A method for locating the Bragg peak of grazing-incidence small-angle X-ray scattering

Abstract

The present application provides a grazing incidence small angle X-ray scattering Bragg peak positioning method, comprising: receiving X-rays grazingly incident to a two-dimensional periodic structure sample at a first angle, wherein the two-dimensional periodic structure sample includes a plurality of particles; determining the real space structure parameters of the two-dimensional periodic structure sample; determining the first scattering vector component and the second scattering vector component corresponding to the particles in the two-dimensional periodic structure sample according to the real space structure parameters, wherein the first scattering vector and the second scattering vector are orthogonal to each other; determining the third scattering vector component and the first scattering angle information according to the first scattering vector component and the second scattering vector component, wherein the third scattering vector component is orthogonal to the first scattering vector and the second scattering vector, and the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak. This scheme can realize the accurate positioning of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample.

Description

Technical Field

[0001] The present application relates to the technical field of small-angle scattering, and in particular to a method for locating a Bragg peak of a grazing-incidence small-angle X-ray scattering. Background Art

[0002] Grazing Incidence Small Angle X-ray Scattering (GISAXS) is a phenomenon in which X-rays grazingly incident on the sample surface interact with the electrons in the material and deviate at a small angle. The spatial distribution of GISAXS signals is closely related to the electron density distribution in the material. It can provide internal statistical structural information of samples over a large range without loss and efficiently, and is widely used in the detection of nanostructures at the scale of 1nm-100nm.

[0003] GISAXS directly obtains the signal of the sample's reciprocal space, and it is necessary to use certain model-based numerical simulation and fitting to extract the structural parameter information of the sample's real space. Therefore, efficient numerical simulation methods for GISAXS signals are critical. Existing GISAXS simulation tools based on the distortion wave-Born approximation theory, such as BornAgain, mainly obtain signals in the form of discrete sampling, and extract Bragg peak data by circle fitting or line fitting, with low calculation accuracy and efficiency; simulation tools based on finite element solution of Maxwell's equations, such as JCMsuite, have huge calculation volume and can only provide fast calculation solutions for relatively simple grating structure samples.

[0004] Existing studies have calculated the Bragg peak position of GISAXS of one-dimensional periodic distribution structure samples by analytical methods, and then quickly simulated the distribution of arbitrary diffraction orders along the Bragg rod; currently, there is still a lack of Bragg peak positioning methods for GISAXS of two-dimensional periodic distribution structure samples.

[0005] How to achieve accurate positioning of the Bragg peak of GISAXS for two-dimensional periodic distribution structure samples has become a key issue that needs to be urgently solved in GISAXS. Summary of the invention

[0006] The present application provides a grazing incidence small angle X-ray scattering Bragg peak positioning method, which can achieve accurate positioning of the GISAXS Bragg peak of a two-dimensional periodically distributed structure sample.

[0007] In a first aspect, an embodiment of the present application provides a grazing incidence small angle X-ray scattering Bragg peak positioning method, which can be performed by a grazing incidence small angle X-ray scattering Bragg peak positioning device, which can be a terminal device or a module for a terminal device, or a server or a module for a server. The present application does not limit the execution subject of the method. The method includes: receiving X-rays grazingly incident to a two-dimensional periodic structure sample at a first angle, wherein the two-dimensional periodic structure sample includes a plurality of particles; determining the real space structure parameters of the two-dimensional periodic structure sample; determining the first scattering vector component and the second scattering vector component corresponding to the particles in the two-dimensional periodic structure sample according to the real space structure parameters, wherein the first scattering vector and the second scattering vector are orthogonal to each other; determining the third scattering vector component and the first scattering angle information according to the first scattering vector component and the second scattering vector component, wherein the third scattering vector component is orthogonal to the first scattering vector and the second scattering vector, and the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak when the first angle is grazingly incident.

[0008] The above scheme, by receiving X-rays that are incident on the two-dimensional periodic structure sample at a first angle, and based on the real-space structural parameters of the two-dimensional periodic structure sample, can achieve accurate positioning of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby achieving accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0009] In a possible implementation method, an X-ray is received that is incident at a second angle on a two-dimensional periodic structure sample; a fourth scattering vector component and a fifth scattering vector component corresponding to particles in the two-dimensional periodic structure sample are determined based on the real-space structure parameters, wherein the fourth scattering vector and the fifth scattering vector are orthogonal to each other; a sixth scattering vector component and second scattering angle information are determined based on the fourth scattering vector component and the fifth scattering vector component, wherein the sixth scattering vector component is orthogonal to the fourth scattering vector and the fifth scattering vector, and the second scattering angle information refers to the scattering angle information corresponding to the Bragg peak when the X-ray is incident at the second angle.

[0010] The above scheme can detect the fourth scattering vector component, the fifth scattering vector component, the sixth scattering vector component and the second scattering angle information corresponding to the Bragg peak of the two-dimensional periodic structure sample rotated at any angle, thereby realizing the accurate positioning of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample after rotation. Furthermore, it can detect the shape and other characteristics of particles in the two-dimensional periodic distribution structure sample at any angle.

[0011] In one possible implementation method, the real-space structural parameters include one or more of the angle between the first oblique direction and the second oblique direction, the particle separation interval of the two-dimensional periodic structure sample along the first oblique direction, and the particle separation interval of the two-dimensional periodic structure sample along the second oblique direction.

[0012] In a possible implementation method, the method further includes: determining an Ewald sphere equation;

[0013] Determining the third scattering vector component and the first scattering angle information according to the first scattering vector component and the second scattering vector component includes: determining the third scattering vector component and the first scattering angle information according to the Ewald sphere equation, the first scattering vector component and the second scattering vector component;

[0014] Determining a sixth scattering vector component and a second scattering angle information according to the fourth scattering vector component and the fifth scattering vector component includes: determining the sixth scattering vector component and the second scattering angle information according to the Ewald sphere equation, the fourth scattering vector component and the fifth scattering vector component.

