Method for obtaining film thickness and refractive index, test system, storage medium and application

Abstract

This invention discloses a method, testing system, storage medium, and application for obtaining thin film thickness and refractive index. The method for obtaining thin film thickness and refractive index includes: using two sets of nonlinear transmission line terahertz frequency comb generators and a broadband mixer to obtain an intermediate frequency (IF) signal carrying transmission phase information; obtaining a measured phase curve based on the IF signal; constructing an equivalent multipath interference model of the thin film; coherently superimposing multiple reflection components of the measured wave signal within the thin film in the complex domain to obtain the complex phase of the total transmission field; obtaining a phase-frequency variation spectrum based on the complex phase as the model phase curve; constructing an error function between the model phase curve and the measured phase curve; and solving for the parameter combination that minimizes the error function by scanning the parameter combination of the thin film's refractive index (n) and thickness (d). This invention avoids thermal or temporal phase drift, thereby avoiding calculation errors caused by phase jumps.

Description

Technical Field

[0001] This invention specifically relates to a method, testing system, storage medium, and application for obtaining thin film thickness and refractive index, belonging to the field of electromagnetic characterization technology for materials and devices. Background Technology

[0002] In the field of electromagnetic characterization of materials and devices, refractive index (or equivalent dielectric constant) and thickness are core parameters determining the propagation, reflection, and transmission characteristics of electromagnetic waves. For dielectric thin films, encapsulation materials, substrate layers, adhesive layers, and multilayer structures, the samples under test often exhibit significant dispersion and loss variations over a wide frequency range, making it difficult to accurately describe their true electromagnetic response using only a single frequency point or narrowband measurement. Therefore, the field typically requires obtaining the transmission / reflection characteristics of the test object within a certain frequency range and using physical models to deduce the variation of refractive index with frequency (or wavelength) and geometric thickness.

[0003] In existing technologies, the approaches used to invert material parameters from spectral response can be broadly categorized into two types: one is the "fringe method" utilizing interference fringe information, and the other is "full-band fitting" incorporating data across the entire frequency band into a single physical model. The fringe method typically relies on Fabry-Pérot interference fringes formed by multiple reflections within the sample. By analyzing the optical path difference relationship between the extreme fringe positions and the fringe spacing, "optical thickness" is separated into refractive index and geometric thickness. In optical thin film testing, a typical approach is to extract the maxima / minimum envelopes of the fringes from the transmission or reflection spectrum to quickly estimate the refractive index and thickness. This type of method is particularly efficient for samples with clear fringes and weak absorption, and is often used to provide initial thickness values ​​or for rapid inversion in transparent regions. The full-band fitting method is more versatile: it treats the air / film / substrate (or more layers) as a multilayer medium system, and establishes a forward model from material parameters {n(f), d} to measurable {T(f), R(f)} or {S11(f), S21(f)} based on Fresnel equations and the transfer matrix method (TMM). It aims to minimize the difference between the model and measured data, and jointly inverts the refractive index dispersion parameters, loss parameters, and thickness. Compared to the fringe method, full-band fitting can handle weak or even no fringes, and is more suitable for scenarios with strong absorption, more complex structures, or where both real and imaginary parameters need to be obtained simultaneously. However, it typically places higher demands on the frequency band continuity, amplitude-phase consistency, and system calibration accuracy of the input data.

[0004] Based on the above ideas, relatively mature measurement platforms have been developed for different frequency bands: In the visible-near infrared band, spectrophotometers are often used to measure transmission / reflection spectra. A monochromator or grating is used to disperse and scan a broadband light source to obtain full-spectrum data, which is then inverted using the fringe method or TMM. In the mid-infrared band, Fourier transform infrared (FTIR) spectrometers are often used. A Michelson interferometer is used to acquire a broadband interferogram in one step, and the full spectrum is obtained through Fourier transform, followed by multi-level model fitting. In the terahertz band, terahertz time-domain spectroscopy (THz-TDS) systems are often used. Ultrashort pulse excitation and time-domain sampling are used to obtain the electric field variation over time, and then Fourier transform is used to obtain amplitude and phase information, making full-band fitting more stable when solving for refractive index and thickness. In optical thin film industrial metrology, spectral ellipsometry is also widely used. It achieves the joint solution of n and d of the thin film by measuring the parameters of polarization state variation with wavelength / angle and performing full-spectrum fitting. The common characteristics of the above systems are: on the one hand, they all revolve around the main line of "acquiring broadband / wideband response - establishing physical model - full spectrum inversion parameters"; on the other hand, they achieve broadband in different ways, including wavelength-by-wave scanning, Fourier transform to obtain the full spectrum in one step, or frequency domain transformation after time domain sampling, etc.

