An exposure writing field splicing method of an electron beam spherical grating

Abstract

The application discloses an exposure writing field splicing method of an electron beam spherical grating, and the splicing process comprises the following steps: calculating the writing field size; calculating the writing field splicing interval of the spherical grating; focusing on a spherical reference point and locally exposing; identifying the writing field splicing error; adjusting and controlling the writing field splicing error; modifying and compensating the consistency of the writing field pattern of each region of the spherical grating; and exposing by the electron beam after converting the error of the whole region writing field. The exposure writing field splicing method of the electron beam spherical grating provided by the application guarantees the consistency of the writing field splicing and the pattern of each region of the spherical grating, reduces the surface roughness of the electron beam spherical grating, avoids the appearance of the secondary peak of the imaging Airy disk caused by the splicing error, and guarantees the imaging quality and the spectral resolution of the spectral instrument.

Description

Technical Field

[0001] This invention relates to the field of spherical grating technology, and in particular to an exposure writing field stitching method for electron beam spherical gratings. Background Technology

[0002] The spectral imaging system is the core component of an imaging spectrometer, determining its spectral resolution. As a crucial part of dispersive spectral imaging systems, the spectroscopic element, specifically the diffraction grating (which consists of equally spaced slits or a periodically distributed diffractive optical element), is a key component. The Offner spectroscopic imaging system, utilizing a convex spherical blazed grating, offers advantages such as compact structure, minimal spectral curvature, and high image quality, making it the preferred choice for spectroscopic imaging spectrometer systems.

[0003] Currently, the main methods for fabricating gratings include mechanical scribing, holographic ion beam etching, and electron beam exposure. Mechanical scribing uses a diamond scribing tool with a suitable angle to etch a blazed grating onto the grating substrate. It has advantages such as ease of operation, low time consumption, and low cost, but is currently only used for planar gratings. Holographic ion beam etching uses light interference to form sawtooth grooves on photoresist, and then uses an ion beam to etch the blazed grooves onto the grating substrate, enabling the etching of convex spherical blazed gratings. However, holographic ion beam etching struggles to achieve high precision in controlling the blazed groove shape of the photoresist and cannot process gratings with low line density. Electron beam exposure offers great flexibility in controlling the grating groove shape and blaze angle. The grating substrate can be spherical, meeting the grating line and surface shape requirements of ultraviolet to very long-wave infrared spectral imaging systems. It is the most precise and diffraction-efficient grating fabrication method.

[0004] When fabricating gratings using electron beam lithography, a field-writing stitching method is employed to stitch together small grating regions into a single grating. For spherical gratings, a larger field-writing curvature and a higher spherical arc increase the likelihood of focusing image distortion during stitching, leading to severe series of field-writing stitching errors. For example, field overlap at the stitching point results in repeated exposure of the overlapping area, causing excessively deep grooves in localized areas; field gaps at the stitching point cause underexposure or no-groove areas; and misalignment between fields can lead to misalignment of grating lines.

[0005] However, currently, no published literature proposes a clear method for writing and stitching blazed gratings during electron beam exposure spherical grating fabrication. Writing and stitching errors can lead to insufficient diffraction efficiency in local areas, affecting the average diffraction efficiency. In severe cases, it can cause sub-peaks and defocusing in the Airy disk, impacting the imaging spectral resolution. Therefore, this invention proposes an exposure and writing stitching method for electron beam spherical gratings. Through error identification, theoretical calculation, and process control, this method significantly reduces spherical writing and stitching errors, achieving precise stitching of spherical blazed grating lines and ensuring consistency in spherical grating lines and diffraction efficiency. Summary of the Invention

[0006] In view of the above-mentioned shortcomings of the prior art, the technical problem to be solved by the present invention is that errors are prone to occur in the electron beam exposure writing field stitching of spherical gratings. The present invention proposes an exposure writing field stitching method to control the writing field stitching error and achieve accurate stitching of spherical grating lines and high consistency of groove shape.

