CN118130390A - Ellipsometry measurement system calibration method, system and ellipsometric measurement method - Google Patents

Abstract

The invention belongs to the field of ellipsometry, and particularly discloses an ellipsometry system calibration method, an ellipsometry system calibration system and an ellipsometry method, which comprise the following steps: s1, measuring a known calibration sample through an ellipsometry system to obtain a detection spectrum signal; s2, modeling an ellipsometry system to obtain a relation between a theoretical spectrum signal and a delay and harmonic coefficients of a photoelastic modulator; s3, constructing an evaluation function based on the detection spectrum signal and the theoretical spectrum signal and solving the evaluation function to obtain the amplitude delay quantity and the harmonic coefficient of the photoelastic modulator; and S4, calibrating parameters of the ellipsometry system according to the obtained amplitude delay quantity and harmonic coefficient of the photoelastic modulator. The invention can realize the simple, quick and high-precision ellipsometry system calibration.

Description

Ellipsometry measurement system calibration method, system and ellipsometric measurement method

Technical Field

The present invention belongs to the field of ellipsometric measurement, and more specifically, relates to an ellipsometric measurement system calibration method, a system and an ellipsometric measurement method.

Background technique

In recent years, with the continuous development of the integration industry, chip structures have become more and more complex, and the thickness has gradually expanded from the original nanometer level to the micrometer level. Defect monitoring of chip structures during the production process provides important guiding significance for improving yield.

In order to meet the needs of online real-time non-destructive measurement, a high-speed ellipsometer system is designed. The specific configuration is shown in Figure 2. The photoelastic modulator (PEM) is a type of compensation device that can change the state of polarized light at a very high frequency. Therefore, building an ellipsometer with an infrared light source and a photoelastic modulator can achieve rapid measurement in the infrared band and realize measurement of three-dimensional stacked structures.

However, the current method for calibrating the parameters of the ellipsometer system relies on changes to the system configuration and even requires the addition of additional devices such as phase-locked amplifiers and choppers. The operation is complex, full-cycle sampling is required, and the accuracy is poor. Therefore, an optimized method for calibrating the parameters of the ellipsometer system is urgently needed.

Summary of the invention

In view of the above defects or improvement needs of the prior art, the present invention provides an ellipsometric measurement system calibration method, system and ellipsometric measurement method, the purpose of which is to achieve simple, fast and high-precision calibration of the ellipsometric measurement system.

To achieve the above object, according to a first aspect of the present invention, a calibration method for an ellipsometric measurement system is proposed, comprising the following steps:

S1. Measure a known calibration sample using an ellipsometric measurement system to obtain a detection spectrum signal;

S2. Model the ellipsometric measurement system and obtain the relationship between the theoretical spectrum signal and the delay and harmonic coefficient of the photoelastic modulator;

S3, constructing and solving an evaluation function based on the detected spectral signal and the theoretical spectral signal to obtain the amplitude delay and harmonic coefficient of the photoelastic modulator;

S4. Calibrate the ellipsometric measurement system parameters according to the obtained amplitude delay and harmonic coefficient of the photoelastic modulator.

As a further preferred embodiment, in the ellipsometric measurement system, the laser emitted by the light source passes through a polarizer and a first photoelastic modulator in sequence and is incident on the sample. After the light is reflected or transmitted by the sample, it passes through a second photoelastic modulator and an analyzer in sequence and is collected by a detector to obtain a spectral signal.

As a further preferred step, in step S2, the ellipsometric measurement system is modeled and the light intensity information is expressed as:

I(t)＝I _dc ′+I _X0 ′X ₀ +I _Y0 ′Y ₀ +I _X1 ′X ₁ +I _Y1 ′Y ₁ +I _X0X1 ′X ₀ X ₁

+I _X0Y1 'X ₀ Y ₁ +I _Y0X1 'Y ₀ X ₁ +I _Y0Y1 'Y ₀ Y ₁

in, A _i represents the amplitude delay of the photoelastic modulator, ω _i represents the modulation frequency of the photoelastic modulator, /> represents the initial phase value of the photoelastic modulator; i=0 represents the corresponding parameter of the first photoelastic modulator, and i=1 represents the corresponding parameter of the second photoelastic modulator; I′ _~ represents the coefficient of the corresponding harmonic ~; the light intensity information at all wavelengths is combined to obtain the theoretical spectrum signal.

