A method for nondestructive extraction of island nanostructure geometry parameters

Abstract

The application discloses a method for nondestructively extracting geometric parameters of island nanostructure, which comprises performing atomic force microscope test, obtaining surface height data of a substrate and a sample respectively and retaining minimum value areas as references; extracting average height and height distribution variance by fitting relative frequency distribution of the surface height data through Gaussian distribution; establishing an island growth physical model in which surface morphology of the sample is equivalent linear superposition of a bottom wet layer and nano island structure; determining surface height data of the bottom wet layer according to surface height data of the substrate; finally, substituting surface height data of the sample extracted from the test and height data of the bottom wet layer determined into mean value equation and variance equation of the island growth physical model to solve the equations simultaneously, so that surface coverage and relative height of the island nanostructure are obtained. The method of the application can accurately and nondestructively extract core geometric parameters of discrete island nano particles without performing destructive characterization and conventional minimum point zero operation.

Description

Technical Field

[0001] This invention belongs to the field of nanomaterial characterization and computational physics, specifically relating to a method for non-destructively extracting geometric parameters of island nanostructures. Background Technology

[0002] As modern nanotechnology and micro / nano devices develop towards high-density integration, zero-dimensional discrete island nanostructures such as semiconductor quantum dots, metal catalytic nanoislands, and magnetic nanoparticles have shown great potential physical advantages over traditional two-dimensional continuous thin films in fields such as photoelectrocatalysis, quantum information, and high-frequency magnetic devices.

[0003] To delve deeper into and manipulate these intrinsic physical correlations at the discrete nanoscale, it is essential to perform high-precision quantitative characterization of their fundamental microscopic geometric parameters, especially the absolute height of discrete particles relative to the substrate and their macroscopic surface coverage on the substrate.

[0004] Currently, the characterization of nanostructure morphology mainly relies on transmission electron microscopy. Although high-resolution cross-sectional transmission electron microscopy has extremely high spatial resolution, it is a destructive characterization method with high sample preparation costs and long processing time. Moreover, it can only observe morphological features in a very small local area, and the extracted data is difficult to represent the global statistical properties of macroscopic large-area thin films.

[0005] Atomic force microscopy (AFM) is a widely used non-destructive method for characterizing the three-dimensional morphology of surfaces. However, conventional AFM depth analysis and image processing algorithms have serious limitations when dealing with sub-nanometer discontinuous epitaxial layers, especially island-like nanostructures. Because the probe cannot penetrate densely grown epitaxial layers to reach the underlying substrate, image processing algorithms typically force zero-order flattening and minimum point zeroing operations to eliminate mechanical drift during scanning. This relative resetting of the Z-axis reference plane causes the average apparent height of a single measurement to completely lose information about the physical thickness of the underlying layer. Particularly for densely packed island-like nanostructures, existing AFM measurement software cannot directly separate the absolute height of the particles relative to the substrate, let alone quantitatively calculate the macroscopic surface coverage of the particles. Summary of the Invention

[0006] In view of the problems existing in the prior art, the purpose of this invention is to overcome the technical defects of existing micro-nano characterization techniques, such as strong destructiveness, lack of global statistical representativeness, and loss of reference plane in conventional atomic force microscopy algorithms. This invention provides a method for non-destructive extraction of geometric parameters of island nanostructures based on statistical analysis of atomic force microscopy. This method can overcome the reference plane drift problem caused by conventional atomic force microscopy image processing algorithms. Without damaging the sample, the core geometric parameters of discrete island nanostructures can be accurately resolved by using only the height statistical data of surface scanning.