[0005] When the test target shifts to the millimeter-wave to Asia-Pacific Hertz band, the most common implementation scheme in existing engineering applications is frequency domain sweep testing centered on a vector network analyzer. This scheme typically excites and receives the sample within the test range using coaxial / waveguide devices or free-space quasi-optical structures, measuring the S-parameters (such as S21 and S11) corresponding to transmission and reflection. Since the test range covers multiple waveguide standard frequency bands, practical systems often use segmented waveguide components, frequency extension modules, or different frequency band front-ends for coverage, and stitch the data together after completing the segmented measurements to obtain the complete spectrum. For sheet-like dielectrics, encapsulation layers, or multilayer structures, in engineering, the sample is often placed between two horn antennas to form a free-space transmission / reflection measurement link, or guided wave measurement is achieved through waveguide fixtures; then the measured S11(f) and S21(f) are input into a multilayer transmission model or equivalent dielectric model, and n(f) and thickness d are obtained by full-band fitting inversion. In addition, there are implementations that use a swept-frequency signal source / stepped frequency source in conjunction with a detector or vector receiver. These also acquire the spectral response by scanning frequency points one by one and rely on a post-processing model to complete parameter inversion. For applications requiring higher signal-to-noise ratios or stronger phase coherence, existing systems also introduce heterodyne down-conversion receiver structures. These down-convert the signal under test to intermediate frequency / baseband via a local oscillator link before performing amplitude and phase measurements and spectral splicing. Existing technologies for extracting the refractive index (or equivalent dielectric constant) and thickness of materials are relatively abundant. These include fringe methods using interference fringes and full-band fitting methods based on multilayer transmission models, as well as platforms for different wavebands such as spectrophotometers, FTIR, ellipsometrics, THz-TDS, and millimeter-wave frequency-domain swept-frequency testing systems. However, the aforementioned existing solutions generally have unavoidable shortcomings in the millimeter-wave and even terahertz frequency bands.

[0006] First, while optical / infrared platforms such as visible-near-infrared spectrophotometers, FTIR, and spectral ellipsometry can obtain thin film n(λ), d relatively well through fringe methods or full-band fitting, their operating frequencies are in the optical / infrared range, not the millimeter-wave band. They measure optical constants at optical frequencies, which are difficult to directly equate to millimeter-wave or terahertz frequencies. Extrapolating the results requires introducing material dispersion models, polarization mechanism assumptions, or additional priors. However, these assumptions are often unreliable for polymers, adhesives, composite media, and porous materials, leading to strong model dependence and uncontrollable errors. Furthermore, the optical fringe method is highly sensitive to ideal conditions such as "uniformity, flatness, weak scattering, and clear fringes" in the sample. Many millimeter-wave and terahertz-related materials in engineering (encapsulating layers, rough surface coatings, multilayer composite structures, and filler-containing materials) often do not meet these conditions, causing the fringes to be washed away or the envelope extraction to be distorted, ultimately resulting in multiple solutions and instability in the inversion results. Ellipsometry, on the other hand, requires the reasonable selection of incident angle, polarization configuration, measurement band, and the establishment of an optical model consistent with the actual structure of the sample (layer structure, rough layer, anisotropy, gradient layer, etc.). If the initial parameter values ​​and model selection are not appropriate, multiple solutions or "fit convergence but physical unreliability" may occur. In practical use, it presents problems such as high learning cost, many operation steps, and limited testing efficiency.

