CN112378860B - Calibration method for system parameters of rotary device type Mueller matrix ellipsometer - Google Patents

Abstract

The invention belongs to the technical field of system calibration of precision optical measuring instruments, and discloses a method for calibrating system parameters of a rotating device type Mueller matrix ellipsometer. The 1/4 standard wave plate and the objective lens are respectively replaced with a 1/4 standard wave plate and a reflector; the azimuth angle of the 1/4 standard wave plate is rotated multiple times, and multiple azimuths are obtained from the detector of the rotating device type Mueller matrix ellipsometer. light intensity information at the angle; perform Fourier analysis on the light intensity information to obtain the Fourier coefficient of the light intensity information; establish a relationship model between the Fourier coefficient of the light intensity information and the parameters of the system to be calibrated; continuously adjust the relationship model to be The values of the system parameters are calibrated until the error between the Fourier coefficients in the relational model and the above-mentioned Fourier coefficients is within a preset range, then the values corresponding to the system parameters to be calibrated are the calibration values. The method can realize the calibration of multiple calibration values through two-step calibration, which is simple and convenient.

Description

Calibration Method of Rotating Device Mueller Matrix Ellipsometer System Parameters

technical field

The invention belongs to the technical field of system calibration of precision optical measuring instruments, and more particularly relates to a method for calibrating system parameters of a rotating device type Mueller matrix ellipsometer.

Background technique

Rotating device ellipsometer is a common type of ellipsometer, which has the advantages of simple modulation, high measurement accuracy, and non-destructive measurement. The rotating device type high-resolution imaging Mueller matrix ellipsometer is based on the double rotating compensator type Mueller matrix ellipsometer. Combined with microscopic imaging technology, the Mueller matrix containing more polarization information can be used to fully characterize the sample. The polarization characteristics, such as depolarization, etc., and high spatial resolution can realize the distribution measurement of micro-area materials, so it has greater advantages than the traditional rotating device ellipsometer. In order to achieve higher resolution, the rotating device type high-resolution imaging Mueller matrix ellipsometer usually adopts a vertical objective lens configuration scheme, in which a beam splitting device and an objective lens are used to form an optical multiplexing system.

In order to ensure the accuracy of the measurement, before using the rotating device type high-resolution imaging Mueller matrix ellipsometer to measure and characterize the material, the system parameters of the instrument need to be calibrated. The parameters to be calibrated include: 1. Polarizer, detector The initial azimuth angle of the polarizer and the first and second rotary compensators; 2, the phase retardation of the first and second rotary compensators; 3, the residual polarization effect of the beam splitting device, the beam splitting film system in the beam splitting device Generally, it will affect the amplitude ratio and phase difference of polarized light; 4. The polarization aberration of the objective lens, usually for the objective lens with a numerical aperture (Numerical Aperture, NA) greater than 0.6, the influence of the polarization aberration must be considered; 5. Rotary device type The relationship between the incident angle of the high-resolution imaging Mueller matrix ellipsometer and the motorized rotation angle of the plane mirror.

The existing calibration methods seldom consider the polarization aberration of the objective lens during calibration, or use offline calibration to calibrate the beam splitter and the objective lens. The calibration process is cumbersome, the calibration error is large, the calibration speed is slow, and the universality is poor. Precision measurement requirements of rotating device type high-resolution imaging Mueller matrix ellipsometer.

SUMMARY OF THE INVENTION

In view of the above defects or improvement requirements of the prior art, the present invention provides a method for calibrating system parameters of a rotating device type Mueller matrix ellipsometer. Replace the 1/4 standard wave plate and mirror respectively, obtain the Fourier coefficient of the light intensity information at this time, and calibrate the Fourier coefficient in the relational model with the Fourier coefficient, because the relational model is the light intensity information The function of the Fourier coefficient of and the parameters of the system to be calibrated, so the azimuth angles of the corresponding polarizer, analyzer, first rotation compensator and second rotation compensator, the first rotation compensator and the second rotation compensator can be obtained. The phase retardation of the compensator and the residual polarization effect of the beam splitting device; secondly, after calibrating the above-mentioned parameters of the system to be calibrated, replace the 1/4 standard wave plate and the reflector with the imaging lens and the objective lens respectively. An isotropic uniform film is set on the sample stage, and the objective lens and the film are regarded as a whole as the sample to be tested, the Mueller matrix of the sample to be tested is obtained, and the calculation model of the Mueller matrix of the sample to be tested is established. The Mueller matrix and the calculation model are used to obtain the calibration value of the polarization aberration of the objective lens and the key parameters of the relationship between the incident angle and the mirror rotation angle of the rotating device Mueller matrix ellipsometer.