As further preferred, step S4 includes: determining a relationship between the ellipsometric measurement system parameters and the harmonic coefficients, and then calibrating the ellipsometric measurement system parameters in combination with the amplitude delay of the photoelastic modulator;

The relationship between the ellipsometric system parameters and the harmonic coefficients is:

I _dc =m ₁₁ +C _b1 (C _m1 m ₂₁ +S _m1 m ₃₁ )+C _b0 {C _m0 [m ₁₂ +C _b1 (C _m1 m ₂₂ +S _m1 m ₃₂ )]+S _m0 [m ₁₃ +C _b1 (C _m1 m ₂₃ +S _m1 m ₃₃ )]}

I _X0 =S _b0 (m ₁₄ +C _b1 C _m1 m ₂₄ +C _b1 S _m1 m ₃₄ )

I _Y0 =S _b0 [S _m0 (m ₁₂ +C _b1 C _m1 m ₂₂ +C _b1 S _m1 m ₃₂ ) -C _m0 (m ₁₃ +C _b1 C _m1 m ₂₃ +C _b1 S _m1 m ₃₃ )]

I _X1 = -S _b1 (m ₄₁ +C _b0 C _m0 m ₄₂ +C _b0 S _m0 m ₄₃ )

I _Y1 =S _b1 [-C _m (m ₃₁ +C _b0 C _m0 m ₃₂ +C _b0 S _m0 m ₃₃ ) + S _m1 (m ₂₁ +C _b0 C _m0 m ₂₂ +C _b0 S _m0 m ₂₃ )]

I _X0X1 = -S _b0 S _b1 m ₄₄

I _X0Y1 = S _b0 S _b1 (-C _m1 m ₃₄ + S _m1 m ₂₄ )

I _Y0X1 = S _b0 S _b1 (C _m0 m ₄₃ -S _m0 m ₄₂ )

I _Y0Y1 = S _b0 S _b1 [C _m0 (C _m1 m ₃₃ -S _m1 m ₂₃ ) + S _m0 (S _m1 m ₂₂ -C _m1 m ₃₂ )]

Wherein, C _θ =cos(2θ), S _θ =sin(2θ), θ=(b _j ,m _j ), j=(0,1); b ₁ represents the difference between the fast axis azimuth of the first photoelastic modulator and the optical axis azimuth of the polarizer, b ₂ represents the difference between the fast axis azimuth of the second photoelastic modulator and the optical axis azimuth of the analyzer, m ₁ and m ₂ represent the fast axis azimuths of the first photoelastic modulator and the second photoelastic modulator, respectively; δ _{static_i} represents the static delay of the photoelastic modulator; _mlk represents the Mueller matrix element in the lth row and kth column of the sample.

As a further preferred embodiment, in step S4, in the relationship between the ellipsometric measurement system parameters and the harmonic coefficients, the static delay of the photoelastic modulator is an uncertain variable; the static delay of the photoelastic modulator is represented by the amplitude delay of the photoelastic modulator:

δ _{static_i} =K _i ×A _i

Among them, _Ki is the corresponding coefficient, and _Ai is the amplitude delay of the photoelastic modulator.

As further preferred, in step S4, the Mueller matrix element m _lk in the relationship between the ellipsometric measurement system parameters and the harmonic coefficients is modeled and characterized using a known calibration sample to obtain the ellipsometric measurement system parameters.

As a further preferred embodiment, in step S3, the evaluation function ψ(P) is:

Wherein, input parameter P = [I' _～ , A ₀ , A ₁ ], _Im (t _p , λ) is the detection spectrum signal, f(I' _～ , A ₀ , A ₁ ,t _p ,λ) is the theoretical spectrum signal; t _p represents the time, λ represents the wavelength, and n represents the total number of data points;

The evaluation function is solved with the goal of minimizing, and the corresponding input parameters, namely the amplitude delay and harmonic coefficient of the photoelastic modulator, are obtained.

As a further preference, in the ellipsometric measurement system, the light source is a pulsed quantum cascade laser, which emits pulsed laser in the mid-infrared band; in step S1, the measured signal is a pulse signal, the pulse signal is integrated and arranged according to the time and wavelength dimensions of the pulse to obtain spectral modulation information, that is, a detected spectral signal.

According to a second aspect of the present invention, there is provided a calibration system for an ellipsometric measurement system, comprising a processor, wherein the processor is configured to execute the above-mentioned calibration method for an ellipsometric measurement system.

