Method and system for constructing moth-eye anti-reflection structure based on dynamic feedback

Abstract

This invention provides a method and system for constructing a moth-eye anti-reflection structure based on dynamic feedback. The method includes: establishing a set of geometric parameters and generating a feasible parameter space; using Latin hypercube sampling, calling scripted tools and a multiphysics numerical simulation platform to jointly calculate the corresponding optical and mechanical performance indicators; forming a data sample library; training a surrogate model based on the initial training sample library, selecting candidate parameters using the expected improvement function for simulation verification and model updating; iterative optimization until the optical performance meets the target, the objective function converges, or the upper limit of the number of simulations is reached, finally outputting the optimal parameter combination. This invention, through pre-constraint of process technology, multiphysics coupled simulation, and an adaptive surrogate model, solves the problems of disconnect between process and performance optimization and low simulation accuracy in existing methods, achieving efficient design of a moth-eye structure that combines manufacturability, high optical performance, and excellent mechanical stability.

Description

Technical Field

[0001] This invention relates to the field of micro-nano structure optical design and manufacturing technology, and in particular to a method and system for constructing a moth-eye anti-reflection structure based on dynamic feedback. Background Technology

[0002] In optoelectronic products such as optical devices, photovoltaic modules, and AR / VR display panels, surface reflection can lead to optical signal attenuation, energy loss, or deterioration of display effects. Therefore, anti-reflection technology is a key technology for improving the core performance of these products. The moth-eye anti-reflection structure, with its unique configuration of a biomimetic nano-protrusion array, achieves a wide-spectrum, large-angle anti-reflection effect through gradient refractive index modulation. Its optical performance is significantly superior to traditional single-layer or multi-layer coating technologies, and it also possesses advantages such as high structural stability and strong resistance to environmental interference. It is currently a research hotspot and key application direction in the field of anti-reflection technology.

[0003] Existing methods for constructing moth-eye anti-reflective structures mainly revolve around three core steps: geometric parameter design, performance simulation, and parameter optimization. However, each step has significant technical shortcomings, and there is a lack of coordination and adaptation between the steps, making it difficult to meet the dual performance and process requirements of high-end applications.

[0004] In the geometric parameter design phase, existing methods often rely on empirical or literature-reported typical parameters, such as a single conical protrusion or a fixed proportion of base diameter and height, to determine the initial parameter range. This only covers a limited number of parameter combinations, and this approach does not fully consider the coupling effects of multi-dimensional parameters such as protrusion shape, number of structural layers, and spacing. In the performance simulation phase, mainstream methods employ a simulation model that separates optical and mechanical performance. For example, optical performance indicators such as reflectivity and transmittance are calculated using optical simulation software, while mechanical performance indicators such as structural stress and deformation are analyzed separately using mechanical simulation tools. This lack of a coupled correlation model between the light field and the structural field results in simulation results that cannot accurately reflect the actual performance of the structure under light-force interaction in real-world applications. In the parameter optimization phase, traditional methods often use uniform sampling or orthogonal experimental design to explore the parameter space. In high-dimensional parameter scenarios, these sampling methods suffer from low sampling efficiency and insufficient sample representativeness, easily leading to insufficient exploration of the parameter space, overlooking potential optimal parameter combinations, and making it difficult to guarantee the global optimality of the optimization results.

[0005] More critically, existing construction methods generally suffer from a disconnect between process constraints and performance optimization. The fabrication of moth-eye antireflective structures relies on precision manufacturing processes such as nanoimprint lithography and electron beam lithography. These processes have clearly defined constraints, including minimum manufacturable feature sizes and manufacturing error compensation. For example, the minimum manufacturable feature size of nanoimprint lithography equipment is typically in the tens to hundreds of nanometers range, and material deformation and mold precision during manufacturing can lead to deviations between the actual structural dimensions and the design dimensions. However, existing methods do not deeply integrate these process constraints into the parameter space definition and performance evaluation process during the parameter design and optimization stages. This results in the designed "optimal parameter combination" potentially exceeding the achievable range of the process. For instance, the designed substrate diameter or spacing might be smaller than the minimum manufacturable feature size of the equipment, or the ratio of the cone height to the substrate diameter might exceed the material forming limit. Ultimately, these structures cannot be fabricated using existing processes, or the fabricated structures may suffer from dimensional deviations that cause optical performance to exceed design thresholds and mechanical properties to fail to meet usage requirements.

[0006] Furthermore, existing methods lack efficient surrogate model selection strategies and termination condition judgment mechanisms during the iterative process of parameter optimization. On the one hand, the selection of surrogate models often relies on fixed models without considering the impact of the number of structural layers on the model fitting accuracy. For example, when there are many structural parameters and the parameter coupling relationships are more complex, the prediction error of the fixed model will increase significantly, leading to a decrease in the reliability of the recommended candidate parameter combinations. On the other hand, the iteration termination condition is based solely on the number of simulations or the achievement of a single performance indicator, without considering the evaluation of the prediction variance of the surrogate model for the optimal parameter combination. If the prediction variance is too large, even if the simulation performance of the current parameter combination meets the standard, its actual service performance still has considerable uncertainty, requiring additional simulation verification costs, ultimately leading to a longer overall optimization cycle and increased computational resource consumption.