[0015] In one possible implementation method, the structure of the Ewald sphere equation is as follows:

[0016]

[0017] Wherein, k0 represents the radius of the Ewald sphere equation, λ represents the wavelength of the X-ray; k ix , k iy and k iz are the kx-axis, ky-axis and kz-axis coordinates corresponding to the wave vector of the incident light in the Ewald sphere.

[0018] The above scheme, by establishing the Ewald sphere equation, can achieve accurate positioning of the Bragg peak of GISAXS for a two-dimensional periodic distribution structure sample, thereby achieving accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0019] In a possible implementation method, the calculation method of the scattering vector is as follows:

[0020]

[0021] Where q represents the scattering vector, α i is the first angle, α f ,θ fis the first scattering angle information, wherein the α f is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere; f is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere.

[0022] The above scheme can determine the Ewald sphere equation based on the scattering vector, and realize the accurate positioning of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing the accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0023] In a possible implementation method, a method for calculating the first scattering vector component and the second scattering vector component is as follows:

[0024]

[0025] Among them, q x represents the first scattering vector component, q y represents the second scattering vector component, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction; p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; θ represents the angle between the first oblique direction and the second oblique direction; n represents the order sequence along the first direction, and m represents the order sequence along the second direction.

[0026] The above scheme, through the calculation method of the first scattering vector component and the second scattering vector component, can accurately determine the X-direction position information and the Y-direction position information of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0027] In one possible implementation,

[0028] The calculation formula of the third scattering vector component is as follows:

[0029]

[0030] Among them, q z represents the third scattered vector component.

[0031] The above scheme, through the calculation method of the third scattering vector component, can accurately determine the Z-direction position information of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0032] In a possible implementation method, the calculation formula of the first scattering angle information is as follows:

[0033]

[0034]

[0035] The above scheme, through the calculation method of the first scattering angle, can accurately determine the scattering angle information of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0036] In a possible implementation method, the calculation methods of the fourth scattering vector component and the fifth scattering vector component are respectively as follows:

[0037]

[0038]

[0039] Among them, q x1 represents the fourth scattered vector component, q y1 represents the fifth scattered vector component, represents the second angle, θ represents the angle between the first oblique direction and the second oblique direction, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction.

[0040] The above scheme, through the calculation method of the fourth scattering vector component and the fifth scattering vector component, can accurately determine the X-direction position information and the Y-direction position information of the Bragg peak of GISAXS of the two-dimensional periodic distribution structure sample after rotating by the second angle, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0041] In a possible implementation method, the calculation formula of the second scattering angle information is as follows:

[0042]

[0043] Among them, α f1 θ is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere when the reflected light is incident at the second angle; f1is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere when the incident light is incident at the second angle; i is the first angle.

[0044] The above scheme, through the calculation method of the second scattering angle, can accurately determine the scattering angle information of the Bragg peak of GISAXS of the two-dimensional periodic distribution structure sample after rotating the second angle, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0045] In one possible implementation method, the structural characteristics of the particles in the two-dimensional periodic structure sample are determined based on the first scattering angle information and / or the second scattering angle information, and a detector; the detector is used to convert the first scattering angle information and / or the second scattering angle information into information that can be analyzed by a two-dimensional planar detector, and determine the structural characteristics of the particles in the two-dimensional periodic structure sample based on the information.

[0046] The above scheme can convert the theoretical Bragg peak position angle coordinates into the pixel index of the two-dimensional planar detector, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample.

[0047] In a second aspect, an embodiment of the present application provides a grazing-incidence small-angle X-ray scattering Bragg peak positioning device, comprising: a receiving unit and a determining unit. The receiving unit is used to receive X-rays that are grazingly incident on a two-dimensional periodic structure sample at a first angle, wherein the two-dimensional periodic structure sample includes a plurality of particles; the determining unit is used to determine the real-space structural parameters of the two-dimensional periodic structure sample; determine the first scattering vector component and the second scattering vector component corresponding to the particles in the two-dimensional periodic structure sample according to the real-space structural parameters, wherein the first scattering vector and the second scattering vector are orthogonal to each other; determine the third scattering vector component and the first scattering angle information according to the first scattering vector component and the second scattering vector component, wherein the third scattering vector component is orthogonal to the first scattering vector and the second scattering vector, and the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak when the first angle is grazingly incident.

[0048] In a possible implementation method, the receiving unit is also used to receive X-rays that are glancingly incident on the two-dimensional periodic structure sample at a second angle; the determining unit is also used to determine a fourth scattering vector component and a fifth scattering vector component corresponding to particles in the two-dimensional periodic structure sample based on the real-space structure parameters, wherein the fourth scattering vector and the fifth scattering vector are orthogonal to each other; and a sixth scattering vector component and second scattering angle information are determined based on the fourth scattering vector component and the fifth scattering vector component, wherein the sixth scattering vector component is orthogonal to the fourth scattering vector and the fifth scattering vector, and the second scattering angle information refers to the scattering angle information corresponding to the Bragg peak when the second angle of incidence is glancingly incident.

[0049] In one possible implementation method, the real-space structural parameters include one or more of the angle between the first oblique direction and the second oblique direction, the particle separation interval of the two-dimensional periodic structure sample along the first oblique direction, and the particle separation interval of the two-dimensional periodic structure sample along the second oblique direction.

[0050] In a possible implementation method, the determining unit is further used to determine the Ewald sphere equation;

[0051] The determining unit is specifically configured to determine a third scattering vector component and first scattering angle information according to the Ewald sphere equation, the first scattering vector component and the second scattering vector component;

[0052] The determining unit is specifically configured to determine a sixth scattering vector component and second scattering angle information according to the Ewald sphere equation, the fourth scattering vector component and the fifth scattering vector component.

[0053] In one possible implementation method, the structure of the Ewald sphere equation is as follows:

[0054]

[0055] Wherein, k0 represents the radius of the Ewald sphere equation, λ represents the wavelength of the X-ray; k ix , k iy and k iz are the kx-axis, ky-axis and kz-axis coordinates corresponding to the wave vector of the incident light in the Ewald sphere.

