A method for manufacturing a low wavefront error double blazed grating by electron beam gray scale lithography

Abstract

The application relates to a method for manufacturing a low-wavefront-error double-flashing grating by electron beam gray-scale lithography, which comprises the following steps: firstly, decomposing dose parameters of an electron beam into average dose and dose difference, decomposing grating parameters into grating height and grating depth, and constructing a mathematical model between the two; secondly, optimizing the relationship between the dose parameters and the grating height and depth through differential calculation and least square fitting, and then realizing high-precision manufacturing of a target grating; and finally, manufacturing the low-wavefront-error double-flashing grating according to the target parameters. The method can effectively reduce the wavefront error, improve the lithography precision, has good manufacturing consistency, and is suitable for the production requirements of high-precision gratings.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of micro-nano processing, and particularly relates to a low-wave-front-error double-blazed grating manufacturing method based on electron beam gray-scale lithography. BACKGROUND

[0002] As a high-resolution dispersive optical element, the blazed grating is widely used in the field of spectral imaging. However, after deviating from the blazed wavelength, the diffraction efficiency of the blazed grating rapidly decreases, and the working bandwidth is limited, which cannot meet the use requirements of the cross-band spectral system. The use of double-blazed gratings can obtain high diffraction efficiency in a wide waveband, which can meet the diffraction requirements of the wideband and promote the development of the cross-band spectral imaging system. However, there are new difficulties in the manufacturing of the double-blazed gratings: the center height matching mode of the gratings in different regions will affect the diffraction wavefront, and only when the center heights of the gratings in different regions are aligned, the diffraction wavefront error can reach the minimum, and the best imaging effect can be achieved. At present, the main manufacturing methods of the double-blazed gratings are mechanical engraving, ion beam etching and electron beam gray-scale lithography, etc. The double-blazed gratings manufactured by the electron beam gray-scale lithography have the characteristics of low roughness and good surface linear degree, and can achieve better spectral splitting and imaging effect. However, the current processing scheme is based on simulation, and there is deviation between the exposure dose distribution and the actual processing, which leads to the fact that the center heights of the gratings in different regions cannot be completely aligned, the quality of the diffraction wavefront decreases, and the application of the double-blazed gratings manufactured by the electron beam gray-scale lithography is affected.

[0003] In view of the above problems, it is urgent to design a low-wave-front-error double-blazed grating manufacturing technology based on electron beam gray-scale lithography to realize the processing of the double-blazed gratings with good wavefront quality. SUMMARY

[0004] The purpose of the application is to overcome the defects of the prior art and provide a low-wave-front-error double-blazed grating manufacturing method based on electron beam gray-scale lithography.

[0005] The purpose of the application can be achieved by the following technical scheme:

[0006] The application provides a low-wave-front-error double-blazed grating manufacturing method based on electron beam gray-scale lithography, which comprises the following steps:

[0007] Step S1: decompose the dose parameters of the electron beam into an average dose and a dose difference, and decompose the grating parameters into a grating height and a grating depth;

[0008] Step S2: construct a first mathematical model between the grating height, the grating depth and the average dose, and the dose difference;

[0009] Step S3: generating a second mathematical model between the grating height variation, the grating depth variation, the average dose variation, and the dose difference variation based on the first mathematical model between the grating height, the grating depth, the average dose, and the dose difference;

[0010] Step S4: Obtaining the relationship data between the average dose, the dose difference, the grating height, and the grating depth in the form of a single variable experiment;

[0011] Step S5: Substituting the relational data into the second mathematical model to obtain coefficient values ​​of the second mathematical model through linear function fitting, and substituting the coefficient values ​​into the second mathematical model;

[0012] Step S6: Obtain target grating parameters, calculate dose parameters corresponding to the target grating according to the target grating parameters and the second mathematical model, and produce the target grating according to the dose parameters corresponding to the target grating.

[0013] Furthermore, the average dose is the average exposure intensity of the electron beam in the photolithography area.

[0014] Furthermore, the dose difference is the absolute value of the difference between the maximum exposure intensity and the minimum exposure intensity of the electron beam in the photolithography area.

[0015] Furthermore, the exposure intensity of the electron beam in a section of the grating area varies linearly.