According to the third aspect of the present invention, an ellipsometric measurement method is provided, in which the ellipsometric measurement system is calibrated by the above-mentioned ellipsometric measurement system calibration method, and then the sample to be measured is measured by the ellipsometric measurement system to obtain the corresponding spectral signal, and then the Mueller matrix of the sample to be measured is obtained based on the calibrated ellipsometric measurement system parameters.

In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

1. The present invention obtains the detection light intensity information through the ellipsometric measurement system, and then obtains the amplitude delay and harmonic coefficient of the photoelastic modulator by combining it with the theoretical light intensity of the system, so as to calibrate the parameters of the ellipsometric measurement system; compared with the traditional method of configuring a chopper, a phase-locked amplifier and a discrete Fourier transform solution, the present invention has the advantages of high precision, simple operation and simple instrument configuration.

2. The present invention is based on the modulation process of the photoelastic modulator. Compared with the traditional method of realizing optical polarization modulation by mechanical rotation, the measurement method of the present invention has the advantages of fast measurement speed and can realize online real-time monitoring.

3. The present invention takes into account that the static delay of the photoelastic modulator is an uncertain variable, and represents the static delay of the photoelastic modulator with the obtained amplitude delay of the photoelastic modulator, so as to realize the accurate calibration of the parameters of the ellipsometric measurement system.

4. The present invention uses quantum cascade lasers to generate mid-infrared spectra. Quantum cascade lasers have the advantages of high intensity, fast tuning speed, wide tuning range, and high signal-to-noise ratio. They are currently one of the best devices for obtaining mid-infrared spectra. As a light source for mid-infrared detection, they can improve detection accuracy.

5. The detection spectrum range adopted by the present invention is the mid-infrared band. The electromagnetic waves in this band have fluctuating absorption and reflectivity for semiconductor materials such as silicon oxide and silicon nitride, that is, different wavelengths have different properties on semiconductor materials. Compared with the traditional wide-spectrum measurement method from near ultraviolet to near infrared, the present invention can measure semiconductor materials with a thickness of tens to hundreds of microns.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a calibration method for an ellipsometric measurement system according to an embodiment of the present invention;

FIG2 is a schematic diagram of the optical system structure of an embodiment of the present invention, wherein (a) is a schematic diagram of an oblique-incidence measurement system, and (b) is a schematic diagram of a straight-through measurement system;

FIG3 is a schematic diagram of an output pulse of a pulsed quantum cascade laser according to an embodiment of the present invention;

FIG4 is a schematic diagram of the tuning modes of a pulsed quantum cascade laser according to an embodiment of the present invention, wherein (a) represents a single wavelength output mode, in which each pulse has the same wavelength; (b) represents a step tuning output mode, in which a fixed time or a fixed number of pulses are emitted at each wavelength and then the next wavelength is tuned; (c) represents a continuous tuning mode, in which each pulse has a different wavelength;

5 is a schematic diagram showing the relationship between the polarization direction of a light beam and the delay amounts of two orthogonal components in ellipsometric measurement according to an embodiment of the present invention;

Figure 6 is a schematic diagram of the pulse modulation process of an embodiment of the present invention, wherein (a) is a schematic diagram of a pulse emitted by a light source; (b) is a schematic diagram of a modulation process; (c) is a schematic diagram of pulse collection, and the collected pulses can be combined into a pulse matrix arranged in time and wavelength dimensions according to the tuning mode of the light source; (d) is an integration process for each pulse, in which the energy of each pulse is represented by integrating the pulses; and (e) is a light intensity curve obtained by combining the energy changes after integrating each pulse in (c).

In all the drawings, the same figure marks are used to represent the same elements or structures, wherein: 1-quantum cascade laser, 2-incident light, 3-polarizer, 4-first photoelastic modulator, 5-sample, 6-sample stage, 7-second photoelastic modulator, 8-polarizer, 9-detector, 10-data collector.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

An embodiment of the present invention provides a method for calibrating an ellipsometric measurement system.

Pre-built ellipsometric measurement systems:

Ellipsometry is an optical measurement method that uses the polarization characteristics of light to measure thin film properties. The measurement principle is that the light beam emitted by the light source is modulated by the analyzer arm and becomes a beam with specific polarization characteristics. The polarization properties change after reflection or transmission by the sample. After modulation by the analyzer arm, the polarization properties of the changed beam can be solved by the detector measurement, and then the properties of the sample surface can be solved. This measurement method can measure the optical properties of thin film materials such as reflectivity, extinction ratio, etc., and can also measure the physical properties of the sample surface, such as roughness, thickness, micro-nano structure, etc.