[0007] To achieve this objective, the present invention adopts the following technical solution: This invention provides a method for non-destructively extracting geometric parameters of island-like nanostructures, comprising the following steps: A substrate and a sample on which island-like nanostructures are grown are provided respectively; The substrate and the sample were subjected to atomic force microscopy to obtain the corresponding surface height data, and the area corresponding to the minimum value was used as the reference surface. The relative frequency distribution of the surface height data is statistically analyzed, and the average height and height distribution variance of the substrate and the sample are extracted by fitting a Gaussian distribution function. The surface morphology of the sample is regarded as a linear superposition of the bottom wetting layer and the island nanostructure, and a physical model of island growth including mean equation and variance equation is constructed. The average height and height distribution variance of the bottom wetting layer are determined based on the average height and height distribution variance of the substrate. Substituting the average height and height distribution variance of the sample with the average height and height distribution variance of the bottom wetting layer into the island growth physical model, the surface coverage and relative height of the island nanostructure are obtained by solving the equations simultaneously.

[0008] The method of this invention performs atomic force microscopy morphological scanning on a substrate (i.e., a blank substrate) and a target sample on which island-like nanostructures are epitaxially grown, respectively, to obtain surface height data of each pixel (test point) within the scanning area (test area). During the scanning and data export process, a minimum pinning mechanism is retained, that is, the minimum value region is used as an implicit physical reference surface to avoid performing a forced minimum point zeroing operation on the morphological image; the minimum value region is a low-level region within the scanning area that can serve as a background reference, preferably an exposed area, a recessed area, or a deep microscopic defect area of ​​the substrate that is not completely covered by the deposited material. Based on this, the relative frequency distribution statistics of the obtained surface height data of the substrate and sample were performed, and Gaussian statistical characteristic parameters were extracted to obtain the average height and height distribution variance of the substrate and sample, respectively. These values ​​were then applied to the construction of the island growth physical model and equation calculation. The island growth physical model is based on the mixed distribution principle in statistics, and regards the surface morphology of the sample as an equivalent linear superposition of the bottom wetting layer and the upper island nanostructure. In order to achieve parameter decoupling, in the statistical calculation, the micromorphology of the island nanostructure is approximated as the vertical height translation of the bottom wetting layer on the Z-axis. This means that the obtained sample height data is equal to the superposition of the height data of the bottom wetting layer and the height data of the island nanostructure. The height data of the bottom wetting layer can be determined based on the height data of the substrate. Therefore, by combining the integral and statistical moment properties of the probability density function, a set of two nonlinear equations containing the target geometric parameters (i.e., the surface coverage and relative height of the island nanostructure) can be constructed. Then, by substituting the average height and height distribution variance of the substrate and sample into the mean equation and variance equation respectively, the target geometric parameters (i.e., the surface coverage and relative height of the island nanostructure) can be obtained by solving the equations simultaneously.

[0009] As can be seen from the above, the method provided by this invention can not only overcome the reference plane drift problem caused by conventional atomic force microscopy image processing algorithms, but also accurately resolve the core geometric parameters of discrete island nanostructures using only surface scanning height statistics without damaging the sample. It has high testing efficiency, accurate results, and practical application value.

[0010] The following are preferred technical solutions of the present invention, but are not intended to limit the technical solutions provided by the present invention. The technical objectives and beneficial effects of the present invention can be better achieved and realized through the following technical solutions.

[0011] As a preferred technical solution of the present invention, the substrate is a flat substrate with a root mean square roughness of no more than 1.0 nm as measured by atomic force microscopy. For example, it can be 1.0 nm, 0.8 nm, 0.6 nm, 0.5 nm, 0.3 nm, 0.2 nm or 0.1 nm, etc. More preferably, the root mean square roughness of the substrate is no more than 0.5 nm.

[0012] As a preferred embodiment of the present invention, the substrate is a single-crystal substrate or an amorphous substrate.

[0013] Preferably, the single-crystal substrate comprises at least one of silicon, sapphire, silicon carbide, garnet, or strontium titanate.

[0014] Preferably, the amorphous substrate includes at least one of amorphous quartz glass, a silicon wafer with a thermal oxide layer on its surface, or an amorphous polymer substrate.

[0015] As a preferred technical solution of the present invention, the material composition of the island nanostructure includes at least one of metal, semiconductor, oxide, non-metallic inorganic material or polymer.

