An efficient computing method for micro-nano structure solar cell cross-scale optical modeling
By combining the finite element method with the transfer matrix theory, the computational efficiency and accuracy problems of traditional simulation methods in the cross-scale structural analysis of crystalline silicon solar cells are solved, and fast and accurate optical simulation and structural optimization are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING UNIV OF TECH
- Filing Date
- 2026-03-06
- Publication Date
- 2026-06-26
AI Technical Summary
Traditional simulation methods struggle to balance computational accuracy and efficiency, and cannot effectively handle the cross-scale structure of crystalline silicon solar cells, resulting in high computational resource consumption, long processing times, and poor design flexibility.
By combining the finite element method (FEM) with the transfer matrix theory (TMT), the micro-nano structure and crystalline silicon substrate of solar cells are processed separately. The calculation results are integrated through coupling formulas to achieve cross-scale optical simulation.
Significantly improves computational efficiency, increasing computational speed by more than 50 times, with high accuracy, reduced resource consumption, suitable for complex structure optimization, and provides support for optoelectronic performance optimization.
Smart Images
Figure FT_1 
Figure FT_2 
Figure FT_3
Abstract
Description
Technical Field
[0001] This invention relates to the field of solar cell design and simulation technology, specifically to an efficient calculation method for cross-scale optical modeling of solar cells that combines the finite element method (FEM) and the transfer matrix theory (TMT). This method is applicable to the analysis of light absorption characteristics, optimization of structural parameters, and prediction of photovoltaic performance of solar cells with micro- and nano-structures on their surfaces, such as TOPCon and HJT. Background Technology
[0002] With the global energy crisis and environmental pollution becoming increasingly prominent, solar energy, as an important component of clean and renewable energy, has received widespread attention. Crystalline silicon solar cells dominate the photovoltaic market due to their high durability, flexible installation, and cost advantages. To further improve the photoelectric conversion efficiency of crystalline silicon solar cells and reduce material costs, researchers commonly employ methods such as introducing micro / nano structures (e.g., pyramid arrays) and multilayer film structures (e.g., anti-reflection layers and passivation layers) onto the cell surface. This enhances light capture capabilities and reduces surface reflection, thereby improving light absorption performance and simultaneously reducing the required thickness of the active layer.
[0003] However, the structure of these solar cells exhibits significant cross-scale characteristics: the size of surface micro- and nanostructures (such as pyramids and nanopores) is typically only a few hundred nanometers to a few micrometers, while the thickness of the crystalline silicon substrate can reach 150 micrometers, and the thickness of surface functional layers (such as anti-reflection layers and passivation layers) is only tens of nanometers. This cross-scale structure presents a huge challenge to optical simulation: traditional single simulation methods struggle to balance computational accuracy and efficiency.
[0004] Currently, the main theoretical methods used for electromagnetic analysis of periodic solar cells include ray tracing, rigorous coupled-wave analysis, finite-difference time-domain (FDTD), and finite element method (FEM). While ray tracing is computationally fast, it is based on geometric optics principles and cannot accurately describe the interference and diffraction effects of micro / nano structures, resulting in insufficient simulation accuracy for nanoscale light field manipulation. FDTD is suitable for simulating the evolution of electromagnetic fields in the time domain, but it relies on cubic meshes, and its memory footprint increases cubically with the simulation area, requiring significant memory resources and limiting computational accuracy. The finite element method (FEM) can discretize irregular nanostructures into small units of arbitrary shapes and achieves accurate calculations of physical quantities in the frequency domain based on Maxwell's equations. It is currently the most widely used and relatively efficient method for photoelectric analysis of micro / nano structure solar cells.
[0005] However, when dealing with multi-scale structures, the finite element method (FEM) faces serious computational efficiency issues: to ensure computational accuracy, high-density meshing of thick crystalline silicon substrates is required, leading to an exponential increase in computational load. This not only consumes a large amount of computational resources but also takes an extremely long time, and may even cause software errors. Furthermore, traditional simulation methods, when optimizing cell structural parameters (such as the apex of a pyramid) or designing complex embedded structures, require extensive experimental verification or full-structure simulation through a "trial and error" approach, further exacerbating time and resource consumption and severely limiting the design flexibility and development progress of solar cells.