The optical system of ellipsometric measurement generally includes a light source, a polarizing arm module, an analyzing arm module and a detector. In different ellipsometric measurement configurations, the configurations of the polarizing arm module and the analyzing arm module are generally different. Generally speaking, both the polarizing arm and the analyzing arm include a polarizer, which converts a non-polarized or other polarized light beam into a linearly polarized light. The polarizer of the polarizing arm is generally called a polarizer, which produces linearly polarized light in a specific direction, while the polarizer of the analyzing arm is generally called an analyzer, which shields the polarized light intensity in other directions, so that the detector can only detect the light intensity in one polarization direction, and then infer the polarized light of the analyzing arm module through the change in light intensity. The polarizing arm and the analyzing arm generally also contain a phase retarder to achieve the modulation of the polarization state of the light beam.

The characterization of sample surface properties is generally accomplished through sample modeling. This model can be established in the form of a 4×4 real matrix or a 2×2 complex matrix, respectively called the Mueller matrix and the Jones matrix. The present invention adopts the Mueller matrix representation.

The ellipsometric measurement system of the present invention is shown in FIG2 , the incident light path includes a quantum cascade laser 1, a polarizer 7, and a first photoelastic modulator 8, the incident light enters the reflection light path after being reflected or transmitted by a sample 5 (placed on a sample stage 6), and the reflection light path includes a second photoelastic modulator 11, an analyzer arm polarizer 12, a detector 4, and a data collector 13. Specifically, the polarizers are all silicon-based mid-infrared polarizers, and the data collector uses a high-speed digital acquisition card with a sampling rate of 1 GHz, so as to completely collect the entire pulse waveform.

The quantum cascade laser 1 is specifically a mid-infrared tunable quantum cascade laser, which can achieve 2-30um wide spectrum tunable light output through grating splitting, and can achieve single wavelength laser output, continuous tuning laser output, step tuning laser output and other functions by controlling the grating. The light output mode of the quantum cascade laser can be divided into continuous light output and pulsed light output. The present embodiment adopts a pulsed quantum cascade laser.

The tuning modes of mid-infrared quantum cascade lasers can be divided into single wavelength output, continuous tuning output and step tuning output, as shown in Figure 4, where (a) indicates single wavelength output mode, where each pulse has the same wavelength; (b) indicates step tuning output mode, where a fixed time or fixed number of pulses are emitted at each wavelength and then tuned to the next wavelength; (c) indicates continuous tuning mode, where the wavelength of each pulse is different. The quantum cascade laser used in this embodiment has a pulse period of T and a pulse duration of t, as shown in Figure 3, and the output mode is continuous tuning or step tuning mode.

The photoelastic modulator is a wave plate that modulates the polarization state of the light beam by changing the phase delay at a fixed frequency. During operation, the transmission delay of the photoelastic modulator changes dynamically in an approximately sinusoidal manner. The relationship between the actual light beam elliptical polarization direction and the delay in the two orthogonal polarization directions is shown in Figure 5. The photoelastic modulator achieves the modulation process by applying different delays to the two polarization directions to change the polarization state.

The calibration method of the above ellipsometric measurement system, as shown in FIG1 , comprises the following steps:

S1. Oblique-incidence measurement is performed on the calibration sample through the ellipsometric measurement system to obtain the detection spectrum signal.

The detector measures a pulse signal, which is integrated and arranged according to the time and wavelength dimensions of the pulse to obtain spectral modulation information, namely the detection spectral signal.

