Smoothing post-processing method and system for low-scattering silicon master and application in plane prescription lenses

Abstract

The application discloses a smoothing post-processing method and system of a low-scattering silicon master mold and application in a plane prescription spectacle lens, and belongs to the technical field of micro-nano optical device manufacturing and eye vision correction. The application comprises the following steps: step one, obtaining a silicon master mold with microstructures formed through an etching process; step two, establishing a quantitative model between surface topography parameters and scattering performance; step three, selecting multiple representative areas on the surface of the silicon master mold; step four, performing a thermal oxidation process on the silicon master mold; step five, simultaneously evaluating smoothing effect and contour fidelity based on initial state data, current data and a target threshold value; and step six, performing an anti-sticking layer treatment on the silicon master mold that meets the standard. The application decomposes scattering into random roughness contribution and periodic scallop contribution, and can accurately predict scattering performance by pre-calibrating coupling coefficients through RCWA. The application ensures that the smoothing process does not damage the optical function of the microstructure, and avoids uncertainty caused by too many empirical coefficients.

Description

Technical Field

[0001] This invention relates to the field of micro-nano optical device manufacturing and optometry technology, specifically to a smoothing post-processing method and system for a low-scattering silicon master mold and its application in planar prescription lenses. Background Technology

[0002] With the convergence of consumer electronics and optometry technology, thinner and flatter prescription lenses have become an industry trend. Optical designs based on diffractive optical elements (DOEs) or Fresnel microstructures can achieve the refractive power of traditional curved lenses on planar substrates, providing a theoretical possibility for realizing completely flat (Flat Optical) prescription lenses. The manufacturing of such lenses typically employs a replication process of "silicon mold + nanoimprint lithography (NIL)," where the quality of the silicon mold directly determines the optical performance of the final lens.

[0003] The mainstream technology for microstructure fabrication of silicon master molds is grayscale photolithography combined with inductively coupled plasma (ICP) etching. However, the ICP etching process has inherent technical limitations: 1. Scallop effect: When using deep silicon etching processes such as Bosch, the alternating etching and passivation cycles cause periodic ripples (scallops) to form on the sidewalls, which can reach a height of tens of nanometers, directly causing light scattering.

[0004] 2. Surface roughness: Ion bombardment during the etching process introduces nanoscale high-frequency roughness on the surface of the microstructure, resulting in an increase in total integrated scattering (TIS) and a decrease in diffraction efficiency.

[0005] 3. Process coupling contradiction: The control of etching parameters on depth, profile and roughness is interdependent, and a single process window cannot take all three into account.

[0006] In existing technologies, thermal oxidation sacrificial layer processes have been used for surface smoothing of semiconductor planar substrates. However, when applied to non-planar microstructures that have already been etched, two key challenges arise: first, the curvature dependence of the oxidation process may lead to contour distortion; second, there is a lack of closed-loop control methods directly related to optical performance. Therefore, this invention provides a post-smoothing method and system for low-scattering silicon master molds, and its application in planar prescription lenses. Summary of the Invention

[0007] To address the aforementioned technical shortcomings, the present invention aims to provide a smoothing post-processing method and system for low-scattering silicon master models, and its application in planar prescription lenses. It decomposes scattering into random roughness contributions and periodic scallop contributions, and accurately predicts scattering performance through RCWA pre-calibration of coupling coefficients. It introduces a contour fidelity evaluation function and a multi-criteria decision mechanism to ensure that the smoothing process does not damage the optical function of the microstructure. It employs a sequential optimization strategy and a local response surface model to make process parameter adjustments engineering-feasible, avoiding uncertainties caused by excessive empirical coefficients. This invention solves the technical problems mentioned in the background art.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The present invention provides a smoothing post-processing method for low-scattering silicon master models, comprising the following steps: Step 1: Obtain a silicon master mold with a microstructure formed by etching process; Step 2: Establish a quantitative model between surface morphology parameters and scattering performance; Step 3: Select multiple representative areas on the surface of the silicon master mold, perform the first multi-point measurement, and obtain the initial roughness parameters, scallop morphology parameters, and initial scattering characteristic data of each area; Step 4: Perform a thermal oxidation process on the silicon master mold to grow a silicon dioxide sacrificial layer on its surface; perform a selective removal process to completely remove the silicon dioxide sacrificial layer; perform a second multi-point measurement to obtain the current roughness parameters, scallop morphology parameters and current scattering characteristic data of each region after processing; measure and record the current contour parameters after processing. Step 5: Based on the initial state data, current data, and target threshold, simultaneously evaluate the smoothing effect and contour fidelity; Step 6: Apply an anti-sticking layer to the qualified silicone master mold.