[0007] THz-TDS, a commonly used method for testing thin film thickness and refractive index in the Asia-Pacific Hertz and Terahertz bands, shares the characteristic of high equipment investment with ellipsometers: high system integration and high cost of key components (such as ultrafast laser sources, precision optomechanical structures, dedicated detectors / optical components, and stable control units), resulting in significantly higher overall procurement and maintenance costs than conventional test systems based on RF / millimeter-wave electronic links.

[0008] To achieve a certain wideband coverage from millimeter waves to terahertz waves, existing engineering systems typically require segmented implementation and module switching, such as switching between different waveguide bands, different harmonic / mixer chains, different front-end components, or different test fixtures / antenna structures. Segmented switching inevitably introduces reference plane changes, amplitude and phase response differences, and calibration residuals; even if calibration is performed separately within each frequency band, it is difficult to guarantee amplitude consistency and phase continuity across frequency bands. Spectral discontinuities, phase jumps, or "step-like" errors often appear at frequency band boundaries, which are then misinterpreted as material dispersion or thickness variations in subsequent fitting and inversion, leading to systematic biases in the inversion parameters. Summary of the Invention

[0009] The main objective of this invention is to provide a method, testing system, storage medium, and application for obtaining thin film thickness and refractive index, thereby overcoming the shortcomings of the prior art.

[0010] To achieve the aforementioned objectives, the technical solution adopted by this invention includes:

[0011] A first aspect of the present invention is a method for obtaining thin film thickness and refractive index, characterized in that it includes:

[0012] Two sets of nonlinear transmission line terahertz frequency comb generators are used to generate a test wave signal and a local oscillator signal covering the millimeter wave to terahertz band, respectively. The test wave signal is transmitted through a thin film to obtain a transmitted test wave signal. A broadband mixer is used to mix the transmitted test wave signal with the local oscillator signal to obtain an intermediate frequency signal carrying the transmission phase information. The phase-frequency change spectrum is obtained based on the intermediate frequency signal as the measured phase curve.

[0013] An equivalent multipath interference model of the wave signal transmitted through the thin film is constructed. The multiple reflection components of the wave signal inside the thin film are coherently superimposed in the complex domain to obtain the complex phase of the total transmission field. Based on the complex phase, the phase-frequency variation spectrum is obtained as the phase curve of the model.

[0014] An error function is constructed between the model phase curve and the measured phase curve. By scanning the parameter combination of the refractive index n and thickness d of the thin film, the parameter combination that minimizes the error function is obtained, which is the refractive index and thickness of the thin film.

[0015] Furthermore, the equivalent multi-path interference model for the transmission thin film of the measured wave signal includes:

[0016] The frequency of the wave signal being measured f The wavelength of the measured wave signal is determined by the independent variable. λ :

[0017] ；

[0018] Let the incident angle of the measured wave signal be α, and the refraction angle of the measured wave signal after it is incident on the thin film be θ. The incident angle α and the refraction angle θ satisfy:

[0019] n sinθ = sinα;

[0020] The equivalent propagation length of the measured wave signal through the thin film in a single pass L 1. Effective optical path compensation term for the air segment related to the reference path of the measured wave signal L 2. Cumulative term of additional path difference caused by multiple reflections of the measured wave signal L 3 are respectively:

[0021] ;

[0022] ;

[0023] .

[0024] Furthermore, the multiple reflection components of the measured wave signal inside the thin film are coherently superimposed in the complex domain to obtain the complex phase of the total transmitted field, specifically including:

[0025] Using the first N reflection components for a finite term approximation, the nth... k Effective length of the first transmission component for:

[0026] ;

[0027] in, N It is a positive integer. N ≥3;

[0028] Definition of the first k Amplitude weighting of the first transmission component for:

[0029] ;

[0030] Calculate any frequency point First k Phase of the path component :

[0031] ;

[0032] The transmission components of each order are coherently superimposed in the complex domain to obtain the total complex amplitude of transmission. :

[0033] .

