A multilayer film thickness measurement method and a measuring instrument based on taylor polynomial fitting coefficient analysis

Abstract

This invention provides a method and instrument for measuring the thickness of multilayer films based on Taylor polynomial fitting coefficient analysis. The method involves acquiring the interference signal of the multilayer film under test output by a shared-arm interference structure, wherein the reference optical path of the shared-arm interference structure and the sample optical path share the same physical transmission optical path. The interference signal is down-processed to obtain a baseband interference signal with a center frequency near zero. Taylor polynomial expansion is performed on the baseband interference signal at the point where the optical path difference is zero, and a Taylor expansion coefficient sequence is obtained. A linear equation system is constructed based on the Taylor expansion coefficient sequence, and the coefficients of the characteristic equation are solved. The optical path difference corresponding to each layer of the multilayer film under test is obtained by solving the characteristic equation. The physical thickness of each layer is calculated based on the optical path difference corresponding to each layer and the refractive index of the film material.

Description

Technical Field

[0001] This invention belongs to the field of optical coherent nondestructive measurement technology, specifically relating to a method and instrument for measuring the thickness of multilayer films based on Taylor polynomial fitting coefficient analysis. Background Technology

[0002] Optical coherence tomography (OCT) is a precision structural measurement technique based on low-coherence interferometry. Traditional frequency-domain OCT analysis methods typically use Fourier analysis to analyze the frequency components of the interference signals acquired by the spectrometer. However, as application scenarios demand increasingly higher analytical resolution and accuracy, this traditional Fourier analysis-based approach has gradually revealed its limitations: it cannot perform frequency analysis on ultrathin film samples, and when the frequency difference of the interference signals is less than its axial resolution, Fourier analysis cannot identify the concentrated frequency components. Improving axial resolution requires replacing the light source with one that has a lower center frequency or a wider bandwidth, which increases system cost and debugging difficulty. Therefore, in the current development of OCT technology, how to achieve super-resolution analysis through algorithm improvement has become an important research direction and technical bottleneck.

[0003] According to optical principles, in a frequency-domain OCT system, the interference signal of a thin-film structure sample (taking a single layer as an example) is: :

[0004] (1-1)

[0005] in Wave number magnitude Let be the power spectral density function of the light source. These are the reflection coefficients of the reference mirror, the upper surface of the film, and the lower surface of the film, respectively. The refractive index of air, The refractive index of the coating material, This represents the distance difference between the upper surface of the film and the reference arm. Let be the thickness of the film. According to equation (1-1): the interference signal can be considered as the sum of three terms, where the first term is the DC term, also called the constant term, which is related to the reflectivity of the reference mirror and the reflection coefficients of the interfaces of each layer of the film under test; the second term is the self-coherence term, which is related to the self-interference of the reflected light from each interface of the film under test; and the third term is the mutual interference term, which is related to the mutual interference between the interfaces of each layer of the film under test and the reference mirror. When When the frequency of mutual interference terms is much greater than that of self-coherent terms, the component frequencies of mutual interference terms can be solved by high-pass filtering and Fourier analysis of the signal, and then the film thickness can be solved by wavelength and material refractive index.

[0006] In practical systems, the charge-coupled device (CCD) of the sampling camera used in spectrometers consists of thousands of pixels, therefore the sampled signal is not continuous but discrete. For discrete signals, traditional data analysis methods typically employ Discrete Fourier Analysis (DFT). Discrete signal at each sampling point Its DFT results for:

[0007] (1-2)

[0008] According to equation (1-2), the discrete Fourier analysis converts the time-domain signal into a frequency-domain signal, and the resulting frequency-domain signal is also discrete, with the frequency axis intervals being: The minimum axial resolution of the corresponding OCT system is:

[0009] (1-3)

[0010] Furthermore, the signal length acquired in actual analysis is limited, so the DFT operation is equivalent to adding a rectangular window to the original signal. According to the Fourier transform and the convolution theorem, the actual Fourier transform image is the result of convolving the ideal spectral function with the Fourier transform result of the window function. This convolution operation causes "leakage" in the spectrum. When frequency components are close together, the "leaked" portions overlap significantly, making it impossible to distinguish frequency peaks, i.e., aliasing.