[0056] In a possible implementation method, the calculation method of the scattering vector is as follows:

[0057]

[0058] Where q represents the scattering vector, α i is the first angle, α f ,θ f is the first scattering angle information, wherein the α f is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere; f is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere.

[0059] In a possible implementation method, a method for calculating the first scattering vector component and the second scattering vector component is as follows:

[0060]

[0061] Among them, q x represents the first scattering vector component, q y represents the second scattering vector component, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction; p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; θ represents the angle between the first oblique direction and the second oblique direction; n represents the order sequence along the first direction, and m represents the order sequence along the second direction.

[0062] In one possible implementation,

[0063] The calculation formula of the third scattering vector component is as follows:

[0064]

[0065] Among them, q z represents the third scattered vector component.

[0066] In a possible implementation method, the calculation formula of the first scattering angle information is as follows:

[0067]

[0068]

[0069] In a possible implementation method, the calculation methods of the fourth scattering vector component and the fifth scattering vector component are respectively as follows:

[0070]

[0071]

[0072] Among them, q x1 represents the fourth scattered vector component, qy1 represents the fifth scattered vector component, represents the second angle, θ represents the angle between the first oblique direction and the second oblique direction, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction.

[0073] In a possible implementation method, the calculation formula of the second scattering angle information is as follows:

[0074]

[0075] Among them, α f1 θ is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere when the reflected light is incident at the second angle; f1 is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere when the incident light is incident at the second angle; i is the first angle.

[0076] In a possible implementation method, the determination unit is also used to determine the structural characteristics of particles in the two-dimensional periodic structure sample based on the first scattering angle information and / or the second scattering angle information, and a detector; the detector is used to convert the first scattering angle information and / or the second scattering angle information into information that can be analyzed by a two-dimensional planar detector, and determine the structural characteristics of particles in the two-dimensional periodic structure sample based on the information.

[0077] In a third aspect, an embodiment of the present application further provides a computing device, including:

[0078] A memory for storing program instructions;

[0079] The processor is used to call the program instructions stored in the memory, and execute any method of implementing the above-mentioned first aspect according to the obtained program instructions.

[0080] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, in which computer-readable instructions are stored. When a computer reads and executes the computer-readable instructions, any method of the above-mentioned first aspect is implemented.

[0081] In a fifth aspect, an embodiment of the present application provides a computer program product, comprising a computer program executable by a computer device, wherein when the program is run on the computer device, the computer device executes any method for implementing the above-mentioned first aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 A schematic diagram of a flow chart of a grazing-incidence small-angle X-ray scattering Bragg peak positioning method provided in an embodiment of the present application;

[0083] Figure 2 A schematic diagram of a flow chart of a grazing-incidence small-angle X-ray scattering Bragg peak positioning method provided in an embodiment of the present application;

[0084] Figure 3 A schematic diagram of the structure of an Ewald sphere provided in an embodiment of the present application;

[0085] Figure 4 A schematic diagram of the real-space structure of a two-dimensional periodic structure sample provided in an embodiment of the present application;

[0086] Figure 5 A schematic diagram of the reciprocal space structure of a two-dimensional periodic structure sample provided in an embodiment of the present application;

[0087] Figure 6 A schematic diagram of the structure of the intersection of the reciprocal space and the Ewald sphere of a two-dimensional periodic structure sample provided in an embodiment of the present application;

[0088] Figure 7 A schematic diagram of the structure of a two-dimensional periodic structure sample provided in an embodiment of the present application after being rotated by a second angle;

[0089] Figure 8 A schematic diagram of a process for converting theoretical Bragg peak position angle coordinates into pixel indexes of a two-dimensional plane detector provided in an embodiment of the present application;

[0090] Fig. 9 A schematic structural diagram of a grazing-incidence small-angle X-ray scattering Bragg peak positioning device provided in an embodiment of the present application;

[0091] Fig.10 A schematic structural diagram of a grazing-incidence small-angle X-ray scattering Bragg peak positioning device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0092] Figure 1 A schematic flow chart of a grazing incidence small angle X-ray scattering Bragg peak positioning method provided in an embodiment of the present application, the method can be performed by a grazing incidence small angle X-ray scattering Bragg peak positioning device, the grazing incidence small angle X-ray scattering Bragg peak positioning device can be a terminal device or a module for a terminal device, or a server or a module for a server. The present application does not limit the execution subject of the method.

[0093] The method comprises the following steps:

[0094] Step 101, receiving X-rays incident at a first angle on a two-dimensional periodic structure sample.

[0095] Wherein, the two-dimensional periodic structure sample includes a plurality of particles.

[0096] In a possible implementation method, the present application does not limit the first angle, and does not limit the shape, material, etc. of multiple particles in the two-dimensional periodic structure sample.

[0097] In a possible implementation method, the two-dimensional periodic structure refers to a periodic array distribution structure generated along two straight lines forming a certain angle with each other in a two-dimensional plane.

[0098] Step 102, determining the real-space structural parameters of the two-dimensional periodic structure sample.

[0099] In one possible implementation method, the real-space structural parameters include one or more of a first oblique direction, a second oblique direction, an angle between the first oblique direction and the second oblique direction, a particle separation interval of the two-dimensional periodic structure sample along the first oblique direction, and a particle separation interval of the two-dimensional periodic structure sample along the second oblique direction.

[0100] Step 103 determines the first scattering vector component and the second scattering vector component corresponding to the particles in the two-dimensional periodic structure sample according to the real space structure parameters.

[0101] The first scattering vector and the second scattering vector are orthogonal to each other.

[0102] Step 104: Determine a third scattering vector component and first scattering angle information according to the first scattering vector component and the second scattering vector component.

[0103] The third scattering vector component is orthogonal to the first scattering vector and the second scattering vector, and the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak at grazing incidence at the first angle.

[0104] The third scattering vector component refers to the position information of the Bragg peak in the kz direction; the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak at grazing incidence at the first angle.