[0006] Transfer Matrix Theory (TMT) is an efficient method for spectral calculations of multilayer planar structures, offering advantages such as high computational speed and accuracy. However, it is only applicable to planar multilayer structures and cannot handle solar cells containing micro- and nano-structures. Therefore, how to integrate the advantages of the Finite Element Method (FEM) and Transfer Matrix Theory (TMT) to construct a cross-scale optical modeling method that balances high accuracy and efficiency, and overcome the limitations of traditional simulation methods in the cross-scale structural analysis of silicon-based solar cells, has become an urgent technical problem to be solved in this field. Summary of the Invention
[0007] To address the limitations of traditional simulation methods in cross-scale structural analysis of micro / nano structure solar cells, this patent provides an efficient computational method for cross-scale optical modeling of micro / nano structure solar cells. By combining the finite element method (FEM) with the transfer matrix theory (TMT), it enables rapid and accurate optical simulation of cross-scale solar cells containing micro / nano structures, providing technical support for cell structure optimization and performance improvement.
[0008] The objective of this invention can be achieved through the following technical solutions:
[0009] An efficient computational method for cross-scale optical modeling of micro / nano-structured solar cells is characterized by splitting the cross-scale structure of the micro / nano-structured solar cell into two independent computational regions. The finite element method (FEM) and transfer matrix theory (TMT) are used for simulation in these regions, respectively. The calculation results are then integrated through a coupling formula to obtain the overall optical characteristic parameters (absorption, reflection, and transmission spectra) of the cell. The specific framework is as follows:
[0010] (1) The upper part, i.e., region one: includes the micro-nano pyramid structure on the top surface of the battery and the pyramid surface functional film. The pyramid surface functional film includes an anti-reflection layer, a passivation layer, etc. For example, the pyramid surface functional film includes Anti-reflective layer (80nm) The passivation layer (50nm) and p emitter layer (25nm) were simulated using the finite element method (FEM) to obtain the transmission and reflection coefficients of S-polarized and P-polarized light in this region; the parameters corresponding to the micro-nano pyramid structure include period, apex angle, etc.
[0011] (2) The lower half, i.e., region two: includes the crystalline silicon substrate and the bottom multilayer planar structure, including Layer (2nm), npoly-Si layer (100nm) and The bottom layer (80nm) was calculated using the transfer matrix theory (TMT), taking into account the influence of different diffraction orders, to obtain the transmission coefficient and reflection coefficient of S-polarized and P-polarized light in this region;
[0012] (3) Results coupling: By establishing the superposition formula of polarized light components, the calculation results of the two regions are integrated to obtain the total transmittance, total reflectance and total absorptivity of the solar cell as a whole, and the photovoltaic performance of the cell is analyzed based on this.
[0013] Further steps (1) FEM simulation steps for Region 1 (top micro / nano structure layer):
[0014] 1.1 Model Establishment and Boundary Condition Setting
[0015] • Construct a three-dimensional model of the top micro / nano structure based on FEM simulation software, including the geometric structure and material parameters of the pyramid array and surface film layer; the material parameters need to be set to the complex refractive index (i.e., including the real and imaginary parts of the refractive index) within the corresponding wavelength range (0.3μm-1.2μm).
[0016] • Boundary condition settings: The vertical boundaries in the x and y directions are set as pyramid periodic boundary conditions (to ensure the periodicity of the pyramid array); the upper and lower boundaries in the z-axis direction are set as perfect matching layers (PML), and the outer terminals are set as scattering boundary conditions;
[0017] 1.2 Mesh Generation and Solver Settings
[0018] • An adaptive mesh generation strategy is adopted to refine the mesh (with relatively high mesh density) in key areas such as pyramid corners and membrane interfaces to ensure computational accuracy; the mesh density is appropriately reduced in other relatively regular areas (preferably to be reduced to about 70% of the fine mesh density in the refined areas) to balance accuracy and efficiency.
[0019] • Solution settings: The incident light direction is set to vertically downward from the air at the top of the pyramid, with a wavelength range covering 0.3μm-1.2μm; the transmission coefficient is solved from the port. ), reflectance coefficient ( ).