[0011] In summary, existing OCT thickness measurement systems based on Fourier analysis cannot effectively and accurately measure close frequency components. Summary of the Invention

[0012] To address the shortcomings and deficiencies of existing technologies, this invention provides a method and apparatus for measuring the thickness of multilayer films based on Taylor polynomial fitting coefficient analysis. This solves the problem that traditional optical coherence tomography techniques have insufficient resolution when measuring ultrathin films and cannot effectively distinguish clustered frequency components with frequency differences smaller than the resolution limit of Fourier transform.

[0013] The core innovation of this invention lies in the following: A shared-arm integrated interference optical path structure is adopted, integrating the reference optical path and the sample optical path into the same transmission optical path, effectively suppressing common-mode noise introduced by environmental vibrations and temperature fluctuations. Based on this, an innovative signal processing method based on Taylor polynomial fitting coefficient analysis is proposed. The baseband signal is obtained by frequency reduction preprocessing of the interference signal. Taylor polynomial expansion is performed at the point where the optical path difference is zero, and the expanded coefficient sequence is obtained by fitting. A linear equation system is constructed based on this coefficient sequence to solve for the characteristic equation coefficients. Finally, the optical path difference corresponding to each film layer is obtained by solving the characteristic equation, and the physical thickness of each thin film layer is calculated by combining the refractive index of the film material.

[0014] This method breaks through the frequency resolution limit of traditional Fourier analysis methods, enabling high-precision measurement of ultrathin film samples. It is particularly suitable for multilayer thin film thickness measurement needs in fields such as optical coating inspection and wafer manufacturing processes. The corresponding measurement device includes components such as a broadband SLD light source, fiber optic coupler, shared-arm interferometric measuring arm, spectrometer, and computer. The computer executes the above method to achieve automated measurement.

[0015] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0016] A method for measuring the thickness of multilayer films based on Taylor polynomial fitting coefficient analysis, comprising:

[0017] The interference signal of the multilayer thin film under test is obtained by the output of the shared-arm interference structure, wherein the reference optical path and the sample optical path of the shared-arm interference structure share the same transmission optical path;

[0018] The interference signal is down-frequency processed to obtain a baseband interference signal with a center frequency near zero frequency;

[0019] The baseband interference signal is subjected to Taylor polynomial expansion at the point where the optical path difference is zero, and the Taylor expansion coefficient sequence is obtained by fitting.

[0020] A system of linear equations is constructed based on the Taylor expansion coefficient sequence, and the coefficients of the characteristic equation are obtained by solving the characteristic equation. The optical path difference corresponding to each layer of the multilayer thin film under test is obtained by solving the characteristic equation.

[0021] The physical thickness of each thin film layer is calculated based on the optical path difference and the refractive index of the film material.

[0022] Furthermore, the reference optical path and the sample optical path of the shared-arm interference structure are integrated in the same transmission optical path.

[0023] Furthermore, before performing frequency reduction processing on the interference signal, an interference signal preprocessing step is also included: performing high-pass filtering on the acquired interference signal to filter out the DC term and self-coherent term in the interference signal, retaining the mutual coherent term carrying the film thickness information, and normalizing and correcting the filtered signal based on the pre-calibrated power spectral density function of the light source.

[0024] Furthermore, the specific method of the frequency reduction processing is as follows: Fourier analysis is performed on the interference signal to obtain the estimated frequency, and frequency shifting processing is performed on the interference signal based on the estimated frequency to complete the frequency reduction.

[0025] Furthermore, the baseband interference signal after Taylor polynomial expansion is fitted using the least squares method. Based on the fitted Taylor expansion coefficient sequence, an overdetermined linear equation system is constructed. The coefficients of the cubic characteristic equation are obtained by solving the cubic characteristic equation. The positive root obtained by solving the cubic characteristic equation is the square term of the cumulative optical path difference of each layer of the multilayer film under test. The optical path difference corresponding to each layer is calculated by the difference of adjacent cumulative optical path differences.

[0026] And, a multilayer film thickness measuring instrument based on Taylor polynomial fitting coefficient analysis, including a broadband SLD light source, a 1×2 fiber coupler, a shared arm interferometric measuring arm, a reflective grating spectrometer and a computer;

[0027] The shared-arm interferometric measurement arm has a built-in beam splitter and a reference mirror, and its reference optical path and sample optical path share the same transmission optical path.