The specific measurement process is shown in FIG6 : As shown in FIG6 (a), the quantum cascade laser emits pulses of the same duration at a fixed frequency. After the modulation process shown in FIG6 (b), the specific optical path is shown in FIG2 . The pulses are modulated into linearly polarized pulse light by the first polarizer, and then become pulses in an elliptically polarized state after being modulated by the first photoelastic modulator. After being reflected by the sample surface or transmitted by the sample, they enter the polarization analyzer arm, and are modulated by the second photoelastic modulator. Then, they enter the detector through the second polarizer. The detector obtains the modulated pulses, which are converted into digital signals after being collected by the data acquisition card. The quantum cascade laser continues to emit pulses. The modulation phase of the photoelastic modulator is different when each pulse is emitted. Therefore, different pulses emitted from the light source will be modulated with different phase delays after entering the photoelastic modulator as linearly polarized light through the first polarizer, thereby generating different polarizations. Since the phase modulation amount of the photoelastic modulator changes periodically, the pulse light transmitted from the photoelastic modulator will change periodically with different polarization states. This cycle will be more complicated under the simultaneous modulation of two photoelastic modulators. In the step tuning mode, the quantum cascade laser will emit a specific number or time of pulses of the current wavelength, and then tune to emit pulses of the next wavelength; in the continuous tuning mode, the pulses emitted by the quantum cascade laser are different each time, but multiple pulse measurements of each wavelength can be achieved through repeated scanning processes. Finally, according to the pulse characteristics under different tuning modes, the detection pulse is represented by the time and wavelength dimensions as shown in Figure 6 (c). The modulation process of the photoelastic modulator is continuous, but the entire pulse duration is at the level of tens of nanoseconds, which can be considered as instantaneous light intensity for the photoelastic modulator, so the light intensity during the entire modulation process can be achieved by integrating the detection pulse. As shown in (d) of Figure 6, each pulse detected is integrated. The integration process is actually the integration of discrete signals. The method of summing discrete data can be adopted, that is, averaging the entire integration interval. In fact, the average detection voltage or current of the entire integration interval is solved. The entire integration covers the entire pulse. The starting point and end point of the integration time in this embodiment are respectively located before and after the pulse, which can ensure that the integration time covers the entire pulse, so that the light intensity can be correctly represented by the integration result. It should be noted that if the energy change of the integration can correctly reflect the change of light intensity, it is not necessary to integrate the entire pulse process, but the pulse part can be integrated. Figure 6 (e) shows that after integrating each pulse collected, a signal matrix of the wavelength-time dimension can be obtained, thereby providing data for subsequent processing.

S2. Model the ellipsometric measurement system and obtain the relationship between the theoretical spectral signal and the delay and harmonic coefficient of the photoelastic modulator.

For the ellipsometric measurement system, the theoretical detection light intensity model is:

Wherein, S _out is the Stokes vector corresponding to the outgoing light, _MA is the Mueller matrix corresponding to the secondary polarization, _MP is the Mueller matrix corresponding to the primary polarization, R(*) represents the Mueller rotation matrix when the rotation angle is *, α ₁ is the azimuth of the optical axis of the polarizer, α ₂ is the azimuth of the optical axis of the analyzer, β ₁ is the fast axis azimuth of the first photoelastic modulator, β ₂ is the fast axis azimuth of the second photoelastic modulator, and under oblique incidence conditions, all azimuths of this system are relative to the incident plane and the positive direction is counterclockwise from the reverse beam viewing angle. M _m0 (δ ₀ ) is the Mueller matrix corresponding to the first photoelastic modulator, M _m1 (δ ₁ ) is the Mueller matrix corresponding to the second photoelastic modulator, M _S is the Mueller matrix corresponding to the sample to be tested, and S _in is the Stokes vector corresponding to the incident light.

In this embodiment, the representation of each matrix vector is as follows:

_MP and _MA correspond to the Mueller matrices for primary and secondary polarization respectively:

M _m1 and M _m0 represent the Mueller matrices of the second photoelastic modulator and the first photoelastic modulator, respectively:

Among them, δ _i (i＝0,1) represents the modulation phase angle of the first photoelastic modulator and the modulation phase angle of the second photoelastic modulator respectively. According to the photoelastic correlation theory, the relationship between the photoelastic phase modulation angle and time t is as follows:

δ(A,ω,t,δ _static )＝Asin(2πωt)+δ _static (4)

Wherein, A represents the amplitude delay of the photoelastic modulator, which is related to the wavelength of the incident light and the applied voltage, ω represents the modulation frequency of the photoelastic modulator, and δ _static represents the static delay of the photoelastic modulator, which is related to the incident wavelength and generally does not change with the applied voltage.

The corresponding Mueller matrix of the sample Ms to be tested is:

R(α) represents the Mueller rotation matrix with a rotation angle of α:

Among them, α=α1, α2; β=β1, β2; α1 and α2 are the optical axis azimuths of the polarizer and the analyzer respectively, and β1 and β2 are the fast axis azimuths of the first photoelastic modulator and the second photoelastic modulator respectively.