[0009] Preferably, step two further includes setting a roughness target threshold Rq according to a preset optical performance target. target and the scattering target threshold TIS target .

[0010] Preferably, step three further includes taking statistical characteristic values ​​as initial state data; and measuring and recording the initial profile reference parameters of the microstructure.

[0011] Preferably, step five further includes adjusting the thermal oxidation process parameters according to the process parameter optimization algorithm if the smoothing effect is not up to standard and the contour fidelity is within the tolerance range, and repeating the thermal oxidation process, sacrificial layer removal process, measurement and evaluation steps until the smoothing effect is up to standard and the contour fidelity is within the tolerance range.

[0012] Preferably, the quantization model decomposes the total scattering into high-frequency random coarse contributions and periodic scallop contributions, expressed as: ; Where λ is the incident light wavelength, R q denoted as root mean square roughness, Δh as the characteristic amplitude of the sidewall scallop, Λ as the scallop period, γ as the coupling coefficient pre-calibrated through rigorous coupled-wave analysis, and ε as the system noise.

[0013] Preferably, the roughness target threshold R q,target Determined by the following formula: ; Among them, TIS target The preset scattering target threshold is used, and Δh and Λ are taken as the median values ​​of the initial measurements.

[0014] Preferably, the multi-point measurement selects at least three different regions, and after obtaining the measurement values, the maximum value of the roughness parameter and scattering characteristic data is taken as the control basis, and the median value of the scallop parameter is taken as the model input.

[0015] Preferably, a smoothing effect evaluation function F is introduced. i Contour fidelity evaluation function G i : ; ; in, This represents the initial maximum roughness. This represents the maximum roughness value after the i-th iteration. These represent the microstructure depth, sidewall angle, and feature line width, respectively. The subscript 0 indicates the initial baseline value, and the subscript tol indicates the preset tolerance. When F i ≥1 and G i If F is ≤1, it is considered to meet the standard. i <1 and G i Continue iterating when G ≤ 1, and when G i When the value is greater than 1, the contour distortion is considered to be excessive.

[0016] Preferably, the process parameter optimization algorithm adopts a sequential optimization strategy based on multi-source data, including: Construct a process parameter vector P = [T, t, atmosphere]; where T is the oxidation temperature and t is the oxidation time; Establish the objective function: ; in, For roughness predicted based on the local response surface model, This represents the increase in oxide layer thickness; The optimal process parameters are solved by minimizing the objective function under the constraint of profile fidelity.

[0017] Preferably, the method further includes a metering backfeeding step: binding the process parameter sequence, metering data sequence and contour data sequence of each iteration to the master mold identifier and storing them in the database, and backfeeding them to the upstream manufacturable design rule library for use in correcting the manufacturing compensation model for subsequent microstructure design.

[0018] A smoothing post-processing system for low-scattering silicon master molds, used to perform the above-described methods, includes: The post-etching master mold input module is used to receive the silicon master mold processed by the etching process; The metrology module includes an atomic force microscope, a total integrating scattering measuring instrument, and a high-precision profilometer; The multi-point sampling control unit is used to control the metrology module to automatically complete the measurement of multiple representative areas and calculate statistical characteristic values; The model and threshold setting module is used to store the quantization model and set the target threshold; The thermal oxidation treatment module includes a precision temperature-controlled oxidation furnace; The wet etching module includes an HF etching tank and an automatic cleaning unit; The closed-loop iterative control module calls the process parameter optimization algorithm to control the thermal oxidation treatment module to perform iterations based on the comparison results of the metering data and the target threshold. Multi-criteria judgment unit, simultaneously evaluating smoothing effect and contour fidelity; The anti-stick coating module is used to apply an anti-stick coating to the qualified silicone master mold. The data traceability and backfeed module is used to record all process and metering data and backfeed it to the upstream design end.

[0019] Preferably, the closed-loop iterative control module has a built-in local response surface model update mechanism to dynamically optimize process parameters based on historical iterative data.

[0020] Preferably, the system further includes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0021] A planar prescription lens, wherein the prescription lens is produced by replicating a low-scattering silicon master mold processed as described above using a nanoimprinting process.