[0028] The probe light emitted by the broadband SLD light source is transmitted to the common arm interferometric measurement arm via a 1×2 fiber coupler. It is then split into sample light and reference light by a beam splitter. The two beams are reflected by the sample and the reference mirror, respectively, and then return to the beam splitter to be combined to form an interference signal. The interference signal is transmitted to the reflection grating spectrometer via a 1×2 fiber coupler.

[0029] The reflective grating spectrometer is used to collect interference signals and transmit them to a computer;

[0030] The computer is configured with an executable program that, when executed, implements the method of any one of claims 1 to 5.

[0031] Furthermore, along the direction of probe light transmission, the common-arm interferometric measuring arm is sequentially provided with an achromatic doublet lens, a microscope objective, an anti-reflection glass plate, and a beam splitter as a beam splitting element, and the reference mirror is fixed at the center of the anti-reflection glass plate.

[0032] Furthermore, the surface of the beam splitter is coated with a semi-transparent and semi-reflective film with a beam splitting ratio of 50:50, the reference mirror is a square silicon mirror, and the surface of the anti-reflection glass sheet is coated with an anti-reflection film for incident light in the 700nm to 1000nm wavelength band.

[0033] Furthermore, the center wavelength range of the broadband SLD light source is 850nm to 950nm.

[0034] Furthermore, it also includes a displacement stage for carrying the multilayer thin film sample to be tested, the displacement stage being used to adjust the spatial position of the sample so that the surface of the sample to be tested is at the focusing position of the sample light; the executable program of the computer also includes a functional module for system calibration.

[0035] Compared with the prior art, the present invention and its preferred embodiments have at least the following beneficial effects:

[0036] At the hardware architecture level, this invention adopts a shared-arm integrated interference optical path design, integrating the reference optical path and the sample optical path into the same transmission optical path. This can effectively suppress common-mode noise introduced by external interference such as environmental vibration and temperature fluctuation, significantly improve the stability of system operation and anti-interference capability in complex environments. At the same time, it can optimize the dispersion balance of the optical path, improve the signal-to-noise ratio of the interference signal, provide a reliable signal foundation for subsequent high-precision signal calculation, and make the overall optical path structure more compact, reducing the difficulty of system assembly and debugging.

[0037] At the signal processing level, this invention innovatively adopts a signal processing scheme based on Taylor polynomial fitting coefficient analysis, which breaks through the inherent frequency resolution limitation of traditional Fourier analysis methods. It can effectively distinguish interference signal components with similar frequency differences that cannot be identified by traditional methods. It can achieve high-precision measurement of ultrathin film samples without replacing them with higher-specification light sources. While reducing system hardware costs and debugging thresholds, it significantly improves the accuracy and reliability of ultrathin film thickness measurement.

[0038] In addition, this invention realizes non-contact, non-destructive measurement of the thickness of multilayer thin films. The measurement process is simple and controllable, and it can be adapted to the detection needs of various industrial scenarios such as optical coating inspection and wafer manufacturing process inspection. It has good engineering practicality and scenario adaptability. Attached Figure Description

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0040] Figure 1 This is a schematic diagram of the system structure of the multilayer film thickness measuring instrument according to an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the optical path structure of the shared-arm interferometric measurement arm according to an embodiment of the present invention;

[0042] Figure 3 This is a physical diagram of the measuring arm and part of the measuring system according to an embodiment of the present invention;

[0043] Figure 4 This is a schematic diagram of the sample interference signal, high-pass filtering result, and spectral power density function correction result in an embodiment of the present invention;

[0044] Figure 5 This is a schematic diagram comparing the high-frequency interference signal before and after frequency reduction in an embodiment of the present invention;

[0045] Figure 6 This is a schematic diagram of the Taylor expansion polynomial fitting and fitting coefficient calculation results in an embodiment of the present invention. Detailed Implementation

[0046] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0047] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0048] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0049] This invention proposes a film thickness measurement instrument based on Taylor polynomial fitting coefficient analysis. Addressing the limitations of traditional optical non-destructive thickness measurement systems, which suffer from insufficient resolution or can only measure single-layer structures when measuring ultrathin films, this invention innovatively employs an analysis method based on Taylor polynomial fitting coefficients. By fitting the interference signal with Taylor polynomials to obtain the fitting polynomial, and analyzing the fitting coefficients, the optical path difference information in the interference signal is solved. Because the analysis algorithm uses Taylor polynomial fitting, it exhibits high local fitting accuracy, demonstrating high measurement accuracy in measuring extremely thin samples. Furthermore, the system utilizes an interference optical path structure design where the sample arm and reference arm share a common arm, enabling the instrument to effectively suppress common-mode noise and enhancing its anti-interference capability and stability in complex environments. This system supports the measurement of two-layer thin films and can be widely applied to optical coating inspection, wafer manufacturing process inspection, and other fields.