[0007] To achieve the above objectives, such as Figure 1 As shown, the present invention provides an exposure writing field stitching method for electron beam spherical gratings, comprising the following steps:

[0008] S1. Calculate the effective writing field size of the spherical grating based on the radius of curvature of the grating spherical substrate, the grating line density, and the electron beam writing field splicing adjustment range.

[0009] Specifically, the radius of curvature of the spherical substrate and the density of the grating lines are determined by the optical design results of the spectrometer, serving as the technical input for the fabrication of the spherical grating. The electron beam exposure writing field size is set to 1200μm*1200μm, the exposure pixel size is 5nm, the total number of writing field pixels is 240000*240000, the grating exposure area, i.e., the effective writing field size range, is 200μm*200μm-1200μm*1200μm, the spherical radius of curvature is greater than 50mm, and the spherical vector height excluding edge thickness is less than 10mm.

[0010] The formula for calculating the effective write field size in the x-direction is:

[0011]

[0012] SF x =N*d (2);

[0013] Where n is an integer representing the number of grating lines in a single write field; d represents the grating line period in mm; r represents the radius of curvature of the grating spherical substrate in mm; and N is an integer representing the maximum value of n, SF xLet n represent the size of the effective write field in the x-direction. The range of n is calculated according to formula (1). Then, after taking the maximum number of grating lines N, the size of the effective write field in the x-direction SF can be determined according to formula (2). x The formula for calculating the effective field size in the y-direction is:

[0014]

[0015] Among them SF y This represents the size of the effective writing field in the y direction, which can be obtained by taking the maximum value according to formula (3).

[0016] S2. Calculate the theoretical write field splicing spacing based on the grating curvature information and write field size.

[0017] Specifically, the theoretical formula for calculating the splicing spacing is as follows:

[0018]

[0019] Dy=SF y (5);

[0020] Where Dx represents the theoretical initial spacing of the writing field in the x-direction, and Dy represents the theoretical initial spacing of the writing field in the y-direction.

[0021] S3. Set reference points according to the ideal spherical grating aperture, focus on the reference points, and perform electron beam exposure and development on a portion of the area; the specific setting of reference points is as follows: set a planar stage reference point on the outer ring of the grating spherical substrate, the size of the planar stage is ≤1mm, and the number of reference points is ≥4.

[0022] Specifically, such as Figure 2 The image shows a cross-sectional view of a convex spherical blazed grating substrate including an edge reference plane. 1 represents the convex spherical region where grating electron beam exposure is performed, and 2 represents the reference plane where electron beam focusing is adjusted at the junction of 1 and 2. Figure 3 The image shows a top view of a convex spherical blazed grating substrate including an edge reference plane. In this view, 1 represents the convex spherical region, with the aperture being the actual effective aperture of the convex spherical grating; 2 is the reference plane, with a width less than 1 mm; and 3 is the electron beam focusing point at the junction of 1 and 2. Before focusing, at least the following steps are performed... Figure 2 The four points shown are located and their x and y positions are recorded to determine the center position of the convex spherical surface in the electron beam exposure system. Then, the leftmost point is selected for focusing adjustment. A satisfactory adjustment is determined by whether the boundary changes of the fine photoresist layer can be clearly seen at magnifications from 100x to 3600x under the electron beam microscope system. After focusing, the electron beam exposure curvature, aperture, and exposure position are set, with an exposure area size of 2*2 write fields. Development is then performed after exposure.

[0023] S4. Identify field splicing errors based on exposure and development results.

[0024] Specifically, such as Figure 4 As shown, 1-4 represent four write fields; 5 represents the write field interval error, that is, there is a gap between write fields, and the area is not exposed by electron beam, resulting in underexposure; 6 represents the write field overlap error, that is, the write fields overlap, and the area is overexposed by electron beam, resulting in overexposure; 7 represents the misalignment error, that is, the write fields are misaligned, causing the same column of grating lines to be not on a straight line, resulting in line misalignment.