[0016] Furthermore, the first mathematical model between the grating height, grating depth, average dose, and dose difference is:

[0017] Depth=F(average dose,dose range)

[0018] Height=G(average dose,dose range)

[0019] Where Depth is the grating depth, Height is the grating height, average dose is the average dose, doserange is the dose difference, F is the function of average dose, dose difference and grating depth, and G is the function of average dose, dose difference and grating height.

[0020] Furthermore, the step S3 includes the following steps: differentiating the first mathematical model to obtain a second mathematical model.

[0021] Furthermore, the second mathematical model is:

[0022]

[0023] Wherein, Δ(Depth) is the grating depth variation, Δ(Height) is the grating height variation, Δ(average dose) is the average dose variation, Δ(dose range) is the dose difference variation, is the first coefficient, is the second coefficient, is the third coefficient, is the fourth coefficient.

[0024] Further, the step S5 comprises the following steps:

[0025] The relationship data of the step S4 comprises the corresponding grating height and grating depth under different average dose and dose difference;

[0026] According to the relationship data, the corresponding grating height variation and grating depth variation under different average dose variation and dose difference variation are calculated;

[0027] The second mathematical model is simplified to obtain a simplified second mathematical model:

[0028] Δ(Depth)=A1×Δ(average dose)+A2×Δ(dose range)

[0029] Δ(Height)=A3×Δ(average dose)+A4×Δ(dose range)

[0030] Wherein, A1, A2, A3, A4 are the first coefficient, the second coefficient, the third coefficient and the fourth coefficient respectively;

[0031] The corresponding grating height variation and grating depth variation under different average dose variation and dose difference variation are substituted into the simplified second mathematical model, the least square method is used to fit the simplified second mathematical model, the coefficients A1, A2, A3, A4 are obtained, and the calculated coefficients A1, A2, A3, A4 are substituted into the second mathematical model.

[0032] Further, the least square method formula is:

[0033]

[0034] Further, the step S6 comprises the following steps:

[0035] The target grating parameters are obtained, including the target grating height and the target grating depth;

[0036] Taking a group of relationship data in the single variable experiment as the initial value, the difference between the target grating height, the target grating depth and the relationship data grating height, grating depth is calculated;

[0037] The calculated difference is substituted into the second mathematical model to obtain the average dose change and the dose difference change. The average dose and the dose difference of the target grating are calculated according to the average dose and the dose difference of the relationship data and the calculated average dose change and the dose difference change. The target grating is produced according to the average dose and the dose difference of the target grating.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (1) By constructing a mathematical model between grating height, grating depth, average dose, and dose difference, the present invention can accurately describe and control the changing relationship between these parameters. The establishment of this mathematical model provides a theoretical basis for subsequent optimization and adjustment, effectively improving the accuracy of the lithography process.

[0040] (2) By fitting the relationship between grating parameters and dose parameters, the present invention can efficiently determine the dose parameters of the target grating using a simplified second mathematical model. This optimization method avoids the wavefront distortion caused by dose errors in traditional electron beam lithography, ensuring high quality and low wavefront error in the final grating.

[0041] (3) The second mathematical model obtained by differential calculation and least square fitting in the present invention can effectively adjust the changes in grating depth and grating height under different conditions, thereby improving the consistency and accuracy of the grating during the lithography process and reducing the lithography error caused by uneven dose.

[0042] (4) The present invention obtains target grating parameters and adjusts the dose parameters based on a mathematical model to ensure that the final grating meets the expected design requirements in terms of height and depth. This method can significantly improve the production accuracy and stability of the target grating in precision manufacturing.