[0007] In summary, current methods for constructing moth-eye anti-reflective structures face a core technical bottleneck: "Under the premise of meeting the manufacturability constraints of nanofabrication processes, it is impossible to efficiently and accurately achieve synergistic optimization of optical and mechanical properties." This problem directly leads to a chain of issues such as insufficient coverage of parameter design, low accuracy of performance simulation, and poor optimization efficiency and reliability. It is difficult to stably output parameter schemes for moth-eye anti-reflective structures that combine process feasibility, excellent optical performance, and high mechanical stability, which seriously restricts the large-scale application of moth-eye anti-reflective technology in high-precision optical devices, long-life photovoltaic modules, and other high-end fields. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for constructing a moth-eye anti-reflection structure based on dynamic feedback. This invention aims to solve the technical problems in existing construction methods, such as the disconnect between process constraints and performance optimization, low efficiency in exploring high-dimensional parameter spaces, insufficient accuracy in optical-mechanical performance simulation, and poor optimization reliability. It achieves efficient output of parameter schemes for moth-eye anti-reflection structures that combine the feasibility of nanofabrication processes with excellent optical performance and stable mechanical properties, providing technical support for the large-scale application of this technology in high-precision optical devices, long-life photovoltaic modules, and other high-end fields.

[0009] In a first aspect, the present invention provides a method for constructing a moth-eye anti-reflective structure based on dynamic feedback, comprising: S1: establishing a set of geometric parameters based on the geometric parameters of the moth-eye anti-reflective structure, and constraining the set of geometric parameters using nano-manufacturing process constraints to obtain a feasible parameter space; S2: sampling within the feasible parameter space using the Latin hypercube sampling method to generate an initial parameter combination set; S3: calling a scripting tool and a multiphysics numerical simulation platform to jointly calculate the optical and mechanical performance indicators of the moth-eye anti-reflective structure corresponding to the initial parameter combination set, forming an initial training sample library; S4: training a surrogate model using the initial training sample library, and calculating the return of candidate geometric parameter combinations in the initial training sample library by combining the expected boost function, inputting the candidate geometric parameter combination with the largest return value into the parameterized simulation model for verification, and adding the simulation verification result to the training sample library to update the surrogate model; S5: repeating step S4 until a preset termination condition is met; S6: selecting the parameter combination that maximizes the objective function from the finally generated sample library as the optimal parameter combination of the moth-eye anti-reflective structure.

[0010] Optionally, in step S1, the geometric parameters include at least one of shape, height, base diameter, top diameter, number of structural layers, and spacing.

[0011] Optionally, in step S4, the selection of the surrogate model is based on the number of layers N of the moth-eye anti-reflection structure. When N=1, a Gaussian regression model is used as the surrogate model; when N=2, a random forest model is used as the surrogate model.

[0012] Optionally, in step S6, the optimal parameter combination P of the moth-eye anti-reflection structure... optimal ={H, D1, D2, δ……} satisfies the manufacturability constraints of nanoimprint lithography, and the geometric parameters satisfy: Min{H, D1, D2, δ……} ≥ η·λ min ; Where η is the manufacturing safety factor, and η>1, λ minH represents the minimum manufacturable feature size of the nanoimprint emulation device, where H is the height, D1 is the substrate diameter, D2 is the top diameter, and δ is the spacing.

[0013] Optionally, in step S4, the formula for calculating the desired lifting function EI is: EI(P) = E[max(f m -f(P), 0)] Among them, f m denoted as the optimal performance value in the current sample library, and f(P) is the predicted value of the surrogate model for the set of geometric parameters.

[0014] Optionally, in step S5, the preset termination condition is any one of the following conditions: (1) The objective function meets the preset design requirements; (2) In k consecutive iterations, the improvement of the objective function is less than the preset tolerance ε; (3) The number of simulation verifications reaches the preset upper limit Nmax.

[0015] Optionally, when the termination condition of reaching a preset upper limit Nmax for the number of simulation verifications is met, if the surrogate model achieves the optimal parameter combination P... optimal Prediction variance Var(f(P) optimal The variance is greater than the prediction variance threshold σ. max If so, incremental sample simulation verification will be automatically initiated, and the surrogate model and optimal parameter combination P will be updated based on the simulation verification results. optimal .

[0016] Optionally, in step S6, the objective function is: F = α·Q + β·M Where α is the optical reflectivity weighting coefficient, β is the peak stress weighting coefficient, Q is the optical performance index, and M is the mechanical performance index.

[0017] Secondly, this invention provides a structural construction system for a moth-eye anti-reflective structure based on dynamic feedback, comprising: a parametric modeling module for configuring the geometric parameters and nano-manufacturing process constraints of the moth-eye anti-reflective structure to generate a feasible parameter space; a dynamic optimization module integrating a Bayesian optimization algorithm library for performing Latin hypercube sampling, training a surrogate model, recommending candidate parameter combinations based on the feasible parameter space, and performing iterative optimization; a multiphysics simulation module for calling scripting tools and a multiphysics numerical simulation platform to batch calculate the optical and mechanical performance indicators corresponding to the parameter combinations; a comparison and verification module for comparing the prediction results of the surrogate model with the simulation verification results of the multiphysics simulation module, and triggering retraining of the surrogate model when the relative error exceeds a preset error threshold; and a report generation module for outputting the optimal parameter combination and sensitivity analysis matrix of the moth-eye anti-reflective structure.

[0018] Optionally, the dynamic optimization module supports batch asynchronous parallel optimization, which can simultaneously generate multiple candidate parameter sets and allocate them to distributed computing nodes for parallel simulation, and the simulation verification results are asynchronously written back to the central database.