[0034] Furthermore, obtaining the phase-frequency change spectrum based on the complex phase includes:

[0035] The total transmission complex amplitude is decomposed into its real part. and the virtual part The total complex amplitude of the transmission is real. and the virtual part sum:

[0036] ;

[0037] Each frequency point is obtained by calculating using the arctangent function. The main phase at the location :

[0038] ;

[0039] The main phase Unfolding along the frequency axis yields continuous phase. This leads to a continuous model phase curve;

[0040] .

[0041] Furthermore, the error function for constructing the model phase curve and the measured phase curve includes:

[0042] Measured phase curve Phase curve with model By comparing at the same frequency points, an error function based on the phase difference is obtained. :

[0043] ;

[0044] Where M is the total number of frequency points. For the model phase curve at frequency Phase value at that point, For the measured phase curve at frequency The phase value at that point.

[0045] Furthermore, the thin film includes a dielectric thin film.

[0046] A second aspect of this invention provides a thickness and refractive index testing system based on a nonlinear transmission line, used to implement the method for obtaining the film thickness and refractive index, comprising:

[0047] A first nonlinear transmission line terahertz frequency comb generator is used to generate a test wave signal covering a wide frequency band from millimeter wave to terahertz, and to incident the test wave signal onto a thin film, wherein the test wave signal is transmitted through the thin film to form a transmitted test wave signal.

[0048] The second nonlinear transmission line terahertz frequency comb generator is used to generate local oscillator signals covering a wide frequency band from millimeter waves to terahertz.

[0049] A wideband mixer is connected to the transmission end of the thin film and the second nonlinear transmission line terahertz frequency comb generator, respectively, to mix the transmitted wave signal under test with the local oscillator signal and output an intermediate frequency signal carrying the transmission phase information of the thin film.

[0050] The data processing module, connected to the broadband mixer, is used to generate a measured phase curve based on the intermediate frequency signal; and to construct an equivalent multipath interference model of the transmitted thin film of the measured wave signal, to coherently superimpose the multiple reflection components of the measured wave signal inside the thin film in the complex domain, to calculate the complex phase of the total transmission field, to generate a model phase curve based on the complex phase, and simultaneously to construct the error function between the model phase curve and the measured phase curve, and to solve the parameter combination that minimizes the error function by scanning the parameter combination of the refractive index n and thickness d of the thin film.

[0051] Furthermore, the equivalent multi-path interference model for the transmission thin film of the measured wave signal includes:

[0052] The frequency of the wave signal being measured f The wavelength of the measured wave signal is determined by the independent variable. λ :

[0053] ；

[0054] Let the incident angle of the measured wave signal be α, and the refraction angle of the measured wave signal after it is incident on the thin film be θ. The incident angle α and the refraction angle θ satisfy:

[0055] n sinθ = sinα;

[0056] The equivalent propagation length of the measured wave signal through the thin film in a single pass L 1. Effective optical path compensation term for the air segment related to the reference path of the measured wave signal L 2. Additional path difference accumulation term caused by multiple reflections L 3 are respectively:

[0057] ;

[0058] ;

[0059] ;

[0060] The calculation of the complex phase of the total transmitted field involves coherently superimposing the multiple reflection components of the measured wave signal inside the thin film in the complex domain.

[0061] Using the first N reflection components for a finite term approximation, the nth... k Effective length of the first transmission component for:

[0062] ;

[0063] in, N It is a positive integer. N ≥3;

[0064] Definition of the first k Amplitude weighting of the first transmission component for:

[0065] ;

[0066] Calculate any frequency point First k Phase of the path component :

[0067] ;

[0068] The transmission components of each order are coherently superimposed in the complex domain to obtain the total complex amplitude of transmission. :

[0069] ;

[0070] Phase curves based on the complex phase generation model include:

[0071] The total transmission complex amplitude is decomposed into its real part. and the virtual part The total complex amplitude of the transmission is real. and the virtual part sum:

[0072] ;

[0073] Each frequency point is obtained by calculating using the arctangent function. The main phase at the location :

[0074] ;

[0075] The main phase Unfolding along the frequency axis yields continuous phase. This leads to a continuous model phase curve;

[0076] ;

[0077] The error function for constructing the model phase curve and the measured phase curve includes:

[0078] Measured phase curve Phase curve with model By comparing at the same frequency points, an error function based on the phase difference is obtained. :

[0079] ;

[0080] Where M is the total number of frequency points. For the model phase curve at frequency Phase value at that point, For the measured phase curve at frequency The phase value at that point.

