Atomic film thickness measuring method based on quasi Brewster angle spectrum

Abstract

The invention provides an atomic film thickness measurement method based on a quasi Brewster angle spectrum. The method comprises the following steps: establishing a layered medium stacking optical model corresponding to a sample according to a substrate and an atomic film structure; calculating an angle resolution spectrum ellipsometry parameter corresponding to the layered medium stacking optical model; establishing a mapping relation between the quasi Brewster angle and the atomic film thickness; carrying out atomic film sample angle resolution spectrum ellipsometry to obtain a quasi Brewster angle measurement value; and measuring the thickness of the atomic film by using the calculated mapping relation and combining a measurement result. According to the method, the atomic film thickness measurement based on the quasi Brewster angle spectrum is realized, the simple, visual, accurate and efficient measurement of the atomic film thickness is realized, the film thickness measurement resolution can reach the atomic weight level, and the method can be applied to the high-sensitivity and high-precision atomic film thickness measurement field in the atomic scale manufacturing field.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical testing of atomic film thickness, and in particular to an atomic film thickness measurement method based on quasi-Brewster angle spectroscopy. BACKGROUND

[0002] With the continuous development of precision manufacturing technology, the processing size and manufacturing precision have reached the atomic / nanometer level. Atomic scale thin film is a key functional material and feature structure in the field of atomic manufacturing, and is an important carrier for realizing micro-macro connection. Atomic film thickness is one of the key indicators for regulating device performance. High-sensitivity and accurate atomic film thickness measurement technology is of great significance for realizing controllable atomic precision manufacturing.

[0003] Currently, atomic force microscopy, scanning electron microscopy, transmission electron microscopy, and ellipsometry are used for precise measurement of film thickness. Atomic force microscopy can achieve atomic level resolution measurement of surface topography, but when applied to thickness measurement, it often needs to artificially prepare steps between the substrate and the film, and the single measurement area is usually small. Scanning and transmission electron microscopy also have high spatial resolution, but they need to be used in a vacuum environment and have high requirements for samples, which limits their application in high-throughput and non-destructive measurement fields. Ellipsometry measures the change in optical polarization state of the measurement beam after reflection / transmission by the film sample, and combines data inversion algorithms to measure the film thickness. Due to the simultaneous analysis of light intensity and phase information of the measurement beam, ellipsometry is widely used in the field of ultra-thin film thickness and related physical / chemical property characterization. However, ellipsometry needs to combine complex data fitting algorithms to achieve the final film thickness measurement. The traditional ellipsometry data fitting process is complex, not intuitive, and has strong dependence on artificial experts, which limits the widespread application of this method.

[0004] To overcome the drawbacks of traditional ellipsometry film thickness measurement methods that rely heavily on data fitting algorithms, the present application proposes an atomic film thickness measurement method based on quasi-Brewster angle spectroscopy. This method uses the mapping relationship between quasi-Brewster angle and atomic film thickness to achieve simple, intuitive, accurate, and efficient measurement of atomic film thickness, and the film thickness measurement resolution can reach the atomic level. In addition, this measurement method is suitable for characterization of atomic film thickness of semiconductor nanomaterials, two-dimensional materials, and perovskite materials, which will help the preparation and application of atomic films. SUMMARY

[0005] Therefore, the present application proposes an atomic film thickness measurement method based on quasi-Brewster angle spectroscopy, which uses the accurate mapping relationship between quasi-Brewster angle and atomic film thickness to achieve simple, intuitive, and high-precision atomic film thickness measurement, greatly reducing the difficulty of data analysis while ensuring atomic-level film thickness measurement resolution. The technical solution is as follows: A method for measuring the thickness of an atomic film based on quasi-Brewster angle spectrum, comprising the following steps: 1) Establishing a layered medium stack optical model corresponding to the sample according to the substrate and the atomic film structure; 2) Calculating the angle-resolved spectroscopic ellipsometric parameters corresponding to the layered medium stack optical model: according to the layered medium stack optical model established in step 1), the simulation results of the angle-resolved spectroscopic ellipsometric parameters are obtained by numerical calculation; 3) Establishing the mapping relationship between the quasi-Brewster angle and the atomic film thickness: using the simulation results of the angle-resolved spectroscopic ellipsometric parameters in step 2), the angle-resolved ellipsometric parameter curve corresponding to the atomic film thickness is extracted, and the mapping relationship between the quasi-Brewster angle and the atomic film thickness is obtained; 4) Carrying out angle-resolved spectroscopic ellipsometric measurement of the atomic film sample to obtain the quasi-Brewster angle measurement value: carrying out angle-resolved spectroscopic ellipsometric measurement of the atomic film sample, and combining the measurement data denoising and smoothing processing algorithm to obtain the quasi-Brewster angle measurement value; 5) Using the calculated mapping relationship and combining the measurement results to realize the measurement of the atomic film thickness: using the quasi-Brewster angle measurement value, substituting into the accurate mapping relationship between the quasi-Brewster angle and the atomic film thickness determined in step 3), and finally solving to obtain the thickness of the atomic film sample.