[0019] This invention constructs a design system for moth-eye anti-reflection structures, encompassing process constraints, multi-physics coupled simulation, and efficient iterative optimization, through an integrated process of "parameter constraints - coupled simulation - intelligent sampling - dynamic optimization - multi-condition termination." First, process constraints define the feasible parameter space, eliminating unmanufacturable parameter combinations. Then, a light field-structure coupled simulation model is established to achieve simultaneous and accurate calculation of optical and mechanical properties. Subsequently, Latin hypercube sampling and hierarchical surrogate models are combined to improve the efficiency and accuracy of exploring high-dimensional parameter spaces. Finally, multi-dimensional termination conditions and incremental verification mechanisms ensure the reliability and efficiency of the optimization results, ultimately outputting the optimal parameter combination.

[0020] Compared with the prior art, the present invention has the following beneficial effects: (1) Improve process adaptability: By deeply binding process constraints and parameter space, ensure that the optimal parameter combination meets the requirements of nano-manufacturing process, avoid the problem of "design is feasible but manufacturing is not feasible", and reduce the cost of R&D trial and error.

[0021] (2) Improve the accuracy of performance simulation: The optical field-structure coupling model can eliminate the error of optical-mechanical performance separation simulation, making the performance indicators more in line with the actual application scenario.

[0022] (3) Improve optimization efficiency and accuracy: Latin hypercube sampling reduces the number of samples by more than 50%, hierarchical proxy model reduces prediction error by more than 30%, and parallel optimization shortens the iteration cycle by more than 40%.

[0023] (4) Improve the reliability of optimization: Multiple termination conditions and incremental verification mechanism enable the performance fluctuation range of the optimal parameter combination to be controlled within 2%, solving the problem of uncertainty in the results of existing methods.

[0024] In summary, this invention, through systematic technical design, comprehensively solves the core technical problems of existing methods for constructing moth-eye anti-reflective structures, providing key technical support for the high-performance, low-cost, and large-scale preparation of this structure. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. By reading the detailed description of the embodiments below, the advantages and benefits of the solutions will become clear to those skilled in the art. The accompanying drawings are only for illustrating preferred embodiments and are not intended to limit the present invention. In the accompanying drawings: Figure 1 This is a flowchart of the steps of the method of the present invention.

[0026] Figure 2 To and Figure 1 The corresponding detailed process diagram of the present invention. Detailed Implementation

[0027] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0028] See Figure 1 The present invention provides a method for constructing a moth-eye anti-reflection structure based on dynamic feedback, which mainly includes: S1: Establish a set of geometric parameters based on the geometric parameters of the moth-eye anti-reflection structure, and constrain the set of geometric parameters using nano-manufacturing process constraints to obtain a feasible parameter space; S2: Sample within the feasible parameter space using the Latin hypercube sampling method to generate an initial parameter combination set; S3: Call the scripting tool and the multiphysics numerical simulation platform to jointly calculate the optical and mechanical performance indicators of the moth-eye anti-reflection structure corresponding to the initial parameter combination set, and form the initial training sample library; S4: Train the surrogate model using the initial training sample library, and calculate the return of candidate geometric parameter combinations in the initial training sample library using the expected boost function. Input the candidate geometric parameter combination with the largest return value into the parameterized simulation model for verification, and add the simulation verification results to the training sample library to update the surrogate model. S5: Repeat step S4 until the preset termination condition is met; S6: Select the parameter combination that maximizes the objective function from the final generated sample library as the optimal parameter combination for the moth-eye anti-reflection structure.

[0029] Optionally, in step S1, the geometric parameters include at least one of shape, height, base diameter, top diameter, number of structural layers, and spacing.

[0030] Optionally, in step S4, the selection of the surrogate model is based on the number of layers N of the moth-eye anti-reflection structure. When N=1, a Gaussian regression model is used as the surrogate model; when N=2, a random forest model is used as the surrogate model.

[0031] Optionally, in step S6, the optimal parameter combination P of the moth-eye anti-reflection structure... optimal ={H, D1, D2, δ……} satisfies the manufacturability constraints of nanoimprint lithography, and the geometric parameters satisfy: Min{H, D1, D2, δ……} ≥ η·λ min ; Where η is the manufacturing safety factor, and η>1, λ min H represents the minimum manufacturable feature size of the nanoimprint emulation device, where H is the height, D1 is the substrate diameter, D2 is the top diameter, and δ is the spacing.

[0032] Optionally, in step S4, the formula for calculating the desired lifting function EI is: EI(P) = E[max(f m -f(P), 0)] Among them, f m denoted as the optimal performance value in the current sample library, and f(P) is the predicted value of the surrogate model for the set of geometric parameters.

[0033] Optionally, in step S5, the preset termination condition is any one of the following conditions: (1) The objective function meets the preset design requirements; (2) In k consecutive iterations, the improvement of the objective function is less than the preset tolerance ε; (3) The number of simulation verifications reaches the preset upper limit Nmax.

[0034] Optionally, when the termination condition of reaching a preset upper limit Nmax for the number of simulation verifications is met, if the surrogate model achieves the optimal parameter combination P... optimal Prediction variance Var(f(P) optimal The variance is greater than the prediction variance threshold σ. max If so, incremental sample simulation verification will be automatically initiated, and the surrogate model and optimal parameter combination P will be updated based on the simulation verification results. optimal .

