A method for bandgap optimization of tandem solar cells based on limiting efficiency

Abstract

This invention discloses a method for optimizing the bandgap of tandem solar cells based on limiting efficiency. First, an overall structural model of the tandem solar cell is established, and material parameters and incident spectrum boundary conditions are set. An optical solution model is established for the top cell region. Optical solutions are then performed on each sub-cell from top to bottom to obtain the photogenerated carrier generation rate distribution and transmission results for each layer. The incident spectrum is updated layer by layer based on the transmission results of the previous layer until the entire layer calculation is completed. The photogenerated carrier generation rate of each layer is used as electrical input for electrical analysis, and the J-V curve of current density-voltage for each sub-cell is obtained through electrical solution. The limiting efficiency is calculated based on the J-V curve to find the maximum power point. The optimal bandgap is determined based on the maximum power point and the limiting efficiency. By using optical-electrical multiphysics coupling modeling and introducing layer-by-layer spectral transfer, a photogenerated carrier generation rate and J-V characteristics that more closely resemble actual operating conditions are obtained, thereby selecting a more realistic optimal bandgap.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic power generation technology, and in particular relates to a method for optimizing the bandgap of tandem solar cells based on extreme efficiency. Background Technology

[0002] Improving solar cell efficiency is one of the core goals of photovoltaic technology development. Tandem solar cells, by allocating the spectrum and performing energy classification conversion of sub-cells with different bandgap sizes, can effectively reduce energy waste in single-junction devices, thus breaking through the efficiency ceiling of single-junction cells and becoming an important development direction for high-efficiency photovoltaic devices. Therefore, evaluating the efficiency ceiling and optimizing the structural parameters of multi-junction solar cells are key tasks in the research and engineering design of high-efficiency photovoltaic devices.

[0003] The prior art patent with publication number CN115659627A discloses a method for optimizing the bandgap combination of multi-junction solar cells. By setting the calculation step size and the number of calculation steps for the bandgap of each junction, the bandgap interval is subdivided, the photoelectric conversion efficiency of multi-junction solar cells under different bandgap combinations is accurately calculated, and the maximum photoelectric conversion efficiency under various bandgap combinations is compared to obtain the optimal bandgap combination. Summary of the Invention

[0004] Current calculations of the limiting efficiency of multi-junction solar cells often employ detailed equilibrium theory or the Shockley-Queisser (SQ) limiting model. This involves deriving the relationship between photocurrent and dark current through integration of the incident spectrum, thereby constructing an idealized current density-voltage characteristic and calculating the theoretical efficiency upper limit. However, these theoretical models are typically based on idealized assumptions, such as approximating material absorption as a step function, considering only the radiative recombination limit, neglecting finite-thickness absorption, non-radiative recombination caused by interfaces and defects, contact and transport losses, temperature effects, and their resulting changes in material parameters. Since the performance of actual multi-junction devices is often significantly affected by factors such as material defects, interface quality, carrier transport, parasitic absorption, and thermal coupling, the efficiency upper limit obtained using idealized detailed equilibrium models deviates significantly from the achievable level of real devices, making it difficult to provide accurate guidance for material selection, structural parameter design, and engineering implementation.

[0005] On the other hand, the finite element method (FEM) can introduce richer material parameters and boundary conditions at the optical and electrical levels, thereby obtaining J-V characteristics that are closer to those of actual devices. However, when the above multiphysics coupling model is applied to multi-junction solar cell structures, there are significant mutual influences between sub-cells: on the one hand, the absorption and filtering of the incident spectrum by the upper sub-cell will change the actual incident spectrum and photogenerated carrier generation rate distribution of the lower sub-cell; on the other hand, the coupling and interconnection losses within the device will also affect the operating state of each sub-cell. Especially for tandem cells with series structures, since each sub-cell needs to work together under the same current conditions, the overall operating point of the system needs to meet the current consistency constraint, which usually requires repeated iterations and simultaneous solutions during the solution process, further increasing the computational complexity and convergence difficulty.

[0006] Therefore, there is an urgent need for a method that can quickly calculate the upper limit of efficiency of multi-junction solar cells under the conditions of considering spectral loss, temperature effect and non-ideal loss mechanism, so as to obtain the optimal solution of bandgap.

