A method and system for characterizing the electro-optic coefficient of a thin film based on the spectral ellipsometry of an external electric field

Abstract

The application discloses a kind of based on external electric field spectrum ellipsometry thin film electro-optic coefficient characterization method and system, specifically relates to optical precision measurement and photoelectric material characterization technical field, including the static ellipsometric parameter of thin film sample when not applying external electric field is collected, constructs multilayer optical model and obtains thin film thickness and static complex refractive index dispersion curve inversion;Sinusoidal alternating modulation voltage is applied, with modulation frequency as the lock-in reference signal, the oscillation amplitude of ellipsometric parameter at modulation frequency is extracted from ellipsometer detection signal;Change modulation voltage amplitude and verify the linear relationship of modulation amplitude and voltage;Refractive index perturbation term is introduced in static optical model, and dynamic optical model is established and the theoretical modulation amplitude of ellipsometric parameter is derived;The measured and theoretical modulation amplitude are globally fitted, with thin film thickness and static refractive index as fixed constraint, iteratively solve electro-optic coefficient, and obtain dispersion distribution by wavelength scanning.

Description

Technical Field

[0001] This invention relates to the field of optical precision measurement and optoelectronic material characterization technology, and more specifically, to a method and system for characterizing the electro-optic coefficient of thin films based on the spectral ellipticity of an external electric field. Background Technology

[0002] The electro-optic coefficient is a key parameter that measures a material's ability to linearly change its refractive index under the influence of an external electric field. It is crucial for the design and performance evaluation of integrated photonic devices such as high-speed electro-optic modulators and switches. Accurate measurement of the electro-optic coefficient of thin films, especially those of III-V compounds (such as AlScN) and ferroelectric oxides, is fundamental to materials research and development and device optimization.

[0003] Currently, the main methods for measuring the electro-optic coefficient of thin films are as follows: Prism coupling method, which calculates the effective electro-optic coefficient by exciting the guided mode and measuring the change in coupling angle with an external electric field, has high sensitivity; interferometry, which calculates the electro-optic coefficient by measuring the intensity or phase change of the interference light caused by the external electric field; and conventional reflection / transmission intensity modulation method, which estimates the coefficient by measuring the change in light intensity before and after applying an electric field. Spectral ellipsometric method is a method that inverts the optical constants (complex refractive index) and thickness of thin films by measuring the change in the polarization state (amplitude ratio and phase difference) of the reflected light after it is obliquely incident on the sample. Traditional ellipsometers are mainly used for static optical parameter measurement. When applied to electro-optic coefficient measurement, two sets of ellipsometric data are measured before and after applying a DC electric field, and the refractive index change is extracted by fitting the difference.

[0004] However, in practical use, it still has some drawbacks. For example, the prism coupling method requires the sample to be optically attached to the prism, which may cause pressure or damage to the sample. It can usually only obtain the effective photoelectric coefficient and it is difficult to separate different tensors. For materials with strong absorption, it is difficult to locate the reflection minimum point of the guided mode, which affects the accuracy. The interferometry method has high requirements for optical path stability and sample preparation (such as Fabry-Perot cavity structure), and the signal is easily affected by environmental disturbances. The conventional reflection / transmission intensity modulation method is easily affected by factors such as light source fluctuations and sample surface scattering, which has limited accuracy and cannot directly obtain the refractive index change. The traditional ellipsometer is very sensitive to the long-term stability of the instrument, environmental micro-vibrations, and thermal effects (thermo-optic effect) caused by the electric field. It is difficult to detect the small refractive index changes caused by the electric field, which limits its measurement accuracy and sensitivity. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method and system for characterizing the electro-optic coefficient of thin films based on the spectral ellipticity of an external electric field, thereby solving the problems mentioned in the background art through the following solutions.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for characterizing the electro-optic coefficient of thin films based on spectral ellipsometrics of an external electric field, comprising S1: placing the thin film sample to be tested in the optical path of a spectral ellipsometer, setting the incident angle and wavelength range under conditions without applying an external electric field, collecting the ellipsometric parameters of the reflected light from the sample, including the amplitude ratio Ψ and the phase difference Δ, constructing a multilayer optical model, and numerically fitting and inverting to obtain the thin film thickness and the static complex refractive index-wavelength dispersion curve; S2: Apply a sinusoidal AC modulation voltage with a frequency of ω to the thin film sample through the sample stage electrode structure. Use ω as the phase-locked reference signal and extract the oscillation amplitudes of Ψ and Δ at ω from the output signal of the spectroscopic ellipsometer detector. These amplitudes are denoted as modulation amplitudes δΨ and δΔ. S3: Change the amplitude of the sinusoidal AC modulation voltage, take different amplitude points, and repeatedly perform signal extraction to obtain δΨ and δΔ at each amplitude point. Determine whether the changes of δΨ and δΔ with the amplitude of the modulation voltage conform to a linear relationship. S4: A perturbation term is superimposed on the refractive index of the thin film. The magnitude of the perturbation term is proportional to the intensity of the modulation electric field of the thin film, the cube of the static refractive index, and the electro-optic coefficient to be measured. For optically anisotropic thin films, the refractive index perturbation is extended to the changes of each component of the refractive index tensor and associated with the tensor elements of different electro-optic coefficients to be measured. The theoretical reflection coefficient is calculated based on the dynamic optical model, and the theoretical dependence of the modulation amplitude of the ellipsoid parameter on the modulation voltage amplitude is derived. S5: Globally fit δΨ and δΔ with the theoretical modulation amplitude. During the fitting process, the film thickness and static complex refractive index dispersion curve are used as fixed input parameters, and the electro-optic coefficient to be measured or the electro-optic coefficient tensor element is used as the variable to be optimized. By minimizing the residual between the measured and theoretical data, the optimal convergence value of the electro-optic coefficient is obtained by iterative solution. Change the measurement wavelength and repeat S2 to S5 to obtain the electro-optic coefficient-wavelength dispersion distribution.

