Design method of X-ray grazing incidence wide spectrum multilayer film structure
Through coupled wave theory and numerical calculation optimization, an X-ray non-periodic multi-layer film structure suitable for soft X-ray and tough X-ray bands was designed, which solved the problem that the existing technology could not effectively adapt to the wide spectrum, and achieved efficient multi-layer Membrane structure design and optimization provide an explanation of the relationship between performance and structure.
Patent Information
- Application Number
- CN202411144212.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-20
- Publication Date
- 2024-12-17
AI Technical Summary
The existing X-ray wide spectrum multi-layer film structure design method cannot effectively adapt to soft X-ray and tough X-ray bands, especially in grazing incident mode, and the existing methods rely on a large number of computing resources and cannot intuitively reveal multi-layers. The relationship between membrane structure and performance.
Based on the coupled wave theory, an analytical theory of X-ray non-periodic multilayer film structure was established, and combined with numerical calculation optimization, a multilayer film structure with high reflectivity performance under the target spectral reflectivity response distribution was obtained, and reflectivity expression was derived through analytical theory. The formula and recursive formula optimize the film layer thickness and film logarithm to achieve efficient numerical optimization.
A multi-layer film structure with high reflectivity performance under a wide spectrum is realized, which significantly shortens the optimization time, improves convergence, and provides a physical explanation of the reflectivity of a non-periodic multi-layer film structure, simplifies the system structure, and is suitable for Soft and tough X-ray bands.
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Abstract
Description
Technical Field
[0001] The invention relates to the technical field of reflectors and diffraction gratings, and in particular to a design method for an X-ray grazing-incidence wide-spectrum multilayer film structure. Background Art
[0002] The soft X-ray and tough X-ray bands cover the characteristic spectral lines of many elements, including the K absorption edge of P, S, and Cl, the L absorption edge of Mo and Ru, and the M absorption edge of Pt and Au. Through spectral detection and analysis, information such as the chemical composition, atomic structure, and electronic configuration of the substance can be obtained, providing a powerful detection tool for multidisciplinary research such as petrochemicals, new energy devices, and life sciences. Mirrors and diffraction gratings are the core components of X-ray monochromators and spectral systems, and their efficiency determines the important indicator of the system's photon flux. The traditional single-layer film grating has low diffraction efficiency, which limits the photon flux of the monochromator and spectrometer system. Coating multilayer films on mirrors and grating elements can greatly improve the efficiency of the X-ray band and significantly improve the performance of the components in this band.
[0003] However, the currently widely used multilayer film reflectors and multilayer film gratings are mainly based on periodic multilayer film structures, and the bandwidth in the X-ray band (Δλ / λ=~1 / 200-1 / 20) is very narrow. To achieve operation under a wide spectrum, the first method is to deposit different multilayer film structures on different areas of the substrate, each structure corresponds to a bandwidth, and adjust the substrate posture to change the incident angle and the multilayer film area to achieve operation under multiple energy points. Due to the limited coating area, it is only suitable for operation at a small number of energy points. The second method is to deposit a non-periodic multilayer film with a wide spectral reflectivity on the substrate. Compared with the former, the latter can simplify the structure of the monochromator or spectrometer, and better integrate with the existing X-ray monochromator and spectrometer structure, and at the same time can achieve a wide spectral response under transient conditions.
[0004] There have been studies on non-periodic multilayer films for near-normal incident extreme ultraviolet bands and hard X-rays with low penetration and absorption, but since various materials have strong absorption for soft X-rays and tough X-rays, and the reflectors and gratings mainly work in grazing incidence mode, the existing theoretical methods for X-ray wide-spectrum multilayer films cannot adapt well to this band. Currently, the multilayer film structure design methods reported internationally for soft X-rays and tough X-rays, such as the Chinese patent CN 105700134 B, which discloses a method for designing X-ray wide-spectrum multilayer film blazed gratings, mainly rely on direct numerical optimization, which usually requires a lot of computing resources and cannot intuitively reveal the relationship between the multilayer film structure and performance. Summary of the invention
[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method for designing X-ray wide spectrum multilayer film structures by combining analytical theory with numerical calculation, so as to obtain a multilayer film structure with high reflectivity performance under the target spectral reflectivity response distribution.