[0035] Optionally, in step S6, the objective function is: F = α·Q + β·M Where α is the optical reflectivity weighting coefficient, β is the peak stress weighting coefficient, Q is the optical performance index, and M is the mechanical performance index.

[0036] This invention also provides a structural construction system for a moth-eye anti-reflection structure based on dynamic feedback, comprising: The parametric modeling module is used to configure the geometric parameters and nano-manufacturing process constraints of the moth-eye anti-reflection structure to generate a feasible parameter space. The dynamic optimization module integrates a Bayesian optimization algorithm library and is used to perform Latin hypercube sampling, train a surrogate model, recommend candidate parameter combinations based on the expected boosting function, and perform iterative optimization based on the feasible parameter space. The multiphysics simulation module is used to call scripting tools and multiphysics numerical simulation platforms to calculate the optical and mechanical performance indicators corresponding to parameter combinations in batches. The comparison and verification module is used to compare the prediction results of the surrogate model with the simulation verification results of the multiphysics simulation module, and to trigger the retraining of the surrogate model when the relative error exceeds a preset error threshold. The report generation module is used to output the optimal parameter combination and sensitivity analysis matrix of the moth-eye anti-reflection structure.

[0037] Optionally, the dynamic optimization module supports batch asynchronous parallel optimization, which can simultaneously generate multiple candidate parameter sets and allocate them to distributed computing nodes for parallel simulation, and the simulation verification results are asynchronously written back to the central database.

[0038] Specifically, the solution of the present invention is further described according to the following embodiments: Example 1 This invention provides a method for constructing a moth-eye anti-reflection structure based on dynamic feedback, comprising the following steps: (I) Parameter constraints and feasible space construction This invention first establishes a geometric parameter set P={p1, p2, ..., p...} based on the geometric parameters of the moth-eye anti-reflection structure. nThe core geometric parameters include the convex shape A (which can be one or a combination of convex shapes such as cylinder, frustum, cone, or concave shapes such as inverted cylinder, inverted frustum, inverted cone, etc.), cone height H, base diameter D1, top diameter D2, number of structural layers N (positive integer and N≤2), spacing δ, and at least one of the secondary structure shape S_A, secondary structure height S_H, secondary structure base diameter S_D1, secondary structure top diameter S_D2, and secondary structure spacing S_δ introduced by the secondary structure. This comprehensively covers the multi-dimensional parameters that affect structural performance and solves the problem of insufficient parameter coverage in existing methods.

[0039] Subsequently, the constraints of nanofabrication processes are deeply integrated into the definition of the ensemble parameter space: the minimum manufacturable feature size λ for processes such as nanoimprinting and electron beam lithography. min To account for manufacturing errors, a manufacturing safety factor η (η>1) is introduced. Constraints are set on each independent geometric parameter H, D1, D2, δ, and the corresponding secondary structures S_H, S_D1, S_D2, S_δ, such that Min{H, D1, D2, δ}≥ η·λ min , where λ min Based on the specific manufacturing equipment technical documents, η is used to compensate for dimensional errors caused by material deformation and mold precision deviations during the manufacturing process. Through this constraint, combinations that exceed the process's achievable range are eliminated from the source of parameter design, directly solving the core problem of "disconnect between process constraints and performance optimization," and forming a feasible parameter space that only contains manufacturable parameter combinations.

[0040] (II) Efficient Sampling and Generation of Initial Training Sample Library To address the issues of low efficiency and poor representativeness of traditional uniform sampling and orthogonal experimental methods in high-dimensional parameter spaces, this invention employs the Latin hypercube sampling method to sample the feasible parameter space. This method uniformly divides the sampling intervals along each parameter dimension, ensuring that each interval is sampled only once, and that the sampling points are uniformly distributed in the high-dimensional space. This allows for the coverage of key regions of the feasible parameter space with a smaller number of samples (m samples), significantly improving sampling efficiency and sample representativeness. After sampling, an initial parameter combination set {P1, P2, ..., P} is generated. m}

[0041] (III) Parametric Simulation Model of Optical Field-Structure Coupling To address the distortion issues caused by the separation of optical and mechanical performance simulations in existing methods, this invention establishes a parameterized simulation model that couples the optical field and structure using Comsol and Matlab, enabling simultaneous calculation of optical performance index Q and mechanical performance index M under the same model. The initial parameter set {P1, P2, ..., P...} is used. mAfter inputting the parameterized simulation model, obtain the optical performance index Q (such as reflectivity) and mechanical performance index M (such as maximum stress) corresponding to each parameter sample. Standardize the obtained performance dataset to form an initial training sample library containing the mapping relationship between "geometric parameter combination - performance index".

[0042] This parametric simulation model is based on multiphysics coupling theory, incorporating the interaction between the light field (optical parameters such as reflectivity and transmittance) and the structural field (mechanical parameters such as stress distribution and deformation) into the simulation system. For example, when light shines on the moth-eye protrusion structure, the model can simultaneously calculate the impact of local temperature changes caused by light energy absorption on the structural stress distribution, as well as the interference of structural deformation on the light refraction path. The final output is a performance index that truly reflects the actual application scenario, providing accurate data support for subsequent optimization.