[0006] Further, in step 2), the ellipsometric parameters include amplitude ratio ψ and phase difference Δ.

[0007] Further, in step 2), the expression of the ellipsometric parameters is:

[0008] In the formula, ψ and Δ represent the amplitude ratio and phase difference of P-polarized and S-polarized reflected light, respectively, i is an imaginary unit, r p and r s are the P and S polarized light reflection coefficients corresponding to the sample, respectively.

[0009] Further, in step 2), the mapping relationship between the quasi-Brewster angle and the atomic film thickness is as follows:

[0010] In the formula, d is the atomic film thickness, the unit is nm; K is the linear correlation coefficient between the atomic film thickness and the quasi-Brewster angle, the unit is degree / nm, which is determined by the optical constant of the atomic film; θ0 is the quasi-Brewster angle corresponding to the bare substrate without film coverage, the unit is degree, which is determined by the optical constant of the substrate.

[0011] Furthermore, in step 2), for the graphene thin film sample on the SiO2 / Si substrate, the simulation process is repeated by changing the graphene thickness to obtain the simulation results of the angle-resolved spectral ellipsoid parameter ψ corresponding to different graphene thicknesses / layer numbers. In step 3), a wavelength of 620 nm is selected, and the angle-resolved ellipsoid parameter curve corresponding to the atomic thin film thickness is extracted to obtain the mapping relationship between the quasi-Brewster angle and the atomic thin film thickness as follows:

[0012] Where L and d are the number and thickness of the Graphene layer, respectively, and θ qB The units for d and d are degree and nm, respectively, and L is an integer between 1 and 10, representing the number of layers in the Graphene.

[0013] Furthermore, in step 4), the angle-resolved spectral ellipsometer measurement is performed using a mechanically variable angle ellipsometer or a back focal plane imaging ellipsometer.

[0014] Furthermore, in step 4), the measurement data denoising and smoothing preprocessing algorithm is a multiple numerical averaging method and a spline curve analytical method based on the Levenberg-Marquard algorithm.

[0015] As can be seen from the above technical solution, the atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy proposed in this invention has at least one or a part of the following beneficial effects: (1) It can achieve highly sensitive, accurate and fast measurement of atomic thin film thickness.

[0016] (2) An approximate linear mapping relationship between the quasi-Brewster angle and the atomic film thickness was proposed.

[0017] (3) Improve the simplicity and intuitiveness of atomic thin film thickness measurement data analysis and enhance the practical application potential of the measurement method.

[0018] (4) It can be extended to various fields of offline measurement and in-situ monitoring of atomic thin film thickness, and help research in fields such as atomic-scale thin film growth dynamics analysis, exploration of novel properties of atomic thin films and large-scale applications. Attached Figure Description

[0019] Figure 1 A flowchart of the atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy provided for this invention; Figure 2 A schematic diagram of the corresponding layered medium stacking optical model constructed for a MoS2 thin film sample on a 300nm SiO2 / Si substrate; Figure 3The simulation results of the angle-resolved spectral ellipsometry parameter ψ for 1-5 layers of MoS2 thin film samples on a 300nm SiO2 / Si substrate, with an incident wavelength of 700nm; Figure 4 The simulation mapping relationship between the quasi-Brewster angle and the thickness of the MoS2 thin film is shown with an incident wavelength of 700 nm. Figure 5 A schematic diagram of the corresponding layered medium stacking optical model constructed for a Graphene thin film sample on a 280nm SiO2 / Si substrate; Figure 6 The simulation mapping relationship between the quasi-Brewster angle and the thickness of the Graphene film is shown with an incident wavelength of 620 nm. Figure 7 The simulation mapping relationship between the quasi-Brewster angle and the thickness of the Graphene film is shown with an incident wavelength of 620 nm. Detailed Implementation