[0006] The purpose of the present invention can be achieved by the following technical solutions:
[0007] A method for designing a X-ray grazing incidence wide spectrum multilayer film structure comprises the following steps:
[0008] Based on coupled wave theory and considering the absorption characteristics of materials to X-rays, an analytical theory of X-ray non-periodic multilayer film structures is established;
[0009] Determine the material, film logarithm, film thickness range and target reflectivity of the non-periodic multilayer film structure according to the X-ray non-periodic multilayer film structure analysis theory and the target band, and obtain an approximate solution for the non-periodic multilayer film structure;
[0010] Taking the target reflectivity curve as the optimization target, an evaluation function is established, and the approximate solution of the non-periodic multilayer film structure is used as the initial structure. The thickness of each layer is used as a variable, and numerical calculation optimization is performed to obtain a multilayer film structure with a target reflectivity curve.
[0011] Furthermore, based on the X-ray non-periodic multilayer film structure analytical theory, an X-ray reflectivity expression for a non-periodic multilayer film in which the film thickness ratio remains unchanged and the multilayer film periodic thickness changes monotonically with the film depth is derived, as well as a recursive formula for the film depth z and wavelength λ of each double-layer film.
[0012] Furthermore, the expression of the X-ray reflectivity is as follows:
[0013]
[0014] κ is the component of the reflected wave vector in the multilayer film in the film layer depth direction z, k is the wave vector in vacuum, is the average repolarization rate of the multilayer film structure, χ A , χ S are the repolarization rates of the absorption layer and the spacer layer, θ is the grazing incidence angle of the multilayer film, Γ is the thickness ratio of the absorption layer material, z sp The physical meaning of is the depth of the multilayer film corresponding to the interface of the film pair, q(z sp ) is the physical meaning of "local period" d m The inverse of q(z sp )=1 / d m (z sp ).
[0015] Furthermore, through the X-ray reflectivity, taking into full account the absorption and refractive index characteristics of the material in different bands of soft X-rays and tough X-rays, the relevant analytical formula between the wavelength λ and the multilayer film depth z is established as follows:
[0016]
[0017]
[0018] In the formula, ± corresponds to the case where the film thickness is monotonically decreasing (+) or monotonically increasing (-);
[0019] Convert continuous variables z and λ into numerical sequences {z l} and {λ l}, the film depth z l With wavelength λ l The recursive formulas are as follows:
[0020]
[0021] z 0 =0,λ 0 =λ max or min , l=0,1,2,...,N-1;
[0022] In the formula, z l is the film depth at the junction of each double-layer film, l is counted from the top of the double-layer film, and is the thickness d of the first l pairs of double-layer films m The sum of l is the wavelength, λ 0 =λ max For the case where the thickness of the double layer decreases monotonically with the depth of the film layer d m+1 <d m ,λ 0 =λ min For the case where the thickness of the double-layer film increases monotonically with the depth of the film layer d m+1 >d m ;
[0023] The double-layer film thickness d m The numerical sequence {d m} can be determined by the film depth z l The numerical sequence of {z l}Calculated, the double-layer film thickness d m , Absorption layer thickness and the thickness of the spacer layer The expressions are as follows:
[0024]
[0025] Where Γ is the thickness ratio of the absorbing layer material, λl is the wavelength corresponding to the double-layer film, z l is the corresponding film depth of the double-layer membrane.
[0026] Furthermore, the {λ l} and {z l} always satisfies that the function F(z,λ) has a real number solution, and the judgment formula for whether the function F(z,λ) has a real number solution is as follows:
[0027]
[0028] In the formula, k=2π / λ, κ is the component of the reflected wave vector in the multilayer film in the film layer depth direction z, k is the wave vector in vacuum, is the average repolarization rate of the multilayer film structure, χ A , χ S are the complex polarizabilities of the absorption layer and the spacer layer, respectively, θ represents the grazing incidence angle of the multilayer film, and Γ is the thickness ratio of the absorption layer material.
[0029] Furthermore, different spectral reflectance response distributions are selected as the target reflectance according to the requirements, and the film layer depth z is l With wavelength λ l The recursive formula of and the judgment formula that the function F(z,λ) has a real number solution are used to obtain the initial solution and the minimum number of film pairs N, and then the film layer structure with the target reflectivity is obtained through numerical optimization.
[0030] Furthermore, in order to obtain a better numerical optimization effect, the number of membrane pairs of the initial membrane structure used for the numerical optimization is increased by 0% to 20% based on the minimum number of membrane pairs N, and the thickness of the increased membrane pairs is equal to the thickness d of the Nth pair of double-layer membranes. N Consistent.