[0022] Preferably, the total integrated scattering (TIS) of the lens at a wavelength of 550 nm is ≤0.3%, and the diffraction efficiency is ≥96%.

[0023] An application of the method described above in the preparation of ultrathin planar ophthalmic prescription lenses.

[0024] The beneficial effects of this invention are as follows: This invention decomposes scattering into random roughness contribution and periodic scallop contribution, and accurately predicts scattering performance by pre-calibrating the coupling coefficient using RCWA. It introduces a profile fidelity evaluation function and a multi-criteria judgment mechanism to ensure that the smoothing process does not damage the optical function of the microstructure. It employs a sequential optimization strategy and a local response surface model to make process parameter adjustments engineering-feasible, avoiding uncertainties caused by excessive empirical coefficients. Multi-point sampling and statistical eigenvalue calculation ensure that the overall performance of the master mold meets standards, providing a guarantee for mass production consistency. Complete process and metrology data are fed back to the design end, enabling subsequent product design to accurately predict and compensate for process deviations. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A flowchart of a smoothing post-processing method for a low-scattering silicon master model provided in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram of the scattering performance model of the present invention.

[0028] Figure 3 This is a schematic diagram illustrating the principle of the thermal oxidation sacrificial layer process of the present invention.

[0029] Figure 4 This is a schematic diagram of the post-processing system for smoothing the low-scattering silicon master mold of the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely 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 without creative effort are within the scope of protection of the present invention.

[0031] Example: Please refer to Figures 1 to 3 As shown, the present invention provides a smoothing post-processing method for a low-scattering silicon master model, comprising the following steps: Step 1: Obtain a silicon master mold with a microstructure formed by etching process; Step 2: Establish a quantitative model between surface topography parameters and scattering performance, and set the roughness target threshold Rq according to the preset optical performance target. target and the scattering target threshold TIS target ; Step 3: Select multiple representative areas on the surface of the silicon master mold, perform the first multi-point measurement, obtain the initial roughness parameters, scallop morphology parameters and initial scattering characteristic data of each area, and take the statistical characteristic values ​​as the initial state data; measure and record the initial profile reference parameters of the microstructure; Step 4: Perform a thermal oxidation process on the silicon master mold to grow a silicon dioxide sacrificial layer on its surface; perform a selective removal process to completely remove the silicon dioxide sacrificial layer; perform a second multi-point measurement to obtain the current roughness parameters, scallop morphology parameters and current scattering characteristic data of each region after processing; measure and record the current contour parameters after processing. Step 5: Based on the initial state data, current data and target threshold, simultaneously evaluate the smoothing effect and contour fidelity. If the smoothing effect does not meet the standard and the contour fidelity is within the tolerance range, adjust the thermal oxidation process parameters according to the process parameter optimization algorithm, and repeat the thermal oxidation process, sacrificial layer removal process, measurement and evaluation steps until the smoothing effect meets the standard and the contour fidelity is within the tolerance range. Step 6: Apply an anti-sticking layer to the qualified silicone master mold.

[0032] In this embodiment, the etched silicon master mold is obtained and the model parameters are calibrated as follows: Fresnel microstructure patterns were exposed on a 6-inch silicon wafer using grayscale photolithography. A microstructure with a depth of 2.8 μm was formed using ICP etching (Bosch process: etching cycles C4F8 / SF6, cycle times 5s / 3s, bias power 50W). An initial master mold, designated M-2026-001, was obtained. RCWA simulation was used to calibrate typical scallop morphology (Δh=5-15nm, Λ=100-150nm), yielding a coupling coefficient γ=0.28±0.03. The measurement noise ε was calibrated by repeated measurements on a blank silicon wafer, and ε≤0.02%. Based on the lens design target (λ=550nm, target diffraction efficiency ≥96%, corresponding to TIS_target≤0.3%), Rq was calculated using the model. target With γ=0.28 and ε=0.02%, the initial Δh0 and Λ0 will be calculated after measurement.

[0033] The initial multi-point measurements and profile datum are as follows: Three regions were selected: the center (C), the half-radius point (M), and the edge (E). Measurement results: Take the maximum value: Rq0 = 4.5nm, TIS0 = 1.58%; take the median: Δh0 = 8.5nm, Λ0 = 120nm.

[0034] Substitute into the model to calculate Rq target =1.08nm; For this, Rq is set... target =1.05nm.