[0020] This invention proposes an atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy. By utilizing the mapping relationship between quasi-Brewster angle and atomic thin film thickness, a simple, intuitive, and high-precision atomic film thickness measurement can be achieved. While ensuring the resolution of atomic-level film thickness measurement, the difficulty of data analysis is greatly reduced.

[0021] The present invention will be further described below with reference to the accompanying drawings and examples, but this is not intended to limit the scope of protection of the present invention.

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0023] Certain embodiments of this disclosure will be described more fully below with reference to the accompanying drawings, some of which, but not all, will be shown. In fact, various embodiments of the invention may be implemented in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided to enable the invention to meet applicable legal requirements.

[0024] Example 1 Specifically, as an exemplary embodiment, the present invention provides an atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy for molybdenum disulfide (MoS2) thin film samples on 300 nm SiO2 / Si substrates.

[0025] like Figure 1 As shown, the atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy proposed in this invention includes the following steps: 1) Establish a layered media stacking optical model for the sample based on the substrate and atomic thin film structure: For the MoS2 thin film sample on a 300nm SiO2 / Si substrate, establish a corresponding layered media stacking optical model, i.e., an "air / MoS2 / SiO2 / Si" four-phase optical model, such as... Figure 2 As shown.

[0026] 2) Calculate the angle-resolved spectral ellipticity parameter corresponding to the layered medium stacked optical model: Using the layered medium stacked optical model established in step 1), the simulation results of the angle-resolved spectral ellipticity parameter ψ of a single layer of MoS2 are obtained by numerical calculation using MATLAB software based on Fresnel reflection law and classical optical transfer matrix theory.

[0027] Specifically, the scattering matrix expression corresponding to the optical model of the layered medium stacked structure is: (1) Among them, superscript p and s The subscripts (m-1)m in the interface matrix I represent the P and S polarization components, respectively. The subscript m in the interface matrix I represents the interface formed by the film layer (m-1) and the film layer m. The subscript m in the film layer matrix L represents the film layer m.

[0028] The expressions for the interface matrix I and the film matrix L are as follows: (2) (3) in, r and t These are the interface reflection and transmission coefficients formed by film layer (m-1) and film layer m, respectively. β The phase thickness of the film is given by the following formula: (4) (5) in, Lambda For wavelength, d m Let m be the physical thickness of the film layer. N m Let m be the complex refractive index of the film layer. Theta m Let m be the incident angle of the light rays entering the film layer.

[0029] Combining formulas (1)-(5), the total polarized light reflection of the layered medium stacked optical model ( ) and transmission coefficient ( The expression for ) is as follows: (6) in, and These are the elements in the first row and first column of the scattering matrix in formula (1), and the elements in the second row and first column, respectively.

[0030] Combining formula (6) and the expressions for the elliptic parameters, including the amplitude ratio ψ and the phase difference Δ, as shown below, the final ψ calculation result is obtained; (7) By varying the MoS2 thickness and repeating the above simulation process, simulation results of the angle-resolved spectral ellipsometry parameter ψ for MoS2 films of different thicknesses / numbers of layers were obtained. Selecting a wavelength of 700 nm, the curves of ψ versus incident angle for 1-5 layers of MoS2 films (thickness 0.65-3.25 nm) were obtained, as shown below. Figure 3 As shown.

[0031] 3) Establish the mapping relationship between the quasi-Brewster angle and the atomic film thickness: Using the simulation results of the angle-resolved spectral ellipticity parameter ψ obtained in step 2), the quasi-Brewster angle is determined; the quasi-Brewster angle is the incident angle corresponding to the minimum value of ψ. The quasi-Brewster angles corresponding to different MoS2 thicknesses are extracted, and finally, a linear mapping relationship between the quasi-Brewster angle and the MoS2 thickness is established, such as... Figure 4 As shown, the corresponding formula is as follows: (8) Where L and d are the number and thickness of MoS2 layers, respectively, and θ qB The units of d and λ are degree and nm, respectively. L is an integer between 1 and 10, representing the number of layers in MoS2. λ is the wavelength, which corresponds to 700 nm in this case.

