Manufacturing method of low-wavefront-error double-blazed grating for electron beam gray lithography

Abstract

The invention relates to a method for manufacturing a low-wavefront-error double-blazed grating for electron beam gray lithography, which comprises the following steps of: 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 average dose and the dose difference; through differential calculation and least square fitting, the relation between the dose parameter and the height and depth of the grating is optimized, and then high-precision manufacturing of the target grating is achieved. The method comprises the following specific steps: firstly, decomposing dose and grating parameters, and establishing a first mathematical model among grating height, depth and dose parameters; and then obtaining relational data through an experiment, performing optimization calculation by using the second mathematical model, and finally obtaining a dose parameter corresponding to the target grating. And finally, manufacturing the double-blazed grating with the low wavefront error according to the target parameters. According to the method, wavefront errors can be effectively reduced, the photoetching precision is improved, and the method has relatively good manufacturing consistency and is suitable for the production requirements of high-precision gratings.

Description

Technical Field

[0001] The invention belongs to the technical field of micro-nano processing, and in particular relates to a method for manufacturing a low-wavefront-error double-blazed grating by electron beam grayscale lithography. Background Art

[0002] Blazed gratings, as a high-resolution dispersive optical element, are widely used in the field of spectral imaging. However, after deviating from the blazing wavelength, the diffraction efficiency of the blazed grating drops rapidly, and the working bandwidth is limited, which cannot meet the use requirements of cross-band spectral systems. The use of double blazed gratings can obtain higher diffraction efficiency over a wider band, which can meet the diffraction requirements of broadband and promote the development of cross-band spectral imaging systems. However, there are new difficulties in the manufacture of double blazed gratings: the center height matching method of gratings in different regions will affect the diffraction wavefront. Only when the center heights of gratings in different regions are aligned can the diffraction wavefront error be minimized and the best imaging effect be achieved. At present, the main production methods of double blazed gratings are mechanical characterization, ion beam etching and electron beam grayscale lithography. Among them, the double blazed gratings manufactured by electron beam grayscale lithography have the characteristics of low roughness and good surface linearity, which can achieve better spectroscopic and imaging effects. However, the current processing scheme is based on simulation, and there is a deviation between the distribution of exposure dose and actual processing, which results in the inability to completely align the center heights of gratings in different areas and the degradation of the diffraction wavefront quality, affecting the application of double-blazed gratings manufactured by electron beam grayscale lithography technology.

[0003] In view of the above problems, it is urgent to design a low wavefront error double blazed grating production technology based on electron beam grayscale lithography to achieve double blazed grating processing with good wavefront quality. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for producing a double-blazed grating with low wavefront error by electron beam grayscale lithography.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The present invention provides a method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography, comprising the following steps:

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

[0008] Step S2: constructing a first mathematical model between grating height, grating depth, average dose and 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 according to 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 relationship data into the second mathematical model to obtain the coefficient value of the second mathematical model through linear function fitting, and substituting the coefficient value 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 lithography 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 between the average dose, dose difference and grating depth, and G is the function between the 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] Among them, 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.

[0024] Furthermore, the step S5 includes the following steps:

[0025] Acquire the relationship data of step S4, including the grating height and grating depth corresponding to different average doses and dose differences;

[0026] According to the relationship data, the corresponding grating height change and grating depth change under different average dose changes and dose difference changes 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] Among them, A1, A2, A3, and A4 are the first coefficient, the second coefficient, the third coefficient, and the fourth coefficient respectively;

[0031] The grating height changes and grating depth changes corresponding to 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 coefficients A1, A2, A3, and A4. The calculated coefficients A1, A2, A3, and A4 are substituted into the second mathematical model.

[0032] Furthermore, the least squares formula is:

[0033]

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

[0035] Obtain target grating parameters, including target grating height and target grating depth;

[0036] Taking a set of relational data in the single variable experiment as the initial value, the difference between the target grating height, the target grating depth and the relational data grating height and 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) The present invention can accurately describe and control the changing relationship between grating height, grating depth, average dose and dose difference by constructing a mathematical model between these parameters. The establishment of this mathematical model provides a theoretical basis for subsequent optimization and adjustment, and effectively improves the accuracy of the lithography process.

[0040] (2) The present invention fits the relationship data between the grating parameters and the dose parameters, and can efficiently obtain the dose parameters of the target grating through the simplified second mathematical model. This optimization method avoids the wavefront distortion caused by dose error in traditional electron beam lithography, and ensures the high quality and low wavefront error of the final grating.

[0041] (3) The second mathematical model obtained by differential calculation and least squares fitting in the present invention can effectively adjust the grating depth and grating height changes 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 the target grating parameters and adjusts the dose parameters in combination with the mathematical model to ensure that the final grating meets the expected design requirements in terms of height and depth. This method can greatly improve the manufacturing accuracy and stability of the target grating in precision manufacturing.

[0043] (5) The present invention establishes a blazed grating model for electron beam grayscale lithography, determines the dose function differential relationship of the grating parameters through experimental fitting, and solves the specific target dose parameters to achieve the center alignment of the blazed gratings in different areas. Compared with the prior art, this technology can effectively realize the double blazed grating processing with low wavefront error, and promotes the application of double blazed gratings. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0045] Figure 2 The electron beam grayscale lithography dose-grating model diagram for the blazed grating;

[0046] Figure 3 Four groups of univariate experimental results of dose parameters and grating parameters;

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

[0048] Figure 5 Wavefront quality measurement results of the fabricated double blazed grating. DETAILED DESCRIPTION

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

[0050] Embodiment 1:

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

[0052] Step S1: decomposing the dose parameter of the electron beam into an average dose and a dose difference, and decomposing the grating parameter into a grating height and a 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 according to 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 relationship data into the second mathematical model to obtain the coefficient value of the second mathematical model through linear function fitting, and substituting the coefficient value 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 lithography area.

