Method for measuring the surface profile of nanostructures

Abstract

The application relates to a nanostructure surface profile measurement method, which comprises the following steps: S100, constructing a scattering intensity calculation model of a target nanostructure, wherein the scattering intensity calculation model comprises key structure parameters for describing a surface profile; S200, performing a small-angle X-ray scattering experiment on a sample with the target nanostructure to obtain scattering experiment data of the target nanostructure; and S300, fitting the scattering intensity calculation model by using the scattering experiment data to obtain key structure parameters of the target nanostructure. The nanostructure surface profile measurement method provided by the application does not need complex sample pretreatment, and has non-destructiveness, high efficiency and high accuracy, and provides a novel technical scheme for high-precision measurement of nanostructures in the field of semiconductor manufacturing.

Description

Technical Field

[0001] This invention relates to the field of semiconductor technology, and more specifically to a method for measuring the surface profile of nanostructures. Background Technology

[0002] With the rapid development of semiconductor technology, the feature size of electronic devices in integrated circuits is constantly shrinking, and traditional planar transistors are gradually transforming into three-dimensional complex architectures. In the semiconductor manufacturing process, the precise measurement of parameters such as the critical dimension (CD), line edge roughness (LER), and surface profile of nanostructures is a core element in ensuring stable device performance and improving production yield. Currently, commonly used nanostructure measurement techniques mainly include scanning electron microscopy (SEM), atomic force microscopy (AFM), and scattering measurement methods.

[0003] Scanning electron microscopy (SEM), with its high resolution, can measure critical dimensions (CD) and line edge roughness (LER). However, high-energy electron beams can easily damage samples and have limitations in accurately characterizing complex three-dimensional surface structures. Atomic force microscopy (AFM), while capable of acquiring high-precision three-dimensional morphology information, is slow and difficult to rapidly characterize large-area samples. Scattering measurements, although non-destructive, lack the ability to resolve details of extremely fine nanoscale features. As the size of nanostructure features continues to shrink, these traditional measurement methods are increasingly revealing their limitations in meeting practical measurement needs.

[0004] Critical-size small-angle X-ray scattering (CD-SAXS) is an emerging nanometrology technique with significant advantages such as non-destructiveness, nanoscale sensitivity, and large-area statistical characterization capabilities. However, existing research largely focuses on the cross-sectional profile of gratings, with less attention paid to the high-precision measurement of surface profile parameters that directly affect device performance. Furthermore, it lacks systematic model support based on kinematic diffraction theory, making it difficult to meet the high-precision metrology requirements of nanostructures in semiconductor manufacturing. Therefore, developing a method for efficiently and accurately measuring the surface profile of nanostructures (such as nanogratings, nanowires, or nanofield-effect transistors) is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method for measuring the surface profile of nanostructures, so as to achieve efficient and high-precision measurement.

[0006] To achieve the above objectives, the present invention provides a method for measuring the surface profile of a nanostructure, comprising the following steps:

[0007] S100: Construct a scattering intensity calculation model for the target nanostructure, wherein the scattering intensity calculation model includes key structural parameters for describing the surface profile;

[0008] S200: Perform small-angle X-ray scattering experiments on the sample with the target nanostructure to obtain scattering experimental data of the target nanostructure;

[0009] S300: The scattering intensity calculation model is fitted using the scattering experimental data to obtain the key structural parameters of the target nanostructure.

[0010] Optionally, step S100 specifically includes the following steps:

[0011] S110: Establish a structural model of the target nanostructure. The structural model is formed by translating polygonal units multiple times along the horizontal and vertical directions. Each polygonal unit is composed of multiple square scattering units. Each polygonal unit includes a first side, a second side, a third side, a fourth side, a fifth side, and a sixth side connected end to end in sequence. The first side, the third side, and the fifth side are all parallel to the horizontal direction, and the second side, the fourth side, and the sixth side are all parallel to the vertical direction. The length of the first side is a×L0, the length of the second side is m×L0, the length of the third side is n×L0, the length of the fourth side is (mb)×L0, the length of the fifth side is (an)×L0, and the length of the sixth side is b×L0. Wherein, L0 is the side length of the scattering unit, a is the side length coefficient of the first side, m is the side length coefficient of the second side, n is the side length coefficient of the third side, and b is the side length coefficient of the sixth side.

[0012] S120: Determine the shape factor of the scattering unit based on kinematic diffraction theory;

[0013] S130: Determine the scattering intensity of the polygonal unit based on the structural model of the target nanostructure and the shape factor of the scattering unit;

[0014] S140: Determine the structure factor based on the periodicity of the target nanostructure;

[0015] S150: Determine the scattering intensity calculation model of the target nanostructure based on the structural factor and the scattering intensity of the polygonal unit.