[0007] A thin film electro-optic coefficient characterization system based on external electric field spectral ellipticity includes a spectral ellipticity measurement module: including a broadband or tunable monochromatic light source, a polarizer, a first compensator, a second compensator, an analyzer, and a photodetector, used to generate polarization probe light and measure the ellipticity parameters of the sample reflected light. Integrated sample stage and electric field application module: including sample clamp and electrode structure integrated on the sample stage, wherein the electrode structure is a vertical electric field configuration or an in-plane electric field configuration, used to carry the sample and apply a sinusoidal AC modulated voltage with frequency ω to the thin film sample; Signal synchronization and data acquisition module: includes a lock-in amplifier, which uses the frequency ω of the modulation voltage as a reference frequency to receive the output signal of the photodetector and extracts the oscillation amplitudes δΨ and δΔ of the ellipsoid parameters that are in sync with the modulation electric field; Central control and data processing module: a computer used to control the wavelength scanning of the spectral ellipsometric measurement module, control the voltage output of the electric field application module, control the signal extraction of the data acquisition module, and run the data processing algorithm of steps S1 to S5 as described in claim 1 to invert and calculate the electro-optic coefficient of the thin film.

[0008] Preferably, when the multilayer optical model is applied to a uniaxial anisotropic thin film, the ordinary light refractive index and the extraordinary light refractive index are described by the Sellmeier dispersion model, the ultraviolet absorption edge is fitted by the Tauc-Lorentz model, and the numerical fitting is performed using the Levenberg-Marquardt nonlinear least squares algorithm.

[0009] Preferably, the frequency of the sinusoidal AC modulation voltage is set in a frequency band that avoids power frequency interference and low-frequency noise from environmental thermal drift.

[0010] Preferably, the oscillation amplitude is extracted after the output signal of the spectral ellipsometer detector is sampled multiple times at each modulation voltage amplitude point and the arithmetic mean is taken.

[0011] Preferably, the modulation voltage amplitude includes at least 5 different amplitude gradients, and each amplitude point is measured repeatedly at least 3 times; Pearson linear regression is used to fit the data as a linear function, and the linear correlation coefficient R is calculated. 2 To determine whether the modulation signal originates from the linear electro-optic effect, for datasets that pass the linearity test, the 3σ criterion is used to remove outlier data points that deviate from the fitted straight line.

[0012] Preferably, the dynamic optical model uses the matrix transmission method to calculate the p-polarization reflection coefficient r under different modulation electric fields. p With s-polarization reflection coefficient r s A first-order Taylor expansion of the reflection coefficient ratio ρ yields the theoretical modulation expression for the ellipticity parameter. The partial derivatives are numerically calculated from the static optical model using the central difference method.