In order to achieve the above object, according to an aspect of the present invention, a method for calibrating parameters of a rotating device type high-resolution imaging Muller matrix ellipsometer system is provided, the method comprising: S1, The imaging lens and objective lens of the resolution imaging matrix ellipsometer are respectively replaced with 1/4 standard wave plate and mirror; S2, rotate the azimuth angle of the 1/4 standard wave plate several times, and rotate the device type Mueller from the rotating device The detectors of the matrix ellipsometer obtain a plurality of light intensity information at the azimuth angles respectively; S3, perform Fourier analysis on the light intensity information to obtain the Fourier coefficients of the light intensity information; S4, establish The relationship model between the Fourier coefficient of the light intensity information and the parameters of the system to be calibrated, wherein the parameters of the system to be calibrated include the polarizer, the analyzer, the azimuth angle of the first rotation compensator and the second rotation compensator, the first Phase delays of a rotary compensator and a second rotary compensator, and the residual polarization effect of the beam splitting device; S5, continuously adjust the values of the system parameters to be calibrated in the relational model until the Fourier value in the relational model If the error between the leaf coefficient and the Fourier coefficient in step S3 is within the preset range, the value corresponding to the parameter of the system to be calibrated at this time is the calibration value.

Preferably, the step S4 specifically includes: S41, obtaining the polarization state of the light received by the detector, and simplifying the polarization state to obtain the light intensity information of the light received by the detector; S42, according to step S41 The light intensity information obtains a relationship model between the Fourier coefficients and the parameters of the system to be calibrated.

Preferably, the expression of the polarization state of the light received by the detector in step S41 is:

S _out =M _a R(A _p )R(-C ₂ )M _c (δ ₂ )R(C ₂ )M _bt *

R(C _s )M _c (δ)R(-C _s )M _s R(-C _s )M _c (δ)R(C _s )M _br *

R(-C ₁ )M _c (δ ₁ )R(C ₁ )R(-P _p )M _p R(P _p )S _in

Among them, S _out is the Stokes vector of the received light of the detector, S _in is the Stokes vector of the outgoing light of the light source, _{Ma , Mc , M p and M s} are the analyzer and the compensator, respectively , the Mueller matrix of the polarizer and the plane mirror, δ ₁ , δ ₂ and δ are the phase retardation of the first rotary compensator, the second rotary compensator and the 1/4 standard wave plate, R(A _p ), R(C ₁ ), R(C ₂ ), R(P _p ), and R(C _s ) are the analyzer, the first rotational compensator, the second rotational compensator, the polarizer, and the The rotation matrix of the 1/4 standard wave plate, A _p , C ₁ , C ₂ , P _p and C _s are the analyzer, the first rotation compensator, the second rotation compensator, the polarizer and the The actual azimuth angle of the 1/4 standard wave plate, wherein, C ₁ =C _s1 -5wt, C ₂ =C _s2 -3wt, C _s1 and C _s2 are respectively the first rotation compensator and the second rotation compensator initial azimuth, w is the rotational fundamental frequency of the servo motor, M _br and M _bt are the Mueller matrices of the non-polarized beam splitter in reflection and transmission, respectively, where,

In the formula, Ψ _r and Δ _r are the amplitude ratio and phase difference of the orthogonally polarized light when reflected by the non-polarizing beam splitter, respectively, Ψ _t and Δ _t are the amplitude of the orthogonally polarized light when the non-polarizing beam splitting device transmits ratio and phase difference.

Preferably, the expression of the light intensity information I(t) of the light received by the detector after simplifying the polarization state in step S41 is:

Among them, I ₀ is the spectral response function, α ₀ is the DC Fourier coefficient, α _2n and β _2n are the Fourier coefficients in the relational model, and M ₁₁ is the Mueller matrix M _s Mueller of the plane mirror Matrix element (1,1).

Preferably, in the step S5:

The formula for calculating the error between the Fourier coefficient in the relational model and the Fourier coefficient in step S3 is:

Wherein, MFc _i is the Fourier coefficient obtained in step S3 of the 1/4 standard wave plate at the ith azimuth angle, and Fc _i is the relationship of the 1/4 standard wave plate at the ith azimuth angle Fourier coefficients in the model.

Preferably, the step S2 includes collecting light intensity information in a plurality of cycles and averaging the light intensity information.

Preferably, the method further includes: S6, replacing the 1/4 standard wave plate and the reflecting mirror with the imaging lens and the objective lens, respectively, setting an isotropic uniform film on the sample stage to replace the The objective lens and the film as a whole are regarded as the sample to be tested; S7, adjust the angle of the plane mirror to change the incident angle of the sample to be tested, the detector obtains the second light intensity information corresponding to the incident angle, and then obtains The Mueller matrix of the sample to be tested; S8, the calculation model of the Mueller matrix of the sample to be tested is established; S9, the parameters in the calculation model are continuously adjusted until the Mueller matrix and steps of the sample to be calculated calculated by the calculation model The error of the Mueller matrix obtained in S7 is within a preset range; in S10, the polarization aberration calibration value of the objective lens can be obtained by substituting the parameters determined in step S9 into the polarization aberration calculation formula of the objective lens.

Preferably, the calculation model of the Mueller matrix of the sample to be tested is:

为入射角

下所述薄膜的穆勒矩阵，M^OB(ρ,θ)为物镜在极角θ和极径ρ下的穆勒矩阵，in,

is the angle of incidence

The Mueller matrix of the film described below, M ^OB (ρ, θ) is the Mueller matrix of the objective lens at the polar angle θ and the polar diameter ρ,

Among them, Ψ _br is the amplitude ratio angle of the objective lens, and Δ _br is the retardation angle of the objective lens.