[0016] Optionally, the shape factor of the scattering unit satisfies the following relationship:

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] Where f0 is the shape factor of the scattering unit, q is the scattering vector, |q| is the magnitude of the scattering vector, and q x q y Let θ be the horizontal and vertical components of the scattering vector, θ be half the scattering angle in the small-angle X-ray scattering experiment, λ be the wavelength of the X-rays in the small-angle X-ray scattering experiment, and α be the rotation angle of the sample. When α = 0°, the X-rays are incident perpendicularly to the sample surface, i.e., perpendicular to the sample surface. Figure 3 The xy plane in the middle.

[0022] Optionally, the scattering intensity of the polygonal unit satisfies the following relationship:

[0023] ,

[0024] ,

[0025] ,

[0026] ,

[0027] in, Let be the scattering intensity of the polygonal unit. Let the scattering intensity be the value of a rectangle with the first and sixth sides as its length and width. Let the scattering intensity be the value of a rectangle with the second and third sides as its length and width. Let N be the scattering intensity of a rectangle with the third and sixth sides as its length and width, and N be the index of the scattering unit.

[0028] Optionally, the structural factors satisfy the following relationship:

[0029] ,

[0030] Wherein, S is the structure factor, X is the period of the target nanostructure in the horizontal direction, Y is the period of the target nanostructure in the vertical direction, δ is the Dirac function, j is the diffraction order index in the horizontal direction, and k is the diffraction order index in the vertical direction.

[0031] Optionally, the scattering intensity calculation model of the target nanostructure satisfies the following relationship:

[0032] I= ×S,

[0033] Where I represents the scattering intensity of the target nanostructure.

[0034] Optionally, the key structural parameters include a, b, m, n, and X, and the scattering experimental data includes q data of the sample having the target nanostructure. x -q y The distribution of scattering intensity on a plane.

[0035] Optionally, step S300 specifically includes the following steps:

[0036] S310: Extract q from the scattering experimental data y =0 and q x The experimental scattering intensity curve within the preset range;

[0037] S320: Using q y =0 and q x The key structural parameters are fitted to the experimental scattering intensity curves within a preset range to obtain the optimal solution for the key structural parameters.

[0038] Optionally, step S320 specifically includes:

[0039] The key structural parameters are iteratively adjusted using one of the differential evolution algorithm, genetic algorithm, and particle swarm optimization algorithm to improve the q predicted by the scattering intensity calculation model. y =0 and q x The mean square error between the scattering intensity curve within the preset range and the experimental scattering intensity curve is minimized until the convergence criterion is met, so as to obtain the optimal solution of the key structural parameters.

[0040] Optionally, the target nanostructure is a nanograting or a nanofield-effect transistor with a periodic concave-convex structure. Attached Figure Description

[0041] Figure 1 This is a flowchart of a method for measuring the surface profile of a nanostructure according to an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of the structural model of the target nanostructure according to an embodiment of the present invention;

[0043] Figure 3 To the q of the HSQ nanograting sample according to an embodiment of the present invention x -q y A schematic diagram of the scattering intensity distribution on a plane;

[0044] Figure 4A To represent the q corresponding to different values ​​of a according to embodiments of the present invention. y =0 and q x A schematic diagram of the scattering intensity curve within a preset range;

[0045] Figure 4B To represent q corresponding to different values ​​of b according to embodiments of the present invention. y =0 and q x A schematic diagram of the scattering intensity curve within a preset range;

[0046] Figure 4C To represent q corresponding to different values ​​of m according to embodiments of the present invention. y =0 and q x A schematic diagram of the scattering intensity curve within a preset range;

[0047] Figure 4D To represent the q corresponding to different values ​​of n according to embodiments of the present invention y =0 and q x A schematic diagram of the scattering intensity curve within a preset range;

[0048] Figure 5 This is a comparison chart of the scattering intensity curve predicted by the scattering intensity calculation model according to an embodiment of the present invention and the experimental scattering intensity curve. Detailed Implementation

[0049] The preferred embodiments of the present invention are given below with reference to the accompanying drawings and described in detail.

[0050] like Figure 1 As shown, this embodiment of the invention provides a method for measuring the surface profile of a nanostructure, which includes the following steps:

[0051] S100: Construct a scattering intensity calculation model for the target nanostructure. The scattering intensity calculation model includes key structural parameters used to describe the surface profile.