[0016] As a preferred technical solution of the present invention, the method for growing the island-like nanostructure includes at least one of physical vapor deposition, chemical vapor deposition, or wet chemical method.

[0017] As a preferred embodiment of the present invention, the island-like nanostructures on the sample are discontinuous discrete islands with a surface coverage greater than zero and less than one.

[0018] As a preferred technical solution of the present invention, the form of the Gaussian distribution function includes: To perform nonlinear least squares fitting; where, The average height of the substrate or the sample. The parameter is the Gaussian peak width and satisfies , The standard deviation of the height distribution (i.e. Standard deviation of height distribution The variance of the height distribution is Specifically, the average height of the base can be obtained separately. and height distribution variance and the average height of the sample and height distribution variance .

[0019] As a preferred embodiment of the present invention, the mean equation in the island growth physical model includes: The variance equation includes: ;in, The average height of the sample. The variance of the height distribution of the sample; The average height of the bottom wetting layer. The variance of the height distribution of the underlying wetting layer; The surface coverage of the island-like nanostructure. The relative height of the island-like nanostructure is given.

[0020] As a preferred technical solution of the present invention, the determination of the average height and height distribution variance of the bottom wetting layer includes: the height distribution variance of the bottom wetting layer is equal to the height distribution variance of the substrate; the average height of the bottom wetting layer is equal to the sum of the average height of the substrate and the theoretical minimum unit structural thickness of the island nanostructure material system; or, it is determined directly by extracting the height statistical characteristics of the non-island regions in the sample.

[0021] The underlying wetting layer described in this invention refers to a thin layer or background region located below the island nanostructure during the formation of the island nanostructure, which can be statistically approximated as a continuous background. Its height statistical characteristics can be determined by the height statistical characteristics of a blank substrate combined with the minimum structural thickness calibration term of the material system of the island nanostructure, or by the height statistical characteristics of non-island regions in the sample. The underlying wetting layer is not limited to being a complete continuous film; its essence is an equivalent statistical layer used to characterize the background term within the framework of mixed distribution inversion.

[0022] Specifically, based on the obtained substrate height data and the thermodynamic characteristics of epitaxial growth, the relevant parameter values ​​of the underlying wetting layer can be calculated. That is, the variance of the height distribution of the underlying wetting layer. It can be equal to the variance of the height distribution of the base. Average height of the underlying wetting layer It can be equal to the average height of the blank substrate. With respect to the theoretical minimum unit structural thickness of this material system The sum of The theoretical minimum unit structure thickness described in this invention refers to the inherent physical thickness of a single unit cell layer, molecular layer, or atomic layer constituting the specific material system, such as the lattice spacing, which can be obtained through theoretical crystallographic calculations or conventional characterization methods (such as X-ray diffraction).

[0023] It should be noted that, due to space limitations and to avoid redundancy, this invention does not exhaustively list all point values ​​within the above numerical range, but it is not limited to the listed values ​​either; other unlisted values ​​within the above numerical range are also applicable.

[0024] Compared with existing technical solutions, the present invention has at least the following beneficial effects: The method for non-destructively extracting geometric parameters of island nanostructures provided by this invention can achieve non-destructive extraction and decoupling of parameters: by cleverly utilizing the statistical characteristics of morphological height data and combining physical growth theory, the complex micro-morphological overlap phenomenon is simplified into a binary algebraic equation, and the height and coverage of nanoparticles are successfully and accurately decoupled from single surface morphological scanning data, completely eliminating the dependence on expensive and destructive cross-sectional transmission electron microscopes.

[0025] The method for non-destructively extracting geometric parameters of island nanostructures provided by this invention can overcome the bottleneck of algorithm reference plane drift: it reveals and utilizes the minimum pinning mechanism in morphology scanning, and through the design of the mean difference model, it bypasses the system limitation of conventional atomic force microscopy measurement software that lacks an absolute depth scale, thus preserving the true physical thickness information.