[0060] The exposure intensity of the electron beam in a section of the grating area varies 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 between the average dose, dose difference and grating depth, and G is the function between the 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] Among them, 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 comprises the following steps:

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

[0071] According to the relationship data, the corresponding grating height change and grating depth change under different average dose changes and dose difference changes are calculated;

[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, the second coefficient, the third coefficient, and the fourth coefficient respectively;

[0076] The grating height changes and grating depth changes corresponding to 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 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 comprises 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, the target grating depth and the relational data grating height and 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] Embodiment 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 manufacturing technology based on electron beam grayscale lithography, comprising the following steps:

[0086] Model establishment of electron beam grayscale lithography of blazed grating:

[0087] like Figure 2 As shown, the dose parameter is decomposed into the average dose and the dose range, and the grating parameter is 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] Expressed in differential form:

[0091]

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

[0093] Univariate Experiments for Grayscale Lithography:

[0094] In a certain small range, the blazed grating in one area is subjected to single variable experiments of average dose and dose difference, and the grating height and grating depth are measured. The corresponding data are fitted with a linear function to obtain the partial derivatives in the above formula.

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

[0096] Taking a set of data in the single variable experiment as the initial value, the target grating height and grating depth are determined according to the structural parameters of the blazed grating in another area, and the target dose parameters are obtained by substituting them into the above formula and performing the final double blazed grating processing.

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

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

[0099] The electron beam grayscale lithography model of double blazed grating replaces the partial derivatives in the differential function relationship between grating parameters and dose parameters with the slope of a linear function fitted by a single variable experiment in a small range.

[0100] The target dose parameters are solved by using the differential relationship after substitution, taking a set of data in the single variable experiment as the initial value, determining the target grating height and grating depth according to the structural parameters of the blazed grating in another area, and calculating the target dose parameters.

[0101] According to the electron beam grayscale lithography process, this embodiment provides a low wavefront error double blazed grating manufacturing technology based on electron beam grayscale lithography. The processing structure is a double blazed grating with a period of 9um at 1.8° and 3.5°. The embodiment is a dose parameter solution process of the 1.8° blazed grating. Figure 2 Shown is a schematic diagram of the electron beam grayscale lithography technology for double blazed gratings, wherein the electron beam grayscale lithography technology for double blazed gratings is to establish an electron beam grayscale lithography model for blazed gratings, and to solve the target dose parameters by calculating partial derivatives through single variable experiments 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 photolithography 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, and their relationship is expressed in differential form as follows:

[0105]

[0106] Univariate Experiments for Grayscale Lithography:

[0107] Single variable experiments of average dose and dose difference were conducted in a certain small range and grating height and grating depth were measured. The specific steps are as follows:

[0108] A 1.5 μm thick PMMA photoresist was spin-coated on the substrate, and 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. A 100 keV electron beam was used for exposure 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 grating:

[0113] A set of data in the single variable experiment is used as the initial value. Here, the average dose of 226 and the dose difference of 50 are selected as the initial values. The target grating height and grating depth are substituted 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, and 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. A 100 keV electron beam was used for exposure 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 below: Figure 4 As shown in Figure 2, the blazed gratings in the two regions are basically aligned. The wavefront quality measurement results of the manufactured double blazed grating are shown in Figure 2. Figure 5 As shown, 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, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0117] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for producing a double-blazed grating with low wavefront error by electron beam grayscale lithography, characterized in that: The following steps are involved: Step S1: decomposing the dose parameter of the electron beam into an average dose and a dose difference, and decomposing the grating parameter into a grating height and a 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 according to 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 relationship data into the second mathematical model to obtain the coefficient value of the second mathematical model through linear function fitting, and substituting the coefficient value into the second mathematical model; 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.

2. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: The average dose is the average exposure intensity of the electron beam in the photolithography area.

3. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: 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.

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

5. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: The first mathematical model between the grating height, grating depth, average dose and dose difference is: Depth=F (average dose, dose range) Height=G(average dose,dose range) Among them, Depth is the grating depth, Height is the grating height, average dose is the average dose, dose range is the dose difference, F is the function between the average dose, dose difference and grating depth, and G is the function between the average dose, dose difference and grating height.

6. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: The step S3 comprises the following steps: differentiating the first mathematical model to obtain a second mathematical model.

7. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: The second mathematical model is: Among them, 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.

8. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: The step S5 comprises the following steps: Acquire the relationship data of step S4, including the grating height and grating depth corresponding to different average doses and dose differences; According to the relationship data, the corresponding grating height change and grating depth change under different average dose changes and dose difference changes are calculated; The second mathematical model is simplified to obtain a simplified second mathematical model: Δ(Depth)=A1×Δ(average dose)+A2×Δ(dose range) Δ(Height)=A3×Δ(average dose)+A4×Δ(dose range) Among them, A1, A2, A3, and A4 are the first coefficient, the second coefficient, the third coefficient, and the fourth coefficient respectively; The grating height changes and grating depth changes corresponding to 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 coefficients A1, A2, A3, and A4. The calculated coefficients A1, A2, A3, and A4 are substituted into the second mathematical model.

9. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 8, characterized in that: The least squares formula is:

10. The method for manufacturing a double-blazed grating with low wavefront error by electron beam grayscale lithography according to claim 1, characterized in that: 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, the target grating depth and the relational data grating height and 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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