[0035] Profile baseline measurement: depth d0 = 2.801 μm, sidewall angle α0 = 87.5°, line width w0 = 1.502 μm. Profile tolerance setting: Δd tol =50nm, Δα tol =1.0°, Δw tol =30nm.

[0036] Iterative smoothing: First iteration: Initial oxidation temperature T = 1050℃, dry oxygen atmosphere, time t1 = 60 min, d ox,1 =48.5nm.

[0037] HF etching → retest: Rq1 = 2.8nm (maximum value of three points), Δh1 = 5.2nm. Λ1=120nm, TIS1=0.72%.

[0038] Profile remeasurement: d1=2.796nm (Δd=5nm<50nm), α1=87.4°, w1=1.500μm.

[0039] Calculate F1 = (4.5 - 2.8) / (4.5 - 1.05) = 0.51 < 1, G1 = max{5 / 50, 0.1 / 1.0, 2 / 30} = 0.1 < 1; Decision: Continue iteration.

[0040] Second iteration: Constructing a local response surface: Fitting Rq and d based on historical data ox The relationship is such that the slope is estimated to be -0.03 nm / nm. Optimize objective J(P), taking w1=0.7 and w2=0.3, and solve for the optimal Δd. ox =26.5nm; Target oxide layer thickness do x,2 =48.5+26.5=75.0nm, therefore t2≈113min; Oxidation (1050℃, 113min, dry oxygen) → HF etching → retesting; Retest results: Rq2 = 1.02 nm, Δh2 = 2.1 nm, TIS2 = 0.27%; Profile re-measurement: d2=2.789μm (Δd=12nm<50nm), α2=87.2°, w2=1.497μm; Calculate F2==0.24<1; Determine: Meets the standard, terminate the iteration.

[0041] Post-compliance processing and data reinjection: RCA standard cleaning; MVD deposition of FDTS anti-stick layer (150℃, 45min); all data stored in the database and then fed back into the DFM rule base.

[0042] Preferably, the quantization model decomposes the total scattering into high-frequency random roughness contributions and periodic scallop contributions. For scattering dominated by high-frequency random roughness, scalar scattering theory is used to describe it. Where λ is the incident light wavelength, and Rq is the root mean square roughness, for perpendicular incidence (i.e., ), simplified to: ; For the periodic structural scattering caused by the sidewall scallop, using the first-order approximation of coupled-wave theory, the resulting diffraction efficiency loss in a specific direction can be expressed as: Where Δh is the characteristic amplitude of the sidewall scallop, Λ is the scallop period, and θ is... m Let η be the m-th order diffraction angle, and η0 be the diffraction efficiency of the ideal structure. In practical engineering applications, a simplified form can be used for scattering evaluation that is not strictly periodic and not for imaging applications: Wherein, γ is the coupling coefficient pre-calibrated through rigorous coupled-wave analysis. For the typical application scenario of this patent (Λ≈100-150nm, λ=550nm), the value of γ ranges from 0.2 to 0.4. The quantization model expression is then: Where ε is the system noise.

[0043] Preferably, the roughness target threshold R q,target Determined by the following formula: ; Among them, TIS target The preset scattering target threshold is used, and Δh and Λ are taken as the median values ​​of the initial measurements.

[0044] Preferably, the multi-point measurement selects at least three different regions. After obtaining the measurement values, the maximum value of the roughness parameter and scattering characteristic data is used as the control basis, and the median value of the scallop parameter is used as the model input. In this embodiment, the root mean square roughness Rq of each region is measured using an atomic force microscope. k scallop amplitude Δh k and period Λ k And take the statistical characteristic value: R q,0 =max{R q,k}, Δh0=median{Δh k},Λ0=median{Λ k The total integrated scattering (TIS) value of each region was measured using a total integrated scattering meter, and the maximum value TIS0 was taken as max{TIS}. k} as initial state data.

[0045] Preferably, a smoothing effect evaluation function F is introduced. i Contour fidelity evaluation function G i : ; ; in, This represents the initial maximum roughness. This represents the maximum roughness value after the i-th iteration. These represent the microstructure depth, sidewall angle, and feature line width, respectively. The subscript 0 indicates the initial baseline value, and the subscript tol indicates the preset tolerance. When F i ≥1 and G i If F is ≤1, it is considered to meet the standard. i <1 and G i Continue iterating when G ≤ 1, and when G i When the value is greater than 1, the contour distortion is considered to be excessive.