[0105] The above scheme, by receiving X-rays that are incident on the two-dimensional periodic structure sample at a first angle, and based on the real-space structural parameters of the two-dimensional periodic structure sample, can achieve accurate positioning of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby achieving accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0106] In a possible implementation method, after step 101 or after step 102, the method further includes: determining an Ewald sphere equation; specifically, establishing a coordinate system with the center of the two-dimensional periodic structure sample as the origin, and determining an Ewald sphere equation; wherein the points in the Ewald sphere are points scattered by the multiple particles after receiving the X-rays. Of course, a coordinate system may also be established with other positions of the two-dimensional periodic structure sample as the origin, and this application does not limit this.

[0107] In one possible implementation method, the Bragg peak principle refers to a phenomenon based on X-ray diffraction. When a beam of monochromatic X-rays passes through a crystal, it will be absorbed and reflected by the atoms of the crystal, causing interference and diffraction effects, forming a complex diffraction pattern. This pattern can be used to determine the structure of the crystal because the structure of the crystal is closely related to its diffraction pattern. This diffraction pattern is composed of a series of peaks, which are called Bragg peaks. The position and intensity of the Bragg peaks depend on various parameters of the crystal structure, such as the lattice constant, interatomic distance, crystal orientation, etc. By measuring the position and intensity of the Bragg peaks, the structural information of the crystal can be obtained.

[0108] In a possible implementation method, the above-mentioned step 103 is specifically as follows: determining the first scattering vector component and the second scattering vector component corresponding to multiple first grating truncated rods in the reciprocal space coordinate system according to the real space structure parameters, the first grating truncated rod refers to the projection of the particles in the two-dimensional periodic structure sample in the reciprocal space; the reciprocal space structure and the real space structure satisfy a certain mathematical transformation; the first scattering vector component refers to the position information of the Bragg peak along the X-axis direction (defined as the kx axis) in the reciprocal space coordinate system, and the second scattering vector component refers to the position information of the Bragg peak along the Y-axis direction (defined as the kx axis) in the reciprocal space coordinate system; determining the third scattering vector component and the first scattering angle information according to the Ewald sphere equation, the first scattering vector component and the second scattering vector component; the third scattering vector component refers to the position information of the Bragg peak along the Z-axis direction (defined as the kz axis) in the reciprocal space coordinate system; the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak when the first angle of grazing incidence is used.

[0109] In a possible implementation method, when the two-dimensional periodic structure sample is rotated around the z-axis by a certain angle in the sample plane, its Bragg peak positioning method is as follows: Figure 2 As shown, the method comprises the following steps:

[0110] Step 201, receiving X-rays incident at a second angle on a two-dimensional periodic structure sample.

[0111] In a possible implementation method, the two-dimensional periodic structure sample is rotated by a second angle.

[0112] In a possible implementation method, the present application does not limit the second angle. Generally, the two-dimensional periodic structure sample is rotated around the z-axis within the sample plane once with the second angle as an interval to obtain information of particles at different angles.

[0113] Step 202: determining a fourth scattering vector component and a fifth scattering vector component corresponding to particles in the two-dimensional periodic structure sample according to the real-space structure parameters.

[0114] The fourth scattering vector and the fifth scattering vector are orthogonal to each other.

[0115] Step 203: Determine a sixth scattering vector component and second scattering angle information according to the fourth scattering vector component and the fifth scattering vector component.

[0116] The sixth scattering vector component is orthogonal to the fourth scattering vector and the fifth scattering vector, and the second scattering angle information refers to the scattering angle information corresponding to the Bragg peak at grazing incidence at the second angle.

[0117] The above scheme can detect the fourth scattering vector component, the fifth scattering vector component, the sixth scattering vector component and the second scattering angle information corresponding to the Bragg peak of the two-dimensional periodic structure sample rotated at any angle, thereby realizing the accurate positioning of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample after rotation. Furthermore, it can detect the shape and other characteristics of particles in the two-dimensional periodic distribution structure sample at any angle.

[0118] In a possible implementation method, after step 201, the above step further includes: determining the Ewald sphere equation; specifically, establishing a coordinate system with the center of the two-dimensional periodic structure sample as the origin, and determining the Ewald sphere equation; wherein the points in the Ewald sphere are the points scattered by the multiple particles after receiving the X-rays. Of course, the coordinate system can also be established with other positions of the two-dimensional periodic structure sample as the origin, and this application does not limit this.

[0119] In a possible implementation method, the above steps 201 to 203 are specifically as follows: receiving X-rays incident at a second angle to a two-dimensional periodic structure sample or rotating the two-dimensional periodic structure sample by a second angle, determining a fourth scattering vector component and a fifth scattering vector component corresponding to a plurality of second grating truncated rods in a reciprocal space coordinate system, wherein the second grating truncated rod refers to the projection of the particle in the reciprocal space after the two-dimensional periodic structure sample is rotated by a second angle; the fourth scattering vector component refers to the position information of the Bragg peak in the kx direction after the rotation by the second angle, and the fifth scattering vector component refers to the position information of the Bragg peak in the ky direction after the rotation by the second angle; determining a sixth scattering vector component and second scattering angle information according to the Ewald sphere equation, the fourth scattering vector component and the fifth scattering vector component; the sixth scattering vector component refers to the position information of the Bragg peak in the kz direction after the rotation by the second angle; and the second scattering angle information refers to the scattering angle information corresponding to the Bragg peak after the rotation by the second angle. In a possible implementation method, the structure of the Ewald sphere equation is shown in the following formula (1):

[0120]

[0121] Wherein, k0 represents the radius of the Ewald sphere equation, λ represents the wavelength of the X-ray; k i refers to the wave vector of the incident light; k ix , k iy and k iz are respectively i The corresponding kx axis, ky axis and kz axis coordinates in the Ewald sphere; q represents the scattering vector, q=k f -k i ,|k f |=|k i |=k0,k f refers to the wave vector of the reflected light; q x ,q y and q z are respectively the kx-axis, ky-axis and kz-axis coordinates of q in the Ewald sphere.