According to the detection light intensity model of formula (1), the first light intensity of S _out can be expressed as follows:

Then we get the expression of light intensity:

in, Where _Ai represents the amplitude delay of the photoelastic modulator, _ωi represents the modulation frequency of the photoelastic modulator, /> represents the initial phase value of the photoelastic modulator, the subscript i=0 represents the corresponding parameter of the first photoelastic modulator, i=1 represents the corresponding parameter of the second photoelastic modulator, and I′ _~ represents the coefficient of the harmonic corresponding to ~ (~=dc, X ₀ …, Y ₀ Y ₁ ).

The light intensity information at all wavelengths is combined to obtain the theoretical spectral signal.

S3. Based on the detected spectral signal and the theoretical spectral signal, an evaluation function is constructed and solved to obtain the amplitude delay and harmonic coefficient of the photoelastic modulator.

The evaluation function ψ(P) is:

Wherein, input parameter P = [I' _～ , A ₀ , A ₁ ], _Im (t _p , λ) is the detection spectrum signal, f(I' _～ , A ₀ , A ₁ ,t _p ,λ) is the theoretical spectrum signal; t _p represents the time, λ represents the wavelength of the incident light, and n represents the total number of data points (pulses);

The solution is performed with the goal of minimizing the evaluation function, that is, using an iterative regression algorithm or a machine learning method to optimize the difference between the light intensity model and the measured light intensity, and the corresponding two photoelastic modulator amplitude delays and 9 harmonic coefficients, namely the input parameter P, are obtained.

S4. Calibrate the ellipsometric measurement system parameters according to the obtained amplitude delay and harmonic coefficient of the photoelastic modulator.

Taking the static delay into consideration, the relationship between the normalized harmonic coefficient and the model normalized coefficient is:

Among them, I' _～ (～＝dc,…,Y ₀ Y ₁ ) is the harmonic coefficient vector obtained by solution, I _～ (～＝dc,…,Y ₀ Y ₁ ) is the model coefficient vector; the relationship between the model coefficient and the system parameters and the sample Mueller matrix is as follows:

Wherein, C _θ =cos(2θ), S _θ =sin(2θ), θ =(b _j ,m _j ), b _j represents the difference between the fast axis azimuth of the photoelastic modulator and the optical axis azimuth of the polarizer, m _j represents the fast axis azimuth of the photoelastic modulator, j =(0,1) represents the corresponding parameters of the polarizer arm and the analyzer arm respectively; _mlk represents the Mueller matrix element with l rows and k columns of the sample.

Specifically, in the oblique incidence calibration process, a sample of known material is used as the measurement sample (such as silicon oxide wafer). In the calibration process, the sample model is considered to be known. When the incident angle and sample thickness are known, its Mueller matrix can be obtained through the model. In the process of beam tuning, the azimuth angle of the polarizer and the fast axis azimuth angle of the photoelastic do not change with the change of wavelength. From this, it can be obtained:

I _i =f(α ₁ ,α ₂ ,β ₁ ,β ₂ ,AOI,λ) (12)

Where AOI is the angle of incidence of the oblique incident beam, which refers to the angle of the incident light relative to the normal line of the sample surface plane. The harmonic coefficient vector of a specific wavelength can be expressed as a function of the polarizer angle, the photoelastic modulator angle, and the incident angle.

For global calibration under multiple wavelengths, the static delay of the photoelastic modulator is an uncertain variable. When the voltage of the photoelastic modulator is fixed, the ratio of the static delay and amplitude delay of the photoelastic modulator is fixed and varies with the wavelength, so it is considered that:

δ _static (λ)＝K(V)×A(λ,V) (13)

The static delays of the two photoelastic modulators (i.e., δ _{static_1} and δ _{static_2} ) satisfy equation (13). During the use of the photoelastic modulator, the voltage value is fixed, so that the K value is a fixed value that does not change with the wavelength. Combining equations (11)-(13), we get:

I _i ′＝f(α ₁ ,α ₂ ,β ₁ ,β ₂ ,K ₁ ,K ₂ ,AOI,λ) (14)

Wherein, K ₁ and K ₂ refer to the ratios of the static delay and amplitude delay of the two photoelastic modulators respectively.