[0031] Furthermore, the target spectral energy range of the multilayer film structure is between 0.1-10 keV, the film period thickness is between 1-20 nm, and the grazing incidence angle θ is in the range of 1.5θ c <θ<90°, where θ c is the critical angle of total reflection, and its value is related to the average polarizability of the material Related.
[0032] Furthermore, the multilayer film structure is placed on the surface of a blazed grating to obtain a grazing-incidence multilayer film blazed grating with a wide spectrum and high efficiency.
[0033] Furthermore, the blazed grating structure is a multilayer film structure after matching optimization, satisfying the following condition:
[0034] Dsinα≈d
[0035] average
[0036] d=L / N
[0037] average
[0038] θ i =θ-α
[0039] Where, d average is the average film thickness of the multilayer film structure, L is the total film thickness, N is the number of film pairs, D is the grating period, α is the blaze angle, θ i is the grating grazing incidence angle, and θ is the multilayer film grazing incidence angle.
[0040] Compared with the prior art, the present invention has the following beneficial effects:
[0041] 1. The present invention is based on coupled wave theory, takes into account the absorption and refractive index characteristics of materials at different wavelengths, and is suitable for soft X-ray and tough X-ray bands. By establishing an analytical theory of X-ray non-periodic multilayer film structure, an analytical relationship between the reflectivity function of the non-periodic multilayer film and the film depth function is obtained, thereby obtaining a recursive formula for the initial film thickness of the wide-spectrum multilayer film, solving the inverse problem of obtaining a non-periodic multilayer film structure according to performance requirements, providing a physical explanation for the reflection of the non-periodic multilayer film structure, clarifying the influence of the non-periodic multilayer film structure on the reflectivity, and providing theoretical guidance for the design of wide-spectrum multilayer film structures.
[0042] 2. The initial non-periodic multilayer film structure obtained by the present invention through analytical theory is an approximate solution to the optimal structure. Combined with numerical calculation optimization, a multilayer film structure with high reflectivity under a wide spectrum can be quickly obtained. The optimization time can be shortened by more than a hundred times and the convergence of the optimization results is higher. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] Figure 1 Schematic diagram of the non-periodic multilayer film structure targeted by the design method of the present invention, wherein θ is the grazing incidence angle of the multilayer film, the Z axis is the depth direction of the multilayer film, and z l is the film depth, d m is the periodic thickness of each film pair from top to base, is the thickness of the absorption layer in each film pair period from top to base, is the thickness of the spacer layer in each film pair period from the top to the base;
[0044] Figure 2 Schematic diagram of the non-periodic multilayer film structure for gratings designed by the present invention, wherein θ i is the grating grazing incidence angle, the Z axis is the depth direction of the multilayer film, and z l is the film depth, θ nis the grating diffraction angle, D is the grating period, α is the blaze angle, d m is the periodic thickness of each film pair from top to base, is the thickness of the absorption layer in each film pair period from top to base, is the thickness of the spacer layer in each film pair period from the top to the base;
[0045] Figure 3 For the 3-4keV broadband reflector, the film thickness distribution curve of the initial multilayer film M1 obtained by analytical theory is combined with the film thickness distribution curve of the multilayer film reflector M2 obtained by numerical calculation optimization;
[0046] Figure 4 In order to simulate the curve of the reflectivity of the multilayer film reflector M2 varying with the wavelength after the process optimization by combining analytical theory with numerical methods, the curve of the reflectivity of the multilayer film reflector M3 varying with the wavelength obtained by directly performing numerical optimization, and the -1 order diffraction efficiency of the multilayer film grating BMG1 obtained by using the multilayer film structure M2 combined with the grating parameters. DETAILED DESCRIPTION
[0047] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.