[0013] Preferably, the global fitting adopts a weighted nonlinear least squares algorithm, and the target residual function is the sum of the squares of the differences between the measured modulation amplitude and the theoretical modulation amplitude divided by the square of the corresponding standard deviation and then accumulated; the iteration adopts the Levenberg-Marquardt algorithm, and after the iteration converges, the measurement uncertainty of the electro-optic coefficient is calculated through the covariance matrix of the residuals.

[0014] The technical effects and advantages of this invention are as follows: 1. This invention uses AC modulation voltage instead of traditional DC bias voltage to separate the weak signal caused by electro-optic effect from low-frequency drift and noise background. By using a lock-in amplifier with the modulation frequency as a reference for phase-sensitive detection, it effectively suppresses low-frequency common-mode interference such as light source power fluctuation, environmental mechanical vibration and thermal drift.

[0015] 2. By controlling the monochromator of the ellipsometer to scan wavelength by wavelength and repeating the dynamic modulation and fitting process, this invention can further obtain the dispersion distribution of the electro-optic coefficient in the entire wavelength range. This ability to acquire multiple parameters simultaneously and resolve spectra provides complete experimental data support for the design and material screening of broadband integrated photonic devices.

[0016] 3. By configuring different electrode configurations such as vertical electric field or in-plane electric field, and combining them with the independent description of the refractive index perturbation of ordinary and extraordinary light in anisotropic optical models, this invention can achieve the separate extraction and differentiation of tensor elements with different electro-optic coefficients. This breaks through the limitation of traditional methods that can only obtain effective electro-optic coefficients and provides a feasible path for the complete tensor characterization of anisotropic electro-optic thin films. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall process of the method of the present invention; Figure 2 These are schematic diagrams of two electrode configurations for the present invention: vertical electric field and in-plane electric field. Figure 3 This is a schematic diagram of the static ellipsometric measurement spectrum of the present invention; Figure 4 This is a schematic diagram illustrating the linear relationship between the modulation amount of the ellipticity parameter and the modulation voltage according to the present invention. Figure 5 This is a schematic diagram illustrating the linear relationship between the refractive index and the modulation voltage according to the present invention. Figure 6 This is a schematic diagram of the overall system structure of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] The specific embodiments of the present invention will be further described in detail below with reference to characterization examples of c-axis oriented AlScN ferroelectric thin films. This embodiment is implemented based on the technical solution of the present invention, and provides detailed implementation steps and specific parameters; however, the scope of protection of the present invention is not limited to the following embodiment.

[0020] like Figures 1-5 As shown, a method for characterizing the electro-optic coefficient of thin films based on spectral ellipsometrics under an external electric field includes S1: placing the thin film sample to be tested in the optical path of a spectral ellipsometer, setting the incident angle and wavelength range under the condition of no external electric field, collecting the ellipsometric parameters of the reflected light from the sample, including the amplitude ratio Ψ and the phase difference Δ, constructing a multilayer optical model, and numerically fitting and inverting to obtain the thin film thickness and the static complex refractive index-wavelength dispersion curve.

[0021] It should be specifically noted that, for uniaxial anisotropic thin films, the multilayer optical model uses the Sellmeier dispersion model to describe the ordinary light refractive index and the extraordinary light refractive index, respectively, and the ultraviolet absorption edge is fitted using the Tauc-Lorentz model. The numerical fitting uses the Levenberg-Marquardt nonlinear least squares algorithm.

[0022] It should be further explained that a rotating compensator type ellipsometry was used as the measurement host, the incident angle was set to 65°, the measurement wavelength range covered the entire band from 400nm to 1600nm, the wavelength sampling step was 5nm, and the sample under test was a structure of "Si substrate / 300nm SiO2 buffer layer / AlScN thin film / 100nm transparent ITO top electrode". A Cu bottom electrode was deposited on the back of the substrate to form a vertical electric field loop.

[0023] Without applying any external electric field, three repeated scans are performed at each wavelength point, and the arithmetic mean is taken to obtain the static ellipticity parameter spectrum Ψ0(λ) and Δ0(λ), thus eliminating the influence of random noise in the optical path.