Therefore, based on equations (10) and (11), the harmonic coefficient vector I' _~ is obtained by solving step S3, the Mueller matrix element _mlk is characterized by modeling a calibration sample of a known material, and the static delay of the photoelastic modulator is represented by the amplitude delay obtained in step S3; then the system parameters (including _α1 , _α2 , _β1 , _β2 , _K1 , _K2 , AOI) are solved by optimizing the fitting, and the calibration of the ellipsometric measurement system parameters is completed.

Furthermore, after the ellipsometric measurement system parameters are calibrated, the sample to be measured can be measured by the ellipsometric measurement system, and the specific method is as follows:

The azimuth angles of the optical axes of the polarizer and the photoelastic modulator are set to differ by 45°. In this configuration, equation (11) can be simplified to:

Wherein, ± _bj indicates that when _bj = 45°, it takes a positive sign, and when _bj = -45°, it takes a negative sign. Under a specific configuration, the Mueller matrix elements and the harmonic coefficients can be corresponded one to one. According to the ratios _K1 and _K2 solved in the calibration process and the amplitude delay of the two photoelastic modulators obtained in solving the harmonic coefficients, the static delay of the two photoelastic modulators can be obtained using equation (13), and then the theoretical harmonic coefficient value can be solved using equation (10). Finally, the Mueller matrix element value is solved according to the system configuration. The specific relationship is as follows:

The black dots represent the elements that cannot be measured in the current configuration, β ₁ and β 2 represent the fast axis azimuth of the first photoelastic modulator and the fast axis azimuth of the second photoelastic modulator respectively. In this configuration, the fast axis of the photoelastic modulator and the optical axis of the polarizer form an angle of 45°.