[0025] S5. Adjust the error based on the field splicing results.

[0026] Specifically, based on step S4, the type of write field error is determined, and the interval compensation method is used for preliminary error adjustment: if a write field interval error occurs, the distance between write fields needs to be reduced; if a write field overlap error occurs, the distance between write fields needs to be increased; if a misalignment error occurs, the write field coordinate deflection angle needs to be changed. Generally, the interval compensation method cannot completely eliminate splicing errors due to coordinate scaling issues. Therefore, three sets of data can be used to derive and fit a formula to calculate the change in write field distance when the splicing error is zero. The write field interval error and write field overlap error can be fitted using the following formula:

[0027] Δx=A1dx 2 +B1dx+a1 (6);

[0028] Δy=A2dy 2 +B2dy+a2 (7);

[0029] Where Δx is the stitching error in the x-direction during the write field stitching process, x represents the change value of the write field spacing in the x-direction, Δy is the stitching error in the y-direction during the write field stitching process, y represents the change value of the write field spacing in the y-direction, and x and y when Δx and Δy are equal to 0 are the ideal interval or overlap error correction values.

[0030] If misalignment error occurs, the calculation formula is as follows:

[0031] C = arctan(c / SF) x (8);

[0032] ΔC=A3dC 2 +B3dC+a3 (9);

[0033] Where C represents the misalignment angle, c represents the misalignment error adjustment value, ΔC represents the misalignment error, and the field coordinate deflection angle needs to be changed. The above formula (9) is obtained by fitting the angle change curve through three angle switching. When ΔC equals 0, c is the ideal misalignment error correction value.

[0034] S6. Perform consistency compensation for writing field and raster pattern based on the multi-region writing field results and raster pattern results.

[0035] Specifically, writing field and raster pattern consistency compensation is achieved by controlling the change in exposure dose (DOSE) values ​​in the edge and center regions. That is, different DOSE values ​​are assigned to the center and edge regions. High consistency is determined by comparing the depth error between the center and edge regions through scanning changes in the DOSE value. The DOSE value range is 0-0.1, with a change precision of 0.01. The judgment criterion is that the edge raster groove corner depth error is less than 2%. The depth error calculation formula is as follows:

[0036]

[0037] Where d1 is the grating groove depth in the central region and d2 is the grating groove depth in the edge region.

[0038] S7. Calculate the full-area writing field error based on the spherical size, calculate the total number of writing fields based on the effective aperture of the grating, assign the correction value from step S5 to all writing fields, and assign the DOSE value from step S6 to the central and edge regions respectively. Then, perform exposure and development on the entire spherical grating. Refer to step S3 for grating electron beam exposure to ensure that the grating writing field distribution covers the effective light-transmitting aperture of the grating. The exposure sequence is S-shaped, with x-direction writing field stitching performed according to array stitching, and y-direction writing field stitching performed according to distance control.

[0039] The method yields a spherical grating with a writing field stitching interval or overlap error of less than 40 nm and a misalignment error angle of less than 0.001°.

[0040] The beneficial effects of this invention are as follows:

[0041] 1. This invention designs a writing field stitching method, which first performs local exposure, identifies the error category, and then performs error correction and process control. This solves the problem of writing field stitching errors that easily occur in the electron beam exposure process of spherical gratings, reduces the surface roughness of the electron beam spherical grating, avoids the occurrence of secondary peaks in the imaging Airy disk caused by stitching errors, achieves accurate stitching of spherical grating lines, and ensures the diffraction efficiency of the spherical grating and the high resolution of the final imaging spectrum.