[0050] This film thickness measuring instrument enables non-contact measurement of the thickness of multilayer nanofilms. The instrument comprises the following main components:

[0051] An 850nm-950nm SLD (Superluminescent Diode) broadband light source is used to emit the probe light. A 1-to-2 fiber optic coupler transmits the light emitted from the light source through the first path to the measurement arm, and transmits the light carrying sample information returning from the measurement arm to the spectrometer. The measurement arm, a shared arm integrating the sample arm and reference arm, is used to focus the probe light and generate interference. The shared arm structure used in the measurement arm has excellent resistance to environmental interference. Since the reference light and sample light propagate in almost identical optical paths, the effects of external vibrations and temperature changes on the two beams manifest as common-mode noise, which cancels each other out during interference, thus significantly improving the stability and reliability of the system. This characteristic allows the system to maintain a high signal-to-noise ratio even in complex operating environments, providing a foundation for the accurate implementation of subsequent algorithms. A beam splitter coated with a semi-transparent, semi-reflective film is installed in the shared arm interference structure. The transmitted light, after passing through the beam splitter, is focused onto the film layer of the sample under test and generates signal light. The reflected light is focused onto a mirror inside the measuring arm and generates reference light. The reference light returned by the mirror and the signal light returned by the sample form an interference signal at the beam splitter, and then return to the fiber coupler and enter the spectrometer via the second path of the fiber coupler; the reflection grating spectrometer reflects different wavelength components of the interference light at different angles through the reflection grating and focuses them onto the pixels of the linear array camera through a lens; the computer processes the coherent signal and analyzes the film thickness information; the displacement stage adjusts the sample position.

[0052] As a more specific implementation, the structure of the multilayer film thickness measuring instrument of the present invention is as follows: Figure 1 As shown, the system includes: a 1-to-2 fiber optic coupler 2; a measuring arm 3; a displacement stage 4; a reflective grating spectrometer 6; and a computer 6. The SLD light source 1 emits broadband infrared light in the 850nm-950nm range. Due to its wide spectral width and short temporal coherence length, the resulting interference pattern has a low spatial frequency component, which is beneficial for noise suppression and improved measurement accuracy. The beam emitted from the laser passes through the fiber optic coupler 2 and enters the measuring arm 3, where interference is generated. The structure of the measuring arm, i.e., the interference generation principle, will be described below. The displacement stage 4 allows adjustment of the sample height so that the sample surface to be measured is located at the focal point of the probe light. The interference signal generated by the measuring arm 3 returns through the original optical path and re-enters the fiber optic coupler, where it is split and enters the reflective grating spectrometer 5. The spectrometer uses the periodic structure of the grating surface to cause diffraction during reflection of the incident light. Light of different wavelengths exhibits different angles after diffraction, thus achieving light separation. The separated beams of different wavelengths are focused by lenses onto pixels of the imaging camera, and the computer 6 collects and analyzes the spectral interference signals.