[0122] For example, Figure 3 As shown in the figure, it is the Ewald sphere equation constructed with k0 as the radius. Figure 3 In the two-dimensional periodic structure sample, there are multiple particles, each particle is Figure 3 As shown in the cylinder in the figure, a coordinate system is established with the center of the two-dimensional periodic structure sample as the origin, where the sample surface is the xy plane, the z axis is perpendicular to the sample surface and the optical axis is the x axis. The X-ray beam is in the xz plane with αi The angle of incidence is k i , the scattered light emission angle is (α f ,θ f ), the wave vector is k f , scattering vector q = k f -k i , which is expressed in the angular coordinate system as shown in the following formula (2):

[0123]

[0124] Wherein, q represents the scattering vector, k0 represents the radius of the Ewald sphere equation, α i is the first angle, α f ,θ f is the first scattering angle information, the α f For the k f The pitch angle in the vertical direction of the Ewald sphere; the θ f For the k f The offset angle of the Ewald sphere in the horizontal direction, sin represents the sine function, and cos represents the cosine function.

[0125] In one possible implementation method, elastic scattering means that during the scattering process, the internal energy and structure of the two particles involved in the scattering do not change. In the elastic scattering process, the system can obey the law of conservation of energy and momentum. Therefore, in elastic scattering, |k f |=|k i |=k0, then

[0126] The above scheme, by establishing the Ewald sphere equation, can achieve accurate positioning of the Bragg peak of GISAXS for a two-dimensional periodic distribution structure sample, thereby achieving accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0127] In a possible implementation method, the real space structure of the two-dimensional periodic structure sample is as follows Figure 4 As shown, it can be seen that the particles in the two-dimensional periodic structure sample generate a periodic array distribution structure in the two-dimensional plane along two straight lines at a certain angle to each other. Among them, the first oblique direction of the two-dimensional periodic structure sample is t1, the second oblique direction is t2, the particle distribution interval along the first oblique direction t1 is d, the particle distribution interval along the first oblique direction t2 is p, and the angle between the first oblique direction t1 and the second oblique direction t2 is θ. Taking the t1 direction parallel to the x-axis direction as an example, it can be known that the grating line period constant distributed in the t1 direction is psinθ, and the grating period constant in the t2 direction is dsinθ.

[0128] In a possible implementation method, the reciprocal space structure of the two-dimensional periodic structure sample is analyzed according to its real space structure. The reciprocal space structure and the real space structure satisfy a certain mathematical transformation. This application does not limit this mathematical transformation, such as Fourier transform, etc. Determine the first scattering vector component q corresponding to the grating truncated rod in the reciprocal space coordinate system x and the second scattering vector component q y .like Figure 5 As shown, the Bragg rod is parallel to k z Directional distribution, in k x -k y In the plane, it falls on the intersection points along the r1 and r2 directions, and the spacing between adjacent Bragg bars along the r1 direction is 2π / psinθ, and the spacing between adjacent Bragg bars along the r2 direction is 2π / dsinθ. Figure 5 In the coordinate system shown, the position of the Bragg rod is also the first scattering vector component q x and the second scattering vector component q y It can be expressed as the following formula (3):

[0129]

[0130] Among them, q x represents the first scattering vector component, q y represents the second scattering vector component, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction; p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; θ represents the angle between the first oblique direction and the second oblique direction; n represents the order sequence along the first direction, and m represents the order sequence along the second direction; the first direction refers to the projection of the first oblique direction in the reciprocal space, and the second direction refers to the projection of the second oblique direction in the reciprocal space, sin represents the sine function, cos represents the cosine function, and tan represents the tangent function.

[0131] The above scheme, through the calculation method of the first scattering vector component and the second scattering vector component, can accurately determine the X-direction position information and the Y-direction position information of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0132] In a possible implementation method, the first scattering vector component and the second scattering vector component are substituted into the Ewald sphere equation to determine the third scattering vector component. Specifically, the position of the intersection point between the reciprocal space of the two-dimensional periodic structure sample and the Ewald sphere is obtained in combination with the Ewald sphere equation, and the spatial angular coordinates corresponding to the diffraction maximum point are calculated, such as Figure 6 As shown. Combining equations (3) and (4), the reciprocal space Bragg rod position coordinates (q x ,q y ) is substituted into the Ewald sphere equation, and the solution below the sample surface is removed, and the calculation formula of the third scattering vector component is obtained as shown in the following formula (4):

[0133]

[0134] Among them, q z represents the third scattering vector component, k0 represents the radius of the Ewald sphere equation, α i is the first angle, θ represents the angle between the first oblique direction and the second oblique direction, λ represents the wavelength of the X-ray, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; the first direction refers to the projection of the first oblique direction in the reciprocal space, the second direction refers to the projection of the second oblique direction in the reciprocal space, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; sin represents the sine function, cos represents the cosine function, and tan represents the tangent function.

[0135] The above scheme, through the calculation method of the third scattering vector component, can accurately determine the Z-direction position information of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0136] In a possible implementation method, the first scattering angle information is determined according to the Ewald sphere equation, the first scattering vector component and the second scattering vector component. Specifically, formulas (2), (3) and (4) are combined to obtain the scattering angle coordinates of the maximum diffraction point in the grazing incidence X-ray small angle scattering field of the two-dimensional periodic structure sample, that is, the first scattering angle coordinates, as shown in formula (5):

[0137]

[0138]

[0139] Among them, α f For the k f The pitch angle in the vertical direction of the Ewald sphere; θ f For the k f The deviation angle in the horizontal direction of the Ewald sphere; α i is the first angle, θ represents the angle between the first oblique direction and the second oblique direction, λ represents the wavelength of the X-ray, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; the first direction refers to the projection of the first oblique direction in the reciprocal space, the second direction refers to the projection of the second oblique direction in the reciprocal space, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; sin represents the sine function, cos represents the cosine function, tan represents the tangent function, arcsin represents the inverse sine function, and arctan represents the inverse tangent function.