[0020] Further, 1.3 Diffraction Order Classification and Data Processing
[0021] Since the incident light wavelength is much smaller than the pyramid array period (P=4μm), many diffraction components will be generated. In FEM data processing tools, by fixing the period p of the pyramid structure, we can automatically output different incident light wavelengths. All diffraction orders (l, m) and their corresponding reflectance and transmittance; according to formula (1), substitute the real part of the known complex refractive index of crystalline silicon. This allows us to obtain the diffraction angles corresponding to all diffraction orders. ;
[0022] (1)
[0023] For ease of subsequent calculations, we will use the diffraction angles corresponding to all diffraction orders. The light was divided into three angular ranges: 0-30°, 30°-60°, and 60°-90°. The transmittance and reflectance of S-polarized light and P-polarized light in different angular ranges were named as follows: , where k=1,2,3 correspond to the three angle ranges of 0-30°, 30°-60°, and 60°-90° respectively;
[0024] Further steps (2) include the TMT calculation and photoelectric property calculation for region two (middle + bottom structure), including the following steps:
[0025] 2.1 Multi-layer planar structure modeling
[0026] The central crystalline silicon substrate layer and the bottom multilayer film structure are considered as a planar multilayer system. The structure of each layer is defined sequentially according to the actual thickness and material order: Si substrate layer (j=1). Layer (j=2), n poly-Si (j=3) Membrane layer (j=4), air layer (j=5);
[0027] 2.2 Construction of the transmission matrix
[0028] •Transmission matrices for each layer Calculated according to formula (2), where For propagation phase, i is the imaginary unit:
[0029] (2)
[0030] Propagation phase With parameters Calculated using formulas (3) and (4) respectively:
[0031] (3)
[0032] (4)
[0033] in Let be the complex refractive index of the j-th layer material. Let the thickness be the j-th layer. Let be the angle of refraction of light in the j-th layer:
[0034] The total transmission matrix M of the multilayer structure is the product of the transmission matrices of each layer, and is calculated according to formula (5):
[0035] (5)
[0036] 2.3 Calculation of Transmission and Reflection Coefficients
[0037] Elements based on the total transfer matrix M Calculate the reflectance of the area using formulas (6) and (7). and transmission coefficient :
[0038]
[0039]
[0040] Further step (3) Integration calculation
[0041] 3.1 Calculation of Total Transmittance and Total Reflectance
[0042] By integrating the calculation results of the two regions using formula (8), the total transmittance of the solar cell is obtained. ) and total reflectance ( ):
[0043]
[0044] 3.2 Calculation of Total Absorption Rate
[0045] According to the law of conservation of energy, the total absorption rate (A) is calculated using formula (9):
[0046]
[0047] 3.3 Photocurrent Calculation
[0048] Based on total absorptivity A(λ) and AM1.5G solar spectrum Calculate the photocurrent according to formula (10). (unit: ),in Here, λ is the wavelength of the incident light, q is the electron charge, h is Planck's constant, and c is the speed of light in a vacuum.
[0049]
[0050] Beneficial effects:
[0051] The cross-scale optical modeling method combining FEM and TMT proposed in this invention has the following significant advantages compared to traditional single simulation methods:
[0052] 1. Significantly Improved Computational Efficiency: By splitting the calculation across scales, the high-density mesh generation of the thick silicon substrate is avoided, resulting in a computational speed more than 50 times faster than traditional full-structure FEM simulation. For example, in spectral calculations within the 0.3μm-1.2μm wavelength range, traditional FEM takes more than 160 hours, while this method only takes less than 4 hours; during structural parameter optimization, this method only requires 4-5 minutes per calculation, significantly reducing the computation time compared to traditional FEM.
[0053] 2. High computational accuracy: This method retains the accurate simulation capability of FEM for interference and diffraction of micro- and nano-structures, while utilizing TMT to ensure the computational accuracy of multilayer planar structures. Compared with the full-structure FEM simulation results, the calculation error of absorptivity, reflectivity, and transmittance of this method is less than 5% across the entire wavelength range, meeting the accuracy requirements for engineering design and scientific research analysis.
[0054] 3. High design flexibility: This method is applicable to various solar cells containing micro / nano structures and can efficiently optimize key parameters at the pyramid apex. Complex structural optimizations that are difficult to achieve with traditional FEM can be quickly accomplished with this method while maintaining accuracy, significantly reducing R&D costs.