Preferably, the calculation formula of the polarization aberration of the objective lens is:

Among them, k is the number of sampling points, Z _l is the coefficient of the lth Zernike polynomial of the corresponding parameter, ε _{k, Ψ} and ε _{k, Δ} are the fitting errors of the corresponding parameters, f _l (ρ _k , θ _k ) is The lth term Zernike polynomial, L is the number of the largest term of the Zernike polynomial.

Preferably, step S10 further includes acquiring the relationship between the incident angle of the rotating device type high-resolution imaging Mueller matrix ellipsometer and the rotation angle of the plane mirror according to the parameters.

In general, compared with the prior art through the above technical solutions conceived by the present invention, a method for calibrating parameters of a rotating device type Mueller matrix ellipsometer system provided by the present invention has at least the following beneficial effects:

1. This application firstly replaces the imaging lens and the objective lens of the rotating device type Mueller matrix ellipsometer with a 1/4 standard wave plate and a reflector, and establishes the Fourier coefficient of the light intensity information and the system parameters to be calibrated. The relational model directly obtains the azimuth angles of the polarizer, the analyzer, the first rotational compensator and the second rotational compensator, the phase retardation of the first rotational compensator and the second rotational compensator, and the residual polarization of the beam splitting device For the calibration value of the effect, since each calibration value is solved at the same time, there is no accumulation of calibration errors, and at the same time, multiple calibration values can be obtained in one step, which is simple and convenient;

2. By setting an isotropic uniform film on the sample stage, using the film and the objective lens as the sample to be tested, and establishing a calculation model of the Mueller matrix of the sample to be tested, the polarization aberration of the objective lens can be calculated according to the calculation model. Calibration values and key parameters of the relationship between the incident angle of the rotating device-type Mueller matrix ellipsometer and the mirror rotation angle;

3. The nonlinear regression fitting method is used to solve the relationship model and the parameters to be calibrated in the calculation model. Compared with the numerical solution method, it has the advantages of high calibration accuracy, good robustness and fast measurement speed;

4. The parameter calibration method of the rotating device type high-resolution imaging Mueller matrix ellipsometer system in this application only needs two-step calibration, and all the parameters to be calibrated can be calibrated, which greatly reduces the complexity of calibration and improves the calibration efficiency. efficiency, and reduces the accumulation of errors between calibration steps.

Description of drawings

1 schematically shows an optical path diagram of a rotating device type high-resolution imaging Mueller matrix ellipsometer system according to an embodiment of the present disclosure;

2 schematically shows a step diagram of a first step calibration method of a rotating device type high-resolution imaging Mueller matrix ellipsometer system according to an embodiment of the present disclosure;

3 schematically shows an optical path diagram of a rotating device type high-resolution imaging Mueller matrix ellipsometer system during the first step of calibration according to an embodiment of the present disclosure;

FIG. 4 schematically shows a step diagram of a second-step calibration method of a rotating device type high-resolution imaging Mueller matrix ellipsometer system according to an embodiment of the present disclosure;

5 schematically shows an optical path diagram of the rotating device type high-resolution imaging Mueller matrix ellipsometer system when the incident angle is changed during the second step of calibration according to an embodiment of the present disclosure;

6 schematically shows a schematic diagram of a data fitting result during the first step of calibration according to an embodiment of the present disclosure;

FIG. 7 schematically shows a schematic diagram of a data fitting result during the second step of calibration according to an embodiment of the present disclosure.

Throughout the drawings, the same reference numbers are used to refer to the same elements or structures, wherein:

101-light source, 102-collimator, 103-plane mirror, 401-polarizer, 402-first compensator, 105-non-polarization beam splitter, 106-lens, 107-objective, 108-sample stage, 901-second compensator, 902-analyzer, 801-1/4 standard wave plate, 802-reflector, 110-detector.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not 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.

The schematic diagram of the optical path of the rotating device type high-resolution imaging Mueller matrix ellipsometer system to be calibrated in the present invention is shown in FIG. 1 . The rotating device type high-resolution imaging Mueller matrix ellipsometer system includes a light source 101, the light source emits a light beam to a collimator 102 for collimation, and then sends the collimated light beam to a flat mirror 103, and the flat mirror 103 reflects The light is sent to the polarizer 401 and the first compensator 402, and the first compensator 402 transmits the light beam to the non-polarization beam splitting device 105, and the non-polarization beam splitting device 105 sends part of the light beam to the lower lens 106 and the objective lens 107, Then the objective lens 107 irradiates the light beam to the sample on the sample stage 108, and the sample on the sample stage 108 reflects the light beam back to the objective lens 107 and the lens 106, and transmits the light beam to the second compensator 901 above it through the non-polarizing beam splitting device 105, and detects the light beam. Polarizer 902 , detector 110 . The polarizer 401 and the first compensator 402 form a polarizing arm, the second compensator 901 and the analyzer 902 form an analyzing arm, and the first compensator 402 and the second compensator 901 are controlled by a servo motor and are installed with High-precision encoder, and based on STM32 to realize the synchronous acquisition of the control system, the objective lens 107 and the lens 106 constitute the imaging system. The function of the plane mirror 103 is to control the incident angle of illumination of the sample. The positions of the objective lens 107 and the lens 106 are in a conjugate relationship, and the offset of the incident beam can be changed by adjusting the rotation angle of the plane mirror 103 . Thus, the angle of the light emitted from the objective lens 107 is changed. The sample stage 108 is composed of an electric rotating stage and an electric positioning stage. The electric rotating stage can realize the change of the azimuth angle of the measurement sample, and the electric displacement stage can realize the adjustment of the focal length of the sample and the movement of the measurement area.

