Large-aperture single-crystalline silicon aspherical surface high-precision polishing method

Abstract

This application relates to the field of optical processing technology. This application provides a high-precision polishing method for large-aperture single-crystal silicon aspheres, which is characterized by including the following steps: S10: Obtain the full-aperture surface shape error distribution of the large-aperture single-crystal silicon aspheres and map it to a discrete grid; S20: Construct an optimized model for dwell time distribution and an optimized model for polishing path planning, using the surface shape error parameters of the large-aperture single-crystal silicon aspheres as inputs, and output the optimal dwell time distribution matrix and polishing path sequence; S30: Based on the optimal dwell time distribution matrix and polishing path sequence, perform polishing treatment on the large-aperture single-crystal silicon aspheres; S40: After each polishing cycle, repeat steps S10-S40 until the number of iterations is reached. This application significantly improves the surface shape accuracy and efficiency of large-aperture aspheric polishing by forming a closed-loop control method of "time allocation-path planning-dynamic calibration".

Description

Technical Field

[0001] The present invention belongs to the field of optical processing, and particularly relates to a high-precision polishing method for large-aperture single-crystal silicon aspheres. Background Art

[0002] Large-aperture single-crystal silicon aspheres are large-sized, aspherical-shaped optical elements made of single-crystal silicon material, including but not limited to extreme ultraviolet lithography machine mirrors and infrared imaging system lenses. The high-precision polishing technology for large-aperture single-crystal silicon aspheres is an advanced manufacturing process for high-performance requirements in optical systems. Its core lies in achieving nanoscale (even sub-nanoscale) surface roughness and sub-micron surface shape accuracy, while overcoming the challenges brought by the characteristics of single-crystal silicon material (such as brittleness and anisotropy) and the complex geometry of aspheres. Nowadays, the high-precision polishing technology for large-aperture single-crystal silicon aspheres is a core problem in the field of optical manufacturing.

[0003] In the high-precision polishing technology for large-aperture single-crystal silicon aspheres, dwell time control and path planning are core process parameters, which directly affect the certainty of material removal, the surface shape convergence efficiency, and the final accuracy. The dwell time refers to the time that the polishing tool (such as a polishing head or a grinding head) stays in a certain local area. The longer the dwell time, the greater the material removal amount in that area; path planning refers to the movement trajectory of the polishing tool, which determines the order in which the polishing head visits each grid point and affects the processing efficiency and surface shape accuracy.

[0004] Traditional methods mainly rely on empirical dwell time allocation and fixed polishing paths (such as spiral or raster paths), and there are the following technical problems: the optimization of local dwell time does not consider the cooperative removal effect of adjacent areas, resulting in limited error correction ability; frequent path switching causes sudden changes in the acceleration of the polishing head, resulting in a decrease in processing efficiency or vibration error. Summary of the Invention

[0005] In view of the above-mentioned defects of the prior art, the present invention proposes a high-precision polishing method for large-aperture single-crystal silicon aspheres. The technical solution designed by the present invention includes the following steps:

[0006] S10: Obtain the full-aperture surface shape error distribution of the large-aperture single-crystal silicon aspherical surface and map it to a discrete grid;

[0007] S20: Construct an optimization model for dwell time distribution and an optimization model for polishing path planning, use the surface shape error parameters of the large-aperture single-crystal silicon aspherical surface as input, and output the optimal dwell time distribution matrix and the polishing path sequence;

[0008] S30: Based on the optimal dwell time distribution matrix and the polishing path sequence, perform polishing treatment on the large-aperture single-crystal silicon aspherical surface;

[0009] S40: After each polishing cycle, repeat steps S10 - S40 until the number of iterations is reached.

[0010] Preferably, S10 includes:

[0011] Measure the large - diameter single - crystal silicon aspheric surface using a phase - shifting interferometer to obtain the full - aperture surface shape error distribution. Divide the surface of the large - diameter single - crystal silicon aspheric surface into grids, record the coordinates and surface shape error parameters for each grid, and store them in matrix form with row and column indices corresponding to spatial positions.