[0024] A five-layer optical model of "air / ITO / AlScN / SiO2 / Si" was established, in which the optical constants of the Si substrate and SiO2 buffer layer were fixed using parameters from a commercial materials database; the thickness and complex refractive index of the ITO layer were set as weakly constrained variables, with the constraint range deviating from the nominal value by no more than 20%; the AlScN layer was treated as uniaxial anisotropy, and the ordinary refractive index n o With the extraordinary refractive index n e The Sellmeier dispersion model was used to describe the light, with the extinction coefficient set to 0 in the transparent band and the Tauc-Lorentz model used to fit the ultraviolet absorption edge; the physical thickness d of AlScN was set as the core fitting variable.

[0025] The Levenberg-Marquardt nonlinear least squares algorithm was used for fitting optimization, with the objective of minimizing the mean square error (MSE) between the measured Ψ and Δ and the calculated model values. The convergence threshold was set to MSE < 1 × 10⁻⁶. -4After fitting, the precise thickness d0 of the AlScN film was obtained, which was measured to be approximately 402.3 nm, and the static ordinary refractive index n across the entire wavelength range was also obtained. o (λ), Extreme optical refractive index n e (λ) Dispersion curve.

[0026] S2: A sinusoidal AC modulation voltage with a frequency of ω is applied to the thin film sample through the sample stage electrode structure. ω is used as the phase-locked reference signal. The oscillation amplitudes of Ψ and Δ at ω are extracted from the output signal of the spectroscopic ellipsometer detector and denoted as the modulation amplitudes δΨ and δΔ.

[0027] It should be specifically noted that the frequency of the sinusoidal AC modulation voltage is set in a frequency band that avoids power frequency interference and low-frequency noise from environmental thermal drift.

[0028] The oscillation amplitude is extracted after the output signal of the spectral ellipsometer detector is sampled multiple times at each modulation voltage amplitude point and the arithmetic mean is taken.

[0029] It should be further explained that the probe electrode of the sample stage forms an electrical connection with the upper and lower electrodes of the sample. The function generator outputs a sinusoidal AC modulation voltage with a frequency of 1kHz. The initial voltage amplitude is set to 10V, and the modulation frequency is selected to avoid the low-frequency noise range of 50Hz power frequency interference and environmental thermal drift, so as to maximize the suppression of common-mode noise.

[0030] The synchronous trigger signal of the function generator is connected to the reference input of the lock-in amplifier. The reference frequency is set to be consistent with the modulation frequency. The time constant of the lock-in amplifier is set to 100ms, and the roll-off slope is 12dB / oct to achieve narrowband filtering. The raw photocurrent signal output from the photodetector of the spectroradiometer is directly input into the lock-in amplifier for orthogonal phase-sensitive detection.

[0031] The lock-in amplifier demodulates the X component, which is in phase with the reference signal, and the Y component, which is orthogonal to it, and then performs a magnitude conversion using the polarization transfer matrix of the elliptic system. Based on the static elliptic parameters Ψ0 and Δ0, a first-order differential approximation is made for the reflection coefficient ratio, and the formula for calculating the reflection coefficient ratio is:

[0032] in, Let i be a constant, and i be the imaginary unit in mathematics, satisfying i 2 =-1, Let δΨ be the amplitude ratio and Δ be the phase difference. The linear mapping relationship between the detector's AC light intensity component and δΨ and δΔ is derived. The modulation amplitudes δΨ and δΔ of the ellipsoid parameters are obtained through the system's pre-calibrated transfer factor. Ten samples are taken at each measurement point, and the average is used to obtain a stable modulation amplitude value.

[0033] S3: Change the amplitude of the sinusoidal AC modulation voltage, take different amplitude points, and repeatedly perform signal extraction to obtain δΨ and δΔ at each amplitude point. Determine whether the changes of δΨ and δΔ with the amplitude of the modulation voltage conform to a linear relationship.

[0034] It should be specifically noted that the modulation voltage amplitude includes at least 5 different amplitude gradients, and each amplitude point is measured repeatedly at least 3 times; Pearson linear regression is used to fit the data as a linear function, and the linear correlation coefficient R is calculated. 2 To determine whether the modulation signal originates from the linear electro-optic effect, for datasets that pass the linearity test, the 3σ criterion is used to remove outlier data points that deviate from the fitted straight line.

[0035] It should be further explained that, keeping the modulation frequency of 1kHz unchanged, the modulation voltage amplitude is set to 0V, 5V, 10V, 15V, 20V, 25V and 30V, a total of 7 gradient points. Each voltage point is measured 5 times according to the process of S2, and two corresponding datasets δΨ(V0) and δΔ(V0) are obtained.