The accuracy of the calibration of the rotating device type high-resolution imaging Mueller matrix ellipsometer system directly affects the measurement accuracy of the instrument, so the error in the instrument must be analyzed and compensated reasonably before measurement.

This application mainly considers the following calibration parameters: (1) the azimuth angle error of the polarizer 401, the analyzer 902, the first compensator 402 and the second compensator 901, the azimuth angle information cannot be accurately obtained when the device is installed; ( 2) The phase retardation of the first compensator 401 and the second compensator 402, the phase retardation is a function of wavelength and is affected by the measurement environment; (3) The residual polarization effect of the non-polarization beam splitter 105, the ideal non-polarization splitter The beam device 105 will not affect the polarization device of the light beam, but due to the complex film system of the actual beam splitter device, it will affect the polarization state of the incident beam; (4) the polarization aberration of the objective lens 107, with the increase of the NA of the objective lens 107. The larger the angle is, the larger the angle of light refraction on the objective lens 107 is. It can be seen from the Fresnel formula that it will have a greater impact on the polarization state of the light. In addition, the birefringence of the coating material is less than the stress birefringence effect will also affect the light. The influence of the polarization state of the objective lens 107 on the polarization state of the light is polarization aberration. Therefore, in order to improve the measurement accuracy of the instrument, the polarization aberration of the objective lens 107 must be considered; (5) The rotation device type Mueller matrix The relationship between the incident angle and the rotation angle of the electric rotating table of the plane reflector 103. The rotating device type Mueller matrix ellipsometer uses the electric rotating table to drive the plane reflector to achieve different illumination incident angles, and the accuracy of the illumination incident angle is highly dependent on the The measurement accuracy of the resolved imaging Mueller matrix ellipsometer has a great influence.

This application realizes the calibration of the above instruments in two steps. The first step is to calibrate: (1) the azimuth angle of the polarizer 401, the analyzer 902, the first compensator 402 and the second compensator 901; (2) the first compensation and (3) the residual polarization effect of the non-polarized beam splitting device 105. The second step of calibration: (4) the polarization aberration of the objective lens 107 and (5) the relationship between the incident angle of the rotating device-type Mueller matrix and the rotation angle of the electric rotating stage of the plane mirror 103 .

First, perform the first step of calibration, as shown in FIG. 2 , which specifically includes the following steps S1 to S5.

S1, replacing the imaging lens and the objective lens of the rotating device type high-resolution imaging Mueller matrix ellipsometer with a 1/4 standard wave plate and a reflector, respectively;

In order to realize this step of calibration, it is necessary to change the optical path configuration of the rotating device type high-resolution imaging Mueller matrix ellipsometer system, and remove the imaging part, namely the objective lens 107 and the lens 106, and replace it with a 1/4 standard wave plate of the calibration sample. 801 and the mirror 802, as shown in Figure 3, place the 1/4 standard wave plate 801 on the mirror 802 to ensure the parallelism between the two. At this time, the system can be regarded as an ordinary mu Ler matrix ellipsometer. The flat mirror 103 is adjusted so that the incident light is perpendicular to the calibration sample.

S2, rotating the azimuth angle of the 1/4 standard wave plate multiple times, and respectively acquiring a plurality of light intensity information at the azimuth angle from the detector of the rotating device type Mueller matrix ellipsometer;

The azimuth angle of the calibration sample is changed at equal intervals by the electric rotating platform, that is, the azimuth angle of the 1/4 standard wave plate is rotated multiple times to measure the calibration sample with the instrument to be calibrated, and several sets of calibration sample azimuths are obtained. The light intensity information under the angle, the light intensity information under each azimuth angle is collected at the detector 110, preferably the light intensity information in multiple periods is collected and the light intensity information is averaged to reduce the stability of the light source. influence, thereby improving the measurement accuracy. The calibrated azimuth angle can be larger than the two groups. With the increase of the number of measurement groups, the final fitting result tends to be stable.

S3, performing Fourier analysis on the light intensity information to obtain the Fourier coefficients of the light intensity information;

The Fourier coefficients required for calibration can be obtained by Fourier analysis of the light intensity information.

