. Optical simulations examine the effects of wavelength, ridge width, and GST thickness on effective refractive index, confinement factor, and effective area. Electrical-thermal simulations determines voltage pulse parameters for phase transitions and analyzed temperature distributions. Opto-thermal simulations explored temperature's influence on the effective refractive index during phase transitions. Results demonstrate the modulator's potential, achieving 160 Mb s<sup>−1</sup> at 1.55 µm. The SiC-GST integration offers high thermal conductivity, low thermo-optic coefficient, and significant refractive index contrast between GST phases, enabling efficient light modulation for high-performance, compact, energy-efficient optical modulators advancing integrated photonics.","PeriodicalId":7219,"journal":{"name":"Advanced Theory and Simulations","volume":"171 1","pages":""},"PeriodicalIF":3.3,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ingvild Bergsbak, Ørnulf Nordseth, Kjetil K. Saxegaard, Vegard S. Olsen, Holger von Wenckstern, Kristin Bergum
The novel, high electron mobility material <span data-altimg="/cms/asset/e9f5e09d-2293-46b4-99bb-9e7dbfc6e7db/adts202400252-math-0002.png"></span><math altimg="urn:x-wiley:25130390:media:adts202400252:adts202400252-math-0002" display="inline" location="graphic/adts202400252-math-0002.png">