[0055] 4. Good functional scalability: This method can not only calculate optical parameters such as light absorption, reflection, and transmission, but also calculate the electrical performance of related cells through photovoltaic current, providing theoretical support for the optimization of the photoelectric performance of solar cells.
[0056] 5. Low resource consumption: This method significantly reduces the requirements for computing hardware, does not rely on supercomputing resources, and can complete high-precision simulation of cross-scale solar cells on ordinary workstations, thus lowering the technical application threshold. Attached Figure Description
[0057] Figure 1 is a schematic diagram of the TOPCon solar cell structure to which this invention applies:
[0058] (a) A two-dimensional schematic diagram of the model structure, showing the division of the two computational regions and the distribution of light rays at different diffraction angles;
[0059] (b) Schematic diagram of the multi-layer planar structure calculated by TMT, with the reflection and transmission relationships of each layer marked.
[0060] Figure 2 shows the reflection and transmission results of the top and bottom regions under S / P polarized light in different angle ranges, obtained from FEM and TMT calculations:
[0061] (a) S / P polarized light reflection and transmission spectra in different angle ranges of the top region calculated by FEM;
[0062] (b) S / P polarized light reflection and transmission spectra in different angle ranges of the bottom region calculated by TMT;
[0063] Figure 3 Comparison of calculation results:
[0064] This method is compared with the total absorption, reflection, and transmission spectra obtained from full FEM simulation;
[0065] Figure 4 shows the results of different pyramid apex angles calculated by the method of the present invention:
[0066] (a) Two-dimensional schematic diagram of the model structure (structural parameter vertex angle β)
[0067] (b) Reflection and transmission curves of the top region under different pyramid apex angles;
[0068] (c) Comparison of absorption, reflection and transmission results at different pyramid apex angles at a wavelength of 0.7 μm (FEM vs. this method);
[0069] (d) Comparison of absorption, reflection and transmission results at different pyramid apex angles at a wavelength of 1 μm (FEM vs. this method). Detailed Implementation
[0070] To make the present invention easier to understand, the present invention will be further described below with reference to the accompanying drawings and examples, but the present invention is not limited to the following embodiments.
[0071] Example 1: TOPCon Solar Cell Cross-Scale Optical Modeling, Performance Calculation, and Structural Optimization
[0072] 1. Device structural parameters
[0073] • Top pyramid structure: apex angle β=70°, period p=4μm; surface layers are sequentially as follows: (80nm) (50nm), p emitter (25nm).
[0074] • Central crystalline silicon layer: 60μm thickness (simulated thickness), with the material refractive index taken in the wavelength range of 0.3μm-1.2μm.
[0075] • Multi-layered bottom structure: (2nm), n poly-Si (100nm), (80nm).
[0076] 2. Simulation Environment and Parameter Settings
[0077] • Simulation software: FEM simulation software, Matlab R2021a (for TMT calculation and result integration).
[0078] • Wavelength range: 0.3μm-1.2μm, step size 0.02μm.
[0079] 3. Implementation of FEM Simulation Steps
[0080] • Model building: A three-dimensional model is built in the FEM simulation software, the geometric parameters of the pyramid array and surface film are imported, and the refractive index of each material is set according to the wavelength range.
[0081] • Boundary conditions: The vertical boundaries in the x / y directions are set as periodic boundary conditions, and the vertical boundaries in the z direction are set as PML boundaries; the incident light is incident vertically from the top (e.g., Figure 1 (a)).
[0082] • Solution and Data Extraction: The transmission and reflection coefficients of S / P polarized light are obtained by solving the problem. The data is divided into three intervals according to the diffraction angle: 0°-30°, 30°-60°, and 60°-90°. The data for each interval are extracted and displayed. Figure 2 (a) in.
[0083] 4. Implementation of TMT Calculation Steps
[0084] • Multilayer structure definition: based on Si substrate layer → →n poly-Si→ →Build a model of the air sequence, and input the thickness and refractive index of each layer.
[0085] • Transfer matrix calculation: Write a program in Matlab to calculate the transfer matrix of each layer and the total transfer matrix according to the transfer matrix formula.