S4, establishing a relationship model between the Fourier coefficient of the light intensity information and the parameters of the system to be calibrated, wherein the parameters of the system to be calibrated include the orientation of the polarizer, the analyzer, the first rotational compensator and the second rotational compensator angle, the phase retardation of the first rotational compensator and the second rotational compensator, and the residual polarization effect of the beam splitting device;

In this relational model, the input is the parameter to be calibrated, and the output is the Fourier coefficient of the measurement signal. Include the following steps:

S41, acquiring the polarization state of the light received by the detector, and simplifying the polarization state to obtain light intensity information of the light received by the detector;

The polarization state expression of the received light of the detector is:

Among them, S _out is the Stokes vector of the received light of the detector, S _in is the Stokes vector of the outgoing light of the light source, _{Ma , Mc , M p and M s} are the analyzer and the compensator, respectively , the Mueller matrix of the polarizer and the plane mirror, δ ₁ , δ ₂ and δ are the phase retardation of the first rotary compensator, the second rotary compensator and the 1/4 standard wave plate, R(A _p ), R(C ₁ ), R(C ₂ ), R(P _p ), and R(C _s ) are the analyzer, the first rotational compensator, the second rotational compensator, the polarizer, and the The rotation matrix of the 1/4 standard wave plate, A _p , C ₁ , C ₂ , P _p and C _s are the analyzer, the first rotation compensator, the second rotation compensator, the polarizer and the The actual azimuth angle of the 1/4 standard wave plate, wherein, C ₁ =C _s1 -5wt, C ₂ =C _s2 -3wt, C _s1 and C _s2 are respectively the first rotation compensator and the second rotation compensator initial azimuth, w is the rotational fundamental frequency of the servo motor, M _br and M _bt are the Mueller matrices of the non-polarized beam splitter in reflection and transmission, respectively, where,

In the formula, Ψ _r and Δ _r are the amplitude ratio and phase difference of the orthogonally polarized light when reflected by the non-polarizing beam splitter, respectively, Ψ _t and Δ _t are the amplitude of the orthogonally polarized light when the non-polarizing beam splitting device transmits ratio and phase difference.

The expression of the light intensity information I(t) of the light received by the detector after simplifying the polarization state is:

Among them, I ₀ is the spectral response function, α ₀ is the DC Fourier coefficient, α _2n and β _2n are the Fourier coefficients in the relational model, and M ₁₁ is the Mueller matrix M _s Mueller of the plane mirror Matrix element (1,1).

S42: Obtain a relationship model between the Fourier coefficients and the parameters of the system to be calibrated according to the light intensity information in step S41.

It can be seen from the analysis and expansion that α ₁ , α ₃ , α ₅ , ..., α ₂₉ , α ₃₁ and β ₁ , β ₃ , β ₅ , ..., β ₂₉ , β ₃₁ are all 0, and the rest of the expressions of the Fourier coefficients The formula is:

α ₂ = -0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r + Δ _t ) · s ₂ · sinδ ₁ · cos2(P _p -A _p ) (6a)

β ₂ = -0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · s ₂ · sinδ ₁ · sin2(P _p -A _p ) (6b)

α ₄ =0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · sinδ ₁ · sinδ ₂ · cos2(P _p -A _p ) (6c)

β ₄ =0.5· _sin2Ψr · _sin2Ψt ·sin( _Δr + _Δt )· _sinδ1 · _sinδ2 · _sin2 (Pp− _Ap ) (6d)

α ₆ =sin2Ψ _r ·sin2Ψ _t ·sin(Δ _r +Δ _t ) · c ₁ ·sinδ ₂ ·sin2P _p ·sin2A _p (6e)

β ₆ = -sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · c ₁ · sinδ ₂ · sin2P _p · cos2A _p (6f)

α ₁₀ = _sin2Ψr · _sin2Ψt ·sin( _Δr + _Δt )·c ₂ · _sinδ1 · _sin2Pp · _sin2Ap (6i)

β ₁₀ = -sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · c ₂ · sinδ ₁ · cos2P _p · sin2A _p (6j)

α ₁₄ = -0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · s ₁ · sinδ ₂ · cos2(P _p -A _p ) (6m)

β ₁₄ = -0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · s ₁ · sinδ ₂ · sin2(P _p -A _p ) (6n)

α ₂₂ =0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · s ₂ · sinδ ₁ · cos2(P+A _p ) (6s)

β ₂₂ =0.5· _sin2Ψr · _sin2Ψt ·sin( _Δr + _Δt )· _{s 2} · _sinδ1 ·sin2(Pp+ _Ap )(6t)

α ₂₆ =0.5 · sin2Ψ _r · sin2Ψ _t · sin(Δ _r +Δ _t ) · s ₁ · sinδ ₂ · cos2(P _p +A _p ) (6u)

β ₂₆ =0.5· _sin2Ψr · _sin2Ψt ·sin( _Δr + _Δt )· _s1 · _sinδ2 · _sin2 (Pp+ _Ap )(6v)

where c _j =cos ² (δ _j /2), and s _j =sin ² (δ _j /2).