[0052] Nanostructures are placed on semiconductor devices, which serve as the physical carriers of these nanostructures. Based on the design drawings of the semiconductor device (such as photolithographic mask images or 3D design models), the core geometric features of the nanostructure can be extracted. Based on these core geometric features, a nanostructure model can be constructed. Then, based on kinematic diffraction theory, a calculation model for the scattering intensity of the nanostructure can be built. The target nanostructure refers to the nanostructure to be measured.

[0053] In some embodiments, the target nanostructure can be a nanograting or a nanofield-effect transistor, and step S110 specifically includes the following steps:

[0054] S110: Establish a structural model of the target nanostructure: such as Figure 2As shown, a nanograting or nanofield-effect transistor with a periodic concave-convex structure is considered to be formed by multiple translations of polygonal units along the x-axis (horizontal direction) and y-axis (vertical direction). The polygonal unit is composed of multiple small squares with a side length of L0 (ranging from 1 to 10 nm), and each small square can be called a scattering unit. The polymorphic unit is L-shaped, consisting of a first side 11, a second side 12, a third side 13, a fourth side 14, a fifth side 15, and a sixth side 16 connected end to end. The first side 11, the third side 13, and the fifth side 15 are all parallel to the x-axis, while the second side 12, the fourth side 14, and the sixth side 16 are all parallel to the y-axis. The length of the first side 11 is a×L0, the length of the second side 12 is m×L0, the length of the third side 13 is n×L0, the length of the fourth side 14 is (mb)×L0, the length of the fifth side 15 is (an)×L0, and the length of the sixth side 16 is b×L0. Here, a is the side length coefficient of the first side 11, m is the side length coefficient of the second side 12, n is the side length coefficient of the third side 13, and b is the side length coefficient of the sixth side 16.

[0055] S120: Based on operational diffraction theory, determine the shape factor of the scattering unit:

[0056] The form factor of a scattering unit (with side length L0 and uniform electron density) can be denoted as f0, and its calculation formula is as follows:

[0057]

[0058] Where, q x q y Let be the components of the scattering vector q in the x and y directions, respectively. The scattering vector q is a two-dimensional vector with a magnitude of . Where θ is half the scattering angle in the small-angle X-ray scattering experiment, and λ is the wavelength of the X-rays in the small-angle X-ray scattering experiment. , α is the rotation angle of the sample. When α = 0°, the X-rays are incident perpendicularly to the sample surface, that is, perpendicular to the sample surface. Figure 3 The xy plane in the middle.

[0059] S130: Determine the scattering intensity of polygonal units based on the structural model of the target nanostructure and the shape factor of the scattering unit.

[0060] Considering the superposition characteristics of polygonal elements, its scattering intensity is obtained by superimposing the scattering contributions from different regions, and its calculation formula is as follows:

[0061]

[0062] in:

[0063]

[0064]

[0065]

[0066] in, Let be the scattering intensity of the polygonal unit. The scattering intensity is represented by a rectangle with the first side 11 and the sixth side 16 as its length and width. The scattering intensity is represented by a rectangle with the second side 12 and the third side 13 as its length and width. Let N be the scattering intensity of a rectangle with the third side 13 and the sixth side 16 as its length and width, and let N be the number of the scattering unit.

[0067] S140: Determining the structure factor based on the periodicity of the target nanostructure.

[0068] To accurately describe the periodicity of the target nanostructure in the x and y directions, a structure factor S is introduced, and its calculation formula is as follows:

[0069]

[0070] Where X is the period of the target nanostructure in the x-direction, Y is the period of the target nanostructure in the y-direction, δ is the Dirac function, j is the diffraction order index in the x-direction, k is the diffraction order index in the y-direction, and j and k take all integer values.

[0071] S150: A calculation model for determining the scattering intensity of a target nanostructure based on structural factors and the scattering intensity of polygonal units.

[0072] The scattering intensity calculation model for the target nanostructure is as follows:

[0073] I= ×S

[0074] Where I represents the scattering intensity of the target nanostructure.

[0075] S200: Perform small-angle X-ray scattering experiments on samples with the target nanostructure to obtain scattering experimental data of the target nanostructure.

[0076] Samples with nanostructures can be prepared using a 50keV electron beam lithography system at the BL08U1B beamline of the Shanghai Synchrotron Radiation Facility (SSRF). Taking the HSQ (hydrosiloxane) nanograting as an example, the process is as follows: Fox16 photoresist is diluted with methyl isobutyl ketone (MIBK) at a ratio of 1:3, spin-coated on a silicon wafer at 4000 rpm for 1 min, and then pre-baked at 180°C for 5 min; the 130 nm thick HSQ layer is exposed using an electron beam lithography (EBL) system, and then the sample is placed in a 25% concentration tetramethylammonium hydroxide (TMAH) developer and developed at 50°C for 30 s. Then it is rinsed with deionized water for 1 min, rinsed with isopropanol (IPA) for 15 s, and finally dried with nitrogen to obtain the nanograting sample.

