Numerical simulation method for evaluating tolerance of metasurface to multiple types of actual machining errors

Abstract

The invention discloses a numerical simulation method for evaluating tolerance of a metasurface to multiple types of actual machining errors, and belongs to the technical field of metasurs.The method comprises the steps that S1, simulation software is initialized, and refractive indexes or relative dielectric constants of a functional layer and a substrate material are imported into a material library; s2, firstly determining the geometrical shape, the structure line width and other dimension parameters of the metasurface structure unit, and then determining the type of an actual machining error to be introduced; and finally modeling the metasurface structure unit. S3, establishing a metasurface simulation model after multiple types of machining errors are introduced at the same time; and S4, carrying out numerical simulation calculation on the metasurface simulation model, continuously changing different types of error parameters by using a control variable method, carrying out statistics on performance results and carrying out comparative analysis on the performance results and ideal conditions, and finally determining the tolerance range of the metasurface to actual machining errors. According to the method, the tolerance degree of the metasurface to various actual machining errors can be rapidly and effectively evaluated.

Description

Technical Field

[0001] The present invention belongs to the technical field of supersurfaces, and in particular relates to a numerical simulation method for evaluating the tolerance of a supersurface to multiple types of actual processing errors. Background Art

[0002] A metasurface is a two-dimensional array of artificial structures composed of sub-wavelength-sized structural units, whose thickness is much smaller than the working wavelength. Although two-dimensional metasurfaces sacrifice some control dimensions compared to three-dimensional metamaterials, they can achieve more precise and efficient control of electromagnetic waves, and the corresponding losses are also significantly reduced. In addition, due to their planar structural characteristics, metasurfaces have significant advantages in processing and integration, which provides a new way for miniaturized and integrated optical devices, making the manipulation of electromagnetic waves more flexible and convenient.

[0003] A complete metasurface micro-nano processing process includes not only the two core processes of electron beam lithography (EBL) and dry etching, but also other key steps such as coating, cleaning, and metal mask removal. However, in this series of complex processes, a variety of processing errors will inevitably occur, such as structural line width error, etching depth error, sidewall angle error, and line edge roughness (LER) error. These processing errors will have a significant impact on the electromagnetic or optical properties of the metasurface, and thus affect the realization of its functions and performance. Therefore, accurately evaluating the tolerance of the metasurface to actual processing errors is of vital importance to the design and application of the metasurface.

[0004] At present, the methods for evaluating the tolerance of metasurfaces to actual processing errors mainly include experimental measurement and numerical simulation. The experimental measurement method refers to evaluating the performance of the metasurface through actual performance testing after the metasurface sample is prepared. Although this method can provide the most direct performance data, it is time-consuming, costly, and difficult to systematically and comprehensively evaluate different types and combinations of processing errors. The numerical simulation method refers to first considering various possible processing errors in the simulation software, and then establishing the corresponding metasurface actual model and simulating and analyzing its performance indicators. However, current research mainly focuses on the modeling of a single type of processing error, and lacks effective means for simultaneously modeling and comprehensively evaluating multiple types of processing errors. Summary of the invention

[0005] The present invention provides a numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors. By utilizing simulation modeling and analysis techniques, the tolerance of a metasurface to various types of actual processing errors can be rapidly and effectively evaluated, thereby providing beneficial assistance and guidance for the simultaneous design and processing of the metasurface.

[0006] The object of the present invention is to provide a numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors, comprising:

[0007] S1. Initialize the simulation software and import the refractive index or relative dielectric constant of the functional layer and substrate materials into the material library;

[0008] S2, first determine the geometric shape, structure line width and other dimensional parameters of the metasurface structure unit, then determine the actual processing error type to be introduced; finally, model the metasurface structure unit;

[0009] S3. Establishing a super surface simulation model after introducing multiple types of processing errors simultaneously; specifically:

[0010] First, the mean and distribution function of each actual machining error type are set;

[0011] Then the error parameters for each actual machining error type are randomly generated;

[0012] Finally, a metasurface simulation model is established based on the generated error parameters;

[0013] S4. Perform numerical simulation calculations on the metasurface simulation model, use the control variable method to continuously change different types of error parameters, perform statistics on the performance results and compare and analyze them with the ideal situation, and finally determine the tolerance range of the metasurface to the actual processing error.

[0014] Preferably, in S1, the initialization setting of the simulation software includes: using the FDTD module in the optical simulation software Ansys Lumerical software to perform initialization setting of the simulation area, boundary conditions, incident light source and monitor.

[0015] Preferably, in S2, the actual processing error types include structure line width error, etching depth error, side wall angle error and LER error.