[0140] The above scheme, through the calculation method of the first scattering angle, can accurately determine the scattering angle information of the Bragg peak of GISAXS for the two-dimensional periodic distribution structure sample, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0141] In one possible implementation method, in order to obtain the information of particles in a two-dimensional periodic structure sample in three-dimensional space, the two-dimensional periodic structure sample is generally rotated around the z-axis within the sample surface to detect the information of each particle at each angle, and then the shape of each particle in three-dimensional space and other information are determined by combining them. When the two-dimensional periodic structure sample is rotated around the z-axis within the sample surface by a certain angle, the position of the reciprocal space Bragg rod will change accordingly, and the angular coordinates corresponding to the diffraction point will be calculated. Figure 7 As shown, when the real-space sample rotates around the z-axis in the plane When the reciprocal space is also around k z Axis rotation angle At this time, the position corresponding to the Bragg rod is the fourth scattering vector component q x1 and the fifth scattered vector component q y1 It can be expressed as shown in the following formula (6):

[0142]

[0143] Among them, q x1 represents the fourth scattered vector component, q y1 represents the fifth scattered vector component, represents the second angle, θ represents the angle between the first oblique direction and the second oblique direction, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; the first direction refers to the projection of the first oblique direction in the reciprocal space, the second direction refers to the projection of the second oblique direction in the reciprocal space, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; sin represents the sine function, cos represents the cosine function, and tan represents the tangent function.

[0144] The above scheme, through the calculation method of the fourth scattering vector component and the fifth scattering vector component, can accurately determine the X-direction position information and the Y-direction position information of the Bragg peak of GISAXS of the two-dimensional periodic distribution structure sample after rotating by the second angle, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0145] In a possible implementation method, the sixth scattering vector component and the second scattering angle information are determined according to the Ewald sphere equation, the fourth scattering vector component and the fifth scattering vector component. Specifically, formulas (1), (2) and (3) are combined to obtain the scattering angle coordinates of the maximum diffraction point in the grazing incidence X-ray small-angle scattering field of the two-dimensional periodic structure sample, that is, the second scattering angle coordinates, as shown in formula (7):

[0146]

[0147] Among them, α f1 is the k at the second angle of incidence f The pitch angle in the vertical direction of the Ewald sphere; θ f1 is the k at the second angle of incidence f The deviation angle in the horizontal direction of the Ewald sphere; α i is the first angle, represents the second angle, θ represents the angle between the first oblique direction and the second oblique direction, λ represents the wavelength of the X-ray, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; the first direction refers to the projection of the first oblique direction in the reciprocal space, the second direction refers to the projection of the second oblique direction in the reciprocal space, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; sin represents the sine function, cos represents the cosine function, tan represents the tangent function, arcsin is the inverse sine function, and arctan is the inverse tangent function.

[0148] The above scheme, through the calculation method of the second scattering angle, can accurately determine the scattering angle information of the Bragg peak of GISAXS of the two-dimensional periodic distribution structure sample after rotating the second angle, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample based on the accurate positioning of the Bragg peak.

[0149] In a possible implementation method, the shape characteristics of the particles in the two-dimensional periodic structure sample are determined based on the first scattering angle information and / or the second scattering angle information and the detector. Specifically, the theoretical Bragg peak position angle coordinates are converted into pixel indices of the two-dimensional plane detector. Figure 8 As shown, the method comprises the following steps:

[0150] Step 801, input structural parameters and rotation angle range, and specify diffraction order.

[0151] In a possible implementation method, structural parameters and a rotation angle range are input, and diffraction orders are specified; the structural parameters and the rotation angle range include The diffraction orders include {m, n}.

[0152] Step 802, calculating the angular coordinates corresponding to the Bragg peak.

[0153] In a possible implementation method, the second scattering angle coordinate (α f1 ,θ f1 ).

[0154] Step 803, input the detector position and pixel size.

[0155] The detector position refers to the distance between the detector and the two-dimensional periodic structure sample. The detector is used to convert the first scattering angle information and / or the second scattering angle information into information that can be analyzed by a two-dimensional planar detector, and determine the structural characteristics of the particles in the two-dimensional periodic structure sample based on the information.

[0156] Step 804 , according to the angular coordinates corresponding to the Bragg peak, the detector position and the pixel size, the plane coordinates are calculated and mapped to the pixel grid according to the pixel size.

[0157] Step 805: remove duplicate coordinate elements to obtain a pixel index matrix.

[0158] The above scheme can convert the theoretical Bragg peak position angle coordinates into the pixel index of the two-dimensional planar detector, thereby realizing accurate detection of the shape and other characteristics of each particle in the two-dimensional periodic distribution structure sample.

[0159] Based on the same technical concept, Fig. 9 A grazing incidence small angle X-ray scattering Bragg peak positioning device 900 provided in an embodiment of the present application is exemplarily shown. Fig. 9 As shown, it includes: a receiving unit 901 and a determining unit 902. The receiving unit 901 is used to receive X-rays incident at a first angle to a two-dimensional periodic structure sample, wherein the two-dimensional periodic structure sample includes a plurality of particles; the determining unit 902 is used to determine the real-space structural parameters of the two-dimensional periodic structure sample; determine the first scattering vector component and the second scattering vector component corresponding to the particles in the two-dimensional periodic structure sample according to the real-space structural parameters, wherein the first scattering vector and the second scattering vector are orthogonal to each other; determine the third scattering vector component and the first scattering angle information according to the first scattering vector component and the second scattering vector component, wherein the third scattering vector component is orthogonal to the first scattering vector and the second scattering vector, and the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak when incident at the first angle.

[0160] In a possible implementation method, the receiving unit 901 is also used to receive X-rays that are glancingly incident on the two-dimensional periodic structure sample at a second angle; the determining unit 902 is also used to determine the fourth scattering vector component and the fifth scattering vector component corresponding to the particles in the two-dimensional periodic structure sample according to the real space structure parameters, wherein the fourth scattering vector and the fifth scattering vector are orthogonal to each other; based on the fourth scattering vector component and the fifth scattering vector component, determine the sixth scattering vector component and the second scattering angle information, wherein the sixth scattering vector component is orthogonal to the fourth scattering vector and the fifth scattering vector, and the second scattering angle information refers to the scattering angle information corresponding to the Bragg peak when the second angle is glancingly incident.