[0077] After sample preparation, small-angle X-ray scattering experiments can be conducted in the SAXS beamline of the SSRF. For example, an X-ray energy of E=10keV (corresponding to a wavelength λ=0.124nm) can be selected, using a PILATUS 2M detector (pixel size 172×172μm). 2 The sample-detector distance was set to 7164.17 nm to ensure coverage of the scattering vector range corresponding to the surface profile of the target nanostructure. Scattering experimental data of the sample were acquired using the detector. The scattering experimental data includes the scattering of the sample with the target nanostructure in reciprocal space. x -q y The distribution of scattering intensity on a plane. For example... Figure 3 The figure shows the q of the HSQ nanograting sample. x -q y The scattering intensity distribution of the plane, which clearly shows The main diffraction peak in the direction and the satellite peaks on both sides.

[0078] S300: The scattering intensity calculation model is fitted using scattering experimental data to obtain the key structural parameters of the target nanostructure.

[0079] The key structural parameters include a, b, m, n, and X. Step S300 specifically includes the following steps:

[0080] S310: Extracting q from scattering experimental data y =0 and q x Within a preset range (e.g., 0.02~0.18nm) -1 The experimental scattering intensity curve of the target nanostructure surface profile is included in the preset range, which contains the scattering peaks corresponding to the key structures. This can effectively reflect the changes in the key structural parameters and provide a reliable data basis for accurate fitting.

[0081] S320: Using q y =0 and qx The key structural parameters a, b, m, n, and X are fitted to the experimental scattering intensity curves within a preset range to obtain the optimal solutions for the key structural parameters a, b, m, n, and X.

[0082] In some embodiments, differential evolution (DE), genetic algorithms, particle swarm optimization, or any other suitable algorithm can be used to iteratively adjust the key structural parameters a, b, m, n, and X, so that the q predicted by the scattering intensity calculation model is obtained. y =0 and q x The mean square error (MSE) between the scattering intensity curve within a preset range and the experimental scattering intensity curve is minimized until the convergence criterion is met, thereby obtaining the optimal solution for the key structural parameters. For example... Figure 4A The figure shows the corresponding values ​​of q for different values ​​of a. y =0 and q x The scattering intensity curve within the preset range, such as Figure 4B The figure shows the corresponding values ​​of q for different values ​​of b. y =0 and q x The scattering intensity curve within the preset range, such as Figure 4C The figure shows the corresponding values ​​of q for different values ​​of m. y =0 and q x The scattering intensity curve within the preset range, such as Figure 4D The figure shows the corresponding q for different values ​​of n. y =0 and q x The scattering intensity curve within the preset range, Figures 4A-4D The influence of each parameter on the scattering intensity is displayed intuitively.

[0083] The parameters of the DE algorithm are set as follows: population size is 50 (this size ensures good global search capability during the optimization process), the mutation factor ranges from (0.1, 1) (to achieve a balance between local and global search), the crossover probability is 0.9 (which is beneficial to improving population diversity), and the convergence criterion is that the relative change of the objective function (i.e., the mean squared error (MSE) between the model prediction and the experimental data) during continuous iterations is less than 1 × 10⁻⁶. -6 Alternatively, the number of iterations can reach 500 (balancing computational efficiency and optimization accuracy).

[0084] like Figure 5 The figure shows a comparison between the scattering intensity curve predicted by the scattering intensity calculation model and the experimental scattering intensity curve. The degree of agreement between the two curves verifies the accuracy of the scattering intensity calculation model.

[0085] The key structural parameters a, b, m, n, and X obtained through fitting (i.e., the optimal solution for the key structural parameters) can be directly converted into actual contour indicators such as linewidth, height, and period of the target nanostructure. Accurate acquisition of these key structural parameters can, in turn, guide the adjustment of process parameters such as photolithography and development in semiconductor manufacturing, reducing device dimensional deviations, thereby ensuring stable device performance, reducing defect rates, and improving production yield.