[0043] (5) This invention establishes a blazed grating model for electron beam grayscale lithography, experimentally fits the dose function differential relationship of the grating parameters, and solves the specific target dose parameters to achieve center alignment of the blazed gratings in different regions. Compared with existing technologies, this technology can effectively achieve low wavefront error in the processing of dual blazed gratings, promoting the application of dual blazed gratings. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart of the method of the present invention;

[0045] Figure 2 This is the electron beam grayscale lithography dose-grating model diagram of the blazed grating;

[0046] Figure 3 The graphs show the four groups of univariate experimental results of dose parameters and grating parameters;

[0047] Figure 4 AFM 3D profile of the final fabricated double blazed grating;

[0048] Figure 5 Figure 2 shows the wavefront quality measurement results of the fabricated double-blazed grating. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0050] Example 1:

[0051] This embodiment provides a method for fabricating a double-blazed grating with low wavefront error using electron beam grayscale lithography. Figure 1 As shown, the following steps are included:

[0052] Step S1: decomposing the electron beam dose parameter into average dose and dose difference, and decomposing the grating parameter into grating height and grating depth;

[0053] Step S2: constructing a first mathematical model between grating height, grating depth, average dose, and dose difference;

[0054] Step S3: generating a second mathematical model between the grating height variation, the grating depth variation, the average dose variation, and the dose difference variation based on the first mathematical model between the grating height, the grating depth, the average dose, and the dose difference;

[0055] Step S4: Obtaining the relationship data between the average dose, the dose difference, the grating height, and the grating depth in the form of a single variable experiment;

[0056] Step S5: Substituting the relational data into the second mathematical model to obtain coefficient values ​​of the second mathematical model through linear function fitting, and substituting the coefficient values ​​into the second mathematical model;

[0057] Step S6: Obtain target grating parameters, calculate dose parameters corresponding to the target grating according to the target grating parameters and the second mathematical model, and produce the target grating according to the dose parameters corresponding to the target grating.

[0058] The average dose is the average exposure intensity of the electron beam in the photolithography area.

[0059] The dose difference is the absolute value of the difference between the maximum exposure intensity and the minimum exposure intensity of the electron beam in the photolithography area.

[0060] The exposure intensity of the electron beam in a section of the grating area changes linearly.

[0061] The first mathematical model between the grating height, grating depth, average dose, and dose difference is:

[0062] Depth=F(average dose,dose range)

[0063] height=G(average dose,dose range)

[0064] Where Depth is the grating depth, Height is the grating height, average dose is the average dose, doserange is the dose difference, F is the function of average dose, dose difference and grating depth, and G is the function of average dose, dose difference and grating height.

[0065] Wherein, step S3 includes the following steps: differentiating the first mathematical model to obtain a second mathematical model.

[0066] Among them, the second mathematical model is:

[0067]

[0068] Wherein, Δ(Depth) is the change of grating depth, Δ(Height) is the change of grating height, Δ(averagedose) is the change of average dose, and Δ(dose range) is the change of dose difference. is the first coefficient, is the second coefficient, is the third coefficient, is the fourth coefficient.

[0069] Wherein, step S5 includes the following steps:

[0070] Obtaining the relationship data of step S4, including the grating height and grating depth corresponding to different average doses and dose differences;

[0071] Calculate the corresponding grating height change and grating depth change under different average dose changes and dose difference changes according to the relationship data;

[0072] The second mathematical model is simplified to obtain a simplified second mathematical model:

[0073] Δ(Depth)=A1×Δ(average dose)+A2×Δ(dose range)

[0074] Δ(Height)=A3×Δ(average dose)+A4×Δ(dose range)

[0075] Among them, A1, A2, A3, and A4 are the first coefficient, second coefficient, third coefficient, and fourth coefficient respectively;

[0076] The corresponding grating height changes and grating depth changes under different average dose changes and dose difference changes are substituted into the simplified second mathematical model, and the simplified second mathematical model is fitted using the least squares method to obtain the coefficients A1, A2, A3, and A4. The calculated coefficients A1, A2, A3, and A4 are substituted into the second mathematical model.

[0077] Among them, the least squares formula is:

[0078]

[0079] Wherein, step S6 includes the following steps:

[0080] Obtain target grating parameters, including target grating height and target grating depth;

[0081] Taking a set of relational data in the single variable experiment as the initial value, the difference between the target grating height, target grating depth and the relational data grating height, grating depth is calculated;

[0082] The calculated difference is substituted into the second mathematical model to obtain the average dose change and the dose difference change. The average dose and the dose difference of the target grating are calculated according to the average dose and the dose difference of the relationship data and the calculated average dose change and the dose difference change. The target grating is produced according to the average dose and the dose difference of the target grating.

[0083] Example 2:

[0084] The parts not mentioned in this embodiment are the same as those in embodiment 1.