[0081] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method steps for obtaining thin film thickness and refractive index.

[0082] The fourth aspect of the present invention provides the use of the method for obtaining thin film thickness and refractive index as described above, or the thickness and refractive index testing system based on nonlinear transmission lines, in the testing of thin film thickness and refractive index in the millimeter-wave to terahertz band.

[0083] Compared with the prior art, the advantages of the present invention include:

[0084] The method for obtaining film thickness and refractive index provided in this invention generates a frequency comb through a nonlinear transmission line, avoiding the need for traditional solutions to segment different frequency bands and then splice them together. This avoids discontinuities at the splicing points caused by hardware switching. The comb teeth are naturally phase coherent, providing a unified phase across the entire frequency band, avoiding thermal or temporal phase drift, and thus avoiding calculation errors caused by phase jumps.

[0085] The present invention provides a thickness and refractive index testing system based on nonlinear transmission lines, which focuses on the refractive index and thickness testing of thin films in a wide frequency band from millimeter wave to terahertz wave. The testing system is simple to build, easy to operate, cost-controllable, and highly repeatable. The inversion method after the test requires a small amount of data, has a fast fitting speed, accurate results, and does not require prior calibration or preparation of a material database. Attached Figure Description

[0086] Figure 1 This is a schematic diagram of a test method based on a nonlinear transmission line terahertz frequency comb generator provided in a typical embodiment of the present invention;

[0087] Figure 2 This is a schematic diagram of phase calculation after the measured wave signal is incident on the thin film in a typical embodiment of the present invention;

[0088] Figure 3 , Figure 4 Examples of model phase curves for different refractive indices and film thicknesses;

[0089] Figure 5 This is a flowchart of a method for testing the thickness and refractive index of a thin film based on a nonlinear transmission line terahertz frequency comb generator, as described in a typical embodiment of the present invention. Detailed Implementation

[0090] In view of the shortcomings of the prior art, the inventors of this invention, through long-term research and extensive practice, have proposed the technical solution of this invention. The following will further explain and illustrate the technical solution, its implementation process and principle in conjunction with the accompanying drawings and specific implementation examples. Unless otherwise specified, the nonlinear transmission line (NLTL) terahertz frequency comb generator, wideband mixer, etc. involved in the embodiments of this invention are all known in the art.

[0091] This invention uses a nonlinear transmission line terahertz frequency comb generator to generate a frequency comb for testing thin film thickness and refractive index in the millimeter wave and terahertz bands. By establishing a multi-path interference model of the thin film, the complex phase of the total transmission field is obtained. Using the error function between this phase curve and the broadband phase curve of the terahertz wave obtained based on the frequency comb test as a benchmark, the refractive index n and thickness d of the thin film are obtained by scanning.

[0092] In a typical implementation scheme, please refer to Figure 5 A method for testing the thickness and refractive index of thin films based on a nonlinear transmission line terahertz frequency comb generator, specifically including:

[0093] 1) The phase-frequency variation spectrum of the thin film under test is obtained by testing with a nonlinear transmission line terahertz frequency comb generator, which is used as the measured phase curve.

[0094] Please see Figure 1 Two sets of nonlinear transmission line (NLTL) terahertz frequency comb generators are used to generate frequency comb signals covering the millimeter wave to terahertz band. One set of NLTL terahertz frequency comb generators is used to generate the measured wave signal RF (i.e., the measured wave, the same below), and the other set is used to generate the local oscillator signal LO (i.e., the local oscillator, the same below). The measured wave signal is transmitted through the thin film under test (DUT) to form the transmitted measured wave signal. A broadband mixer is used to mix the transmitted measured wave signal with the local oscillator signal to obtain an intermediate frequency signal (IF) carrying the transmitted phase information. Based on the IF signal, a broadband phase-frequency variation spectrum (phase-frequency variation spectrum) from the millimeter wave to the terahertz band is plotted, which is the measured phase curve.