[0007] To solve the above-mentioned technical problems, the technical solution provided by the present invention is: a method for optimizing the bandgap of tandem solar cells based on limiting efficiency, comprising the following steps: S1. Establish an overall structural model of the tandem battery, set material parameters and incident spectrum boundary conditions, and establish an optical solution model for the top battery region. S2. Perform optical solutions for each sub-cell from top to bottom to obtain the photogenerated carrier generation rate distribution and transmission results of each sub-cell. Update the incident spectrum layer by layer based on the transmission results of the previous layer until the full layer calculation is completed. S3. Using the photogenerated carrier generation rate of each layer as the electrical input, perform electrical analysis and obtain the JV curve of current density-voltage of each sub-cell through electrical solution. S4. Calculate the limiting efficiency based on the JV curve, find the maximum power point, and determine the optimal bandgap based on the maximum power point and the limiting efficiency.

[0008] Specifically, in step S4, the device is determined to be either a series or independent architecture based on the terminal structure, and different limiting efficiency calculation methods are selected accordingly. Based on the electrical connection relationship between the terminals and interconnect layers of the solar cell, when each sub-cell has an independent external terminal and is electrically isolated, it is determined to be an independent architecture; when each sub-cell shares an external terminal and is electrically connected in series, it is determined to be a series architecture.

[0009] Specifically, in step S4, when determining whether the device is a series or independent architecture based on the terminal structure, if it is an independent architecture, the maximum power point of each sub-cell is determined based on the JV curve of each sub-cell, and the maximum power of each sub-cell is summed to obtain the total output power density of the independent architecture. The total output power density of the independent architecture is then normalized with the incident power density to calculate the limiting efficiency. If it is a series architecture, the VJ expression of each sub-cell is constructed by inverting the JV curve of each sub-cell. The voltage of each sub-cell is summed with the current density as a common variable to obtain the total VJ function of the series architecture. Based on the VJ function of the series architecture, a global maximum power point search is performed on the total power within a preset current density range to obtain the current density and total output power density corresponding to the maximum power point. The total output power density and incident power density are then normalized to calculate the efficiency of the series architecture, which is used as the limiting efficiency calculation result of the multi-junction solar cell.

[0010] Specifically, when performing a global maximum power point search, a database containing multiple sets of JV curve samples is pre-built. The maximum power point search model is trained based on the database to learn the mapping relationship between JV curve features and the voltage position of the maximum power point. For the device to be solved, its open-circuit voltage and JV curve features are extracted and input into the maximum power point search model to obtain the candidate voltage range corresponding to the maximum power point. Then, the output power is calculated within the candidate voltage range, and the maximum power point is finely located through local dense sampling, interpolation fitting, or range optimization.

[0011] Specifically, in step S1, the silicon textured surface structure of the overall structure model of the stacked battery is pyramid-shaped.

[0012] Specifically, in step S2, during the optical solution, considering the refraction of light by the silicon pyramid textured surface, electromagnetic field boundary condition constraints are first established. Based on the principle that the electric field distribution is determined by the dielectric properties of the material and the space charge, and the principle that there are no isolated magnetic charge sources during the propagation of the magnetic field, the electromagnetic field boundary conditions in the sub-cell are constrained. Then, electromagnetic field propagation calculations are performed. Based on the principle that a time-varying magnetic field can induce an electric field, and that the electromagnetic propagation relationship of the magnetic field response is determined by the time-varying electric field and the conductivity of the material, the electric field and magnetic field distributions at various locations of the sub-cell are solved. Based on the electric field and magnetic field distributions at various locations of the sub-cell, the transmission results and photogenerated carrier generation rate distribution in each region of the sub-cell are calculated. The transmission results include light absorption characteristics and transmission characteristics.

[0013] Specifically, in step S2, when performing optical solutions for each sub-cell from top to bottom, if the top-layer sub-cell is optically solved, its incident spectrum is the incident spectrum set in step S1; if non-top-layer sub-cells are optically solved, their incident spectrum is the incident spectrum corrected based on the transmission results of the previous layer sub-cell.