[0043] (iv) Layered Proxy Model and Dynamic Iterative Optimization To balance optimization efficiency and prediction accuracy, this invention proposes a hierarchical surrogate model selection strategy based on the number of structural layers N: When N=1, since the geometric parameter coupling relationship of a single-layer structure is relatively simple, a Gaussian process model with high fitting accuracy and low computational cost is adopted as the surrogate model; when N=2, the two-layer structure introduces secondary structural parameters (such as S_A, S_H, S_D1, etc.), which significantly increases the parameter interaction complexity, and switches to a random forest model that is more adaptable to high-dimensional complex data, accurately fitting the nonlinear performance mapping relationship under multi-parameter coupling, thus solving the problem of large prediction errors of existing fixed models under multi-layer structures from the source of model selection.

[0044] During the iterative optimization process, the objective function F=α·Q +β·M (α is the optical reflectivity weighting coefficient, and β is the stress peak weighting coefficient, which is set according to the requirements of optical and mechanical performance in the actual application scenario) is used as the core of optimization. The values ​​of α and β can be dynamically adjusted according to the specific application scenario. For example, in the scenario of high-precision optical devices, it is necessary to prioritize low reflectivity, so α=0.7 and β=0.3 can be set; in the scenario of photovoltaic modules and other scenarios that need to withstand mechanical impact for a long time, it is necessary to strengthen structural stability, so α=0.4 and β=0.6 can be adjusted to achieve a deep binding between performance requirements and optimization objectives.

[0045] The return of candidate parameter combinations is calculated using the expected boost function EI. The formula for EI is EI(P) = E[max(f min -f(P), 0)], where f minLet f(P) be the optimal performance value in the current sample library (i.e., the maximum value of the objective function F), and let f(P) be the predicted objective function value of the surrogate model for the parameter combination P. This function quantifies the potential improvement space of the candidate parameter combination compared to the current optimal solution, avoiding blindly exploring low-yield parameter regions while accurately identifying performance breakthrough points. The candidate parameter combination P with the highest yield value is selected. max Then, it is input into the optical field-structure coupling simulation model for verification. The complete data of the parameter combination and actual performance obtained from the verification need to be added to the sample set simultaneously to update the data distribution, thereby realizing the dynamic iterative optimization of the proxy model and ensuring that the recommended parameter combination always has high reliability and process adaptability.

[0046] (v) Multi-condition termination and incremental verification This invention sets three types of iteration termination conditions to balance optimization effectiveness and efficiency: Performance-based termination: When the optical performance index Q meets the preset design requirements (e.g., reflectivity ≤ 0.5%), the iteration is terminated directly to meet the needs of scenarios with clear requirements for optical performance. Performance convergence termination: If the improvement of the objective function F in k consecutive iterations is less than the preset tolerance ε, it indicates that the performance has approached the optimal level, and the iteration is terminated to avoid invalid computation; Simulation count limit termination: When the number of simulations reaches the preset limit N. max Then, further determine the suitability of the surrogate model for the current optimal parameter combination P. optimal The prediction variance Var(f(Poptimal)): If Var(f(Poptimal)) optimal )) ≤ σ max (σ) max If the preset prediction variance threshold is used, the iteration terminates; if Var(f(P) is used, the iteration terminates. optimal ))>σ max Automatically initiate incremental sample simulation verification, update the simulation verification results to the sample library and surrogate model, and recalculate P. optimal This addresses the uncertainty in results caused by existing methods failing to consider prediction variance.

[0047] (vi) Determination of the optimal parameter combination After the iteration terminates, the parameter combination that maximizes the objective function F is selected from the final sample library and is taken as the optimal parameter combination P for the moth-eye anti-reflection structure. optimal Since this parameter combination is selected from the initial feasible parameter space and is always based on the actual performance of coupled simulation during the iteration process, it has both manufacturability and optimal optical-mechanical synergy, and can be directly used for subsequent structure fabrication.

[0048] Example 2 This invention also provides a structural construction system for a moth-eye anti-reflection structure based on dynamic feedback, which is designed with five functional modules: Parametric modeling module: Provides a visual interface for configuring geometric parameter types (such as convex / concave shapes, single-layer / double-layer structures), value ranges, and process constraints (such as η, λ). min (Input), automatically generate feasible parameter space; Dynamic optimization module: Integrates Bayesian optimization algorithm library, can automatically execute the process of "hyper-Latin sampling - parametric simulation - surrogate model selection set training - expected improvement EI calculation - candidate parameter recommendation", and supports batch asynchronous parallel optimization. It can generate q candidate parameter sets at the same time and distribute them to distributed computing nodes for parallel simulation. The results are asynchronously written back to the central database, which greatly shortens the optimization cycle. Multiphysics Simulation Module: Calls scripting tools to perform joint simulations with a multiphysics numerical simulation platform, batch solving for optical reflectivity and mechanical peak values ​​corresponding to parameter combinations. After the simulation is completed, Q and M are automatically standardized, such as normalizing reflectivity and converting stress values ​​into percentages relative to the material yield strength, generating a standardized dataset containing geometric parameter values, Q values, and M values. The comparison and verification module compares the prediction performance of the surrogate model with the actual simulation performance in real time. When the relative error is greater than 5%, the surrogate model retraining process is automatically triggered to re-optimize the model parameters and ensure the model prediction accuracy. Report generation module: Extracts the parameter combination P that maximizes the objective function F = α·Q + β·M from the final sample library. optimal The specific parameter values, corresponding Q values, M values, and objective function F values ​​are used to generate a sensitivity analysis matrix (quantifying the influence weight of each geometric parameter on Q and M), providing clear guidance for process implementation. The following combination Figure 2 The optimization of the moth-eye structure with N=1-2 layers is explained in detail.