[0095] 2) Data processing after testing.

[0096] An equivalent multi-path interference model of the wave signal under test transmitted through the thin film under test is constructed. Multiple internal reflection components are coherently superimposed in the complex domain to obtain the complex phase of the total transmission field. Based on the complex phase, the phase-frequency change spectrum is obtained as the phase curve of the model.

[0097] The error function between the model phase curve and the measured phase curve is constructed. By scanning the parameter combination of the refractive index n and thickness d of the thin film under test, the parameter combination that minimizes the error function is obtained, thereby inverting the refractive index and thickness of the thin film under test.

[0098] It should be noted that, due to the need for mixing to generate an intermediate frequency signal, there will be a small, fixed frequency difference between the measured wave signal and the local oscillator signal. This is necessary for mixing and is known in the art. Furthermore, both the model phase curve and the measured phase curve are broadband. In addition, the incident angle and other parameters of the measured wave signal used in constructing the equivalent multi-path interference model of the measured wave signal transmitting through the measured thin film are consistent with those used in the actual measurement.

[0099] like Figure 2 As shown, after the measured wave signal enters the measured thin film, it forms a series of multiple reflection components of different orders. Each component has a different effective optical path and amplitude weight. By treating these components as coherent superposition, the total complex amplitude can be obtained, thereby extracting the total phase. To avoid the phase principal value [ The transition of π,π] affects the error evaluation. This invention expands the phase curve and outputs it in a unified angle system to obtain the measured phase curve.

[0100] This invention uses the frequency of the measured wave signal f (GHz) is the independent variable, representing the wavelength of the measured wave signal. λ (mm) is calculated using the following formula:

[0101] ；

[0102] Let the incident angle of the measured wave signal be α, and the angle of refraction of the measured wave signal after it is incident on the film under test (specifically, the angle of refraction at the end of the film after the first incident on the film under test) be θ. The incident angle α and the angle of refraction θ satisfy: n sinθ = sinα; for example, if the incident angle α is 45°, then .

[0103] Combination Figure 2 Given the geometric relationships shown, the equivalent propagation length and compensation term for a single propagation are defined as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] in, L 1. Characterizes the equivalent propagation length of the measured wave signal through the measured thin film in a single pass. L2. Characterize the effective optical path compensation term in the air segment related to the reference path of the measured wave signal. L 3. Characterizes the additional path difference accumulation term caused by multiple reflections of the measured wave signal. 。

[0108] It should be noted that, without a thin film, the portion of the path that light travels normally is called the reference path-dependent air segment.

[0109] Using the first N reflection components for a finite term approximation, the nth... k Effective length of the first transmission component for:

[0110] .

[0111] in, N It is a positive integer. N ≥3 (usually around 10 is sufficient to achieve the desired result), this formula reflects the first [value] in the transmission channel. k The first-order component undergoes an additional (k) compared to the first-order component. 1) The internal round trip is therefore calculated based on its propagation within the tested thin film. Incremental and superimposed Additional path difference.

[0112] The magnitude weight of each component is given by the series expansion formed by the interface reflection / transmission coefficients, defining the first... k Amplitude weighting of the first transmission component for:

[0113] .

[0114] Therefore, at any frequency point Place, No. k Phase of the path component for:

[0115] .

[0116] The transmission components of each order are coherently superimposed in the complex domain, and the total complex amplitude of the transmission is obtained. Represented as:

[0117] .

[0118] For ease of numerical implementation, the total complex amplitude of transmission can be written as its real part. and the virtual part sum:

[0119]

[0120] Each frequency point is obtained by calculating using the arctangent function. The main phase at the location :

[0121] .

[0122] The main phase Unfolding along the frequency axis yields continuous phase. , To prevent the influence of phase jumps on calculation errors and thus obtain a continuous model phase curve. Specifically, examples of model phase curves for different refractive indices and film thicknesses are provided. Figure 3 , Figure 4 As shown.