[0046] Preferably, the process parameter optimization algorithm adopts a sequential optimization strategy based on multi-source data, including: Construct a process parameter vector P = [T, t, atmosphere]; where T is the oxidation temperature and t is the oxidation time; Establish the objective function: ; in, For roughness predicted based on the local response surface model, This represents the increase in oxide layer thickness; The optimal process parameters are solved by minimizing the objective function under the constraint of profile fidelity.

[0047] A sequential optimization strategy is adopted: a local response surface model is constructed; based on historical iteration data, R is fitted. q With d ox Local relationships; Solving for the optimal dox: Minimizing the objective function J while satisfying the contour fidelity constraint; Back-deriving process parameters: Based on the optimal d ox The oxidation time t is determined by the Deal-Grove model.

[0048] Preferably, the method further includes a metering backfeeding step: binding the process parameter sequence, metering data sequence and contour data sequence of each iteration to the master mold identifier and storing them in the database, and backfeeding them to the upstream manufacturable design rule library for use in correcting the manufacturing compensation model for subsequent microstructure design.

[0049] When F i ≥1 and G i When the value is ≤1, the iteration is terminated. The qualified master mold undergoes standard RCA cleaning, followed by anti-stick coating using molecular vapor deposition. All process parameter sequences { P i}、Measurement data sequence { Rq i , Δh i , Λ i TIS i} and contour data sequence { d i , α i , w i The master model ID is bound and stored in the database, and then fed back to the upstream Design for Manufacturability (DFM) rule base to correct the manufacturing compensation model for subsequent microstructure designs.

[0050] Please see Figure 4 As shown, a smoothing post-processing system for a low-scattering silicon master mold, used to perform the above-described method, includes: The post-etching master mold input module is used to receive the silicon master mold processed by the etching process; The metrology module includes an atomic force microscope, a total integrating scattering measuring instrument, and a high-precision profilometer; The multi-point sampling control unit is used to control the metrology module to automatically complete the measurement of multiple representative areas and calculate statistical characteristic values; The model and threshold setting module is used to store the quantization model and set the target threshold; The thermal oxidation treatment module includes a precision temperature-controlled oxidation furnace; The wet etching module includes an HF etching tank and an automatic cleaning unit; The closed-loop iterative control module calls the process parameter optimization algorithm to control the thermal oxidation treatment module to perform iterations based on the comparison results of the metering data and the target threshold. Multi-criteria judgment unit, simultaneously evaluating smoothing effect and contour fidelity; The anti-stick coating module is used to apply an anti-stick coating to the qualified silicone master mold. The data traceability and backfeed module is used to record all process and metering data and backfeed it to the upstream design end.

[0051] Preferably, the closed-loop iterative control module has a built-in local response surface model update mechanism to dynamically optimize process parameters based on historical iterative data.

[0052] Preferably, the system further includes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0053] A planar prescription lens, wherein the prescription lens is produced by replicating a low-scattering silicon master mold processed as described above using a nanoimprinting process.

[0054] Preferably, the total integrated scattering (TIS) of the lens at a wavelength of 550 nm is ≤0.3%, and the diffraction efficiency is ≥96%.

[0055] An application of the method described above in the preparation of ultrathin planar ophthalmic prescription lenses.

[0056] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for smoothing and post-processing a low-scattering silicon master model, characterized in that, Includes the following steps: Step 1: Obtain a silicon master mold with a microstructure formed by etching process; Step 2: Establish a quantitative model between surface morphology parameters and scattering performance; Step 3: Select multiple representative areas on the surface of the silicon master mold, perform the first multi-point measurement, and obtain the initial roughness parameters, scallop morphology parameters, and initial scattering characteristic data of each area; Step 4: Perform a thermal oxidation process on the silicon master mold to grow a silicon dioxide sacrificial layer on its surface; perform a selective removal process to completely remove the silicon dioxide sacrificial layer; perform a second multi-point measurement to obtain the current roughness parameters, scallop morphology parameters and current scattering characteristic data of each region after processing; measure and record the current contour parameters after processing. Step 5: Based on the initial state data, current data, and target threshold, simultaneously evaluate the smoothing effect and contour fidelity; Step 6: Apply an anti-sticking layer to the qualified silicone master mold.

2. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, Step two also includes setting a roughness target threshold R based on a preset optical performance target. targe t and scattering target threshold TIS target .

3. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, Step three also includes taking statistical characteristic values ​​as initial state data; and measuring and recording the initial profile reference parameters of the microstructure.

4. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, Step five also includes adjusting the thermal oxidation process parameters according to the process parameter optimization algorithm if the smoothing effect is not up to standard and the contour fidelity is within the tolerance range, and repeating the thermal oxidation process, sacrificial layer removal process, measurement and evaluation steps until the smoothing effect is up to standard and the contour fidelity is within the tolerance range.

5. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, The quantization model decomposes the total scattering into high-frequency random coarse contributions and periodic scallop contributions, expressed as follows: ； Where λ is the incident light wavelength, R q denoted as root mean square roughness, Δh as the characteristic amplitude of the sidewall scallop, Λ as the scallop period, γ as the coupling coefficient pre-calibrated through rigorous coupled-wave analysis, and ε as the system noise.

6. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, The roughness target threshold R q,target Determined by the following formula: ； Among them, TIS target The preset scattering target threshold is used, and Δh and Λ are taken as the median values ​​of the initial measurements.

7. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, The multi-point measurement selects at least three different regions, and after obtaining the measurement values, the maximum value of the roughness parameter and scattering characteristic data is used as the control basis, and the median value of the scallop parameter is used as the model input.

8. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, Introducing a smoothing effect evaluation function F i Contour fidelity evaluation function G i : ； ； in, This represents the initial maximum roughness. This represents the maximum roughness value after the i-th iteration. These represent the microstructure depth, sidewall angle, and feature line width, respectively. The subscript 0 indicates the initial baseline value, and the subscript tol indicates the preset tolerance. When F i ≥1 and G i If F is ≤1, it is considered to meet the standard. i < 1 and G i Continue iterating when G ≤ 1, and when G i > 1 indicates that the contour distortion exceeds the limit.

9. The smoothing post-processing method for low-scattering silicon master molds as described in claim 1, characterized in that, The process parameter optimization algorithm adopts a sequential optimization strategy based on multi-source data, including: Construct a process parameter vector P = [T, t, atmosphere]; where T is the oxidation temperature and t is the oxidation time; Establish the objective function: ； in, For roughness predicted based on the local response surface model, This represents the increase in oxide layer thickness; The optimal process parameters are solved by minimizing the objective function under the constraint of profile fidelity.

10. The smoothing post-processing method for a low-scattering silicon master model as described in claim 1, characterized in that, It also includes a metering backfeeding step: binding the process parameter sequence, metering data sequence and contour data sequence of each iteration to the master mold identifier and storing them in the database, and backfeeding them to the upstream manufacturable design rule library, which is used to correct the manufacturing compensation model for subsequent microstructure design.

11. The smoothing post-processing system for a low-scattering silicon master model as described in claim 1, for performing the method as described in any one of claims 1-10, characterized in that, include: The post-etching master mold input module is used to receive the silicon master mold processed by the etching process; The metrology module includes an atomic force microscope, a total integrating scattering measuring instrument, and a high-precision profilometer; The multi-point sampling control unit is used to control the metrology module to automatically complete the measurement of multiple representative areas and calculate statistical characteristic values; The model and threshold setting module is used to store the quantization model and set the target threshold; The thermal oxidation treatment module includes a precision temperature-controlled oxidation furnace; The wet etching module includes an HF etching tank and an automatic cleaning unit; The closed-loop iterative control module calls the process parameter optimization algorithm to control the thermal oxidation treatment module to perform iterations based on the comparison results of the metering data and the target threshold. Multi-criteria judgment unit, simultaneously evaluating smoothing effect and contour fidelity; The anti-stick coating module is used to apply an anti-stick coating to the qualified silicone master mold. The data traceability and backfeed module is used to record all process and metering data and backfeed it to the upstream design end.

12. The smoothing post-processing system for low-scattering silicon master molds as described in claim 11, characterized in that, The closed-loop iterative control module incorporates a local response surface model update mechanism to dynamically optimize process parameters based on historical iterative data.

13. The smoothing post-processing system for low-scattering silicon master molds as described in claim 11, characterized in that, It also includes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method as described in any one of claims 1-10.

14. A planar prescription lens, characterized in that, The prescription lens is produced by replicating a low-scattering silicon master mold processed by any one of claims 1-8 using a nanoimprinting process.

15. A planar prescription lens as described in claim 14, characterized in that, The lens has a total integrated scattering TIS ≤ 0.3% at a wavelength of 550 nm and a diffraction efficiency ≥ 96%.

16. The application of the method as described in any one of claims 1-10 in the preparation of ultrathin planar ophthalmic prescription lenses.

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