[0016] Preferably, in S2, when the super surface structure unit is a cylindrical structure, the modeling step includes:

[0017] Determine the basic parameters: radius is r, height is h;

[0018] According to the actual structure line width error and etching depth error, the radius is changed from r to r 1 , the structure height changes from h to h 1 ; The side wall angle is θ, 0°<θ≤90°, the structural shape changes from a cylinder to a truncated cone, and the upper base width of the truncated cone is still r 1 , the lower base width is r 1 becomes r 2 =r 1 +h1 *tanθ;

[0019] Then the frustum is evenly split from top to bottom. After splitting, the frustum is equivalent to being composed of n small cylinders, each with a height of h. 1 / n, the bottom width from top to bottom is r 1 、r 1 +△r、r 1 +2*△r、……、r 1 +n*△r、……、r 2 ;

[0020] Use the Rough cylinder model in the Object Library for each height h 1 / n small cylinder is modeled, and the LER is changed by setting the seed, corr length, amplitude and resolution to complete the modeling of a single structural unit.

[0021] Preferably, in S3, the structure line width error, etching depth error and side wall angle error obey a normal distribution.

[0022] Preferably, in S3, the corr length, amplitude and resolution are kept unchanged, and LER errors of other structures are simulated by randomly generating different seed integer values.

[0023] The advantages and positive effects of the present invention are:

[0024] The present invention uses the FDTD module in Ansys Lumerical software for simulation to simulate and analyze the impact of errors that may occur in the actual processing of the metasurface structure on the performance. Specifically, the present invention considers four common processing errors, including structural line width error, etching depth error, sidewall angle error, and line edge roughness (LER) error. In order to more accurately simulate the impact of these errors on the performance of the metasurface, the present invention adopts a uniform splitting method from top to bottom, and first models a single metasurface structure unit in detail.

[0025] In the modeling process, the present invention assumes that the structural line width error follows the normal distribution law, and simulates the line width fluctuation that may occur in actual processing by randomly generating multiple different structural line width values. Then, the same method is used to model other metasurface structural units, thereby realizing the establishment of a simulation model for the metasurface when multiple processing errors exist at the same time.

[0026] After completing the model establishment, the present invention carried out numerical simulation calculations, and obtained the performance of the metasurface under different processing error conditions through simulation calculations. Subsequently, the simulation results were statistically analyzed to evaluate the specific effects of various processing errors on the performance of the metasurface. Finally, the present invention determined the tolerance range of the metasurface to the actual processing errors, and proposed corresponding processing accuracy requirements based on the analysis results to ensure that the metasurface can meet the expected performance standards in practical applications. Through this series of simulation and analysis processes, the present invention provides important theoretical basis and technical guidance for the precise processing of the metasurface. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flowchart of a preferred embodiment of the present invention;

[0028] Figure 2 This is a structural diagram of the supersurface simulation model of the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to further understand the content, features and effects of the present invention, the following embodiments are given as examples and described in detail with reference to the accompanying drawings:

[0030] The technical solution of the present invention is:

[0031] See also Figure 1 and Figure 2 , a numerical simulation method for evaluating the tolerance of metasurfaces to multiple types of actual processing errors, including:

[0032] Step 1: When using the FDTD module of the optical simulation software Ansys Lumerical, a series of initialization settings must be performed first, including defining the simulation area, setting boundary conditions, configuring the incident light source, and installing the monitor. Subsequently, the refractive index or relative dielectric constant of the functional layer and substrate materials must be imported into the material database.

[0033] In the process of using the optical simulation software Ansys Lumerical to design and analyze optoelectronic devices, you first need to use its built-in FDTD (finite time-domain difference method) module to perform simulation calculations. In order to ensure the accuracy of the simulation, you first need to accurately set the simulation area, including defining the spatial range and grid division of the simulation. Next, you need to set appropriate boundary conditions to simulate the actual physical environment and prevent boundary effects from interfering with the simulation results. In addition, it is necessary to define the parameters of the incident light source in detail, including wavelength, intensity, polarization state, and incident angle, to ensure that the characteristics of the light source match the actual application scenario.

[0034] After completing the above settings, it is also necessary to set up appropriate monitors in the simulation software to record and analyze the electromagnetic field distribution, power flow density and other related parameters at each key position during the simulation process. The setting of the monitor is crucial for subsequent analysis and optimization design.

[0035] Next, in order to simulate the actual optoelectronic device structure, it is necessary to import the relevant optical parameters of the required functional layers and substrate materials from the material library of Ansys Lumerical. These parameters usually include the refractive index or relative dielectric constant of the material, which determines the absorption, reflection and transmission characteristics of the material to light waves. By accurately importing these parameters, it can be ensured that the simulation results can truly reflect the optical behavior of the material in actual applications.

[0036] In summary, by carefully setting the simulation area, boundary conditions, incident light source, and monitor, and importing accurate material parameters from the material library, the FDTD module in Ansys Lumerical software can be used to perform efficient and accurate optical simulation, thereby providing strong theoretical support for the design and optimization of optoelectronic devices.