S5, continuously adjust the values of the system parameters to be calibrated in the relational model, until the error between the Fourier coefficients in the relational model and the Fourier coefficients in step S3 is within a preset range, then the system parameters to be calibrated at this time The corresponding value is the calibration value.

From the above formulas (6a) to (6x), it can be seen that the input variables in the formula whose Fourier coefficient is the output are the parameter variables to be calibrated, that is, the Fourier coefficient Fc _i at the ith azimuth angle of the calibration sample is A function of the parameters to be calibrated (A _p , P _p , C _s1 , C _s2 , C _s , δ ₁ , δ ₂ , δ, Ψ _r , Ψ _t , Δ _r , Δ _t ). Combined with the Fourier coefficient MFc _i obtained in step S3, the calculation formula for the error of the two is obtained as follows:

Wherein, MFc _i is the Fourier coefficient obtained in step S3 of the 1/4 standard wave plate at the ith azimuth angle, and Fc _i is the relationship of the 1/4 standard wave plate at the ith azimuth angle Fourier coefficients in the model. The corresponding parameters to be calibrated can be obtained by solving according to the nonlinear regression method. The fitting result is shown in Figure 6, where the abscissa is the 24 Fourier coefficients, and the ordinate is the value of the Fourier coefficients.

So far, the first step of calibration has been completed. After the corresponding device is calibrated using the data after the first step of calibration, the above calibration sample is removed, and the imaging part (lens 106 and objective lens 107) is re-installed. The objective lens 107 is high resolution. As the core component of the imaging system, with the increase of the objective lens 107NA, the angle of light refraction on the NA is also larger, which will have a greater impact on the polarization state of the light. In addition, the birefringence effect and stress of the coating material will also be It affects the polarization state of the light, and the effect of the objective lens on the polarization state of the light becomes the polarization aberration, especially the polarization aberration of the high NA objective lens with NA greater than 0.6 is more obvious. In order to improve the measurement accuracy of the instrument, the polarization aberration of the objective lens 107 must be considered; another purpose of the second calibration step is to calibrate the relationship between the measurement incident angle and the angle of rotation of the mirror motorized rotary table. The specific steps of the second calibration are as follows, as shown in FIG. 4 , including steps S6 to S10.

S6, replace the 1/4 standard wave plate and the reflecting mirror with the imaging lens and the objective lens respectively, and set an isotropic uniform film on the sample stage, and regard the objective lens and the film as a whole as a sample to be tested;

The objective lens 107 is adjusted so that the axis of the light rays and the objective lens 107 coincide, so that the incident angle of the light emitted from the objective lens 107 is 0°. An isotropic uniform thin film 803 is placed on the sample stage, with the objective lens 107 and the isotropic sample as a whole.

S7, adjusting the angle of the mirror to change the incident angle of the sample to be tested, the detector obtains second light intensity information corresponding to the incident angle, and then obtains the Mueller matrix of the sample to be tested;

A measurement is performed using the instrument already calibrated in the first step, and the light intensity information at the incident angle of 0° is obtained at the detector 110 . As shown in FIG. 5 , by adjusting the rotation angle of the plane mirror 103 to change the incident angle of the sample to be tested, the detector obtains the second light intensity information corresponding to the incident angle, and then obtains the information of the second light intensity of the sample to be tested. Mueller matrix, the Mueller matrix at this time is the Mueller matrix required for the calibration of the subsequent steps.

S8, establishing a calculation model of the Mueller matrix of the sample to be tested;

The calculation model of the calculation model of the Mueller matrix of the sample to be tested in this application is established based on the Zernike polynomial. Zernike polynomial is a set of functions defined on the unit circle, with completeness and orthogonality. Since the form of Zernike polynomial is almost the same as the aberration of optical system, Zernike polynomial is usually used to describe wavefront aberration , any image in the unit circle can be expanded using the Zernike polynomial, where the Zernike polynomial is defined as follows:

为径多项式。Among them, n is the order of the polynomial, m is the angular frequency of the sine component, (ρ, θ) are the polar diameter and polar angle in the corresponding polar coordinates, N is the normalization factor,

is the diameter polynomial.

The calculation model of the Mueller matrix of the sample to be tested in this application is:

为入射角

下所述薄膜的穆勒矩阵，可以由薄膜传输矩阵计算得到，M^OB(ρ,θ)为物镜在极角θ和极径ρ下的穆勒矩阵。原有的校准方式利用球面镜特性，将物镜当作样品，测量了物镜的偏振特性，研究中用穆勒矩阵表征的物镜偏振特性，从穆勒矩阵元素中可以看出，物镜的偏振特性没有明显的各向异性，因此，可以用偏振参数振幅比角和相位差角来表征物镜偏振像差。由此，物镜上每一点的穆勒矩阵可以用下式表示：in,

is the angle of incidence

The Mueller matrix of the thin film described below can be calculated from the thin film transmission matrix, where M ^OB (ρ, θ) is the Mueller matrix of the objective lens at the polar angle θ and the polar diameter ρ. The original calibration method utilizes the characteristics of spherical mirrors, takes the objective lens as a sample, and measures the polarization characteristics of the objective lens. In the study, the polarization characteristics of the objective lens are characterized by the Mueller matrix. It can be seen from the elements of the Mueller matrix that the polarization characteristics of the objective lens are not obvious. The anisotropy of , therefore, can be used to characterize the objective polarization aberration by the polarization parameters, amplitude ratio angle and retardation angle. Thus, the Mueller matrix of each point on the objective can be expressed as:

Among them, Ψ _br is the amplitude ratio angle of the objective lens, and Δ _br is the retardation angle of the objective lens.