[0161] In one possible implementation method, the real-space structural parameters include one or more of the angle between the first oblique direction and the second oblique direction, the particle separation interval of the two-dimensional periodic structure sample along the first oblique direction, and the particle separation interval of the two-dimensional periodic structure sample along the second oblique direction.

[0162] In a possible implementation method, the determining unit 902 is further used to determine an Ewald sphere equation;

[0163] The determination unit 902 is specifically used to determine the third scattering vector component and the first scattering angle information based on the Ewald sphere equation, the first scattering vector component and the second scattering vector component; the determination unit 902 is specifically used to determine the sixth scattering vector component and the second scattering angle information based on the Ewald sphere equation, the fourth scattering vector component and the fifth scattering vector component.

[0164] In one possible implementation method, the structure of the Ewald sphere equation is as follows:

[0165]

[0166] Wherein, k0 represents the radius of the Ewald sphere equation, λ represents the wavelength of the X-ray; k ix , k iy and k iz are the kx-axis, ky-axis and kz-axis coordinates corresponding to the wave vector of the incident light in the Ewald sphere.

[0167] In a possible implementation method, the calculation method of the scattering vector is as follows:

[0168]

[0169] Where q represents the scattering vector, α i is the first angle, α f ,θ f is the first scattering angle information, wherein the α f is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere; f is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere. In a possible implementation method, the calculation method of the first scattering vector component and the second scattering vector component is as follows:

[0170]

[0171] Among them, qx represents the first scattering vector component, q y represents the second scattering vector component, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction; p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; θ represents the angle between the first oblique direction and the second oblique direction; n represents the order sequence along the first direction, and m represents the order sequence along the second direction.

[0172] In a possible implementation method, the determining unit 902 is used to substitute the first scattering vector component and the second scattering vector component into the Ewald sphere equation to determine the third scattering vector component;

[0173] The calculation formula of the third scattering vector component is as follows:

[0174]

[0175] Among them, q z represents the third scattered vector component.

[0176] In a possible implementation method, the calculation formula of the first scattering angle information is as follows:

[0177]

[0178]

[0179] In a possible implementation method, the calculation methods of the fourth scattering vector component and the fifth scattering vector component are respectively as follows:

[0180]

[0181]

[0182] Among them, q x1 represents the fourth scattered vector component, q y1 represents the fifth scattered vector component, represents the second angle, θ represents the angle between the first oblique direction and the second oblique direction, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction.

[0183] In a possible implementation method, the calculation formula of the second scattering angle information is as follows:

[0184]

[0185] Among them, α f1 θ is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere when the reflected light is incident at the second angle; f1 is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere when the incident light is incident at the second angle; i In a possible implementation method, the determination unit 902 is further used to determine the structural characteristics of particles in the two-dimensional periodic structure sample according to the first scattering angle information and / or the second scattering angle information and a detector; the detector is used to convert the first scattering angle information and / or the second scattering angle information into information that can be analyzed by a two-dimensional planar detector, and determine the structural characteristics of particles in the two-dimensional periodic structure sample according to the information.

[0186] Based on the same technical concept, the embodiment of the present application provides a grazing incidence small angle X-ray scattering Bragg peak positioning device 1000, which can be a computing device, for example. Fig.10 As shown, a grazing-incidence small-angle X-ray scattering Bragg peak positioning device 1000 includes at least one processor 1001 and a memory 1002 connected to the at least one processor. The specific connection medium between the processor 1001 and the memory 1002 is not limited in the embodiment of the present application. Fig.10 For example, the processor 1001 and the memory 1002 are connected via a bus. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0187] In an embodiment of the present application, the memory 1002 stores instructions that can be executed by at least one processor 1001. The at least one processor 1001 can execute the above-mentioned grazing-incidence small-angle X-ray scattering Bragg peak positioning method by executing the instructions stored in the memory 1002.

[0188] Among them, the processor 1001 is a control center of the grazing-incidence small-angle X-ray scattering Bragg peak positioning device 1000, which can use various interfaces and lines to connect various parts of the computer device, and perform resource settings by running or executing instructions stored in the memory 1002 and calling data stored in the memory 1002. Optionally, the processor 1001 may include one or more determination units, and the processor 1001 may integrate an application processor and a modem processor, wherein the application processor mainly processes an operating system, a user interface, and an application program, etc., and the modem processor mainly processes wireless communication. It can be understood that the above-mentioned modem processor may not be integrated into the processor 1001. In some embodiments, the processor 1001 and the memory 1002 may be implemented on the same chip, and in some embodiments, they may also be implemented separately on independent chips.

[0189] Processor 1001 can be a general-purpose processor, such as a central processing unit (CPU), a digital signal processor, an application-specific integrated circuit (ASIC), a field programmable gate array or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, and can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present application. A general-purpose processor can be a microprocessor or any conventional processor, etc. The steps of the method disclosed in the embodiments of the present application can be directly embodied as a hardware processor to be executed, or can be executed by a combination of hardware and software modules in the processor.

[0190] The memory 1002 is a non-volatile computer-readable storage medium that can be used to store non-volatile software programs, non-volatile computer executable programs and modules. The memory 1002 may include at least one type of storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory, a random access memory (Random Access Memory, RAM), a static random access memory (Static Random Access Memory, SRAM), a programmable read-only memory (Programmable Read Only Memory, PROM), a read-only memory (Read Only Memory, ROM), an electrically erasable programmable read-only memory (Electrically Erasable Programmable Read-Only Memory, EEPROM), a magnetic memory, a disk, an optical disk, etc. The memory 1002 is any other medium that can be used to carry or store a desired program code in the form of an instruction or data structure and can be accessed by a computer, but is not limited thereto. The memory 1002 in the embodiment of the present application can also be a circuit or any other device that can realize a storage function, for storing program instructions and / or data.