[0086] • Coefficient Calculation: Calculates the S / P polarized light transmission and reflection coefficients for three angular intervals, and displays them in... Figure 2 (b) in.
[0087] 5 Results Integration and Analysis
[0088] The total absorption, reflection, and transmission spectra were calculated, and the results are shown in Figure 3. Compared with the full FEM simulation results, the absorption rate reached over 90% in the wavelength range of 0.7μm-0.95μm, and the trends of the two methods were highly consistent, with an error of less than 3%.
[0089] · Calculate the photocurrent using formula (10) =33.161mA / cm², which is within a reasonable range, verifying the strong scalability of the method.
[0090] 6. Calculation Time Statistics
[0091] As shown in Table 1, our algorithm outperforms traditional simulations in both overall spectral plot calculation and apex corner optimization. When calculating the 0.3–1.2 μm spectrum of the entire TOPCon structure, traditional FEM simulations take over 160 hours, while our proposed algorithm reduces the computation time to less than 4 hours. In optimizing the pyramid apex corner parameters, our algorithm takes only 4 minutes, representing a speedup of over 50 times compared to FEM simulations.
[0092] 7. Calculation of Pyramid Vertex Parameters
[0093] • Adjust the pyramid apex angle β to 30°-100°, and use this method to calculate the photocurrent at 60°-80°. .
[0094] • Absorption, reflectance, and transmittance results are displayed in Figure 4 In our study, we found that as the apex angle of the pyramid increases from 30° to 100°, the pyramid structure gradually approaches a planar structure, the reflectivity gradually increases, and the absorptivity decreases.
[0095] Photocurrent The results are shown in Table 2: The value first increases and then decreases with increasing apex angle, reaching a peak of 33.309 mA / cm² at β=65°.
[0096] Table 1. Comparison of computation time for different models using different simulation methods
[0097] Table 2 Photovoltaic current under different pyramid structure parameters (Unit: mA) )
[0098] This invention solves the problem of balancing accuracy and efficiency in cross-scale structural modeling using traditional single simulation methods. The calculation speed is more than 50 times faster than traditional full FEM simulation, with an error of less than 5%. It can achieve parameter optimization of pyramid structures and design of complex structures, and is suitable for the research and optimization of various solar cells with micro-nano structures.
[0099] In summary, this invention provides an efficient computational method for cross-scale optical modeling of micro / nano structured solar cells. By combining the finite element method (FEM) with the transfer matrix theory (TMT), it enables rapid and accurate optical simulation of cross-scale solar cells containing micro / nano structures.
Claims
1. An efficient computational method for cross-scale optical modeling of micro / nano structure solar cells, characterized in that, The computational method divides the multi-scale structure of micro / nano solar cells into two independent computational regions, which are simulated using the finite element method (FEM) and the transfer matrix theory (TMT) respectively. The calculation results are then integrated through a coupling formula to obtain the overall optical characteristic parameters (absorption, reflection, and transmission spectra) of the cell.
2. The method according to claim 1, characterized in that, The specific framework is as follows: (1) The upper part, i.e., region one: includes the micro-nano pyramid structure on the top surface of the battery and the pyramid surface functional film. The pyramid surface functional film includes an anti-reflection layer, a passivation layer, etc. For example, the pyramid surface functional film includes Anti-reflective layer (80nm) The passivation layer (50nm) and p emitter layer (25nm) were simulated using the finite element method (FEM) to obtain the transmission and reflection coefficients of S-polarized and P-polarized light in this region; the parameters corresponding to the micro-nano pyramid structure include period, apex angle, etc. (2) The lower half, i.e., region two: includes the crystalline silicon substrate and the bottom multilayer planar structure, including Layer (2nm), npoly-Si layer (100nm) and The bottom layer (80nm) was calculated using the transfer matrix theory (TMT), taking into account the influence of different diffraction orders, to obtain the transmission coefficient and reflection coefficient of S-polarized and P-polarized light in this region; (3) Results coupling: By establishing the superposition formula of polarized light components, the calculation results of the two regions are integrated to obtain the total transmittance, total reflectance and total absorptivity of the solar cell as a whole, and the photovoltaic performance of the cell is analyzed based on this.