[0085] This embodiment provides a low wavefront error double-blazed grating fabrication technology based on electron beam grayscale lithography, including the following steps:

[0086] Establishment of electron beam grayscale lithography model of blazed grating:

[0087] like Figure 2 As shown in Figure 2, the dose parameters are decomposed into the average dose and the dose range, and the grating parameters are decomposed into the grating height and the grating depth. Obviously, the grating height and the grating depth are related to the average dose and the dose range, that is:

[0088] Depth = F(average dose, dose range)

[0089] Height = G(average dose, dose range)

[0090] In differential form, it is:

[0091]

[0092] In a certain range, the partial derivative in the above formula is the slope of the corresponding function.

[0093] Univariate experiment of gray scale lithography:

[0094] In a small range, univariate experiments of average dose and dose difference are respectively performed on one area of the blazed grating, and the grating height and grating depth are measured. The corresponding data is fitted by a linear function respectively, and the partial derivative in the above formula is obtained.

[0095] Solution of dose parameters and processing of double blazed gratings:

[0096] Using a set of data in the univariate experiment as the initial value, the target grating height and grating depth are determined according to the structure parameters of the blazed grating in another area, and the target dose parameters are solved by substituting into the above formula and finally processed into double blazed gratings

[0097] The electron beam gray scale lithography model of double blazed gratings decomposes the grating parameters of blazed gratings into grating height and grating depth, and decomposes the dose parameters into average dose and dose difference.

[0098] The electron beam gray scale lithography model of double blazed gratings expresses the functional relationship of grating parameters and dose parameters as a differential relationship.

[0099] The electron beam gray scale lithography model of double blazed gratings substitutes the slope of the linear function fitted by the univariate experiment in the partial derivative of the differential functional relationship of grating parameters and dose parameters in a small range.

[0100] The solution of target dose parameters uses the substituted differential relationship, uses a set of data in the univariate experiment as the initial value, determines the target grating height and grating depth according to the structure parameters of the blazed grating in another area, and calculates the target dose parameters.

[0101] According to the electron beam grayscale lithography process, this embodiment provides a low wavefront error double blazed grating production technology based on electron beam grayscale lithography. The processing structure is a double blazed grating with a period of 9um and 1.8° and 3.5°. The embodiment is the dose parameter solution process of the 1.8° blazed grating. Figure 2 The figure shows a schematic diagram of the electron beam grayscale lithography technology for double blazed gratings, which is to establish an electron beam grayscale lithography model for blazed gratings, calculate partial derivatives through single variable experiments to solve the target dose parameters to achieve center-aligned double blazed grating processing.

[0102] Next, a method embodiment of the present invention is given, wherein the method comprises the following steps:

[0103] Grayscale lithography model of blazed grating:

[0104] The dose parameters are decomposed into average dose and dose range, and the grating parameters are decomposed into grating height and grating depth. Their relationship is expressed in differential form as follows:

[0105]

[0106] Univariate experiment for grayscale lithography:

[0107] Conduct single-variable experiments on average dose and dose difference within a certain small range and measure grating height and grating depth. The specific steps are as follows:

[0108] A 1.5 μm thick PMMA photoresist was spin-coated on the substrate. The exposure pattern was evenly divided into 20 layers within a 9 μm period. The dose parameters of each layer were determined by the average dose and the dose difference. Exposure was performed using a 100 keV electron beam at 30 nA, followed by development in an IPA:H2O=2:1 solution for 4 min.

[0109] Fit the corresponding data with a linear function to obtain the partial derivatives in the above formula, such as Figure 3 As shown, the relationship obtained here is:

[0110] Δ(Depth)=6.5×Δ(average dose)-1.6×Δ(dose range)

[0111] Δ(Height)=2×Δ(average dose)+2.5×Δ(dose range)

[0112] Solution of dose parameters and processing of double-blazed gratings:

[0113] Taking a set of data from the single-variable experiment as the initial value, here we select the average dose of 226 and the dose difference of 50 as the initial value, and substitute the target grating height and grating depth into the above formula to solve. According to the structural parameters of the 3.5° blazed grating, the target grating height of the 1.8° blazed grating here is 280nm, and the target grating depth is 550nm. The target dose parameters calculated are the average dose of 230μC / cm 2 , dose difference 48μC / cm 2 , and perform the final double blazed grating processing. The specific steps are:

[0114] A 1.5 μm thick PMMA photoresist was spin-coated on the substrate. The exposure pattern was evenly divided into 20 layers within a 9 μm period. The dose parameters of each layer were determined by the average dose and the dose difference. Exposure was performed using a 100 keV electron beam at 30 nA, followed by development in an IPA:H2O=2:1 solution for 4 min.