[0123] This invention will measure the phase curve (Based on measured data) and model phase curve By comparing at the same frequency points, an error function based on the phase difference is obtained, such as the mean square error function. :

[0124] .

[0125] Where M is the total number of frequency points. For the model phase curve at frequency Phase value at that point, For the measured phase curve at frequency The phase value at that point.

[0126] By scanning the parameter combination of the refractive index n and thickness d of the thin film under test, the parameter combination that minimizes the error function is obtained, thereby inverting the refractive index and thickness of the thin film under test.

[0127] Current mainstream film thickness testing methods and instruments mainly test in the optical and infrared frequency bands. This invention focuses on the refractive index and thickness testing of thin films in a wide frequency band from millimeter wave to terahertz wave. The testing system is simple to set up, easy to operate, cost-controllable, and highly repeatable. The inversion method after the test requires a small amount of data, has a fast fitting speed, accurate results, and does not require prior calibration or preparation of a material database.

[0128] This invention generates a frequency comb using a nonlinear transmission line, avoiding the need for traditional solutions to segment different frequency bands and then splice them together. This also avoids discontinuities at the splicing points caused by hardware switching. The comb teeth are naturally phase coherent, providing a unified phase across the entire frequency band, avoiding thermal or temporal phase drift, and thus avoiding calculation errors caused by phase jumps.

[0129] It should be understood that the above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for obtaining the thickness and refractive index of a thin film, characterized in that, include: Two sets of nonlinear transmission line terahertz frequency comb generators are used to generate a test wave signal and a local oscillator signal covering the millimeter wave to terahertz band, respectively. The test wave signal is transmitted through a thin film to obtain a transmitted test wave signal. A broadband mixer is used to mix the transmitted test wave signal with the local oscillator signal to obtain an intermediate frequency signal carrying the transmission phase information. The phase-frequency change spectrum is obtained based on the intermediate frequency signal as the measured phase curve. An equivalent multipath interference model of the wave signal transmitted through the thin film is constructed. The multiple reflection components of the wave signal inside the thin film are coherently superimposed in the complex domain to obtain the complex phase of the total transmission field. Based on the complex phase, the phase-frequency variation spectrum is obtained as the phase curve of the model. The error function between the model phase curve and the measured phase curve is constructed. By scanning the parameter combination of the refractive index n and thickness d of the thin film, the parameter combination that minimizes the error function is obtained, which is the refractive index and thickness of the thin film. Constructing an equivalent multi-path interference model for the transmission thin film of the measured wave signal includes: Determine the wavelength λ of the measured wave using the frequency f of the measured wave signal as the independent variable: ； Let the incident angle of the measured wave signal be α, and the refraction angle of the measured wave signal after it is incident on the thin film be θ. The incident angle α and the refraction angle θ satisfy: n·sinθ=sinα; The equivalent propagation length L1 of the measured wave signal passing through the thin film in a single pass, the effective optical path compensation term L2 related to the reference path of the measured wave signal in the air segment, and the additional path difference accumulation term L3 caused by multiple reflections of the measured wave signal are respectively: ； ； ； The complex phase of the total transmitted field is obtained by coherently superimposing the multiple reflection components of the measured wave signal inside the thin film in the complex domain, specifically including: Using the first N reflection components as a finite term approximation, the effective length of the k-th order transmission component is defined. for: ； Where N is a positive integer, N≥3; Define the amplitude weight of the k-th order transmission component. for: ； Calculate any frequency point Phase of the k-th path component : ； The transmission components of each order are coherently superimposed in the complex domain to obtain the total complex amplitude of transmission. : ； The phase-frequency change spectrum obtained based on the complex phase includes: The total transmission complex amplitude is decomposed into its real part. and the virtual part The total complex amplitude of the transmission is real. and the virtual part sum: ； Each frequency point is obtained by calculating using the arctangent function. The main phase at the location : ； The main phase Unfolding along the frequency axis yields continuous phase. This leads to a continuous model phase curve; ； The error function for constructing the model phase curve and the measured phase curve includes: Measured phase curve Phase curve with model By comparing at the same frequency points, an error function based on the phase difference is obtained. : ； Where M is the total number of frequency points. For the model phase curve at frequency Phase value at that point, For the measured phase curve at frequency The phase value at that point.