[0048] This embodiment provides a method for designing a non-periodic multilayer film structure for a reflector and a grating for the 3-4 keV energy range with the goal of obtaining a high and flat reflectivity. The non-periodic multilayer film structure designed for the reflector is as follows: Figure 1 As shown in Figure 2, the non-periodic multilayer film structure designed for grating is as follows: Figure 2 The design method includes the following steps:
[0049] S1. Based on coupled wave theory and considering the absorption characteristics of materials to X-rays, an analytical theory of X-ray non-periodic multilayer film structure is established;
[0050] The X-ray reflectivity expression of the non-periodic multilayer film whose double-layer film thickness changes monotonically with depth is obtained as follows:
[0051]
[0052] In order to solve the inverse problem from the target reflectivity to the multilayer film structure, the absorption and refractive index characteristics of the material in different bands of soft X-rays and tough X-rays are fully considered, and the relevant analytical formula between the wavelength λ and the multilayer film depth z is established as follows:
[0053]
[0054] In the formula, ± corresponds to the case where the film thickness is monotonically decreasing (+) or monotonically increasing (-);
[0055] Convert continuous variables z and λ into numerical sequences {z l} and {λ l}, the film depth z l With wavelength λ l The recursive formulas are as follows:
[0056]
[0057] z 0 =0,λ 0 =λ max or min , l=0,1,2,...,N-1;
[0058] In the formula, z l is the film depth at the junction of each double-layer film, l is counted from the top of the double-layer film, and is the thickness d of the first l pairs of double-layer films m The sum of l is the wavelength, λ 0 =λ max For the case where the thickness of the double layer decreases monotonically with the depth of the film layer d m+1 <d m ,λ 0 =λ min For the case where the thickness of the double-layer film increases monotonically with the depth of the film layer d m+1 >d m ;
[0059] Double layer film thickness d m The numerical sequence {d m} can be determined by the film depth z l The numerical sequence of {z l}Calculated, the double-layer film thickness d m , Absorption layer thickness and the thickness of the spacer layer The expressions are as follows:
[0060]
[0061] Where Γ is the thickness ratio of the absorbing layer material, λ l is the wavelength corresponding to the double-layer film, z l is the corresponding film depth of the double-layer membrane.
[0062] At the same time {λ l} and {z l}It is necessary to satisfy that the function F(z,λ) has a real number solution. The judgment formula for whether the function F(z,λ) has a real number solution is as follows:
[0063]
[0064] In the formula, k=2π / λ, κ is the component of the reflected wave vector in the multilayer film in the film layer depth direction z, k is the wave vector in vacuum, is the average repolarization rate of the multilayer film structure, χ A , χ S are the complex polarizabilities of the absorption layer and the spacer layer, respectively, θ represents the grazing incidence angle of the multilayer film, and Γ is the thickness ratio of the absorption layer material.
[0065] S2. Determine the material, film pair number, film thickness range and target reflectivity R of the non-periodic multilayer film structure based on analytical theory and target waveband. 0 , an approximate solution for the non-periodic multilayer film structure is given;
[0066] By analyzing the recursive formula and iterative recursion of the judgment formula, the highest efficiency R(λ) achievable in the target band and the corresponding multilayer film thickness distribution {d m},m=1,2,...,N, where N is the corresponding minimum number of membrane pairs. In order to obtain better numerical optimization results, the number of membrane pairs in the final initial membrane structure can be increased by 0% to 20% based on the minimum number of membrane pairs, and the thickness of the increased membrane pairs is equal to the thickness of the Nth pair of double-layer membranes d N Consistent.
[0067] The target spectral energy range is between 0.1-10keV, and the film period thickness is between 1-20nm.
[0068] The analytical theory is not applicable in the total reflection region, so the grazing incidence angle range is 1.5θ c <θ<90°, where θ c is the critical angle of total reflection, and its value is related to the average polarizability of the material Related.
[0069] For the 3-4keV band, select [Cr / C / ] N / substrate (Si) combination, thickness ratio 0.4, N in the square brackets represents the number of film pairs. For the multilayer film reflector working at a grazing incidence angle of 1.85°, the corresponding target reflectivity is finally selected as 29% through recursive formula iteration, and the minimum required number of film pairs is 67. The initial film system selects the number of film pairs N = 80, and the double-layer film thickness exceeding 67 is the 67th double-layer film thickness. The initial multilayer film structure approximate solution M1 obtained by analytical expression has a distribution of each film thickness as follows Figure 3 as shown in .
[0070] S3, taking the target reflectivity curve as the optimization target, establishing the evaluation function, taking the non-periodic multilayer film structure obtained in S2 as the initial structure, and taking the thickness of each layer as the variable, using the Levenberg-Marquardt algorithm, performing numerical calculation optimization, and obtaining the multilayer film reflector structure with the target reflectivity curve, such as Figure 1 shown.