[0036] Pearson linear regression was used to fit a linear function to the δΨ-V0 and δΔ-V0 data respectively, and the linear correlation coefficient R was calculated. 2 When R 2 When R ≥ 0.99, the modulation signal is determined to originate from the linear electro-optic effect, and the data is valid; if R 2 If the value is below the threshold, investigate for problems such as sample leakage, thermo-optical interference, or poor electrode contact. After eliminating the interference, measure again.

[0037] For the dataset that passes the linearity test, outlier data points that deviate from the fitted straight line are removed using the 3σ criterion. Then, the remaining valid data are weighted and averaged to obtain the modulation amplitude-voltage response curve for subsequent inversion.

[0038] S4: A perturbation term is superimposed on the refractive index of the thin film. The magnitude of the perturbation term is proportional to the intensity of the modulation electric field of the thin film, the cube of the static refractive index, and the electro-optic coefficient to be measured. For optically anisotropic thin films, the refractive index perturbation is extended to the changes of each component of the refractive index tensor and associated with the tensor elements of different electro-optic coefficients to be measured. The theoretical reflection coefficient is calculated based on the dynamic optical model, and the theoretical dependence of the modulation amplitude of the ellipsometric parameter on the modulation voltage amplitude is derived.

[0039] It should be specifically noted that the dynamic optical model uses the matrix transmission method to calculate the p-polarization reflection coefficient r under different modulation electric fields. p With s-polarization reflection coefficient r s A first-order Taylor expansion of the reflection coefficient ratio ρ yields the theoretical modulation expression for the ellipticity parameter. The partial derivatives are numerically calculated from the static optical model using the central difference method.

[0040] It should be further explained that, based on the tensor form of the linear electro-optic effect, for a c-axis oriented hexagonal AlScN thin film, the electric field E perpendicular to the thin film plane is... Z Only stimulate r 13 and r 33 The refractive index perturbations of the two electro-optic coefficient tensors satisfy the following:

[0041]

[0042] electric field strength in the formula , The effective spacing between the upper and lower electrodes is defined as follows: an electric field uniformity correction factor f is introduced, specifically, f takes values ​​from 0.92 to 0.98, pre-calibrated by capacitance-voltage testing, to correct electric field non-uniformity caused by electrode depletion layer and edge effects.

[0043] Based on the multilayer optical model of S1, the refractive index tensor of the AlScN layer is replaced with a dynamic tensor after superposition and perturbation. The p-polarized and s-polarized reflection coefficients r under different modulation electric fields are calculated using the 4×4 matrix transmission method. p r s .

[0044] For reflection coefficient ratio Performing a first-order Taylor expansion yields the theoretical modulation amount of the ellipticity parameters:

[0045]

[0046] The partial derivatives in the formula are obtained numerically from the static optical model using the central difference method. The final derivation is... , The linear dependence of the modulation voltage amplitude V0 corresponds to the slope determined by the electro-optic coefficient tensor element r. 13 and r 33 A joint decision.

[0047] S5: Globally fit δΨ and δΔ with the theoretical modulation amplitude. During the fitting process, the film thickness and static complex refractive index dispersion curve are used as fixed input parameters, and the electro-optic coefficient to be measured or the electro-optic coefficient tensor element is used as the variable to be optimized. By minimizing the residual between the measured and theoretical data, the optimal convergence value of the electro-optic coefficient is obtained by iterative solution. Change the measurement wavelength and repeat S2 to S5 to obtain the electro-optic coefficient-wavelength dispersion distribution.

[0048] It should be specifically noted that the global fitting adopts a weighted nonlinear least squares algorithm, and the target residual function is the sum of the squares of the differences between the measured modulation amplitude and the theoretical modulation amplitude divided by the square of the corresponding standard deviation and then summed; the iteration adopts the Levenberg-Marquardt algorithm, and after the iteration converges, the measurement uncertainty of the electro-optic coefficient is calculated through the covariance matrix of the residuals.

[0049] It should be further explained that the film thickness d0 and the full-band static refractive index n obtained in S1 o (λ), n e (λ), and the pre-calibrated electric field uniformity correction factor f are all set to fixed input parameters, only the electro-optic coefficient r is set. 13 and r 33 Set them as the free variables to be optimized to avoid fitting divergence caused by parameter coupling from the root.