[0037] Step 2: After clarifying the geometric shape of the metasurface structural unit, such as circular or rectangular, and determining the relevant dimensional parameters such as the structure line width and height, further identify and select four types of errors that may be introduced in actual processing, including structure line width error, etching depth error, sidewall angle error, and LER error. After completing the above steps, start modeling the structural unit.

[0038] When designing a metasurface structural unit, it is first necessary to clarify the specific type of its geometric shape, such as a circle, rectangle or any other suitable shape. Next, the dimensional parameters of the structural unit need to be set in detail, including but not limited to key dimensions such as structural line width and height. After these basic parameters are determined, the next step is to introduce four major error factors that may occur in the actual processing process. These errors include deviations in structural line width, inconsistencies in etching depth, deviations in sidewall angles, and errors in line edge roughness (LER). After clarifying these geometric shapes, dimensional parameters and processing errors, detailed modeling of the metasurface structural unit can be started. This step is crucial because it will directly affect the performance and application effect of the final metasurface. Through accurate modeling, problems that may occur in the actual processing process can be better predicted and controlled, thereby improving the reliability and consistency of the metasurface structural unit.

[0039] Step 3: Taking a cylinder as an example, the theoretical radius is r and the height is h. According to the actual structure line width error and etching depth error, the radius is changed from r to r. 1 , the structure height changes from h to h1 ; After considering the side wall angle θ (in the case of a regular trapezoid, 0°<θ≤90°), the structural shape changes from a cylinder to a truncated cone, and the upper base width of the truncated cone is still r 1 , the lower base width is r 1 becomes r 2 =r 1 +h 1 *tanθ; then the frustum is evenly split from top to bottom. After splitting, the frustum is equivalent to being composed of n small cylinders, each with a height of h 1 / n, the bottom width from top to bottom is r 1 、r 1 +△r、r 1 +2*△r、……、r 1 +n*△r、……、r 2 . Use the Rough cylinder model in the Object Library for each height h 1 / n small cylinders are modeled, and LER is changed by setting parameters such as seed, corr length, amplitude and resolution, thus completing the modeling of a single structural unit.

[0040] Take a cylinder as an example, assuming that its theoretical radius is r and its height is h. In the actual manufacturing process, due to various factors, such as structural line width error and etching depth error, the original radius r will change, which is expressed as r 1 Similarly, the height of the structure will change from h to h 1 When the side wall angle θ is further considered (here it is assumed to be a regular trapezoid, i.e. 0°<θ≤90°), the original cylindrical structure will change into a truncated cone shape. The upper base width of the truncated cone remains r 1 remains unchanged, and the bottom width will become r 2 , where r 2 =r 1 +h 1 *tanθ.

[0041] Next, the frustum is evenly split from top to bottom. After splitting, the frustum can be regarded as a structure composed of n small cylinders. The height of each small cylinder is h 1 Divide by n, that is h 1 / n. The base width of each small cylinder from top to bottom is r 1 、r 1 +△r、r 1 +2*△r、……、r 1 +n*△r、……、r 2, use the Roughcylinder model in the Object Library for each height h 1 / n small cylinders are used for modeling. In the modeling process, different parameters such as seed, corr length, amplitude and resolution are set to simulate and change the local edge roughness (LER). In this way, the detailed modeling process of a single structural unit can be completed.

[0042] Step 4: The error of the structure line width follows the law of normal distribution. By randomly generating multiple different structure line width values ​​and modeling other structural units one by one according to the above method, the work of introducing multiple types of processing errors in the metasurface simulation model is completed. The etching depth error and the sidewall angle error also obey the normal distribution and fluctuate randomly around the error mean according to the law of normal distribution. The LER error cannot be measured by normal distribution. In this case, keeping the corr length, amplitude and resolution unchanged, the LER error of other structures can be simulated by randomly generating different seed integer values.

[0043] In the process of establishing the metasurface simulation model, the first thing to consider is the distribution characteristics of the structural line width error. According to statistical principles, these errors usually follow the law of normal distribution, which means that the probability of error values ​​appearing near the mean is higher, while the probability of appearing away from the mean gradually decreases. In order to more accurately simulate the errors that may occur in the actual processing process, random number generation technology is used to generate multiple different structural line width values. These values ​​are randomly selected, but their distribution follows the law of normal distribution, thus ensuring the statistical significance of the simulation results.

[0044] Next, we will not only limit ourselves to the error of a single structural line width, but also extend this method to other types of structural units. This means that in the modeling process, each structural unit needs to be treated similarly to consider its possible processing errors. For example, there may be errors in the height, angle or other key dimensions of the structural unit, and these errors can also be assumed to obey the normal distribution. By introducing the corresponding error model for each structural unit, various errors that may occur in the actual processing process can be more comprehensively simulated.