[0115] The AFM three-dimensional profile of the final double blazed grating is shown in Figure 2. Figure 4 As shown in Figure 2, the blazed gratings in the two regions are basically aligned. The wavefront quality measurement results of the fabricated double blazed grating are shown in Figure 2. Figure 5 As shown in the figure, the measured value of the wavefront error PV of the 0th order diffraction is lower than 0.2λ (test wavelength 632.8nm).

[0116] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0117] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for fabricating a double-blazed grating with low wavefront error using electron beam grayscale lithography, characterized in that: The following steps are involved: Step S1: decomposing the electron beam dose parameter into average dose and dose difference, and decomposing the grating parameter into grating height and grating depth; Step S2: constructing a first mathematical model between grating height, grating depth, average dose, and dose difference; Step S3: generating a second mathematical model between the grating height variation, the grating depth variation, the average dose variation, and the dose difference variation based on the first mathematical model between the grating height, the grating depth, the average dose, and the dose difference; Step S4: Obtaining the relationship data between the average dose, the dose difference, the grating height, and the grating depth in the form of a single variable experiment; Step S5: Substituting the relational data into the second mathematical model to obtain coefficient values ​​of the second mathematical model through linear function fitting, and substituting the coefficient values ​​into the second mathematical model; Step S6: acquiring target grating parameters, calculating dose parameters corresponding to the target grating according to the target grating parameters and the second mathematical model, and producing the target grating according to the dose parameters corresponding to the target grating; The average dose is the average exposure intensity of the electron beam in the photolithography area; The dose difference is the absolute value of the difference between the maximum exposure intensity and the minimum exposure intensity of the electron beam in the lithography area; The first mathematical model between the grating height, grating depth, average dose and dose difference is: in, is the grating depth, is the grating height, is the average dose, is the dose difference, is a function of the average dose, dose difference and grating depth, It is a function of the average dose, dose difference and grating height; Said step S3 comprises the following steps: differentiating the first mathematical model to obtain a second mathematical model; The second mathematical model is: in, is the grating depth variation, is the grating height variation, is the average dose change, is the dose difference variation, is the first coefficient, is the second coefficient, is the third coefficient, is the fourth coefficient.

2. The method for fabricating a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, wherein: The exposure intensity of the electron beam in a section of the grating area varies linearly.

3. The method for fabricating a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, wherein: The step S5 comprises the following steps: Obtaining the relationship data of step S4, including the grating height and grating depth corresponding to different average doses and dose differences; Calculate the corresponding grating height change and grating depth change under different average dose changes and dose difference changes according to the relationship data; The second mathematical model is simplified to obtain a simplified second mathematical model: in, 、 They are the first coefficient, the second coefficient, the third coefficient, and the fourth coefficient respectively; Substitute the corresponding grating height changes and grating depth changes under different average dose changes and dose difference changes into the simplified second mathematical model, and use the least squares method to fit the simplified second mathematical model to obtain the coefficients 、 , the calculated coefficients 、 Substitute into the second mathematical model.

4. The method for fabricating a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 3, wherein: The least squares formula is: 。 5. The method for fabricating a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, wherein: The step S6 comprises the following steps: Obtain target grating parameters, including target grating height and target grating depth; Taking a set of relational data in the single variable experiment as the initial value, the difference between the target grating height, target grating depth and the relational data grating height, grating depth is calculated; The calculated difference is substituted into the second mathematical model to obtain the average dose change and the dose difference change. The average dose and the dose difference of the target grating are calculated according to the average dose and the dose difference of the relationship data and the calculated average dose change and the dose difference change. The target grating is produced according to the average dose and the dose difference of the target grating.

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