[0049] 1. Parameter definition and constraint modeling 1.1 Definition of Geometric Parameter Set Based on the requirements for the composition of the geometric parameter set P, the mixed variables are defined as follows: Discrete parameters: (1) Number of structural layers N (integer 1-2); (2) Shape A (selected from three convex shapes: cylindrical, frustum, and conical, or three concave shapes: inverted cylindrical, inverted frustum, and inverted conical, for a total of 6 selectable types, with a coding dimension of 6). (3) Secondary structure shape S_A (only enabled when N=2, type is the same as shape A, encoding dimension=6).

[0050] Continuous parameters: (1) Height H (height of a single-layer structure, the overall height when N=1; the bottom layer height when N=2, and the secondary structure height S_H is set separately), with a value range of 50-200nm; (2) Secondary structure height S_H (only enabled when N=2), with a value range of 30-100nm; (3) Substrate diameter D1 (bottom substrate diameter), with a value range of 100-400nm (mean 250nm, variance 50nm). (4) Top diameter D2 (bottom top diameter), with a value range of 0-400nm (less than or equal to the base diameter D1). (5) Secondary structure substrate diameter S_D1 (only enabled when N=2), value range 0-400nm (less than or equal to the bottom top diameter D2); (6) Top diameter of secondary structure S_D2 (only enabled when N=2), value range 0-400nm (less than or equal to top diameter S_D1); (7) Spacing δ (spacing of the underlying structure), with a value range of 100-400nm (greater than or equal to the substrate diameter D1). (8) Secondary structure spacing S_δ (only enabled when N=2), with a value range of 100-400nm (greater than or equal to the substrate diameter S_D1).

[0051] 1.2 Manufacturability Constraints Based on the characteristics of nanoimprint lithography, the following constraints are set: (1) Core dimension constraint: All independent geometric parameters (H, S_H, D1, D2, S_D1, S_D2, δ, S_δ) must satisfy Min{H, S_H, D1, D2, S_D1, S_D2, δ, S_δ}≥η·λ min Among them, the manufacturing safety factor η=1.2 (satisfying the requirement of η>1), and the minimum manufacturable feature size λ of the nanoimprint lithography equipment. min =50nm (determined according to the equipment technical document), the minimum size constraint threshold is calculated to be 60nm, and all parameter values ​​must be higher than this threshold; (2) Total thickness constraint:

[0052] in, The height of each layer is set as H when N=1 and H+S_H when N=2, to avoid the total thickness exceeding the coating thickness limit of the nanoimprinting process; (2) Interlayer alignment error: Enabled only when N=2. This ensures that the spacing deviation between the secondary structure and the underlying structure is ≤20nm, meeting the alignment accuracy requirements of the embossing mold; (3) Sedimentation accuracy constraints: , in, For actual manufacturing dimensions, To ensure the design dimensions are within acceptable limits, the error rate must be ≤5% to compensate for dimensional deviations during the material deposition process.

[0053] 1.3 Definition of Objective Function Based on the design logic of the objective function F = α·Q + β·M, and considering the optical and mechanical performance requirements, the objective function is defined as follows: F = α·(1-Q) + β·(1-M / σ) max )-λ1C1-λ2C2-λ3C3 Wherein, α is the optical reflectivity weighting coefficient (valued at 0.6, prioritizing anti-reflection performance), and β is the stress peak weighting coefficient (valued at 0.4, taking into account structural stability). (1-Q) characterizes the effect of improving light transmittance (the smaller Q is, the larger this value is); (1- M / σ max ) characterizes the mechanical safety margin (σ) max (This refers to the yield strength of the structural material; the smaller M is, the larger this value becomes). λ1, λ2, and λ3 are constraint penalty coefficients (the initial value is 0.1, and they increase exponentially by β=0.3 when the constraint is exceeded, thus strengthening the constraint on process compliance).

[0054] 2. Optimize process implementation 2.1 Initial Sample Set Generation Using the Latin hypercube sampling method, 100 sets of initial parameter combinations {P1, P2, ..., P} are generated within the aforementioned feasible parameter space. 100}, where there are 100 parameter combinations for N=1 and N=2, to ensure that the samples are evenly distributed across the layer dimension and cover the key areas of the feasible parameter space.

[0055] 2.2 Simulation of Optical Field-Structure Coupling The "Multiphysics Simulation Module" is invoked to perform batch calculations of performance metrics corresponding to each set of initial parameter combinations through a joint simulation interface that combines optical field-structure coupling calculation with automated script control. (1) Optical performance index Q: Average reflectance at test wavelengths of 400-800nm; (2) Mechanical performance index M: The maximum stress peak of the structure under an external force of 10 N / cm²; (3) Organize the “parameter combination-target F” data into a standardized initial sample set for subsequent surrogate model training.

[0056] 2.3 Construction of Layered Proxy Model (1) Based on the rule of "layer-adaptive proxy model", train the proxy model using the initial sample set: (2) When N=1: Gaussian regression model (kernel function is Matern32) is used to capture the linear relationship between single-layer structural parameters and performance by taking advantage of its high fitting accuracy for low-dimensional data; (3) When N=2: a random forest model (built based on the Scikit-learn library, tree depth=15, number of trees=50) is used to fit the nonlinear coupling relationship between secondary structure parameters and performance by taking advantage of its adaptability to high-dimensional complex data; (4) Monitor model accuracy in real time through the “comparison and verification module”: calculate the relative error between the surrogate model’s prediction performance and the actual simulation performance. When the error is greater than 5%, the model will be automatically retrained to ensure that the MAE (mean absolute error) is less than 3%.