[0032] 4) Angular-resolved ellipsometry measurement of atomic thin film samples to obtain quasi-Brewster angle measurements: Based on the incident angle and wavelength range corresponding to the quasi-Brewster angle, angular-resolved ellipsometry measurement of MoS2 thin film samples is performed using a mechanical variable angle ellipsometer or a back focal plane imaging ellipsometer; the measurement results are denoised and smoothed using multiple numerical averaging and spline curve analysis based on the Levenberg-Marquard algorithm to obtain quasi-Brewster angle measurements.

[0033] 5) Using the simulation mapping relationship and combined with the measurement results, the atomic thin film thickness is measured: Using the quasi-Brewster angle measurement value in step 4) and the mapping relationship between the quasi-Brewster angle and the MoS2 thickness established in step 3), the final measured value of the MoS2 thin film sample thickness is obtained.

[0034] Example 2 Specifically, as an exemplary embodiment, the present invention provides an atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy for graphene thin film samples on 280 nm SiO2 / Si substrates.

[0035] like Figure 1 As shown, the atomic thin film thickness measurement method based on quasi-Brewster angle spectroscopy proposed in this invention includes the following steps: 1) Establish a layered media stacking optical model for the sample based on the substrate and atomic thin film structure: For the graphene thin film sample on a 280nm SiO2 / Si substrate, establish a corresponding layered media stacking optical model, namely a "air / graphene / SiO2 / Si" four-phase optical model, such as... Figure 5 As shown.

[0036] 2) Calculate the angle-resolved spectral ellipticity parameter corresponding to the layered medium stacked optical model: Using the layered medium stacked optical model established in step 1), the simulation results of the angle-resolved spectral ellipticity parameter ψ of a single-layer Graphene are obtained by numerical calculation using MATLAB software based on Fresnel reflection law and classical optical transfer matrix theory.

[0037] By varying the graphene thickness and repeating the above simulation process, simulation results of the angle-resolved spectral ellipsometry parameter ψ for graphene films of different thicknesses / numbers of layers were obtained. Selecting a wavelength of 620 nm, the curves of ψ versus incident angle for 1-5 layers of graphene films (thickness 0.35-1.75 nm) were obtained, as shown below. Figure 6 As shown.

[0038] The relevant formulas are the same as those in Formulas (1)-(7) in Example 1, and will not be listed here again.

[0039] 3) Establish the mapping relationship between the quasi-Brewster angle and the atomic thin film thickness: Using the simulation results of the angle-resolved spectral ellipticity parameter ψ obtained in step 2), determine the quasi-Brewster angle; the quasi-Brewster angle is the incident angle corresponding to the minimum value of ψ. Extract the quasi-Brewster angles corresponding to different graphene thicknesses, and finally establish a linear mapping relationship between the quasi-Brewster angle and the graphene thickness, such as... Figure 7 As shown, the corresponding formula is as follows: (9) Where L and d are the number and thickness of the Graphene layer, respectively, and θ qB The units for d and λ are degree and nm, respectively. L is an integer between 1 and 10, representing the number of layers in the Graphene. λ is the wavelength, which corresponds to 620 nm in this case.

[0040] 4) Angular-resolved ellipsometry measurement of atomic thin film samples to obtain quasi-Brewster angle measurements: Based on the incident angle and wavelength range corresponding to the quasi-Brewster angle, angular-resolved ellipsometry measurement of Graphene thin film samples is performed using a mechanical variable angle ellipsometer or a back focal plane imaging ellipsometer; the measurement results are denoised and smoothed using multiple numerical averaging and spline curve analysis based on the Levenberg-Marquard algorithm to obtain quasi-Brewster angle measurements.

[0041] 5) Using the simulation mapping relationship and combined with the measurement results, the atomic thin film thickness is measured: Using the quasi-Brewster angle measurement value in step 4) and the mapping relationship between the quasi-Brewster angle and the Graphene thickness established in step 3), the final measurement value of the Graphene thin film sample thickness is obtained.