[0191] An embodiment of the present application also provides a computer-readable storage medium, which stores a computer-executable program, and the computer-executable program is used to enable a computer to execute a grazing-incidence small-angle X-ray scattering Bragg peak positioning method listed in any of the above methods.

[0192] An embodiment of the present application provides a computer program product, including a computer program executable by a computer device. When the program is run on the computer device, the computer device executes a grazing-incidence small-angle X-ray scattering Bragg peak positioning method listed in any of the above-mentioned methods.

[0193] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0194] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0195] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0196] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0197] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for locating the Bragg peak of grazing-incidence small-angle X-ray scattering, characterized in that: include: Receiving an X-ray incident at a first angle to a two-dimensional periodic structure sample, wherein the two-dimensional periodic structure sample includes a plurality of particles; Determining the real-space structural parameters of the two-dimensional periodic structure sample; Determine a first scattering vector component and a second scattering vector component corresponding to particles in the two-dimensional periodic structure sample according to the real space structure parameters, wherein the first scattering vector and the second scattering vector are orthogonal to each other; the first scattering vector component represents the position of the Bragg peak along the X-axis direction in the reciprocal space coordinate system, and the second scattering vector component represents the position of the Bragg peak along the Y-axis direction in the reciprocal space coordinate system; A third scattering vector component and first scattering angle information are determined based on the first scattering vector component and the second scattering vector component, wherein the third scattering vector component is orthogonal to the first scattering vector and the second scattering vector, and the third scattering vector component represents the position of the Bragg peak along the Z-axis direction in the reciprocal space coordinate system; and the first scattering angle information refers to the scattering angle information corresponding to the Bragg peak at grazing incidence at the first angle.

2. The method according to claim 1, characterized in that After the third scattering vector component and the scattering angle information are determined, the method further includes: receiving an X-ray incident at a second angle to the two-dimensional periodic structure sample; Determine a fourth scattering vector component and a fifth scattering vector component corresponding to particles in the two-dimensional periodic structure sample according to the real space structure parameters, wherein the fourth scattering vector and the fifth scattering vector are orthogonal to each other; the fourth scattering vector component refers to the position information of the Bragg peak in the X-axis direction after rotating the second angle, and the fifth scattering vector component refers to the position information of the Bragg peak in the Y-axis direction after rotating the second angle; A sixth scattering vector component and second scattering angle information are determined according to the fourth scattering vector component and the fifth scattering vector component, wherein the sixth scattering vector component is orthogonal to the fourth scattering vector and the fifth scattering vector, and the sixth scattering vector component refers to position information of the Bragg peak in the Z-axis direction after rotation by the second angle; and the second scattering angle information refers to scattering angle information corresponding to the Bragg peak at grazing incidence at the second angle.

3. The method according to claim 2, characterized in that The real space structural parameters include one or more of the angle between the first oblique direction and the second oblique direction, the particle separation interval of the two-dimensional periodic structure sample along the first oblique direction, and the particle separation interval of the two-dimensional periodic structure sample along the second oblique direction.

4. The method according to claim 2, characterized in that The method further comprises: determining an Ewald sphere equation; Determining a third scattering vector component and first scattering angle information according to the first scattering vector component and the second scattering vector component includes: Determine a third scattering vector component and first scattering angle information according to the Ewald sphere equation, the first scattering vector component and the second scattering vector component; The determining, according to the fourth scattering vector component and the fifth scattering vector component, a sixth scattering vector component and second scattering angle information comprises: A sixth scattering vector component and second scattering angle information are determined according to the Ewald sphere equation, the fourth scattering vector component and the fifth scattering vector component.

5. The method according to claim 4, characterized in that The structure of the Ewald sphere equation is as follows: Wherein, k0 represents the radius of the Ewald sphere equation, λ represents the wavelength of the X-ray; k ix , k iy and k iz are the kx-axis, ky-axis and kz-axis coordinates corresponding to the wave vector of the incident light in the Ewald sphere.

6. The method according to claim 5, characterized in that The calculation method of the scattering vector is as follows: Where q represents the scattering vector, α i is the first angle, α f ,θ f is the first scattering angle information, wherein the α f is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere; f is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere.

7. The method according to claim 1, characterized in that The calculation method of the first scattering vector component and the second scattering vector component is as follows: Among them, q x represents the first scattering vector component, q y represents the second scattering vector component, d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction; p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction; θ represents the angle between the first oblique direction and the second oblique direction; n represents the order sequence along the first direction, and m represents the order sequence along the second direction.

8. The method according to claim 7, characterized in that The calculation formula of the third scattering vector component is as follows: Among them, q z represents the third scattered vector component.

9. The method according to claim 8, characterized in that The calculation formula of the first scattering angle information is as follows:

10. The method according to claim 2, characterized in that The calculation methods of the fourth scattering vector component and the fifth scattering vector component are respectively as follows: Among them, q x1 represents the fourth scattered vector component, q y1 represents the fifth scattered vector component, represents the second angle, θ represents the angle between the first oblique direction and the second oblique direction, n represents the order sequence along the first direction, and m represents the order sequence along the second direction; d represents the particle division interval of the two-dimensional periodic structure sample along the first oblique direction, and p represents the particle division interval of the two-dimensional periodic structure sample along the second oblique direction.

11. The method according to claim 10, characterized in that The calculation formula of the second scattering angle information is as follows: Among them, α f1 θ is the pitch angle of the wave vector of the reflected light in the vertical direction of the Ewald sphere when the incident light is incident at the second angle; f1 is the deviation angle of the wave vector of the reflected light in the horizontal direction of the Ewald sphere when the reflected light is incident at the second angle; i is the first angle.

12. The method according to any one of claims 1 to 11, characterized in that The method further comprises: The first scattering angle information and / or the second scattering angle information are converted into information that can be analyzed by a two-dimensional planar detector, and the structural characteristics of the particles in the two-dimensional periodic structure sample are determined based on the information.

13. A computer-readable storage medium, characterized in that: The method comprises computer-readable instructions, and when a computer reads and executes the computer-readable instructions, the method according to any one of claims 1 to 12 is implemented.

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