[0053] The optical path structure of the shared-arm integrated measuring arm is as follows: Figure 2As shown, the system includes: an achromatic cemented doublet lens 11; a microscope objective 12; an antireflective glass plate 13; a reflector 14; and a beam splitter 15. A low-coherence light beam guided by an optical fiber first passes through the achromatic cemented doublet lens 11, after which the beam exits as a parallel beam. This parallel beam is focused by the microscope objective 12. The combination of the lens and the microscope objective allows for the convergence of a high-energy-density focal point on both the reference plane and the sample surface, thereby improving the detection signal-to-noise ratio and reducing the influence of chromatic aberration and aberrations on the interference signal. The converged beam then passes through the antireflective glass plate 13. This glass plate uses a special coating process to improve the transmittance of light in the 700nm-1000nm wavelength range, reducing beam energy loss. Furthermore, a square silicon reflector 14 with a side length of 1mm is glued to the center of the glass plate. The silicon reflector 14 has high and stable reflectivity in the infrared and near-infrared bands and is lower in cost and easier to cut and process compared to gold and silver reflectors. The focused light beam illuminates the beam splitter 15 through the unobstructed portion of the antireflective glass plate. The beam splitter has a semi-transparent, semi-reflective coating with a splitting ratio of (50:50), causing the beam to split at this interface. The transmitted light, after passing through the beam splitter, is focused onto the surface of the sample under test, becoming the sample light. This sample light then returns to the detector arm after passing through the various layers of the surface coating. Simultaneously, the reflected light is reflected and focused onto the aforementioned silicon mirror, and then reflected back to the beam splitter as reference light. Finally, these two beams, originating from the same light source and having undergone almost identical optical paths, converge again at the beam splitter, satisfying the coherence condition and interfering. Figure 3 A physical image of the measuring arm is shown.

[0054] After the system underwent light source and wavelength calibration, an experiment was conducted using a silicon wafer nominally coated with 530nm silicon oxide and 200nm silicon nitride thin films as the sample. The collected interference signals are as follows: Figure 4 The above figure shows the signal being processed using a high-pass filter to remove the calibrated spectral power density function (e.g., Figure 4 (As shown in the middle figure) the final result is Figure 4 The signal is shown in the lower figure. Because the interference signal is a high-frequency signal, directly fitting the signal will result in an ill-conditioned fitting matrix due to numerical oscillations, making it impossible to obtain an accurate solution. Therefore, the signal needs to be down-frequency processed before fitting, such as... Figure 5 The center frequency of the down-frequency signal shown is near 0. A Taylor expansion polynomial fitting is performed on the down-frequency signal curve, as follows: Figure 6 As shown, the fitting approximation error is less than 0.04. The optical path difference between each film layer can be solved by substituting the coefficients of the fitting polynomial into the characteristic equation. The obtained optical path differences are as follows: and Under infrared light irradiation, the refractive index of silicon nitride is approximately 1.95, and that of silicon oxide is approximately 1.45. Based on these refractive indices, the thickness of the silicon nitride film is calculated to be 213.92 nm, and the thickness of the silicon oxide film is calculated to be 529.41 nm. This example demonstrates the reliability of the measuring instrument for non-destructive optical measurements of ultrathin film structures.

[0055] Based on the system provided above, the specific steps for implementing the measurement include the following:

[0056] The light emitted from the S1 and SLD broadband light sources enters the measurement arm via an optical fiber coupler. It is focused onto the sample by the microscope objective in the probe arm. The signal light reflected from the sample returns along the original beam path. The shared-arm interference structure consists of an achromatic cemented doublet lens, a microscope objective, a beam splitter, and a glass substrate with a centrally mounted mirror. By adjusting the beam splitter's position, the reference light is focused onto the mirror at the center of the glass substrate. The displacement stage is adjusted so that the sample surface to be measured is located at the focal point of the sample light. The sample light and the reference light interfere within the shared-arm interference structure and are transmitted to the spectrometer via the optical fiber coupler. The spectrometer receives the signal and transmits it to the computer.

[0057] S2. Perform spectral calibration of the system using 850nm and 950nm single-frequency lasers respectively. Connect the single-frequency lasers to the system's light source, record the corresponding pixel coordinates, and then export the wavelength data after supplementing it using an interpolation algorithm.

[0058] S3. Place the mirror on the sample arm and adjust the displacement stage so that the mirror surface is at the focal point of the reference light. Collect the interference signal of the mirror for light source calibration and dispersion compensation. Place the sample to be tested on the sample arm and adjust the displacement stage so that the mirror surface is at the focal point of the reference light. Collect the interference signal of the sample. The interference signal collected by the system can be expressed as Equation (1-1). Preferably, dispersion compensation is performed by polynomial fitting of the phase of the mirror interference signal to compensate for the dispersion phase deviation introduced by the optical elements in the optical path. This is a conventional dispersion compensation method for frequency domain OCT systems.