[0026] The method for non-destructively extracting geometric parameters of island nanostructures provided by this invention yields data with high global statistical representativeness: the calculation process can be based on the global frequency probability density function of tens of thousands of pixels within a region of hundreds of nanometers, effectively suppressing random fluctuation errors in local geometric morphology, and the extracted geometric parameters have extremely high macroscopic statistical representativeness. Attached Figure Description

[0027] Figure 1 This is a flowchart of the method for non-destructive extraction of geometric parameters of island nanostructures provided in Embodiment 1 of the present invention.

[0028] Figure 2 This is an atomic force microscope image of the substrate in Example 2.

[0029] Figure 3 This is an atomic force microscope image of the sample from Example 2.

[0030] Figure 4 This is a comparison curve of the relative frequency distribution of the height between the substrate and the sample surface and its Gaussian distribution fitting in Example 2. Detailed Implementation

[0031] The technical solution of the present invention will be further illustrated below through specific embodiments.

[0032] Those skilled in the art will understand that the embodiments described are merely illustrative of the invention and should not be construed as limiting the invention.

[0033] Example 1 This embodiment provides a method for non-destructively extracting the geometric parameters of island-like nanostructures, such as... Figure 1 As shown, the method includes the following steps: S1. Obtain surface height data: Atomic force microscopy (AFM) was used to scan the morphology of both the substrate (blank substrate) and the sample with epitaxially grown island nanostructures to obtain the surface height data of each pixel within the scanned area. During the scanning and data export process, a minimum pinning mechanism was retained, that is, the minimum value region was used as an implicit physical reference surface to avoid performing a forced minimum point zeroing operation on the morphology image. The minimum value region is a low-level region within the scanned area that can be used as a background reference, preferably an exposed area, a recessed area, or a deep micro-defect area of ​​the substrate that is not completely covered by the deposited material. S2. Extract Gaussian statistical feature parameters: The relative frequency distribution of the surface height data obtained in step S1 is statistically analyzed using a Gaussian distribution function. A nonlinear least-squares fit was performed on the relative frequency distribution data. Two statistical parameters were extracted from the fit result: mean height. and height distribution standard deviation The variance of the height distribution was calculated. ,in Specifically, this step yields the average height of the blank substrate. and height distribution variance and the average height of the target sample and height distribution variance ; S3. Construct a physical model for island growth: Based on the principle of mixed distribution in statistics, an equivalent physical model describing the growth of island nanostructures is established. The surface morphology of the target sample is considered as an equivalent linear superposition of the bottom wetting layer and the upper island nanostructure. To achieve parameter decoupling, in statistical calculations, the microstructure of the island nanostructure is approximated as a vertical height translation of the bottom wetting layer along the Z-axis. Based on the integral and statistical moment properties of the probability density function, a system of two nonlinear equations containing the geometric parameters of the target is constructed: The mean equation is: ; The variance equation is: ; in, This represents the average height of the bottom wetting layer. The variance of the height distribution of the bottom wetting layer. The (equivalent) surface coverage of the island-like nanostructure. The (equivalent) relative height of the island-like nanostructure; S4. Determine the parameters of the underlying wetting layer: Based on the thermodynamic characteristics of epitaxial growth, calculate the parameters of the bottom wetting layer. Calculate the variance of the height distribution of the bottom wetting layer. Equal to the height distribution variance of the blank substrate Average height of the underlying wetting layer Equal to the average height of the blank substrate With respect to the theoretical minimum unit structure thickness of this material system The sum of The theoretical minimum unit structural thickness is described. It refers to the inherent physical thickness of a single unit cell layer, molecular layer or atomic layer that constitutes the specific material system, which can be obtained through theoretical crystallographic calculations or conventional characterization methods; Steps S3 and S4 are not in any particular order; S5. Solve for geometric parameters simultaneously: The target sample statistical parameters extracted in step S2 and and the parameters of the underlying wetting layer determined in step S4. and Substituting these equations into the system of two nonlinear equations described in S3, and solving the system simultaneously, the surface coverage of the island-like nanostructure can be calculated. and relative height .