[0050] Iterative optimization is performed using a weighted nonlinear least squares algorithm, and the objective residual function is defined as follows:

[0051] In the formula, N is the total number of modulation voltage gradient points, and σΨ and σΔ are the standard deviations of δΨ and δΔ obtained from multiple measurements in S2, serving as weighting factors to reflect the confidence levels of different data. The iteration uses the Levenberg-Marquardt algorithm, with the convergence condition being the sum of the values ​​of χ² in two consecutive iterations. 2 The relative change is less than 1×10 -6 .

[0052] After iterative convergence, r at the current measurement wavelength is obtained. 13 r 33 The optimal value is obtained, and the measurement uncertainty is calculated using the covariance matrix of the residuals. Taking a wavelength of 1550 nm as an example, r is obtained through fitting. 33 =1.56 pm / V, uncertainty ±0.2 pm / V, r 13 =0.42pm / V, uncertainty ±0.3pm / V.

[0053] The ellipsometer monochromator is controlled to scan wavelength by wavelength in 10 nm steps within the range of 400 nm to 1600 nm. The measurement and fitting process from S2 to S5 is repeated at each wavelength point, and the electro-optic coefficient r of the entire wavelength range is finally output. 13 (λ), r 33 (λ) Dispersion distribution curve.

[0054] like Figure 6As shown, a thin film electro-optic coefficient characterization system based on external electric field spectral ellipticity includes a spectral ellipticity measurement module: including a broadband or tunable monochromatic light source, a polarizer, a first compensator, a second compensator, an analyzer, and a photodetector, used to generate polarization probe light and measure the ellipticity parameters of the sample reflected light.

[0055] Integrated sample stage and electric field application module: including sample clamp and electrode structure integrated on the sample stage, wherein the electrode structure is a vertical electric field configuration or an in-plane electric field configuration, used to carry the sample and apply a sinusoidal AC modulated voltage with frequency ω to the thin film sample.

[0056] Signal synchronization and data acquisition module: includes a lock-in amplifier, which uses the frequency ω of the modulation voltage as a reference frequency to receive the output signal of the photodetector and extracts the oscillation amplitudes δΨ and δΔ of the ellipsoid parameters that are in sync with the modulation electric field.

[0057] Central control and data processing module: a computer used to control the wavelength scanning of the spectral ellipsometric measurement module, control the voltage output of the electric field application module, control the signal extraction of the data acquisition module, and run the data processing algorithm of steps S1 to S5 as described in claim 1 to invert and calculate the electro-optic coefficient of the thin film.

[0058] Secondly: The accompanying drawings of the embodiments disclosed in this invention only involve the structures involved in the embodiments disclosed in this invention. Other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of this invention can be combined with each other. In conclusion, 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 characterizing the electro-optic coefficient of thin films based on spectral ellipsometrics of an external electric field, characterized in that, include: S1: Place the thin film sample to be tested in the optical path of the spectrometer ellipsometer. Set the incident angle and wavelength range without applying an external electric field. Collect the ellipsometric parameters of the reflected light from the sample, including the amplitude ratio Ψ and the phase difference Δ. Construct a multilayer optical model and obtain the thin film thickness and static complex refractive index-wavelength dispersion curve by numerical fitting and inversion. S2: Apply a sinusoidal AC modulation voltage with a frequency of ω to the thin film sample through the sample stage electrode structure. Use ω as the phase-locked reference signal and extract the oscillation amplitudes of Ψ and Δ at ω from the output signal of the spectroscopic ellipsometer detector. These amplitudes are denoted as modulation amplitudes δΨ and δΔ. S3: Change the amplitude of the sinusoidal AC modulation voltage, take different amplitude points, and repeatedly perform signal extraction to obtain δΨ and δΔ at each amplitude point. Determine whether the changes of δΨ and δΔ with the amplitude of the modulation voltage conform to a linear relationship. S4: A perturbation term is superimposed on the refractive index of the thin film. The magnitude of the perturbation term is proportional to the intensity of the modulation electric field of the thin film, the cube of the static refractive index, and the electro-optic coefficient to be measured. For optically anisotropic thin films, the refractive index perturbation is extended to the changes of each component of the refractive index tensor and associated with the tensor elements of different electro-optic coefficients to be measured. The theoretical reflection coefficient is calculated based on the dynamic optical model, and the theoretical dependence of the modulation amplitude of the ellipsoid parameter on the modulation voltage amplitude is derived. S5: Globally fit δΨ and δΔ with the theoretical modulation amplitude. During the fitting process, the film thickness and static complex refractive index dispersion curve are used as fixed input parameters, and the electro-optic coefficient to be measured or the electro-optic coefficient tensor element is used as the variable to be optimized. By minimizing the residual between the measured and theoretical data, the optimal convergence value of the electro-optic coefficient is obtained by iterative solution. Change the measurement wavelength and repeat S2 to S5 to obtain the electro-optic coefficient-wavelength dispersion distribution.