[0071] The evaluation function is as follows:
[0072]
[0073] λ min ≤λ i ≤λ max ,i=1,2,...,I
[0074] In the formula, R(λ i ) is the wavelength λ of the multilayer film structure i The reflectivity under 0 (λ i ) is the wavelength λ i The target reflectivity under i For each wavelength involved in calculating the reflectivity during numerical optimization, an appropriate number of calculation points can be selected based on the actual calculation accuracy requirements within the wavelength range. The total number of points I should be greater than the number of variables, that is, the total number of film layers 2N. In this embodiment, I=201 is selected.
[0075] The convergence of optimizing multilayer films by combining analytical theory with numerical optimization in step S1 to step S3 is higher than that of optimizing by numerical optimization alone. For the optimization of multilayer film thickness with flat reflectivity as the target, the convergence RD calculation formula is as follows:
[0076]
[0077] λ min ≤λ i ≤λ max ,i=1,2,...,I
[0078] In the formula, R aver Represents the average reflectivity of the optimized multilayer film structure in the target band.
[0079] The Levenberg-Marquardt algorithm was used to optimize M1 with a target reflectivity of 29%. After M1 was optimized, the film thickness distribution of the multilayer film structure M2 of the reflector was obtained as follows: Figure 3 As shown, the corresponding reflectivity curve at 1.85° grazing incidence angle is as follows Figure 4 As shown in , M2 convergence RD = 2.1 × 10 -3 A high reflectivity with a flat average efficiency of 28.8% was obtained in the 3–4 keV range.
[0080] Taking the periodic multilayer film d = 5.4nm as the initial structure, numerical calculation is directly used for optimization, and the genetic algorithm, a global optimization algorithm, is selected for optimization. The reflectivity of the optimized multilayer film M3 is as follows Figure 4 As shown in , the M3 convergence RD = 0.03. Figure 4 The reflectivity curves of non-periodic multilayer films obtained by the two optimization methods M2 and M3 show that the average reflectivity of the two structures is close, but the reflectivity curve M3 obtained by the method of numerical optimization using genetic algorithm using the internationally commonly used multilayer film calculation software IMD has worse convergence and obvious oscillation. The numerical optimization process of M2 only takes 8 seconds, while the numerical optimization time of M3 is 5 hours using genetic algorithm. The design method that combines analytical theory and numerical calculation can more quickly obtain a multilayer film structure with a flatter reflectivity curve.
[0081] The blazed grating structure matches the optimized multilayer film structure and satisfies the following conditions:
[0082] Dsinα≈d
[0083] average
[0084] d=L / N
[0085] average
[0086] θ i =θ-α
[0087] Where, d average is the average film thickness of the multilayer film structure, L is the total film thickness, N is the number of film pairs, D is the grating period, α is the blaze angle, θ i is the grating grazing incidence angle, and θ is the multilayer film grazing incidence angle.
[0088] The average period thickness d of the multilayer film structure M2 average =5.41nm, for grating period D = 416.67nm, grating order n = -1, the blaze angle is selected as 0.75°, and the grating grazing angle is 1.1°. The -1 order diffraction efficiency of the multilayer film blazed grating BMG1 at 1.1° under grazing angle is as follows: Figure 4 As shown, the multilayer blazed grating BMG1 achieves a high diffraction efficiency of 29.8% on average in the range of 2.91-4.26keV.
[0089] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.
Claims
1. A method for designing a wide spectrum multilayer film structure with grazing incidence X-rays, characterized in that: The following steps are involved: Based on coupled wave theory and considering the absorption characteristics of materials to X-rays, an analytical theory of X-ray non-periodic multilayer film structures is established; Determine the material, film logarithm, film thickness range and target reflectivity of the non-periodic multilayer film structure according to the X-ray non-periodic multilayer film structure analysis theory and the target band, and obtain an approximate solution for the non-periodic multilayer film structure; Taking the target reflectivity curve as the optimization target, an evaluation function is established, and the approximate solution of the non-periodic multilayer film structure is used as the initial structure. The thickness of each layer is used as a variable, and numerical calculation optimization is performed to obtain a multilayer film structure with a target reflectivity curve.
2. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 1, characterized in that: According to the X-ray non-periodic multilayer film structure analytical theory, the X-ray reflectivity expression of the non-periodic multilayer film with a constant film thickness ratio and a monotonically changing multilayer film periodic thickness with film depth and the recursive formula of the film depth z and wavelength λ of each double-layer film are derived.
3. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 2, characterized in that: The expression of the X-ray reflectivity is as follows: In the formula, k=2π / λ, κ is the component of the reflected wave vector in the multilayer film in the film layer depth direction z, k is the wave vector in vacuum, is the average repolarization rate of the multilayer film structure, χ A , χ S are the repolarization rates of the absorption layer and the spacer layer, θ is the grazing incidence angle of the multilayer film, Γ is the thickness ratio of the absorption layer material, z sp The physical meaning of is the depth of the multilayer film corresponding to the interface of the film pair, q(z sp ) is the physical meaning of "local period" m The inverse of q(z sp )=1 / d m (z sp ).
4. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 3, characterized in that: Through the X-ray reflectivity, taking into full consideration the absorption and refractive index characteristics of the material in different bands of soft X-rays and tough X-rays, the relevant analytical formula between the wavelength λ and the multilayer film depth z is established as follows: In the formula, ± corresponds to the case where the film thickness is monotonically decreasing (+) or monotonically increasing (-); Convert continuous variables z and λ into numerical sequences {z l } and {λ l }, the film depth z l With wavelength λ l The recursive formulas are as follows: z0=0,λ0=λ max or min ,l=0,1,2,...,N-1; In the formula, z l is the film depth at the junction of each double-layer film, l is counted from the top of the double-layer film, and is the thickness d of the first l pairs of double-layer films m The sum of l is the wavelength, λ0=λ max For the case where the thickness of the double layer decreases monotonically with the depth of the film layer d m+1 <d m ,λ0=λ min For the case where the thickness of the double-layer film increases monotonically with the depth of the film layer d m+1 >d m ; The double-layer film thickness d m The numerical sequence {d m } can be determined by the film depth z l The numerical sequence of {z l }Calculated, the double-layer film thickness d m , Absorption layer thickness and the thickness of the spacer layer The expressions are as follows: Where Γ is the thickness ratio of the absorbing layer material, λ l is the wavelength corresponding to the double-layer film, z l is the corresponding membrane depth of the double-layer membrane.
5. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 4, characterized in that: The {λ l } and {z l } always satisfies that the function F(z,λ) has a real number solution, and the judgment formula for whether the function F(z,λ) has a real number solution is as follows: In the formula, k=2π / λ, κ is the component of the reflected wave vector in the multilayer film in the film layer depth direction z, k is the wave vector in vacuum, is the average repolarization rate of the multilayer film structure, χ A , χ S are the complex polarizabilities of the absorption layer and the spacer layer, respectively, θ represents the grazing incidence angle of the multilayer film, and Γ is the thickness ratio of the absorption layer material.
6. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 5, characterized in that: According to the requirements, different spectral reflectance response distributions are selected as the target reflectance, and the film layer depth z is l With wavelength λ l The recursive formula of and the judgment formula that the function F(z,λ) has a real number solution are used to obtain the initial solution and the minimum number of film pairs N, and then the film layer structure with the target reflectivity is obtained through numerical optimization.
7. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 6, characterized in that: In order to obtain a better numerical optimization effect, the number of membrane pairs of the initial membrane layer structure used for the numerical optimization is increased by 0% to 20% based on the minimum number of membrane pairs N, and the thickness of the increased membrane pairs is equal to the thickness d of the Nth pair of double-layer membranes. N Consistent.
8. The method for designing a wide spectrum X-ray grazing incidence multilayer film structure according to claim 1, characterized in that: The target spectral energy range of the multilayer film structure is between 0.1-10 keV, the film period thickness is between 1-20 nm, and the grazing incidence angle θ is in the range of 1.5θ c <θ<90°, where θ c is the critical angle of total reflection, and its value is related to the average polarizability of the material Related.
9. The method for designing a multilayer film structure with grazing incidence X-rays and wide spectrum according to claim 1, characterized in that: The multilayer film structure is placed on the surface of a blazed grating to obtain a grazing-incidence multilayer film blazed grating with a wide spectrum and high efficiency.
10. The method for designing a multilayer film structure with grazing incidence X-rays and wide spectrum according to claim 9, characterized in that: The blazed grating structure is a multilayer film structure after matching optimization, and the conditions satisfied are as follows: Dsinα≈d average d=L / N average i i =θ-α Where, d average is the average film thickness of the multilayer film structure, L is the total film thickness, N is the number of film pairs, D is the grating period, α is the blaze angle, θ i is the grating grazing incidence angle, and θ is the multilayer film grazing incidence angle.
Citation Information
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