[0012] Preferably, the dwell - time distribution optimization model in S20 has the following formula:

[0013]

[0014] In the formula, is the set of surface discretization grid regions of the large - diameter single - crystal silicon aspheric surface, and are the surface shape error parameters of regions x and y, is the collaborative removal efficiency function of regions x and y.

[0015] Preferably, the collaborative removal efficiency function has the following formula:

[0016]

[0017] In the formula, is the anti - zero constant, is the Euclidean distance between regions x and y, is the Gaussian kernel width.

[0018] Preferably, the polishing path planning optimization model in S20 has the following formula:

[0019]

[0020] In the formula, is the surface shape error parameter of the next polishing path point adjacent to region x, is the path - switching cost function.

[0021] Preferably, the path - switching cost function has the following formula:

[0022]

[0023] In the formula, is the error - smoothing weight, is the time - efficiency weight, is the speed of the polishing head moving from region x to x + 1, is the actual distance of the polishing head moving from region x to x + 1.

[0024] Preferably, the output of the optimal dwell time distribution matrix and the polishing path sequence includes:

[0025] Using the NSGA-II multi-objective genetic algorithm to perform Pareto front optimization on the dwell time distribution optimization model and the polishing path planning optimization model, with the material removal per pass and the polishing head acceleration as the constraint conditions, to output the optimal dwell time distribution matrix and the polishing path sequence.

[0026] Beneficial effects:

[0027] Through the collaborative removal effect modeling, multi-objective joint optimization and dynamic compensation mechanism, the present invention systematically solves the problems of surface shape convergence efficiency, path planning contradiction and process stability in the polishing of large-aperture single-crystalline silicon aspheres, significantly superior to traditional single-objective and static optimization methods, and has high engineering application value. Description of the Drawings

[0028] Figure 1 It is a schematic flow chart of a preferred embodiment of the present invention. Detailed Embodiments

[0029] The following will describe in detail the embodiments of the present invention. The following embodiments are implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given. However, the protection scope of the present invention is not limited to the following embodiments.

[0030] The present invention designs a high-precision polishing method for large-aperture single-crystalline silicon aspheres, as Figure 1 shown, the technical solution includes the following steps, specifically including:

[0031] S10: Obtain the full-aperture surface shape error distribution of the large-aperture single-crystalline silicon aspheric surface and map it to a discrete grid;

[0032] S20: Construct a dwell time distribution optimization model and a polishing path planning optimization model, using the surface shape error parameters of the large-aperture single-crystalline silicon aspheric surface as inputs, and output the optimal dwell time distribution matrix and the polishing path sequence;

[0033] S30: Based on the optimal dwell time distribution matrix and the polishing path sequence, perform polishing treatment on the large-aperture single-crystalline silicon aspheric surface;

[0034] S40: After each polishing cycle, repeat steps S10 - S40 until the number of iterations is reached.

[0035] Preferably, S10 includes:

[0036] A phase-shifting interferometer is used to measure the large-aperture single-crystal silicon aspheric surface to obtain the full-aperture surface error distribution. The surface of the large-aperture single-crystal silicon aspheric surface is divided into grids. Each grid records the coordinates and surface error parameters, which are stored in a matrix form, with row and column indexes corresponding to spatial positions.

[0037] Specifically, in surface measurement, the sampling resolution must be greater than or equal to 1mm 2 , noise suppression uses median filtering + Zernike polynomial fitting to remove the adjustment error; in grid discretization, the grid is divided into 1×1mm² grids, and the coordinates of each grid are recorded as .

[0038] Preferably, the residence time distribution optimization model in S20 is formulated as follows:

[0039]

[0040] Where, is the surface discretization grid area set of large-aperture single-crystal silicon aspheric surface, and are the surface error parameters of regions x and y, is the synergistic removal efficiency function of regions x and y.