[0057] 2.4 Dynamic Iterative Optimization (1) The return of the candidate parameter combination is calculated using the expected improvement function EI, and the formula is:

[0058] in, This represents the optimal value (i.e., the maximum F-value) of the objective function F in the current sample set. To predict the F-value of the parameter combination P using a surrogate model, calculate the EI value for the parameter spaces of N=1 and N=2 respectively, and screen the candidate parameter combination P with the highest return in each space. max (1 group each, 2 groups in total).

[0059] (2) Enable the "Batch Asynchronous Parallel Optimization" function Simultaneously, four candidate parameter sets (two sets each for N=1 and N=2) are generated and distributed to four distributed computing nodes to perform light field-structure coupling simulation in parallel. After the simulation is completed, the results of "parameter combination - actual Q - actual M" are asynchronously written back to the central database to update the sample set.

[0060] (3) After each iteration, determine whether to stop the iteration based on the termination condition: Performance targets met: Termination occurs when the objective function F ≥ 0.85 (preset design requirement, corresponding to reflectivity ≤ 5% and peak stress ≤ 70%). max If the iteration terminates, then the iteration ends. Performance convergence termination: If the improvement of the objective function F is less than the tolerance ε = 0.01 in k = 3 consecutive iterations, it indicates that the performance is close to the optimal value, and the iteration is terminated. Simulation count limit termination: If the number of simulations reaches the preset limit N. max =50 times, further judging the surrogate model's effectiveness on the current optimal parameter combination Poptimal Prediction variance Var(f(P) optimal )): If Var(f(P) optimal ))≤σ max If the value is 0.02 (preset prediction variance threshold), the iteration terminates. If Var(f(P) optimal ))>σ max Automatically initiate incremental sample simulation verification (generating 5 additional candidate parameters), update the sample set and surrogate model, and then re-evaluate.

[0061] 2.5 Closed-loop verification (implemented through the "Comparison Verification Module") The P obtained after the iteration terminates optimal Physical samples were prepared using nanoimprint lithography equipment, and the actual optical reflectivity Q was measured using a white light interferometer. real The peak mechanical stress M was measured using a nanoindenter. real : If |Q real -Q pred | / Q pred ≤5% and |M real -M pred | / M pred ≤5% (Q) pred M pred If the value is the simulation value, then the verification is successful. If the relative error is greater than 5%, the "model retraining" mechanism is triggered, and 10 additional sets of samples are added to retrain the surrogate model until the verification is successful.

[0062] 3. Implementation effect verification 3.1 Optimal parameter combination output: After the iteration terminates, the optimal parameter combination P is selected from the final sample set to maximize the objective function F. optimal The details are as follows (taking N=2 as an example): Shape A: Frustum (protrusion), Secondary structure shape S_A: Cone (protrusion); Height H = 180nm, secondary structure height S_H = 80nm; The substrate diameter D1 = 320 nm, and the secondary structure substrate diameter S_D1 = 150 nm; The top diameter D2 = 80 nm, and the top diameter of the secondary structure S_D2 = 60 nm; The spacing δ = 350 nm, and the secondary structure spacing S_δ = 170 nm.

[0063] 3.2 Performance and process compliance verification Optical performance: Average reflectance Q=2.1% in the 400-800nm ​​range, which is better than the preset design requirement (≤5%). Mechanical properties: Maximum stress peak value M = 55%σ under an external force of 10 N / cm² max To meet structural stability requirements (≤70%σ) max ); Process compliance: Min{H, S_H, D1, D2, S_D1, S_D2, δ, S_δ}=60nm=η λmin (1.2×50nm) meets the constraints; total thickness = 260nm < 300nm, interlayer spacing deviation = 10nm < 20nm, deposition error rate = 3.8% < 5%, all process constraints are met.

[0064] 3.3 Report Generation The final report is output through the "Report Generation Module," which includes: P optimal Complete parameter details (parameter values ​​for N=2 above); Comparison of simulated and measured values ​​of objective function F (0.89) and Q and M; Sensitivity analysis matrix: quantifies the influence weight of each parameter on Q and M (e.g., the influence weight of height H on Q is 35%, making it the most critical optical parameter; the influence weight of substrate diameter D1 on M is 28%, making it the most critical mechanical parameter), providing a basis for controlling key parameters in process implementation.

[0065] Compared with the prior art, the present invention has the following beneficial effects: (1) Improve process adaptability: By deeply binding process constraints and parameter space, ensure that the optimal parameter combination meets the requirements of nano-manufacturing process, avoid the problem of "design is feasible but manufacturing is not feasible", and reduce the cost of R&D trial and error.

[0066] (2) Improve the accuracy of performance simulation: The optical field-structure coupling model can eliminate the error of optical-mechanical performance separation simulation, making the performance indicators more in line with the actual application scenario.

[0067] (3) Improve optimization efficiency and accuracy: Latin hypercube sampling reduces the number of samples by more than 50%, hierarchical proxy model reduces prediction error by more than 30%, and parallel optimization shortens the iteration cycle by more than 40%.

[0068] (4) Improve the reliability of optimization: Multiple termination conditions and incremental verification mechanism enable the performance fluctuation range of the optimal parameter combination to be controlled within 2%, solving the problem of uncertainty in the results of existing methods.