[0014] Specifically, during the electromagnetic field propagation calculation, the electromagnetic field distribution at adjacent time points and spatial locations is iteratively calculated. For the time dimension, the discrete solution of the continuous time process is achieved by setting the solver step size. For the spatial dimension, a training sample set is constructed based on experimentally obtained silicon pyramid textured surface structure data. This training sample set includes geometric morphology parameters, interlayer interface position parameters, and corresponding high-precision mesh division settings for different silicon pyramid textured surface regions. Based on the training sample set, an optical solution model is trained to learn the correspondence between the silicon pyramid textured surface structure features and the mesh node distribution. The structural parameters of the battery device to be solved are input into the optical solution model, which outputs the node division density or local refinement scheme for different regions, rapidly generating computational nodes for electromagnetic field propagation calculation.

[0015] Specifically, during the electrical analysis in step S3, the photogenerated carrier generation rate of each sub-cell is mapped to the electrical model as the input of the photogenerated term. The Poisson equation, continuity equation, and drift-diffusion equation are solved for each sub-cell to obtain the potential distribution, electron / hole concentration distribution, and corresponding carrier current density distribution inside the device. The applied terminal voltage is scanned, and the terminal current density corresponding to each scan voltage point is calculated to obtain the JV characteristic curve of each sub-cell.

[0016] Specifically, in the electrical analysis process, the transport process of electrons and holes in tandem solar cells involves numerical solutions at different spatial locations, so the computational domain is discretized; based on the training sample set, the electrical analysis model is trained, the electrical solution domain is inferred and predicted, and the node density and cell size corresponding to different regions are output, so as to adaptively divide the electrical solution domain.

[0017] The beneficial effects of this invention are as follows: by using optical-electrical multiphysics coupling modeling and introducing layer-by-layer spectral transfer, the photogenerated carrier generation rate and JV characteristics of each sub-cell can be obtained that are closer to actual operating conditions. This improves the engineering guidance significance of the calculation results of the limiting efficiency of multi-junction solar cells and enables the selection of an optimal bandgap that is more in line with reality. For series-tandem cells, the monotonic intervals of the JV curves of each sub-cell are segmented within a preset effective operating current range, and VJ inversion is performed. The total voltage function is synthesized with current density as a common variable, and a global maximum power point search is further performed. The series current constraint is embedded in the solution process, avoiding the computational overhead caused by explicit current matching iteration or repeated simultaneous solutions in traditional methods. This significantly reduces the overall simulation computation and improves the solution stability. At the same time, this method has modularity and reusability, which facilitates multi-dimensional scanning and overall efficiency evaluation of material systems, structural parameters, and variable bandgap designs. It can also be combined with experimental data to calibrate model parameters, thereby supporting efficiency fitting and prediction analysis under actual operating conditions. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention.

[0019] Figure 2 This is a schematic diagram of the overall structure of the stacked battery.

[0020] Figure 3 This is a graph showing the JV curve results in the example.

[0021] Figure 4 The graph shows the limiting efficiency results in the embodiments.

[0022] Figure 5 The results are from the optical verification experiment in the examples.

[0023] Figure 6 The results are from the electrical verification experiments in the examples. Detailed Implementation

[0024] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] Example 1: A method for optimizing the bandgap of tandem solar cells based on limiting efficiency, comprising the following steps: S1. Establish an overall structural model of the tandem battery, set material parameters and incident spectrum boundary conditions, and establish an optical solution model for the top battery region. S2. Perform optical solutions for each sub-cell from top to bottom to obtain the photogenerated carrier generation rate distribution and transmission results of each sub-cell. Update the incident spectrum layer by layer based on the transmission results of the previous layer until the full layer calculation is completed. S3. Using the photogenerated carrier generation rate of each layer as the electrical input, perform electrical analysis and obtain the JV curve of current density-voltage of each sub-cell through electrical solution. S4. Calculate the limiting efficiency based on the JV curve, find the maximum power point, and determine the optimal bandgap based on the maximum power point and the limiting efficiency.

[0026] The material parameters of the overall structure model of the tandem battery include the functional layer sequence, thickness range, and interconnection layer settings of each sub-cell; construct the material parameter set corresponding to the layer structure, which includes at least the material band gap, refractive index, extinction coefficient, electron affinity, carrier mobility, recombination coefficient, doping concentration, and work function; and set the incident spectral boundary conditions, including spectral distribution, incident power density, and incident angle.