[0042] In summary, this invention provides a method for measuring atomic thin film thickness based on quasi-Brewster angle spectroscopy. The quasi-Brewster angle-to-atomic thin film thickness mapping relationship established in this invention enables highly sensitive and accurate measurement of atomic thin film thickness, improves the simplicity and intuitiveness of atomic thin film thickness measurement data analysis, and enhances the practical application potential of the measurement method.

[0043] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the thickness of an atomic film based on quasi-Brewster angle spectroscopy, characterized in that, The method comprises the following steps: 1) establishing a layered medium stack optical model corresponding to a sample according to a substrate and an atomic thin film structure; 2) calculating angle-resolved spectroscopic ellipsometric parameters corresponding to the layered medium stack optical model: according to the layered medium stack optical model established in step 1), a simulation result of the angle-resolved spectroscopic ellipsometric parameters is obtained by numerical calculation; 3) establishing a mapping relationship between a quasi-Brewster angle and an atomic thin film thickness: using the simulation result of the angle-resolved spectroscopic ellipsometric parameters in step 2), an angle-resolved ellipsometric parameter curve corresponding to the atomic thin film thickness is extracted, and a mapping relationship between the quasi-Brewster angle and the atomic thin film thickness is obtained; 4) performing angle-resolved spectroscopic ellipsometric measurement on an atomic thin film sample to obtain a quasi-Brewster angle measurement value: performing angle-resolved spectroscopic ellipsometric measurement on the atomic thin film sample, and combining measurement data denoising and smoothing processing algorithms to obtain the quasi-Brewster angle measurement value; 5) using the calculated mapping relationship and combining the measurement result to realize atomic thin film thickness measurement: using the quasi-Brewster angle measurement value, substituting the quasi-Brewster angle and the atomic thin film thickness into the accurate mapping relationship determined in step 3), and finally solving to obtain the atomic thin film sample thickness.

2. The quasi-Brewster angle spectroscopy based atomic thin film thickness measurement method according to claim 1, wherein, In step 2), the ellipsometric parameters include a magnitude ratio ψ and a phase difference Δ.

3. The quasi-Brewster angle spectroscopy based atomic thin film thickness measurement method according to claim 2, wherein, In step 2), the expression of the ellipsometric parameters is as follows: ； where ψ and Δ represent the amplitude ratio and phase difference of P- and S-polarized reflected light, respectively, i is the imaginary unit, r p and r s are the P- and S-polarized light reflection coefficients of the sample, respectively.

4. The quasi-Brewster angle spectroscopy based atomic thin film thickness measurement method of claim 1, wherein, In step 2), the mapping relationship between the quasi-Brewster angle and the atomic thin film thickness is as follows: ； In the formula, d is the atomic thin film thickness, the unit is nm; K is a linear correlation coefficient between the atomic thin film thickness and the quasi-Brewster angle, the unit is degree / nm, which is determined by atomic thin film optical constants; θ0 is a quasi-Brewster angle corresponding to a bare substrate without film coverage, the unit is degree, which is determined by substrate optical constants.

5. The quasi-Brewster angle spectroscopy based atomic thin film thickness measurement method of claim 1, wherein, In step 2), for a Graphene thin film sample on a SiO2 / Si substrate, by changing the Graphene thickness, the simulation process is repeated to obtain angle-resolved spectroscopic ellipsometric parameter ψ simulation results corresponding to Graphene of different thicknesses / layers.

6. The quasi-Brewster angle spectroscopy based atomic thin film thickness measurement method of claim 5, wherein, In step 3), the wavelength is selected as 620 nm, the angle-resolved ellipsometric parameter curve corresponding to the atomic thin film thickness is extracted, and the mapping relationship between the quasi-Brewster angle and the atomic thin film thickness is as follows: ； where L and d are the number of layers and thickness of graphene, respectively, and θ qB and d are in units of degree, nm, respectively, and L is an integer between 1 and 10, representing the number of layers of graphene.

7. The quasi-Brewster angle spectroscopy based atomic thin film thickness measurement method of claim 1, wherein, In step 4), the angle-resolved spectroscopic ellipsometric measurement is measured by using a mechanical variable angle ellipsometer or a back focal plane imaging ellipsometer; the measurement data denoising and smoothing preprocessing algorithm is a multiple numerical average method and a spline curve analysis method based on a Levenberg-Marquard algorithm.

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