[0042] 2. The present invention also achieves consistency compensation of writing field and grating pattern by controlling the change of exposure dose DOSE value in the edge region and the center region, thereby improving the consistency of groove shape and further ensuring the consistency of spherical grating scribing and diffraction efficiency. Attached Figure Description

[0043] Figure 1This is a schematic flowchart of the method of the present invention;

[0044] Figure 2 Cross-sectional view showing the distribution of the grating convex region and the reference surface region;

[0045] Figure 3 A top view showing the distribution of the grating's convex surface region and the reference surface region;

[0046] Figure 4 A schematic diagram illustrating the writing field splicing error of the grating convex surface;

[0047] Figure 5 Low-magnification optical microscope photograph before correction of grating convex surface splicing error;

[0048] Figure 6 This is a high-magnification optical microscope photograph after correction of splicing errors of the grating convex surfaces;

[0049] Figure 7 The test results show the groove shape in the central region of the grating convex surface;

[0050] Figure 8 The results show the groove shape test results for the edge region of the grating convex surface. Detailed Implementation

[0051] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present invention are shown in the accompanying drawings, and not all of them.

[0052] Example 1

[0053] This embodiment provides an exposure spelling method and analysis for spherical gratings, including the following steps:

[0054] S1. Based on the grating's spherical radius of curvature of 68.23 mm, grating line density of 710 lp / mm, and effective aperture of 24 mm, calculate the dimension SF of the writing field in the x-direction. x The size is 720.896 μm, and the dimension in the y direction is 772.335 μm.

[0055] S2. Based on the grating curvature information and the writing field size, the theoretical writing field splicing spacing Dx is calculated to be 724.552μm and Dy is 772.335μm.

[0056] S3. Set reference points according to the ideal spherical grating aperture, focus on the reference points, and set the reference positions as four points: up, down, left, and right. After adjusting the position of the exposure area, perform electron beam exposure and development.

[0057] S4. Identify writing field splicing errors based on exposure and development results; writing field overlap error occurs in the x-direction, writing field interval error occurs in the y-direction, and writing field misalignment error also occurs, such as... Figure 5 This is a schematic diagram of the initial write field splicing error. It can be seen that the write field splicing error can be clearly seen under a low-magnification optical microscope before the write field splicing error is corrected.

[0058] S5. Adjust the error based on the field splicing results;

[0059] Three sets of data were used to derive the formula and calculate the change in write distance when the stitching error is 0. The three sets of x-direction write distance changes were 1μm, 2μm, and 3μm, with corresponding stitching errors of Δx = -1.5μm, -0.3μm, and 0.7μm, respectively. Negative values ​​indicate write overlap error. The three sets of y-direction write distance changes were 1μm, 2μm, and 3μm, with corresponding stitching errors of Δy = -0.2μm, -0.9μm, and -1.7μm, respectively. Formulas (6) and (7) were obtained by fitting. Then, when Δx = 0, x = 2.335 μm (indicating that the writing distance should be increased) and when Δy = 0, y = -0.331 μm (indicating that the writing distance should be decreased) were calculated. At the same time, a misalignment error occurred, and the calculated misalignment angle was about 0.05°. The misalignment error was corrected by adjusting the writing angle. The misalignment error angles were corrected by 0.05°, 0.1°, and 0.15° respectively, and the corresponding misalignment angle errors were 0.01°, 0.08°, and 0.013°. Formula (9) was obtained by fitting. Then, when ΔC is 0, the misalignment angle correction value is 0.06°. After the splicing error correction, the x-direction error Δx is about 20 nm, the y-direction error Δy is about 30 nm, and the misalignment error angle value is close to 0°. Figure 6 The diagram shows the corrected field stitching. It can be seen that after the field stitching error is corrected, the field stitching error under a high-magnification optical microscope is almost eliminated.

[0060] S6. Perform consistency compensation for writing field and raster pattern based on the multi-region writing field results and raster pattern results.

[0061] Writing field and raster pattern consistency compensation is achieved by controlling the exposure DOSE values ​​of the edge and center regions to ensure consistency. The center DOSE value is 0.31, and the edge DOSE value is 0.30. The test results for local groove shapes at these two locations are as follows: Figure 7 and Figure 8 As shown, the depth of the grating groove at the center is 126nm, and the depth of the grating groove at the edge is 122nm, with a depth error of 1.6%, which is less than 2%.