[0034] Example 2 This embodiment provides a method for non-destructively extracting the geometric parameters of yttrium iron garnet island nanostructures. Taking the preparation and characterization of yttrium iron garnet island nanostructures on a gadolinium gallium garnet substrate as an example, this embodiment details the technical solution of Example 1. Those skilled in the art should understand that this embodiment is only for verifying the accuracy and operability of the method provided in Example 1 of this invention. The method provided in Example 1 of this invention is also applicable to other metal, semiconductor, or oxide nanostructure systems prepared by physical vapor deposition processes. Furthermore, as an extension and example, the single-crystal substrates involved in the method of Example 1 of this invention include, but are not limited to: silicon (Si), sapphire (Al2O3), silicon carbide (SiC), various garnets, or strontium titanate (SrTiO3) and other conventional epitaxial single-crystal substrates; the amorphous substrates include, but are not limited to: amorphous quartz glass, silicon wafers with a thermally oxidized layer on the surface, or flat amorphous polymer substrates. The materials of the island nanostructures are not limited to magnetic materials, but can also broadly encompass metals, semiconductors, oxides, non-metallic inorganic materials, or polymer materials. Specifically, the method for non-destructively extracting the geometric parameters of yttrium iron garnet island nanostructures in this embodiment includes the following steps: S0, Sample preparation: Take a substrate (blank substrate) with a gadolinium gallium garnet crystal plane orientation of (111), immerse it in acetone for ultrasonic cleaning for 10 min, then in isopropanol for ultrasonic cleaning for 5 min, rinse with flowing deionized water, and then dry with high-purity nitrogen. Then, yttrium iron garnet (YFeG) material was deposited on the cleaned blank substrate using radio frequency magnetron sputtering to obtain the target sample. The sputtering process parameters were set as follows: sputtering power 80W, working atmosphere consisting of 5% oxygen and 95% argon (by volume), target-substrate distance 18cm, and deposition time 8min. After sputtering, the target sample was annealed at 800℃ for 60min to form a YFeG island-like nanostructure, thus obtaining the target sample. S1. Obtain surface height data: The morphology of the treated blank substrate and the prepared target sample was scanned using an atomic force microscope (AFM). The scanning range was set to 500 nm × 500 nm, and the results were as follows: Figure 2 and Figure 3 The image shows the microscopic morphology of the atomic force microscope; the height data of all pixels in the image is exported without performing zero-order flattening. S2. Extract Gaussian statistical feature parameters: Frequency distribution statistics were performed on the altitude data, and a Gaussian distribution function was fitted to obtain the following results: Figure 4 The comparison fitting curve is shown below. Figure 4 As shown, the horizontal axis of the figure represents surface height, and the vertical axis represents relative frequency. The legend independently indicates the original data points and their corresponding Gaussian fitting curves for the blank substrate and the target sample deposited for 8 minutes. The coefficient of determination... All values ​​are better than 0.99, indicating that the height fluctuations strictly follow a normal distribution. Extracting parameters from the fitted curve: For blank substrates: average height Standard deviation of height distribution The variance of the height distribution was calculated. .

[0035] For the target sample: average height Standard deviation of height distribution The variance of the height distribution was calculated. ; S3. Determine the physical model for island growth: The mean equation is: ; The variance equation is: ; S4. Determine the parameters of the underlying wetting layer: Based on theoretical crystallographic calculations and transmission electron microscopy calibration, the theoretical minimum unit thickness of yttrium iron garnet epitaxial growth on the gadolinium gallium garnet (111) crystal plane is the characteristic geometric thickness of a single-crystal oxygen polyhedron layer, i.e. .

[0036] Calculate the average height of the bottom wetting layer: .

[0037] Determine the standard deviation of the height distribution of the underlying wetting layer: Corresponding variance ; S5. Solve for geometric parameters simultaneously: Substituting the above parameters into the equations of the island growth physical model, we get: First move: ; Second move: ; The above system of two nonlinear equations was solved using numerical methods, and the relative height was directly obtained. Surface coverage That is, 80.8%.