The formula for calculating the polarization aberration of the objective lens is:

Among them, k is the number of sampling points, Z _l is the coefficient of the lth Zernike polynomial of the corresponding parameter, ε _{k, Ψ} and ε _{k, Δ} are the fitting errors of the corresponding parameters, f _l (ρ _k , θ _k ) is The lth term Zernike polynomial, L is the number of the largest term of the Zernike polynomial.

The Zernike decomposition of formulas (11) and (12) is carried out. From the decomposition results of the first 49 Zernike coefficients, it can be found that only a few coefficients have relatively large values, and it can be observed that the larger Zernike coefficients are of the same type. Zernike moment, the multi-pattern corresponding to the Zernike coefficient whose coefficient value is greater than 1% is selected to describe the polarization aberration of the objective lens, and the decomposed data is used as the initial value of the subsequent fitting.

正弦值为正比例关系，但是由于仪器光路缺陷和硬件的噪声，实际的关系可以表示为：The relationship between the incident angle of the rotating device type Mueller matrix ellipsometer and the mirror rotation angle can be obtained according to Abbe's sine theorem, the sine value of the mirror deflection angle α and the illumination incident angle

The sine value is proportional to the relationship, but due to the optical path defect of the instrument and the noise of the hardware, the actual relationship can be expressed as:

It can be seen from the above analysis that the above formulas (11) to (13) contain 12 unknowns, namely 8 Zernike coefficients, slope K, intercept D, and the fitting thickness d of the standard film sample.

S9, continuously adjust the parameters in the calculation model until the error between the Mueller matrix of the sample to be tested calculated by the calculation model and the Mueller matrix obtained in step S7 is within a preset range;

Still using the nonlinear regression fitting method to solve the following nonlinear equation (14) to obtain the above 12 unknown parameters, the expression of the nonlinear equation (14) is:

Wherein, M _simu (ρ, θ) is the sample Mueller matrix obtained by the calculation model, and the Mueller matrix obtained in the above step S7.

S10, the parameter determined in step S9 is substituted into the polarization aberration calculation formula of the objective lens to obtain the polarization aberration calibration value of the objective lens.

From this formula (14), the above 12 unknowns can be solved, and the unknown quantities can be substituted into the above (11) and (12) to obtain the polarization aberration of the objective lens; the solved K and D can be substituted into formula (13) The relationship between the incident angle of the rotating device type Mueller matrix ellipsometer and the rotation angle of the mirror is obtained.

Figure 7 shows the measurement and fitting results of the calibrated Mueller matrix, where the abscissa is the incident angle, and the ordinate is the value of the Mueller matrix. It can be seen from the figure that the measured data indicates that the polarization effect of the objective is isotropic, that is, the elements of the Mueller matrix in the off-diagonal part are close to 0. And with the increase of the incident angle, the change range of the Mueller matrix increases, which is due to the increase of the deflection of the light near the edge of the objective lens, and the increase of the influence on the polarized light.

To sum up, the present application can obtain calibration parameters of multiple devices through two-step calibration, which greatly reduces the complexity of calibration, improves the efficiency of calibration, and reduces the accumulation of errors between calibration steps; The regression fitting method solves the parameters to be calibrated in the relational model and the calculation model. Compared with the numerical solution method, it has the advantages of high calibration accuracy, good robustness, and fast measurement speed.

Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, etc., All should be included within the protection scope of the present invention.

Claims (6)

1. A calibration method for system parameters of a rotary device type Mueller matrix ellipsometer is characterized by comprising the following steps:

s1, replacing an imaging lens and an objective lens of the rotary device type high-resolution imaging Mueller matrix ellipsometer with a 1/4 standard wave plate and a reflector respectively;

s2, rotating the azimuth angle of the 1/4 standard wave plate for multiple times, and respectively acquiring light intensity information under the multiple azimuth angles from a detector of the rotary device type high-resolution imaging Mueller matrix ellipsometer;

s3, carrying out Fourier analysis on the light intensity information to obtain Fourier coefficients of the light intensity information;

s4, establishing a relationship model between a fourier coefficient of the light intensity information and a parameter of the system to be calibrated, where the parameter of the system to be calibrated includes azimuth angles of a polarizer, an analyzer, a first rotating compensator and a second rotating compensator, phase delay amounts of the first rotating compensator and the second rotating compensator, and a residual polarization effect of the beam splitting device, and the step S4 specifically includes:

s41, obtaining the polarization state of the received light of the detector, and simplifying the polarization state to obtain the light intensity information of the received light of the detector; the polarization state expression of the received light of the detector is as follows:

S_out＝M_aR(A_p)R(-C₂)M_c(δ₂)R(C₂)M_bt*R(C_s)M_c(δ)R(-C_s)M_sR(-C_s)M_c(δ)R(C_s)M_br*R(-C₁)M_c(δ₁)R(C₁)R(-P_p)M_pR(P_p)S_in

wherein S is_outIs the Stokes vector of the received light of the detector, S_inStokes vector of the light emitted by the light source, M_a、M_c、M_pAnd M_sMueller matrices, delta, of analyzers, compensators, polarizers and flat mirrors, respectively₁、δ₂And δ is the phase retardation of the first rotation compensator, the second rotation compensator and the 1/4 standard waveplate, R (A)_p)、R(C₁)、R(C₂)、R(P_p) And R (C)_s) Rotation matrices of the analyzer, the first rotation compensator, the second rotation compensator, the polarizer and the 1/4 standard wave plate, A_p、C₁、C₂、P_pAnd C_sActual azimuth angles of the analyzer, the first rotation compensator, the second rotation compensator, the polarizer and the 1/4 standard wave plate respectively, wherein C₁＝C_s1-5ω t，C₂＝C_s2-3ω t，C_s1And C_s2Initial azimuth angles of the first rotary compensator and the second rotary compensator respectively, omega is the rotation fundamental frequency of the servo motor, M_brAnd M_btRespectively, the mueller matrices of the non-polarizing beam splitting device in reflection and in transmission, wherein,

in the formula, Ψ_rAnd Δ_rAmplitude ratio and phase difference, psi, of orthogonally polarized light, respectively, upon reflection by the non-polarizing beam splitting means_tAnd Δ_tThe amplitude ratio and the phase difference of the polarized light in the orthogonal direction when the non-polarization beam splitting device transmits are respectively obtained; the expression of the light intensity information i (t) received by the detector after the polarization state is simplified is as follows:

wherein, I₀As a function of the spectral response, α₀Is a direct Fourier coefficient, alpha_2nAnd beta_2nI.e. the Fourier coefficients, M, in the relational model₁₁Mueller matrix M as a flat mirror_sMueller matrix elements (1, 1);

s42, acquiring a relation model of the Fourier coefficient and the system parameter to be calibrated according to the light intensity information in the step S41;

s5, continuously adjusting the value of the system parameter to be calibrated in the relational model until the error between the Fourier coefficient in the relational model and the Fourier coefficient in the step S3 is within a preset range, wherein the value corresponding to the system parameter to be calibrated is a calibration value, and the calculation formula of the error between the Fourier coefficient in the relational model and the Fourier coefficient in the step S3 is as follows:

wherein, MFC_iThe Fourier coefficient, Fc, obtained in step S3 at the i azimuth angle of the 1/4 standard waveplate_iFor the 1/4 standard wave plate at the i azimuth angleFourier coefficients in the relational model.

2. The calibration method according to claim 1, wherein step S2 comprises collecting light intensity information over a plurality of periods and averaging the light intensity information.

3. The calibration method according to claim 1, wherein the method further comprises:

s6, the 1/4 standard wave plate and the reflector are respectively replaced by the imaging lens and the objective lens, and the objective lens and the film are taken as a whole to be a sample to be measured by arranging an isotropic uniform film on a sample stage;

s7, adjusting the angle of the plane mirror to change the incident angle of the sample to be detected, and obtaining second light intensity information corresponding to the incident angle by the detector to further obtain a Mueller matrix of the sample to be detected;

s8, establishing a computational model of the Mueller matrix of the sample to be measured;

s9, continuously adjusting parameters in the calculation model until the error between the Mueller matrix of the sample to be measured calculated by the calculation model and the Mueller matrix obtained in the step S7 is within a preset range;

and S10, substituting the parameters determined in the step S9 into the polarized aberration calculation formula of the objective lens to obtain the polarized aberration calibration value of the objective lens.

4. The calibration method according to claim 3, wherein the computational model of the Mueller matrix of the sample to be measured is:

wherein,

is the angle of incidence

Mueller matrix of the said film, M^OB(rho, theta) is the Mueller matrix of the objective lens under the polar angle theta and the polar diameter rho,

therein, Ψ_brIs the amplitude ratio angle, Δ, of the objective lens_brIs the phase difference angle of the objective lens.

5. The calibration method according to claim 4, wherein the calculation formula of the polarization aberration of the objective lens is:

wherein k is the number of sampling points, Z_lThe coefficients of the Zernike polynomials of the first term, ε, for the corresponding parameters_k，ΨAnd ε_k，ΔFitting error for corresponding parameter, f_l(ρ_k，θ_k) Is Zernike polynomial of the I term, and L is the number of the maximum term of the Zernike polynomial.

6. The calibration method according to claim 5, wherein the step S10 further comprises obtaining a relationship between an incident angle and a rotation angle of the plane mirror of the rotating device type high resolution Mohler matrix ellipsometer according to the parameter.

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