[0045] After completing the error modeling of all key structural units, these units are combined to form a complete metasurface model. This model not only considers a single type of processing error, but also integrates multiple types of processing errors, so that the simulation results are closer to the actual processing situation. In this way, the performance of the metasurface in practical applications can be more accurately predicted, providing strong theoretical support and data basis for subsequent design optimization and process improvement.

[0046] Step 5. We conducted in-depth numerical simulations on the metasurface simulation model that incorporates various types of processing errors. In this process, we systematically adjusted key variables such as structure line width, etching depth, and sidewall angle using the control variable method. Subsequently, we conducted a comprehensive statistical analysis of the obtained performance results and compared them with the ideal conditions. Based on the above research, we finally determined the tolerance threshold of the metasurface to actual processing errors, and proposed corresponding processing accuracy requirements accordingly.

[0047] In the process of studying the simulation model of the metasurface, various types of processing errors were introduced, including but not limited to structure line width, etching depth, and sidewall angle. In order to more accurately evaluate the impact of these errors on the performance of the metasurface, the control variable method was used for numerical simulation calculations. Specifically, the values ​​of these variables were changed one by one to observe their specific impact on the performance of the metasurface.

[0048] After each change in variables, a series of numerical simulations are performed to obtain the performance results of the metasurface under different processing error conditions. By conducting detailed statistics and analysis on these results, we can more comprehensively understand the specific impact of various processing errors on the performance of the metasurface.

[0049] Next, these performance results are compared and analyzed with the ideal metasurface performance. Through this comparison, the error range that the metasurface can tolerate during actual processing can be clearly identified. The determination of this range is of great significance in guiding the actual processing process because it can help formulate reasonable processing accuracy requirements.

[0050] Finally, based on the statistical and comparative analysis of the performance results, actual machining accuracy requirements for metasurfaces were proposed. These requirements not only ensure that the performance of the metasurface in actual applications meets expectations, but also provide clear guidance for the machining process, thereby improving machining efficiency and product quality. In this way, it can be ensured that the metasurface can still maintain its excellent performance in the face of actual machining errors.

[0051] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are within the scope of the technical solution of the present invention.

Claims

1. A numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors, characterized in that: include: S1. Initialize the simulation software and import the refractive index or relative dielectric constant of the functional layer and substrate materials into the material library; S2, first determine the geometric shape, structure line width and other dimensional parameters of the metasurface structure unit, then determine the actual processing error type to be introduced; finally, model the metasurface structure unit; S3. Establishing a super surface simulation model after introducing multiple types of processing errors simultaneously; specifically: First, the mean and distribution function of each actual machining error type are set; Then the error parameters for each actual machining error type are randomly generated; Finally, a metasurface simulation model is established based on the generated error parameters; S4. Perform numerical simulation calculations on the metasurface simulation model, use the control variable method to continuously change different types of error parameters, perform statistics on the performance results and compare and analyze them with the ideal situation, and finally determine the tolerance range of the metasurface to the actual processing error.

2. The numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors according to claim 1, characterized in that: In S1, the initialization setting of the simulation software includes: using the FDTD module in the optical simulation software Ansys Lumerical software to perform initialization setting of the simulation area, boundary conditions, incident light source and monitor.

3. The numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors according to claim 1, characterized in that: In S2, the actual processing error types include structure line width error, etching depth error, side wall angle error and LER error.

4. The numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors according to claim 1, characterized in that: In S2, when the super surface structural unit is a cylindrical structure, the modeling step includes: Determine the basic parameters: radius is r, height is h; According to the actual structure line width error and etching depth error, the radius is changed from r to r1, and the structure height is changed from h to h1; the side wall angle is θ, 0°<θ≤90°, and the structure shape is changed from a cylinder to a truncated cone. The upper base width of the truncated cone is still r1, and the lower base width is changed from r1 to r2=r1+h1*tanθ; Then the frustum is evenly split from top to bottom. After splitting, the frustum is equivalent to being composed of n small cylinders. The height of each small cylinder is h1 / n, and the bottom widths from top to bottom are r1, r1+△r, r1+2*△r, ..., r1+n*△r, ..., r2 respectively. The Rough cylinder model in the Object Library is used to model each small cylinder with a height of h1 / n, and the LER is changed by setting the seed, corr length, amplitude and resolution to complete the modeling of a single structural unit.

5. The numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors according to claim 1, characterized in that: In S3, the structure line width error, etching depth error, and sidewall angle error follow a normal distribution.

6. The numerical simulation method for evaluating the tolerance of a metasurface to multiple types of actual processing errors according to claim 1, characterized in that: In S3, the corr length, amplitude, and resolution are kept unchanged, and the LER errors of other structures are simulated by randomly generating different seed integer values.

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