[0059] S4. Obtain the upper and lower envelopes of the mirror interference signal using Hilbert transform. for:

[0060] (2-1)

[0061] The upper and lower envelopes of the interference signal are respectively:

[0062]

[0063] (2-2)

[0064] Power spectral density function of the light source This can be expressed as:

[0065] (2-3)

[0066] S5. Perform high-pass filtering on the interference signal of the sample to remove the DC term and self-coherence terms. Then remove the power spectral density function of the light source. Treating the surface reflection coefficients of each layer as constants, the remaining mutual interference terms can be simplified as follows:

[0067] (2-4)

[0068] right Fourier analysis can be used to obtain the estimated frequencies. ,right Frequency reduction processing can achieve the following:

[0069] (2-5)

[0070] because These are three approximate components that approach 0, so we can... The expression in Perform a Taylor polynomial expansion at this point. The expanded polynomial can be written as:

[0071] +C (2-6)

[0072] Written in matrix form:

[0073]

[0074] (2-7)

[0075] in Let be the order of the Taylor expansion. Based on the matrix pair... Perform least squares fitting, the fitting coefficient matrix is ​​as follows (2-8). Based on the coefficient matrix 2-8, construct the following system of linear algebraic equations:

[0076] (2-9)

[0077] Because of the physical structure and optical properties of thin films, Therefore, this system of equations has a unique solution. Constructing matrix (2-10), the three roots of its characteristic equation system (2-11) are... .

[0078] (2-10)

[0079] (2-11)

[0080] Obviously there is ; The optical path difference is calculated using the above operations. .

[0081] S6. The thickness of each thin film layer is calculated by processing the optical path difference obtained from the refractive index of the material and the environment.

[0082] In summary, the present invention, based on the shared-arm integrated measurement arm technology and the Taylor multiplication polynomial fitting coefficient analysis technology, uses sample light to illuminate the thin film structure and generates interference fringes through a reasonably designed optical path difference and the reference light reflected by the reference mirror. In the design of the interference optical path, the integrated interference arm and reference arm optical paths ensure that the interference light and reference light follow the same path within the optical fiber, thereby reducing common-mode noise. An integrated microscope objective is used to reduce chromatic aberration and aberrations generated by the measurement optical path. This achieves stable and accurate generation of interference fringes. In the calibrated system, the Taylor multiplication polynomial fitting coefficient analysis method is used to analyze the mathematical characteristics of the sinusoidal function clustered components in the interference fringe signal, examining the relationship between the Taylor multiplication polynomial fitting coefficients and the components of the original sinusoidal function. The clustered sinusoidal function components are calculated by analyzing the fitting coefficients. Ultimately, film thickness measurement exceeding the resolution of Fourier analysis is achieved.

[0083] Compared with existing technologies, the key advantages of this invention include:

[0084] The shared-arm integrated measurement arm combines the two separate reference arms and sample arms of a traditional fiber optic interferometer into one. Compared to existing fiber optic interferometers, this design ensures that environmental disturbances have the same impact on each reference and sample beam without sacrificing the inherent flexibility of the fiber, effectively reducing the impact of environmental interference on the detection results. Simultaneously, this structure ensures minimal dispersion imbalance while maintaining high interference fringe contrast, resulting in a more compact structure.

[0085] A numerical analysis method based on Taylor polynomial fitting coefficients is employed to analyze the inherent limitations of existing Fourier analysis methods when analyzing clustered sinusoidal components. A method based on Taylor polynomial fitting coefficients is proposed to address the mathematical characteristics of clustered sinusoidal components in interference fringes. Compared to existing Fourier analysis methods, this method achieves extremely high frequency resolution for signals clustered from multiple sinusoidal functions.

[0086] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0088] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other forms of multilayer film thickness measurement methods and instruments based on Taylor polynomial fitting coefficient analysis. All equivalent variations and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A method for measuring the thickness of multilayer films based on Taylor polynomial fitting coefficient analysis, characterized in that, include: The interference signal of the multilayer thin film under test is obtained by the output of the shared-arm interference structure, wherein the reference optical path and the sample optical path of the shared-arm interference structure share the same transmission optical path; The interference signal is down-frequency processed to obtain a baseband interference signal with a center frequency near zero frequency; The baseband interference signal is subjected to Taylor polynomial expansion at the point where the optical path difference is zero, and the Taylor expansion coefficient sequence is obtained by fitting. A system of linear equations is constructed based on the Taylor expansion coefficient sequence, and the coefficients of the characteristic equation are obtained by solving the characteristic equation. The optical path difference corresponding to each layer of the multilayer thin film under test is obtained by solving the characteristic equation. The physical thickness of each thin film layer is calculated based on the optical path difference and the refractive index of the film material.