[0027] In this embodiment, a 2T perovskite-crystalline silicon tandem solar cell structure model is first established, such as... Figure 2As shown in the figure, the pyramid is a silicon textured surface structure. Incident light is incident from the air side perpendicular to the sample surface. The overall device current is extracted from the ITO and Ag electrodes. MAPbI3 is the wide bandgap top cell, and Si is the narrow bandgap bottom cell. The functional layer between ITO / SnO2 / C60 is set with equivalent parameters according to the actual doping and bandgap conditions. The donor doping concentration is 10. 18 [1 / cm 3 The acceptor doping concentration is 10. 18 [1 / cm 3 To support subsequent bandgap optimization calculations, the bandgap of MAPbI3 was taken as the research object and set as a function x. The bandgap of Si is 1.12 eV, and x > 1.12 eV satisfies the basic premise of tandem cells. The purpose of setting the function is to optimize the bandgap later. Other material parameters, such as relative permittivity, are taken from commonly used parameters in material parameter libraries and reference books. To simulate the working state of solar photovoltaic cells under standard solar irradiance conditions, the incident spectrum adopts the AM1.5G standard solar spectrum, that is, the ground-based global solar spectrum with an air quality coefficient of 1.5, corresponding to a total irradiance of 1000 W / m². 2 .

[0028] Based on the overall structural model of the tandem battery, an optical solution model is established for the top battery region. Considering the refraction of light by the silicon pyramid textured surface structure, electromagnetic field boundary condition constraints are first established. Based on the principle that the electric field distribution is jointly determined by the dielectric properties of the material and the space charge, and the principle that there are no isolated magnetic charge sources during the propagation of the magnetic field, the electromagnetic field boundary conditions in the sub-battery are constrained. Then, electromagnetic field propagation calculations are performed. Based on the principle that a time-varying magnetic field can induce an electric field, and that the electromagnetic propagation relationship of the magnetic field response is jointly determined by the time-varying electric field and the conductivity of the material, the electric field distribution and magnetic field distribution at each location of the sub-battery are solved. Based on the electric field distribution and magnetic field distribution at each location of the sub-battery, the transmission results and photogenerated carrier generation rate distribution in each region of the sub-battery are calculated. The transmission results include light absorption characteristics and transmission characteristics. Photogenerated carrier generation rate = incident photon flux × absorption rate.

[0029] In the specific solution process, this invention solves for the incident electromagnetic field based on initial state constraints and iteratively calculates the electromagnetic field distribution at adjacent time points and spatial locations based on the coupling relationship between the electric and magnetic fields. For the time dimension, discrete solutions for continuous-time processes can be achieved by setting the solver step size. For the spatial dimension, since the studied device contains a non-ideal silicon pyramid textured surface structure and local narrow regions, simple uniform mesh partitioning is not suitable for spatial nodes. To improve the solution accuracy and computational efficiency under complex structures, a training sample set is constructed based on experimentally obtained silicon pyramid textured surface structure data. The training sample set includes geometric topography parameters, interlayer interface position parameters, and corresponding high-precision mesh partitioning settings for different silicon pyramid textured surface regions.

[0030] Based on the training sample set, the neural network model is trained to learn the correspondence between the textured surface features of the silicon pyramid and the distribution of mesh nodes. After training, the structural parameters of the device to be solved are input into the neural network model, which outputs the node partitioning density or local refinement scheme for different regions to quickly generate computing nodes for electromagnetic field propagation calculations.

[0031] Multiplying the transmittance of the top cell by the AM1.5G spectrum yields the incident spectrum of the subsequent sub-cells. This allows for optical solutions to be performed on each sub-cell from top to bottom, updating the incident spectrum layer by layer based on the transmission results of the previous layer until the calculation of the entire layer is completed.

[0032] The calculated photogenerated carrier generation rate of each sub-cell is used as input for electrical analysis. The photogenerated carrier generation rate of each sub-cell is mapped to the electrical model as the input for the photogenerated term. The Poisson equation, continuity equation, and drift-diffusion equation are solved for each sub-cell to obtain the potential distribution, electron / hole concentration distribution, and corresponding carrier current density distribution inside the device. The applied terminal voltage is scanned, and the terminal current density corresponding to each scanned voltage point is calculated to obtain the JV characteristic curve of each sub-cell.