2. The method for characterizing the electro-optic coefficient of a thin film based on the spectral ellipticity of an external electric field according to claim 1, characterized in that: For uniaxial anisotropic thin films, the multilayer optical model uses the Sellmeier dispersion model to describe the ordinary and extraordinary refractive indices, respectively, and the ultraviolet absorption edge is fitted using the Tauc-Lorentz model. The numerical fitting uses the Levenberg-Marquardt nonlinear least squares algorithm.

3. The method for characterizing the electro-optic coefficient of a thin film based on the spectral ellipticity of an external electric field according to claim 1, characterized in that: The frequency of the sinusoidal AC modulation voltage is set in a frequency band that avoids power frequency interference and low-frequency noise from environmental thermal drift.

4. The method for characterizing the electro-optic coefficient of thin films based on the spectral ellipsometrics of an external electric field according to claim 1, characterized in that: The oscillation amplitude is extracted after the output signal of the spectral ellipsometer detector is sampled multiple times at each modulation voltage amplitude point and the arithmetic mean is taken.

5. The method for characterizing the electro-optic coefficient of a thin film based on the spectral ellipticity of an external electric field according to claim 1, characterized in that: The modulation voltage amplitude includes at least five different amplitude gradients, and each amplitude point is measured at least three times. Pearson linear regression is used to fit the data as a linear function, and the linear correlation coefficient R is calculated. 2 To determine whether the modulation signal originates from the linear electro-optic effect, for datasets that pass the linearity test, the 3σ criterion is used to remove outlier data points that deviate from the fitted straight line.

6. The method for characterizing the electro-optic coefficient of a thin film based on the spectral ellipticity of an external electric field according to claim 1, characterized in that: The dynamic optical model uses the matrix transmission method to calculate the p-polarization reflection coefficient r under different modulation electric fields. p With s-polarization reflection coefficient r s A first-order Taylor expansion of the reflection coefficient ratio ρ yields the theoretical modulation expression for the ellipticity parameter. The partial derivatives are numerically calculated from the static optical model using the central difference method.

7. The method for characterizing the electro-optic coefficient of a thin film based on the spectral ellipticity of an external electric field according to claim 1, characterized in that: The global fitting uses a weighted nonlinear least squares algorithm. The target residual function is the sum of the squares of the differences between the measured modulation amplitude and the theoretical modulation amplitude, divided by the square of the corresponding standard deviation, and then accumulated. The iteration uses the Levenberg-Marquardt algorithm. After the iteration converges, the measurement uncertainty of the electro-optic coefficient is calculated through the covariance matrix of the residuals.

8. A thin film electro-optic coefficient characterization system based on external electric field spectral ellipsoidization, used to implement the thin film electro-optic coefficient characterization method based on external electric field spectral ellipsoidization as described in any one of claims 1-7, characterized in that, include: Spectral ellipticity measurement module: includes a broadband or tunable monochromatic light source, a polarizer, a first compensator, a second compensator, an analyzer, and a photodetector, used to generate polarization probe light and measure the ellipticity parameters of the sample reflected light; Integrated sample stage and electric field application module: including sample clamp and electrode structure integrated on the sample stage, wherein the electrode structure is a vertical electric field configuration or an in-plane electric field configuration, used to carry the sample and apply a sinusoidal AC modulated voltage with frequency ω to the thin film sample; Signal synchronization and data acquisition module: includes a lock-in amplifier, which uses the frequency ω of the modulation voltage as a reference frequency to receive the output signal of the photodetector and extracts the oscillation amplitudes δΨ and δΔ of the ellipsoid parameters that are in sync with the modulation electric field; Central control and data processing module: a computer used to control the wavelength scanning of the spectral ellipsometric measurement module, control the voltage output of the electric field application module, control the signal extraction of the data acquisition module, and run the data processing algorithm of steps S1 to S5 as described in claim 1 to invert and calculate the electro-optic coefficient of the thin film.

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