3. The method according to claim 2, characterized in that, Step (1) FEM simulation steps for the top micro / nano structure layer of region 1: 1.1 Model Establishment and Boundary Condition Setting • Construct a 3D model of the top micro / nano structure based on FEM simulation software, including the geometric structure and material parameters of the pyramid array and surface film; the material parameters need to be set to the complex refractive index of 0.3μm-1.2μm in the corresponding wavelength range; • Boundary condition settings: The vertical boundaries in the x and y directions are set as pyramidal periodic boundary conditions; the upper and lower boundaries in the z direction are set as perfectly matched layers (PML); and the outer terminals are set as scattering boundary conditions. 1.2 Mesh Generation and Solver Settings • An adaptive mesh generation strategy is adopted to refine the mesh in key areas such as pyramid corners and membrane interfaces to ensure computational accuracy; the mesh density is appropriately reduced in other relatively regular areas to balance accuracy and efficiency. • Solution settings: The incident light direction is set to vertically downward from the air at the top of the pyramid, with a wavelength range covering 0.3μm-1.2μm; the transmission coefficient is solved from the port. Reflection coefficient .
4. The method according to claim 3, characterized in that, It also includes diffraction order classification and data processing: Since the incident light wavelength is much smaller than the period of the pyramid array, many diffraction components are generated. In FEM data processing tools, by fixing the period p of the pyramid structure, different incident light wavelengths can be automatically output. All diffraction orders (l, m) and their corresponding reflectance and transmittance; according to formula (1), substitute the real part of the known complex refractive index of crystalline silicon. This allows us to obtain the diffraction angles corresponding to all diffraction orders. ; (1) For ease of subsequent calculations, the diffraction angles corresponding to all diffraction orders are... The light was divided into three angular ranges: 0-30°, 30°-60°, and 60°-90°. The transmittance and reflectance of S-polarized light and P-polarized light in different angular ranges were named as follows: , and , , where k=1,2,3 correspond to the three angle ranges of 0-30°, 30°-60°, and 60°-90° respectively.
5. The method according to claim 3, characterized in that, Step (2) includes the following steps for calculating the TMT and photoelectric properties of the middle and bottom structures in region two: 2.1 Multi-layer planar structure modeling The central crystalline silicon substrate layer and the bottom multilayer film structure are considered as a planar multilayer system. The structure of each layer is defined sequentially according to the actual thickness and material order: Si substrate layer (j=1). Layer (j=2), n poly-Si (j=3) Membrane layer (j=4), air layer (j=5); 2.2 Construction of the transmission matrix •Transmission matrices for each layer Calculated according to formula (2), where For propagation phase, i is the imaginary unit: (2) Propagation phase With parameters Calculated using formulas (3) and (4) respectively: (3) (4) in Let be the complex refractive index of the j-th layer material. Let the thickness be the j-th layer. Let be the angle of refraction of light in the j-th layer: The total transmission matrix M of the multilayer structure is the product of the transmission matrices of each layer, and is calculated according to formula (5): M = (5) 2.3 Calculation of Transmission and Reflection Coefficients Elements based on the total transfer matrix M The reflectance coefficient of the region is calculated according to formulas (6) and (7). and transmission coefficient : (6) (7) TMT calculated the diffraction angles corresponding to the three diffraction orders respectively. Transmission coefficients of internally S-polarized and P-polarized light , With reflection coefficient , , where k=1,2,3 correspond to the three angle ranges of 0-30°, 30°-60°, and 60°-90° respectively.
6. The method according to claim 3, characterized in that, Step (3) Integration Calculation 3.1 Calculation of Total Transmittance and Total Reflectance By integrating the calculation results of the two regions using formula (8), the total transmittance of the solar cell is obtained. ) and total reflectance ( ): (8) 3.2 Calculation of Total Absorption Rate According to the law of conservation of energy, the total absorption rate (A) is calculated using formula (9): (9) 3.3 Photocurrent Calculation Based on total absorptivity A(λ) and AM1.5G solar spectrum Calculate the photocurrent according to formula (10). (unit: ),in Here, λ is the wavelength of the incident light, q is the electron charge, h is Planck's constant, and c is the speed of light in a vacuum. (10)。