[0062] S7. After converting the full-area writing field error according to the spherical size, expose and develop the entire spherical blazed grating. Refer to step S3 for grating electron beam exposure to ensure that the grating writing field distribution covers the effective light-passing aperture of the grating is 24mm and the number of grating writing fields is 896.

Claims

1. A method for exposure writing field stitching of an electron beam spherical grating, characterized in that, Includes the following steps: S1. Calculate the writing field size of the spherical grating; the formula for calculating the writing field size of the spherical grating is: ； ； Where n is an integer representing the number of grating lines in a single write field; d represents the grating line period in mm; r represents the radius of curvature of the grating spherical substrate in mm; and N is an integer representing the maximum value of n. Indicates the size of the write field in the x-direction; ； in This represents the dimension of the field in the y-direction, and the maximum value is taken according to the formula. S2. Calculate the theoretical write field splicing spacing; the formula for calculating the theoretical write field splicing spacing is: ； ； in This represents the theoretical initial spacing of the writing field in the x-direction. This represents the theoretical initial spacing of the writing field in the y-direction; S3. Perform partial electron beam exposure and development; S4. Identify field splicing errors based on exposure and development results; S5. Adjust the error based on the field splicing results.

2. The writing field splicing method as described in claim 1, characterized in that, The method further includes the following steps: S6. Perform consistency compensation for writing fields and raster patterns; S7. After converting the full-area writing field error according to the spherical size, expose and develop the entire spherical grating.

3. The writing field splicing method as described in claim 2, characterized in that, In step S1, the size of the spherical grating writing field is calculated based on the radius of curvature of the grating sphere, the grating line density, and the electron beam writing field splicing adjustment range.

4. The writing field splicing method as described in claim 1, characterized in that, In step S3, a reference point is set according to the ideal spherical grating aperture, the reference point is focused, and partial area electron beam exposure and development are performed. The method for setting reference points based on the ideal spherical grating aperture is as follows: set a planar stage reference point on the outer ring of the grating spherical substrate, with the size of the planar stage ≤ 1 mm and the number of reference points ≥ 4.

5. The writing field splicing method as described in claim 3, characterized in that, The types of writing field splicing errors in step S4 include: overlap error and interval error.

6. The writing field splicing method as described in claim 5, characterized in that, If overlap error or interval error occurs in step S5, the calculation formula for the write field error adjustment method is as follows: ； ； in dx represents the stitching error in the x-direction during the write field stitching process, and dx represents the change in the write field spacing in the x-direction. Let dy represent the stitching error in the y-direction during the write field stitching process, where dy represents the change in the write field spacing in the y-direction. A1, B1, a1, A2, B2, and a2 are all formula coefficients. , When x and y are equal to 0, they are the overlap error or interval error correction values.

7. The writing field splicing method as described in claim 2, characterized in that, The writing field and raster pattern consistency compensation in step S6 is achieved by controlling the change of exposure dose DOSE values ​​in the edge and center regions. Specifically, different DOSE values ​​are assigned to the center and edge regions. High consistency is determined by comparing the depth error between the center and edge regions through scanning changes in the DOSE value. The DOSE value range is 0-0.1, with a change precision of 0.

01. The consistency judgment criterion is that the edge raster groove corner depth error is less than 2%, and the depth error calculation formula is: ； Where d1 is the grating groove depth in the central region and d2 is the grating groove depth in the edge region.

8. The field splicing method as described in claim 7, characterized in that, The full-area write field error conversion in step S7 involves calculating the total number of write fields based on the effective aperture size of the grating, assigning the correction value from step S5 to all write fields, assigning the DOSE value from step S6 to the central and edge regions respectively, and then exposing and developing the entire spherical grating. The exposure sequence is S-shaped, the x-direction write field stitching is performed according to array stitching, and the y-direction write field stitching is performed according to distance control.

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