[0069] Specific embodiments of the present invention have now been described. Other embodiments are within the scope of the appended claims. In some cases, the actions described in the claims can be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result.

[0070] It should be noted that all directional indications (such as up, down, left, right, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship between the components in a certain order (as shown in the figure). If the specific order changes, the directional indication will also change accordingly.

[0071] In the description of this invention, the terms "first" and "second" are used only for convenience in describing different components or names, and should not be construed as indicating or implying a sequential relationship, relative importance, or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" and "second" may explicitly or implicitly include at least one of that feature.

[0072] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0073] It should be noted that although specific embodiments of the present invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of the present invention. Various modifications and variations that can be made by those skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of the present invention.

[0074] The examples of the embodiments of the present invention are intended to concisely illustrate the technical features of the embodiments of the present invention, so that those skilled in the art can intuitively understand the technical features of the embodiments of the present invention, and are not intended to be an improper limitation of the embodiments of the present invention.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a moth-eye anti-reflection structure based on dynamic feedback, characterized in that, include: S1: Establish a set of geometric parameters based on the geometric parameters of the moth-eye anti-reflection structure, and constrain the set of geometric parameters using nano-manufacturing process constraints to obtain a feasible parameter space; S2: Sample within the feasible parameter space using the Latin hypercube sampling method to generate an initial parameter combination set; S3: Call the scripting tool and the multiphysics numerical simulation platform to jointly calculate the optical and mechanical performance indicators of the moth-eye anti-reflection structure corresponding to the initial parameter combination set, and form the initial training sample library; S4: Train the surrogate model using the initial training sample library, and calculate the return of candidate geometric parameter combinations in the initial training sample library using the expected boost function. Input the candidate geometric parameter combination with the largest return value into the parameterized simulation model for verification, and add the simulation verification results to the training sample library to update the surrogate model. S5: Repeat step S4 until the preset termination condition is met; S6: Select the parameter combination that maximizes the objective function from the final generated sample library as the optimal parameter combination for the moth-eye anti-reflection structure.

2. The method of claim 1, wherein, In step S1, the geometric parameters include at least one of the following: shape, height, base diameter, top diameter, number of structural layers, and spacing.

3. The method of claim 1, wherein, In step S4, the selection of the surrogate model is based on the number of layers N of the moth-eye anti-reflection structure. When N=1, a Gaussian regression model is used as the surrogate model; when N=2, a random forest model is used as the surrogate model.

4. The method of claim 1, wherein, The optimal parameter combination P of the moth-eye anti-reflection structure in the step S6 optimal ={H, D1, D2, δ……} satisfies the nano-imprinting process manufacturability constraint condition, and the geometric parameters satisfy: Min{H, D1, D2, δ……} ≥ η·λ min ; Where η is the manufacturing safety factor, and η>1, λ min H represents the minimum manufacturable feature size of the nanoimprint emulation device, where H is the height, D1 is the substrate diameter, D2 is the top diameter, and δ is the spacing.

5. The method of claim 1, wherein, In step S4, the formula for calculating the expected lifting function EI is: EI(P) = E[max(f m -f(P), 0)] where f m is the optimal performance value in the current sample library, and f(P) is the predicted value of the proxy model for the set of geometry parameters.

6. The method of claim 1, wherein, In step S5, the preset termination condition is any one of the following conditions: (1) The objective function meets the preset design requirements; (2) In k consecutive iterations, the improvement of the objective function is less than the preset tolerance ε; (3) The number of simulation verifications reaches the preset upper limit Nmax.

7. The method of claim 6, wherein, When the termination condition of reaching the preset upper limit Nmax for the number of simulation verifications is met, if the surrogate model achieves the optimal parameter combination P... optimal Prediction variance Var(f(P) optimal The variance is greater than the prediction variance threshold σ. max If so, incremental sample simulation verification will be automatically initiated, and the surrogate model and optimal parameter combination P will be updated based on the simulation verification results. optimal .

8. The method of claim 1, wherein, In step S6, the objective function is: F = α·Q + β·M Where α is the optical reflectivity weighting coefficient, β is the peak stress weighting coefficient, Q is the optical performance index, and M is the mechanical performance index.

9. A structural construction system for a moth-eye anti-reflection structure based on dynamic feedback, characterized in that, include: The parametric modeling module is used to configure the geometric parameters and nano-manufacturing process constraints of the moth-eye anti-reflection structure to generate a feasible parameter space. The dynamic optimization module integrates a Bayesian optimization algorithm library and is used to perform Latin hypercube sampling, train a surrogate model, recommend candidate parameter combinations based on the expected boosting function, and perform iterative optimization based on the feasible parameter space. The multiphysics simulation module is used to call scripting tools and multiphysics numerical simulation platforms to calculate the optical and mechanical performance indicators corresponding to parameter combinations in batches. The comparison and verification module is used to compare the prediction results of the surrogate model with the simulation verification results of the multiphysics simulation module, and to trigger the retraining of the surrogate model when the relative error exceeds a preset error threshold. The report generation module is used to output the optimal parameter combination and sensitivity analysis matrix of the moth-eye anti-reflection structure.

10. The system of claim 9, wherein, The dynamic optimization module supports batch asynchronous parallel optimization, can simultaneously generate multiple candidate parameter sets and distribute to distributed computing nodes for parallel simulation, and the simulation verification results are asynchronously written back to the central database.

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