[0038] The results show that the non-destructive extraction method of this invention can accurately determine the formation of three-dimensional island-like nanoparticles with a relative height of approximately 0.73 nm and an area coverage of approximately 80.8% on the surface of the target sample. This extraction result is in high agreement with the subsequent angle-resolved X-ray photoelectron spectroscopy equivalent chemical thickness measurement results, verifying the extremely high accuracy of this method.

[0039] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that any equivalent mathematical transformations made based on the statistical distribution analysis and physical superposition model framework disclosed in this invention, or any application of it to the geometric parameter derivation of other micro / nano characterization datasets, fall within the scope of protection and disclosure of this invention.

[0040] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

Claims

1. A method for non-destructively extracting geometric parameters of island-like nanostructures, characterized in that, Includes the following steps: A substrate and a sample on which island-like nanostructures are grown are provided respectively; The substrate and the sample were subjected to atomic force microscopy to obtain the corresponding surface height data, and the area corresponding to the minimum value was used as the reference surface. The relative frequency distribution of the surface height data is statistically analyzed, and the average height and height distribution variance of the substrate and the sample are extracted by fitting a Gaussian distribution function. The surface morphology of the sample is regarded as a linear superposition of the bottom wetting layer and the island nanostructure, and a physical model of island growth including mean equation and variance equation is constructed. The average height and height distribution variance of the bottom wetting layer are determined based on the average height and height distribution variance of the substrate. Substituting the average height and height distribution variance of the sample with the average height and height distribution variance of the bottom wetting layer into the island growth physical model, the surface coverage and relative height of the island nanostructure are obtained by solving the equations simultaneously.

2. The method for non-destructively extracting geometric parameters of island nanostructures according to claim 1, characterized in that, The substrate is a flat substrate with a root mean square roughness of no more than 1.0 nm as measured by atomic force microscopy. Preferably, the root mean square roughness of the substrate is no greater than 0.5 nm.

3. The method for non-destructively extracting geometric parameters of island nanostructures according to claim 1 or 2, characterized in that, The substrate is a single-crystal substrate or an amorphous substrate; Preferably, the single-crystal substrate comprises at least one of silicon, sapphire, silicon carbide, garnet, or strontium titanate; Preferably, the amorphous substrate includes at least one of amorphous quartz glass, a silicon wafer with a thermal oxide layer on its surface, or an amorphous polymer substrate.

4. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-3, characterized in that, The material composition of the island-like nanostructure includes at least one of metal, semiconductor, oxide, non-metallic inorganic material or polymer.

5. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-4, characterized in that, The method for growing the island-like nanostructures includes at least one of physical vapor deposition, chemical vapor deposition, or wet chemical methods.

6. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-5, characterized in that, The island-like nanostructures on the sample are discontinuous, discrete islands with a surface coverage greater than zero and less than one.

7. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-6, characterized in that, The form of the Gaussian distribution function includes: ,in, The average height of the substrate or the sample. The parameter is the Gaussian peak width and satisfies , Let be the standard deviation of the height distribution, and let be the variance of the height distribution. .

8. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-7, characterized in that, The physical model for island growth includes: considering the surface morphology of the sample as a linear superposition of the underlying wetting layer and the island nanostructure.

9. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-8, characterized in that, The mean equation in the physical model of island growth includes: The variance equation includes: ;in, The average height of the sample. The variance of the height distribution of the sample; The average height of the bottom wetting layer. The variance of the height distribution of the underlying wetting layer; The surface coverage of the island-like nanostructure. The relative height of the island-like nanostructure is given.

10. The method for non-destructively extracting geometric parameters of island nanostructures according to any one of claims 1-9, characterized in that, The methods for determining the average height and height distribution variance of the bottom wetting layer include: the height distribution variance of the bottom wetting layer being equal to the height distribution variance of the substrate; the average height of the bottom wetting layer being equal to the sum of the average height of the substrate and the theoretical minimum unit structural thickness of the island nanostructure material system; or, being directly extracted and determined from the height statistical characteristics of the non-island regions in the sample.

Images