[0086] The surface profile measurement method for nanostructures presented in this invention requires no complex sample pretreatment and combines non-destructive, high efficiency, and high accuracy, providing a novel technical solution for high-precision metrology of nanostructures in the semiconductor manufacturing field. The method is applicable to the surface profile and roughness characterization of nanowires, nanotrenches, and periodic micro / nanostructures in semiconductor manufacturing.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. That is, all simple and equivalent changes and modifications made based on the claims and description of this invention fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A method for measuring the surface profile of a nanostructure, characterized in that, Includes the following steps: S100: Construct a scattering intensity calculation model for the target nanostructure, wherein the scattering intensity calculation model includes key structural parameters for describing the surface profile; S200: Perform small-angle X-ray scattering experiments on the sample with the target nanostructure to obtain scattering experimental data of the target nanostructure; S300: The scattering intensity calculation model is fitted using the scattering experimental data to obtain the key structural parameters of the target nanostructure; Step S100 specifically includes the following steps: S110: Establish a structural model of the target nanostructure. The structural model is formed by multiple translations of polygonal units along the horizontal and vertical directions. Each polygonal unit is composed of multiple square scattering units. Each polygonal unit includes a first side, a second side, a third side, a fourth side, a fifth side, and a sixth side connected end-to-end in sequence. The first side, the third side, and the fifth side are all parallel to the horizontal direction, and the second side, the fourth side, and the sixth side are all parallel to the vertical direction. The length of the first side is a×L0, the length of the second side is m×L0, the length of the third side is n×L0, the length of the fourth side is (mb)×L0, the length of the fifth side is (an)×L0, and the length of the sixth side is b×L0. Wherein, L0 is the side length of the scattering unit, a is the side length coefficient of the first side, m is the side length coefficient of the second side, n is the side length coefficient of the third side, and b is the side length coefficient of the sixth side. The key structural parameters include a, b, m, n, and X. S120: Determine the shape factor of the scattering unit based on kinematic diffraction theory; S130: Determine the scattering intensity of the polygonal unit based on the structural model of the target nanostructure and the shape factor of the scattering unit; S140: Determine the structure factor based on the periodicity of the target nanostructure; S150: Determine the scattering intensity calculation model of the target nanostructure based on the structural factor and the scattering intensity of the polygonal unit; The shape factor of the scattering unit satisfies the following relationship: ， ， ， ， Where f0 is the shape factor of the scattering unit, q is the scattering vector, |q| is the magnitude of the scattering vector, and q x q y θ represents the horizontal and vertical components of the scattering vector, θ is half the scattering angle during the small-angle X-ray scattering experiment, λ is the wavelength of the X-rays during the small-angle X-ray scattering experiment, and α is the rotation angle of the sample. The scattering intensity of the polygonal unit satisfies the following relationship: ， ， ， ， in, Let be the scattering intensity of the polygonal unit. Let the scattering intensity be the value of a rectangle with the first and sixth sides as its length and width. Let the scattering intensity be the value of a rectangle with the second and third sides as its length and width. The scattering intensity is represented by the third and sixth sides of a rectangle, where N is the number of the scattering unit. The structural factors satisfy the following relationship: ， Wherein, S is the structure factor, X is the period of the target nanostructure in the horizontal direction, Y is the period of the target nanostructure in the vertical direction, δ is the Dirac function, j is the diffraction order index in the horizontal direction, and k is the diffraction order index in the vertical direction. The scattering intensity calculation model of the target nanostructure satisfies the following relationship: I= ×S, Where I represents the scattering intensity of the target nanostructure.

2. The surface profile measurement method for nanostructures according to claim 1, characterized in that, The key structural parameters include a, b, m, n, and X, and the scattering experimental data includes q values ​​of samples with the target nanostructure. x -q y The distribution of scattering intensity on a plane.

3. The surface profile measurement method for nanostructures according to claim 2, characterized in that, Step S300 specifically includes the following steps: S310: Extract q from the scattering experimental data y =0 and q x The experimental scattering intensity curve within the preset range; S320: Using q y =0 and q x The key structural parameters are fitted to the experimental scattering intensity curves within a preset range to obtain the optimal solution for the key structural parameters.

4. The surface profile measurement method for nanostructures according to claim 3, characterized in that, Step S320 specifically includes: The key structural parameters are iteratively adjusted using one of the differential evolution algorithm, genetic algorithm, and particle swarm optimization algorithm to improve the q predicted by the scattering intensity calculation model. y =0 and q x The mean square error between the scattering intensity curve within the preset range and the experimental scattering intensity curve is minimized until the convergence criterion is met, so as to obtain the optimal solution of the key structural parameters.

5. The method for measuring the surface profile of nanostructures according to claim 1, characterized in that, The target nanostructure is a nanograting or a nanofield-effect transistor with a periodic concave-convex structure.

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