[0041] Preferably, the collaborative removal efficiency function is as follows:

[0042]

[0043] Where, To prevent division by zero constant, is the Euclidean distance between regions x and y, is the Gaussian kernel width.

[0044] Specifically, for the residence time distribution optimization model, since the Gaussian removal function of the polishing area is localized and the synergistic effect of the distant area can be ignored, a distance threshold is introduced to calculate only The dwell time distribution optimization model uses a Gaussian kernel function to quantify the collaborative correction capability of adjacent areas, suppressing local over- / under-polishing. A distance threshold is introduced to calculate effective neighborhood pairs, reducing the amount of meaningless calculations. Ultimately, the polishing tool's dwell time in each area is optimized, maximizing the efficiency of surface error correction and enhancing the ability to simultaneously correct large-area errors through synergistic effects.

[0045] Preferably, the polishing path planning optimization model in S20 is formulated as follows:

[0046]

[0047] Where, is the surface shape error parameter of the next polishing path point adjacent to region x. is the path switching cost function.

[0048] Preferably, the path switching cost function has the following formula:

[0049]

[0050] In the formula, is the error smoothing weight, is the time efficiency weight, is the speed of the polishing head moving from region x to x + 1, is the actual distance of the polishing head moving from region x to x + 1.

[0051] Specifically, through the polishing path planning optimization model, the path switching cost function combines error smoothness and time efficiency to achieve the balance of process goals. In addition, the path speed and distance are adjusted in real time to suppress mechanical vibration (acceleration constraint), and the error smoothing weight preferentially connects regions with similar errors to avoid sudden changes in surface shape caused by path switching. Finally, the moving path of the polishing head is planned to minimize the efficiency loss and sudden change in surface shape error caused by path switching, and improve the processing efficiency.

[0052] Preferably, the optimal dwell time distribution matrix and polishing path sequence are output, including:

[0053] The NSGA-II multi-objective genetic algorithm is used to perform pareto front optimization on the dwell time distribution optimization model and the polishing path planning optimization model. With the single-pass polishing removal amount and the polishing head acceleration as constraint conditions, the optimal dwell time distribution matrix and polishing path sequence are output.

[0054] Specifically, since there is a natural contradiction between dwell time optimization and path planning, a trade-off is needed. NSGA-II can output a non-dominated solution set, support the joint optimization of continuous variables (dwell time) and discrete variables (path sequence), and provide multi-dimensional optimization options for process decision-making. Therefore, the dwell time and removal amount are correlated through the Preston equation to avoid subsurface damage, and acceleration limits are introduced in path planning to suppress mechanical vibration. Among them, the single-pass polishing removal amount of the constraint condition is less than 50 nm (to prevent subsurface damage), and the polishing head acceleration is less than 0.5 m / s 2 (to avoid vibration exceeding the limit), output the optimal dwell time distribution matrix and polishing path sequence, drive the subsequent polishing operation, and retain the strategy and fast non-dominated sorting. For example, input the surface shape error matrix , maximize the total synergistic effect , under the Preston variance ( ) and process constraints, inversely solve the dwell time distribution , where is the removal rate coefficient, is the pressure distribution.

[0055] In addition, for the joint optimization of dwell time optimization and path planning, since the collaborative efficiency affects the dwell time distribution and the path planning requires the dwell time matrix as input, the two are coupled through iterative optimization, including first optimizing the dwell time distribution, generating a path according to the dwell time distribution (such as a dense path in a high dwell time area), dynamically compensating for the deviation between the actual removal amount and the theory, and finally optimizing the dwell time distribution and path planning, outputting the Preston front solution set, and providing multi-dimensional process options.