It will be easily understood by those skilled in the art that 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 and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A method for calibrating an ellipsometric measurement system, comprising the following steps: S1. Measure a known calibration sample using an ellipsometric measurement system to obtain a detection spectrum signal; S2. Model the ellipsometric measurement system and obtain the relationship between the theoretical spectrum signal and the delay and harmonic coefficient of the photoelastic modulator; S3, constructing and solving an evaluation function based on the detected spectral signal and the theoretical spectral signal to obtain the amplitude delay and harmonic coefficient of the photoelastic modulator; S4. Calibrate the ellipsometric measurement system parameters according to the obtained amplitude delay and harmonic coefficient of the photoelastic modulator. 2. The ellipsometric measurement system calibration method as described in claim 1 is characterized in that, in the ellipsometric measurement system, the laser emitted by the light source is incident on the sample after passing through a polarizer and a first photoelastic modulator in sequence, and the light is reflected or transmitted by the sample and then passes through a second photoelastic modulator and an analyzer in sequence before being collected by a detector to obtain a spectral signal. 3. The ellipsometric measurement system calibration method according to claim 2, characterized in that, in step S2, the ellipsometric measurement system is modeled and the light intensity information is expressed as: I(t)＝I _dc ′+I _X0 ′X ₀ +I _Y0 ′Y ₀ +I _X1 ′X ₁ +I _Y1 ′Y ₁ +I _X0X1 ′X ₀ X ₁ +I _X0Y1 'X ₀ Y ₁ +I _Y0X1 'Y ₀ X ₁ +I _Y0Y1 'Y ₀ Y ₁ in, A _i represents the amplitude delay of the photoelastic modulator, ω _i represents the modulation frequency of the photoelastic modulator, /> represents the initial phase value of the photoelastic modulator; i=0 represents the corresponding parameter of the first photoelastic modulator, i=1 represents the corresponding parameter of the second photoelastic modulator; I′ _~ represents the coefficient of the corresponding harmonic ~; the light intensity information at all wavelengths is combined to obtain the theoretical spectrum signal. 4. The ellipsometric measurement system calibration method according to claim 3, characterized in that step S4 comprises: determining a relationship between the ellipsometric measurement system parameters and the harmonic coefficients, and then calibrating the ellipsometric measurement system parameters in combination with the amplitude delay of the photoelastic modulator; The relationship between the ellipsometric system parameters and the harmonic coefficients is: I _dc =m ₁₁ +C _b1 (C _m1 m ₂₁ +S _m1 m ₃₁ )+C _b0 {C _m0 [m ₁₂ +C _b1 (C _m1 m ₂₂ +S _m1 m ₃₂ )]+S _m0 [m ₁₃ +C _b1 (C _m1 m ₂₃ +S _m1 m ₃₃ )]} I _X0 =S _b0 (m ₁₄ +C _b1 C _m1 m ₂₄ +C _b1 S _m1 m ₃₄ ) I _Y0 =S _b0 [S _m0 (m ₁₂ +C _b1 C _m1 m ₂₂ +C _b1 S _m1 m ₃₂ ) -C _m0 (m ₁₃ +C _b1 C _m1 m ₂₃ +C _b1 S _m1 m ₃₃ )] I _X1 = -S _b1 (m ₄₁ +C _b0 C _m0 m ₄₂ +C _b0 S _m0 m ₄₃ ) I _Y1 =S _b1 [-C _m (m ₃₁ +C _b0 C _m0 m ₃₂ +C _b0 S _m0 m ₃₃ ) + S _m1 (m ₂₁ +C _b0 C _m0 m ₂₂ +C _b0 S _m0 m ₂₃ )] I _X0X1 = -S _b0 S _b1 m ₄₄ I _X0Y1 = S _b0 S _b1 (-C _m1 m ₃₄ + S _m1 m ₂₄ ) I _Y0X1 = S _b0 S _b1 (C _m0 m ₄₃ -S _m0 m ₄₂ ) I _Y0Y1 = S _b0 S _b1 [C _m0 (C _m1 m ₃₃ -S _m1 m ₂₃ ) + S _m0 (S _m1 m ₂₂ -C _m1 m ₃₂ )] Wherein, C _θ =cos(2θ), S _θ =sin(2θ), θ=(b _j ,m _j ), j=(0,1); b ₁ represents the difference between the fast axis azimuth of the first photoelastic modulator and the optical axis azimuth of the polarizer, b ₂ represents the difference between the fast axis azimuth of the second photoelastic modulator and the optical axis azimuth of the analyzer, m ₁ and m ₂ represent the fast axis azimuths of the first photoelastic modulator and the second photoelastic modulator, respectively; δ _{static_i} represents the static delay of the photoelastic modulator; _mlk represents the Mueller matrix element in the lth row and kth column of the sample. 5. The ellipsometric measurement system calibration method according to claim 4, characterized in that, in step S4, in the relationship between the ellipsometric measurement system parameters and the harmonic coefficients, the static delay of the photoelastic modulator is an uncertain variable; the static delay of the photoelastic modulator is represented by the amplitude delay of the photoelastic modulator: δ _{static_i} =K _i ×A _i Among them, _Ki is the corresponding coefficient, and _Ai is the amplitude delay of the photoelastic modulator. 6. The ellipsometric measurement system calibration method as claimed in claim 5, characterized in that, in step S4, the Mueller matrix element m _lk in the relationship between the ellipsometric measurement system parameters and the harmonic coefficients is modeled and characterized using a known calibration sample to obtain the ellipsometric measurement system parameters. 7. The ellipsometric system calibration method according to claim 3, wherein in step S3, the evaluation function ψ(P) is: Wherein, input parameter P = [I' _～ , A ₀ , A ₁ ], _Im (t _p , λ) is the detection spectrum signal, f(I' _～ , A ₀ , A ₁ ,t _p ,λ) is the theoretical spectrum signal; t _p represents the time, λ represents the wavelength, and n represents the total number of data points; The evaluation function is solved with the goal of minimizing, and the corresponding input parameters, namely the amplitude delay and harmonic coefficient of the photoelastic modulator, are obtained. 8. The ellipsometric measurement system calibration method according to any one of claims 1 to 7, characterized in that, in the ellipsometric measurement system, the light source is a pulsed quantum cascade laser, which emits a pulsed laser in the mid-infrared band; in step S1, the measured signal is a pulse signal, the pulse signal is integrated, and the spectral modulation information is obtained according to the time and wavelength dimensions of the pulse, that is, the spectral signal is detected. 9. A calibration system for an ellipsometric measurement system, comprising a processor, wherein the processor is used to execute the calibration method for an ellipsometric measurement system according to any one of claims 1 to 8. 10. An ellipsometric measurement method, characterized in that an ellipsometric measurement system is calibrated by using the ellipsometric measurement system calibration method as described in any one of claims 1 to 8, and then the sample to be measured is measured by the ellipsometric measurement system to obtain a corresponding spectral signal, and then the Mueller matrix of the sample to be measured is obtained based on the calibrated ellipsometric measurement system parameters.