[0033] Specifically, by imposing continuity constraints on the relationship between electron and hole currents, the following equations are applied: Number of electrons = Electron inflow - Electron outflow + Number of electrons generated under illumination G - Loss R caused by recombination of electrons and holes; Number of holes = Hole inflow - Hole outflow + Number of holes generated under illumination G - Loss R caused by recombination of electrons and holes; Electron current = Directed migration current of electrons generated under the electric field + Diffusion current caused by uneven electron concentration distribution; Hole current = Directed migration current of holes generated under the electric field + Diffusion current caused by uneven hole concentration distribution. Based on these constraints, an electrical solution is performed.

[0034] The transport of electrons and holes in devices also involves numerical solutions at different spatial locations, thus requiring discrete partitioning of the computational domain in the electrical analysis step. Since tandem solar cells contain heterojunction interfaces, local narrow-layer regions, and areas with drastic changes in carrier concentration and potential, uniform partitioning can easily lead to excessive computation or insufficient local solution accuracy. Therefore, this embodiment also employs a neural network model trained on a training sample set to infer and predict the electrical solution domain, outputting the node density and cell size corresponding to different regions, thereby achieving adaptive partitioning of the electrical computational domain. This method reduces the overall number of computational nodes while maintaining the accuracy of electron and hole transport solutions, improving the solution efficiency. In the specific application of this embodiment, the JV curve calculated using a typical perovskite bandgap of x=1.68eV is shown below. Figure 3 As shown.

[0035] After obtaining the JV characteristic curves of each sub-cell, the multi-junction solar cell is determined to be either an independent architecture or a series architecture based on the terminal lead-out method of the multi-junction solar cell. The independent architecture is in which each sub-cell is isolated and has its own terminal lead-out, while the series architecture is in which each sub-cell is connected in series and shares an external terminal.

[0036] When the architecture is determined to be independent, the maximum power point of each sub-cell is determined based on the JV curve of each sub-cell. The maximum power of each sub-cell is summed to obtain the total output power density of the independent architecture. The total output power density of the independent architecture is normalized with the incident power density to calculate the limiting efficiency.

[0037] When the structure is determined to be a series structure, the VJ expression of each sub-cell is constructed by inversion based on the JV characteristic curves of each sub-cell. The voltages of each sub-cell are then summed using current density as a common variable to obtain the overall VJ function of the series structure. Based on the series structure VJ function, a global maximum power point search is performed on the total power within a preset current density range to obtain the current density and total output power density corresponding to the maximum power point. The efficiency of the series structure is then calculated by normalizing the total output power density and the incident power density, and this efficiency is used as the limiting efficiency calculation result for the multi-junction solar cell.

[0038] The method for inverting VJ from JV is as follows: Within a preset current density range, the J-V characteristic curves of each sub-cell are selected and segmented to obtain monotonic effective operating intervals. The preset current density range is from 0 to the minimum short-circuit current density of each sub-cell. Due to the preprocessing dividing it into monotonic intervals, the JV curves exhibit an inverse mapping relationship, thus yielding the VJ curve. The V-J expressions of each sub-cell are summed using current density as a common variable to obtain the overall VJ function of the series architecture. This setting ensures that the current density of each sub-cell is equal under series constraints and embeds the current constraint within the overall voltage function construction process, thereby avoiding explicit current matching iterations and reducing the overall simulation computational load.

[0039] When performing a global maximum power point search, since the maximum power point usually appears within a specific proportion of the open-circuit voltage rather than distributed across the entire voltage range, this invention does not employ a point-by-point traversal of the entire voltage range to determine the maximum power point. Instead, a database containing multiple sets of JV curve samples is pre-constructed. This database includes at least the open-circuit voltage, short-circuit current, fill factor, curve curvature, local slope features, and the corresponding maximum power point location. A neural network model is trained based on this database to learn the mapping relationship between JV curve features and the voltage location of the maximum power point. For the device to be solved, its open-circuit voltage and JV curve features are first extracted and input into the neural network model to obtain the candidate voltage range corresponding to the maximum power point. Subsequently, the output power is calculated only within the candidate voltage range, and the maximum power point is precisely located through local dense sampling, interpolation fitting, or range optimization. This reduces the number of searches and improves computational efficiency while ensuring the accuracy of maximum power point extraction.

[0040] The optimal bandgap can be determined based on the maximum power point. In this embodiment, with a bottom cell bandgap of 1.12 eV, the maximum power is calculated for different top cell bandgap values. Dividing this power by the incident light power of 1000 W / m² gives the limiting efficiency of the cell under the research model. The calculated results are obtained by scanning the perovskite top cell bandgap, as shown in the figure below. Figure 4 As shown. According to the calculation results, when the bottom cell is a 1.12eV crystalline silicon cell, the top cell should be a perovskite cell with a voltage of around 1.65-1.71eV.