2. The method for obtaining thin film thickness and refractive index according to claim 1, characterized in that: The thin film includes a dielectric thin film.

3. A thickness and refractive index testing system based on a nonlinear transmission line, used to implement the method for obtaining the film thickness and refractive index as described in any one of claims 1-2, characterized in that, include: A first nonlinear transmission line terahertz frequency comb generator is used to generate a test wave signal covering a wide frequency band from millimeter wave to terahertz, and to incident the test wave signal onto a thin film, wherein the test wave signal is transmitted through the thin film to form a transmitted test wave signal. The second nonlinear transmission line terahertz frequency comb generator is used to generate local oscillator signals covering a wide frequency band from millimeter waves to terahertz. A wideband mixer is connected to the transmission end of the thin film and the second nonlinear transmission line terahertz frequency comb generator, respectively, to mix the transmitted wave signal under test with the local oscillator signal and output an intermediate frequency signal carrying the transmission phase information of the thin film. The data processing module, connected to the wideband mixer, is used to generate a measured phase curve based on the intermediate frequency signal; Furthermore, an equivalent multi-path interference model of the transmitted thin film of the wave signal under test is constructed. The multiple reflection components of the wave signal under test inside the thin film are coherently superimposed in the complex domain, the complex phase of the total transmission field is calculated, and the model phase curve is generated based on the complex phase. At the same time, the error function between the model phase curve and the measured phase curve is constructed, and the parameter combination of the refractive index n and thickness d of the scanned thin film is solved to obtain the parameter combination that minimizes the error function.

4. The thickness and refractive index testing system based on nonlinear transmission lines according to claim 3, characterized in that: The equivalent multi-optical-path interference model for thin films includes: Determine the wavelength λ of the measured wave signal using the frequency f as the independent variable: ； Let the incident angle of the measured wave signal be α, and the refraction angle of the measured wave signal after it is incident on the thin film be θ. The incident angle α and the refraction angle θ satisfy: n·sinθ=sinα; The equivalent propagation length L1 of the measured wave signal passing through the thin film in a single pass, the effective optical path compensation term L2 related to the reference path of the measured wave signal passing through the thin film, and the additional path difference accumulation term L3 caused by multiple reflections of the measured wave signal are respectively: ； ； ； The calculation of the complex phase of the total transmitted field involves coherently superimposing the multiple reflection components of the measured wave signal inside the thin film in the complex domain. Using the first N reflection components as a finite term approximation, the effective length of the k-th order transmission component is defined. for: ； Where N is a positive integer, N≥3; Define the amplitude weight of the k-th order transmission component. for: ； Calculate any frequency point Phase of the k-th path component : ； The transmission components of each order are coherently superimposed in the complex domain to obtain the total complex amplitude of transmission. : ； Phase curves based on the complex phase generation model include: The total transmission complex amplitude is decomposed into its real part. and the virtual part The total complex amplitude of the transmission is real. and the virtual part sum: ； Each frequency point is obtained by calculating using the arctangent function. The main phase at the location : ； The main phase Unfolding along the frequency axis yields continuous phase. This leads to a continuous model phase curve; ； The error function for constructing the model phase curve and the measured phase curve includes: Measured phase curve Phase curve with model By comparing at the same frequency points, an error function based on the phase difference is obtained. : ； Where M is the total number of frequency points. For the model phase curve at frequency Phase value at that point, For the measured phase curve at frequency The phase value at that point.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the method steps for obtaining the film thickness and refractive index as described in any one of claims 1-2.

6. The method for obtaining thin film thickness and refractive index as described in any one of claims 1-2, or the thickness and refractive index testing system based on nonlinear transmission lines as described in claim 3 or 4, for the testing of thin film thickness and refractive index in the millimeter-wave to terahertz band.

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