[0056] Preferably, the method further includes:

[0057] Construct a dynamic removal rate compensation model for minimizing the cumulative deviation between the theoretical removal rate and the actual removal rate, dynamically correcting the optimal dwell time matrix. The dynamic removal rate compensation model has the following formula:

[0058]

[0059] In the formula, is the set of time segments in the polishing process, is a specific time period in the set, is the expected removal amount calculated based on the dwell time distribution optimization model, is the measured removal amount.

[0060] Specifically, the removal amount data of each area is collected every 10 seconds to update , and the extended Kalman filter (EKF) is used to update the optimal dwell time matrix online to compensate for the removal rate drift. The single compensation amount does not exceed ±20% of the theoretical value to prevent overshoot. Finally, the dynamic removal rate compensation model is seamlessly connected with the dwell time optimization model to form a "prediction-execution-feedback" closed-loop control architecture, and the deviation between the theoretical removal rate and the actual removal rate is corrected in real time to ensure the stability of the polishing accuracy.

[0061] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations according to the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning, or limited experiments should be within the protection scope determined by the claims.

Claims

1. A high-precision polishing method for a large-aperture single-crystal silicon aspherical surface, characterized in that, It includes the following steps: S10: Obtain the full-aperture surface shape error distribution of the large-aperture single-crystal silicon aspheric surface and map it to a discrete grid; S20: Construct an optimized model for dwell time distribution and an optimized model for polishing path planning. Using the surface shape error parameters of the large-aperture single-crystal silicon aspheric surface as input, output the optimal dwell time distribution matrix and the polishing path sequence; S30: Based on the optimal dwell time distribution matrix and the polishing path sequence, perform polishing on the large-aperture single-crystal silicon aspheric surface; S40: After each polishing cycle, repeat steps S10 - S40 until the number of iterations is reached; For the optimized model of dwell time distribution in S20, the formula is as follows: Where W is the set of surface discretization grid regions of the large-aperture single-crystal silicon aspheric surface, Region x and Region y are the surface shape error parameters of regions x and y, and Synergy(Region x , Region y ) is the collaborative removal efficiency function of regions x and y.

2. The aspherical high-precision polishing method for large-diameter single-crystalline silicon according to claim 1, characterized in that S10 includes: Use a phase-shifting interferometer to measure the large-aperture single-crystal silicon aspheric surface, obtain the full-aperture surface shape error distribution, divide the surface of the large-aperture single-crystal silicon aspheric surface into grids, record the coordinates and surface shape error parameters for each grid, store them in matrix form, and the row and column indices correspond to the spatial positions.

3. A high-precision polishing method for a large-aperture single-crystal silicon aspherical surface according to claim 1, characterized in that For the collaborative removal efficiency function, the formula is as follows: where ∈ is the zero-eliminating constant, d xy is the Euclidean distance between regions x and y, and σ is the Gaussian kernel width.

4. A method for high-precision polishing of a large-aperture single-crystal silicon aspherical surface according to claim 1, characterized in that, For the optimized model of polishing path planning in S20, the formula is as follows: In the formula, Region x+1 is the surface form error parameter of the next polishing path point adjacent to region x, and Path(Regon x , Region x+1 ) is the path switching cost function.

5. A high-precision polishing method for a large-aperture single-crystal silicon aspherical surface according to claim 4, characterized in that, For the path switching cost function, the formula is as follows: where α is the error smoothing weight, β is the time efficiency weight, v x，x+1 is the speed of the polishing head moving from area x to x + 1, and d x，x+1 is the actual distance of the polishing head moving from area x to x + 1.

6. A method for high-precision polishing of a large-aperture single-crystal silicon aspherical surface according to claim 1, characterized in that, The output of the optimal dwell time distribution matrix and the polishing path sequence includes: Use the NSGA-II multi-objective genetic algorithm to perform pareto front optimization on the optimized model of dwell time distribution and the optimized model of polishing path planning. With the single-pass removal amount and the acceleration of the polishing head as constraint conditions, output the optimal dwell time distribution matrix and the polishing path sequence.

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