[0041] To verify the accuracy of the computational model of this invention, experiments were conducted on both the optical and electrical computational steps. The results of the optical verification experiment are as follows: Figure 5 As shown, the thickness of the top cell, as the functional layer that directly interacts with the incident light, has a significant impact on the cell's optical performance. Therefore, cell samples with different perovskite layer thicknesses were fabricated to alter the light reflection characteristics of the stacked cells, thus verifying the accuracy of the optical calculations. Furthermore, to reduce testing errors, the electrodes were positioned around the perimeter of the device, ensuring the test light spot fell entirely within the central region of the device. Comparison between the experimental and calculated results shows a deviation of approximately 10 nm, with a relative error of approximately 2.8%.

[0042] The results of the electrical verification are as follows Figure 6 As shown, three identical batches of samples were prepared under the same model conditions. Each batch yielded at least 10 sets of test data, and the comparison between the experimental results and the calculated results for each batch was statistically analyzed. The results are as follows: Figure 6 As shown, the simulation model can accurately represent the experimental results, with a relative error within 3%.

[0043] Example 2: A method for optimizing the bandgap of tandem solar cells based on limiting efficiency, comprising the following steps: Step 1: Establish a device structure model of a multi-junction solar cell, and establish optical, electrical and thermal models corresponding to the device structure model; set material parameters and device structure parameters, and set incident spectrum boundary conditions, incident power density and thermal boundary conditions.

[0044] Step 2: Perform optical solutions for the sub-cells from top to bottom. If it is the top layer sub-cell, its incident spectrum is set in Step 1. The incident spectra of other layers are set in Step 3. Obtain the spectral absorption results, transmission results and photogenerated carrier generation rate of the sub-cells.

[0045] Step 3: Update the incident spectrum boundary conditions of the next sub-cell based on the transmission results of the previous sub-cell, and repeat the optical solution and photogenerated carrier generation rate calculation until the optical calculation of all sub-cells is completed, and obtain the photogenerated carrier generation rate of each sub-cell.

[0046] Step 4: Use the obtained photogenerated carrier generation rate of each sub-cell as input to the electrical model, and solve the Poisson equation, continuity equation and drift-diffusion equation based on the boundary conditions to obtain the JV characteristic curve of each sub-cell.

[0047] Step 5: Determine whether the multijunction solar cell is an independent structure or a series structure based on the terminal lead-out method of the multijunction solar cell; where the independent structure is that each sub-cell is isolated and has its own terminal lead-out, and the series structure is that each sub-cell is connected in series and shares an external terminal.

[0048] Step 6: When the independent architecture is determined, the maximum power point of each sub-cell is determined based on the JV curve of each sub-cell obtained in Step 4. The maximum power of each sub-cell is summed to obtain the total output power density of the independent architecture. The total output power density of the independent architecture is normalized with the incident power density to calculate the limiting efficiency.

[0049] Step 7: When the system is determined to be a series architecture, the JV characteristic curves of each sub-cell obtained in Step 4 are inverted to construct the VJ expression of each sub-cell; and the voltage of each sub-cell is summed with the current density as a common variable to obtain the total VJ function of the series architecture.

[0050] Step 8: Based on the series architecture VJ function obtained in Step 7, perform a global maximum power point search within a preset current density range to obtain the current density and total output power density corresponding to the maximum power point. Then, normalize the total output power density and incident power density to calculate the series architecture efficiency, which serves as the limiting efficiency calculation result for the multi-junction solar cell. Based on the limiting efficiency, the optimal bandgap can be determined.