2. The method for measuring the thickness of a multilayer film based on Taylor polynomial fitting coefficient analysis according to claim 1, characterized in that: The reference optical path and sample optical path of the shared-arm interference structure are integrated in the same transmission optical path.

3. The method for measuring the thickness of a multilayer film based on Taylor polynomial fitting coefficient analysis according to claim 1, characterized in that: Before performing frequency reduction processing on the interference signal, an interference signal preprocessing step is also included: performing high-pass filtering on the acquired interference signal to filter out the DC term and self-coherent term in the interference signal, retaining the mutual coherent term carrying the film thickness information, and normalizing and correcting the filtered signal based on the pre-calibrated power spectral density function of the light source.

4. The method for measuring the thickness of a multilayer film based on Taylor polynomial fitting coefficient analysis according to claim 1, characterized in that: The specific method of frequency reduction processing is as follows: Fourier analysis is performed on the interference signal to obtain the estimated frequency, and frequency shifting processing is performed on the interference signal based on the estimated frequency to complete the frequency reduction.

5. The method for measuring the thickness of a multilayer film based on Taylor polynomial fitting coefficient analysis according to claim 1, characterized in that: The baseband interference signal after Taylor polynomial expansion is fitted by the least squares method. Based on the fitted Taylor expansion coefficient sequence, an overdetermined linear equation system is constructed. The coefficients of the cubic characteristic equation are obtained by solving the cubic characteristic equation. The positive root obtained by solving the cubic characteristic equation is the square term of the cumulative optical path difference of each film layer of the multilayer film under test. The optical path difference corresponding to each film layer is calculated by the difference of adjacent cumulative optical path differences.

6. A multilayer film thickness measuring instrument based on Taylor polynomial fitting coefficient analysis, characterized in that, Includes a broadband SLD light source, a 1×2 fiber coupler, a shared-arm interferometric measurement arm, a reflective grating spectrometer, and a computer; The shared-arm interferometric measurement arm has a built-in beam splitter and a reference mirror, and its reference optical path and sample optical path share the same transmission optical path. The probe light emitted by the broadband SLD light source is transmitted to the common arm interferometric measurement arm via a 1×2 fiber coupler. It is then split into sample light and reference light by a beam splitter. The two beams are reflected by the sample and the reference mirror, respectively, and then return to the beam splitter to be combined to form an interference signal. The interference signal is transmitted to the reflection grating spectrometer via a 1×2 fiber coupler. The reflective grating spectrometer is used to collect interference signals and transmit them to a computer; The computer is configured with an executable program that, when executed, implements the method of any one of claims 1 to 5.

7. A multilayer film thickness measuring instrument based on Taylor polynomial fitting coefficient analysis according to claim 6, characterized in that, Along the direction of probe light transmission, the common-arm interferometric measuring arm is sequentially provided with an achromatic doublet lens, a microscope objective, an anti-reflection glass plate, and a beam splitter as a beam splitting element, and the reference mirror is fixed at the center of the anti-reflection glass plate.

8. A multilayer film thickness measuring instrument based on Taylor polynomial fitting coefficient analysis according to claim 7, characterized in that, The surface of the beam splitter is coated with a semi-transparent and semi-reflective film with a beam splitting ratio of 50:

50. The reference mirror is a square silicon mirror. The surface of the anti-reflective glass sheet is coated with an anti-reflective film for incident light in the 700nm to 1000nm wavelength band.

9. A multilayer film thickness measuring instrument based on Taylor polynomial fitting coefficient analysis according to claim 6, characterized in that, The center wavelength range of the broadband SLD light source is 850nm to 950nm.

10. A multilayer film thickness measuring instrument based on Taylor polynomial fitting coefficient analysis according to claim 6, characterized in that, It also includes a displacement stage for carrying the multilayer thin film sample to be tested, the displacement stage being used to adjust the spatial position of the sample so that the surface of the sample to be tested is at the focal position of the sample light; the executable program of the computer also includes a functional module for system calibration.

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