[0051] In this specific application, the limiting efficiency of a two-terminal perovskite-crystalline silicon tandem solar cell (2T tandem, sub-cells connected in series) is calculated to determine its optimal bandgap. The specific steps are as follows: Step 1: Establish a 2T perovskite-crystalline silicon tandem solar cell structure model, such as... Figure 2 As shown, the incident light is perpendicular to the sample surface from the air side. The overall device current is extracted from the ITO and Ag electrodes. MAPbI3 is the wide bandgap top cell, and Si is the narrow bandgap bottom cell. The functional layers between ITO / MAPbI3 / Si / Ag are set with equivalent parameters according to the actual doping and bandgap conditions. In this example, the donor doping concentration is 1e18[1 / cm²]. 3 The acceptor doping concentration is 1e18[1 / cm]. 3 To support subsequent bandgap optimization calculations, the bandgap of MAPbI3 is set as a function x, and the bandgap of Si is set as a function y, with x > y satisfying the basic premise of tandem solar cells. The purpose of setting the functions is to optimize the bandgap later. Other material parameters, such as relative permittivity, are taken from commonly used parameters in material parameter libraries and reference books. To simulate the working state of solar photovoltaic cells under standard solar irradiance conditions, the incident spectrum adopts the AM1.5G standard solar spectrum, that is, the ground-based global solar spectrum with an air quality coefficient of 1.5, corresponding to a total irradiance of 1000 W / m². 2 .

[0052] Step Two: Based on the device structure model established in Step One, an optical solution model is established for the top battery region. The electromagnetic wave frequency domain equations (Maxwell's equations in frequency domain form) are solved under preset incident spectral boundary conditions to obtain the battery distribution and optical response at different wavelengths. During the solution process, a plane wave normal incidence condition is applied at the incident boundary. Based on the frequency domain electromagnetic field solution results, the absorptivity and transmittance of the top battery are obtained as follows: Figure 3 As shown. The carrier generation rate of the top cell is obtained by combining the spatial distribution.

[0053] Step 3: Multiply the transmittance of the top cell obtained in Step 2 by the AM1.5G spectrum to obtain the incident spectrum of the bottom cell. Repeat the operation in Step 2 to calculate the carrier generation rate of the bottom cell.

[0054] Step 4: Use the obtained photogenerated carrier generation rate s of each sub-cell as input to the electrical model, and solve the Poisson equation, drift-diffusion equation, and continuity equation system. Obtain the JV curve of the sub-cell.

[0055] Step 5: Determine that the sub-batteries are connected in series, then proceed to Step 7.

[0056] Step 7: By differentiating the JV curve, it can be determined that the JV obtained from the model in Step 4 are all monotonically decreasing functions. Therefore, there exists a VJ curve in the range from 0V to the open-circuit voltage.

[0057] Step 8: For the VJ curve obtained at specified x and y coordinates, calculate V×J, perform a global maximum power point search, determine the maximum power under this condition, and divide it by the incident light power of 1000 W / m. 2 This represents the limiting efficiency of the battery under the research model. By scanning the x and y values, the limiting efficiency of the 2T tandem battery with different bandgap combinations is obtained. Under the optical and electrical model conditions used in this embodiment, the tandem battery efficiency reaches its maximum, approximately 43%, when the top cell bandgap is approximately 1.62 eV and the bottom cell bandgap is approximately 0.94 eV.

Claims

1. A method for optimizing the bandgap of tandem solar cells based on limiting efficiency, characterized in that, Includes the following steps: S1. Establish an overall structural model of the tandem battery, set material parameters and incident spectrum boundary conditions, and establish an optical solution model for the top battery region. S2. Perform optical solutions for each sub-cell from top to bottom to obtain the photogenerated carrier generation rate distribution and transmission results of each sub-cell. Update the incident spectrum layer by layer based on the transmission results of the previous layer until the full layer calculation is completed. S3. Using the photogenerated carrier generation rate of each layer as the electrical input, perform electrical analysis and obtain the JV curve of current density-voltage of each sub-cell through electrical solution. S4. Calculate the limiting efficiency based on the JV curve, find the maximum power point, and determine the optimal bandgap based on the maximum power point and the limiting efficiency.

2. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 1, characterized in that, In step S4, the device is determined to be either a series or independent architecture based on the terminal structure, and different limiting efficiency calculation methods are selected accordingly. Based on the electrical connection relationship between the terminals and interconnect layers of the solar cell, when each sub-cell has an independent external terminal and is electrically isolated, it is determined to be an independent architecture; when each sub-cell shares an external terminal and is electrically connected in series, it is determined to be a series architecture.

3. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 2, characterized in that, In step S4, when determining whether the device is a series or independent architecture based on the terminal structure, if it is an independent architecture, the maximum power point of each sub-cell is determined based on the JV curve of each sub-cell, and the maximum power of each sub-cell is summed to obtain the total output power density of the independent architecture. The total output power density of the independent architecture is then normalized with the incident power density to calculate the limiting efficiency. If it is a series architecture, the VJ expression of each sub-cell is constructed by inverting the JV curve of each sub-cell. The voltage of each sub-cell is summed with the current density as a common variable to obtain the total VJ function of the series architecture. Based on the VJ function of the series architecture, a global maximum power point search is performed on the total power within a preset current density range to obtain the current density and total output power density corresponding to the maximum power point. The total output power density and incident power density are then normalized to calculate the series architecture efficiency, which is used as the limiting efficiency calculation result of the multi-junction solar cell.

4. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 1 or 3, characterized in that, When performing a global maximum power point search, a database containing multiple sets of JV curve samples is pre-built. The maximum power point search model is trained based on the database to learn the mapping relationship between JV curve features and the voltage position of the maximum power point. For the device to be solved, its open-circuit voltage and JV curve features are extracted and input into the maximum power point search model to obtain the candidate voltage range corresponding to the maximum power point. Then, the output power is calculated within the candidate voltage range, and the maximum power point is finely located through local dense sampling, interpolation fitting, or range optimization.

5. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 1, characterized in that, In step S1, the silicon textured surface structure of the overall structure model of the stacked battery is pyramid-shaped.

6. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 1, characterized in that, In step S2, during the optical solution, considering the refraction of light by the silicon pyramid textured surface, electromagnetic field boundary condition constraints are first established. Based on the principle that the electric field distribution is determined by the dielectric properties of the material and the space charge, and the principle that there are no isolated magnetic charge sources during the propagation of the magnetic field, the electromagnetic field boundary conditions in the sub-cell are constrained. Then, electromagnetic field propagation calculations are performed. Based on the principle that a time-varying magnetic field can induce an electric field, and that the electromagnetic propagation relationship of the magnetic field response is determined by the time-varying electric field and the conductivity of the material, the electric field and magnetic field distributions at various locations of the sub-cell are solved. Based on the electric field and magnetic field distributions at various locations of the sub-cell, the transmission results and photogenerated carrier generation rate distribution in each region of the sub-cell are calculated. The transmission results include light absorption characteristics and transmission characteristics.

7. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 1, characterized in that, In step S2, when performing optical solutions for each sub-cell from top to bottom, if the top-layer sub-cell is optically solved, its incident spectrum is the incident spectrum set in step S1; if the non-top-layer sub-cell is optically solved, its incident spectrum is the incident spectrum corrected based on the transmission results of the previous layer sub-cell.

8. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 6, characterized in that, In the electromagnetic field propagation calculation process, the electromagnetic field distribution at adjacent time points and adjacent spatial locations is iteratively calculated. For the time dimension, the discrete solution of the continuous time process is achieved by setting the solver step size. For the spatial dimension, a training sample set is constructed based on the silicon pyramid textured surface structure data obtained from experimental tests. The training sample set includes the geometric morphology parameters, interlayer interface position parameters, and corresponding high-precision mesh division settings of different silicon pyramid textured surface regions. Based on the training sample set, the optical solution model is trained to learn the correspondence between the silicon pyramid textured surface structure features and the mesh node distribution. The structural parameters of the battery device to be solved are input into the optical solution model, which outputs the node division density or local refinement scheme for different regions, quickly generating calculation nodes for electromagnetic field propagation calculation.

9. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 1, characterized in that, In step S3, during the electrical analysis, the photogenerated carrier generation rate of each sub-cell is mapped to the electrical model as the input of the photogenerated term. The Poisson equation, continuity equation, and drift-diffusion equation are solved for each sub-cell to obtain the potential distribution, electron / hole concentration distribution, and corresponding carrier current density distribution inside the device. The applied terminal voltage is scanned, and the terminal current density corresponding to each scan voltage point is calculated to obtain the JV characteristic curve of each sub-cell.

10. The method for optimizing the bandgap of tandem solar cells based on limiting efficiency according to claim 9, characterized in that, During the electrical analysis, the transport process of electrons and holes in tandem solar cells involves numerical solutions at different spatial locations. Therefore, the computational domain is discretized. Based on the training sample set, the electrical analysis model is trained, and the electrical solution domain is inferred and predicted. The node density and cell size corresponding to different regions are output, and the electrical solution domain is adaptively partitioned.

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