METHOD FOR CONDUCTING OPTICAL MEASUREMENT USINGFULL MUELLER MATRIX ELLIPSOMETER

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First Claim
1. A method for conducting optical measurement with a full Mueller matrix ellipsometer, comprising the following steps:
 constructing an experimental optical path of the full Mueller matrix ellipsometer, the experimental optical path of the full Mueller matrix ellipsometer including a light source, a polarizer, a first phase compensator, an analyzer, a second phase compensator, a spectrometer, and a sample stage;
performing a total regression calibration on operating parameters of the full Mueller matrix ellipsometer;
placing a sample to be tested on the sample stage, and obtaining experimental Fourier coefficients of the sample to be tested with the full Mueller matrix ellipsometer;
obtaining information of the sample to be tested based on the experimental Fourier coefficients of the sample to be tested;
wherein a method for calibrating the full Mueller matrix ellipsometer comprises the following steps;
setting rotational speeds of the first phase compensator and the second phase compensator;
setting a frequency of the spectrometer for measuring light intensity data, so that the spectrometer measures the light intensity data every T/N time, wherein a total of N sets of light intensity data are acquired, where N≥
25, and T is a period of measurement;
acquiring the light intensity data measured by the spectrometer;
obtaining respective experimental Fourier coefficients α
′
_{2n}, β
′
_{2n }from N relation formulas between the light intensity data and experimental Fourier coefficients formed by the N sets of light intensity data, based on the light intensity data acquired by a data acquisition module of the spectrometer;
obtaining respective theoretical Fourier coefficients α
_{2n}, β
_{2n }based on the respective experimental Fourier coefficients, an initial polarization angle C_{s1 }of the first phase compensator and an initial polarization angle C_{s2 }of the second phase compensator which have been calibrated;
obtaining, by a phase retardation calculation module for the first phase compensator, a phase retardation δ
_{1 }of the first phase compensator based on the respective theoretical Fourier coefficients, a polarization angle P_{s }of the polarizer and a polarization angle A_{s }of the analyzer which have been calibrated, on the basis that a reference sample is isotropic and uniform;
obtaining, by a phase retardation calculation module for the second phase compensator, a phase retardation δ
_{2 }of the second phase compensator, based on the respective theoretical Fourier coefficients, the polarization angle P_{s }of the polarizer and the polarization angle A_{s }of the analyzer which have been calibrated, on the basis that the reference sample is isotropic and uniform;
obtaining accurate values of all operating parameters (d, θ
, P_{s}, A_{s}, C_{s1}, C_{s2}, δ
_{1}, δ
_{2}) of the full Mueller matrix ellipsometer through least square fitting according to the relation formulas between the theoretical Fourier coefficients and the operating parameters, with (d, θ
, P_{s}, A_{s}, C_{s1}, C_{s2}, δ
_{1}, δ
_{2}) being as variables, and with the initial polarization angle C_{s1 }of the first phase compensator, the initial polarization angle C_{s2 }of the second phase compensator, the polarization angle P_{s }of the polarizer, the polarization angle A_{s }of the analyzer, the phase retardation δ
_{1 }of the first phase compensator and the phase retardation δ
_{2 }of the second phase compensator, which have been calibrated, being as initial values, where d is a thickness of the reference sample, and θ
is an angle at which light is incident on the reference sample.
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Abstract
A method for conducting optical measurement using a full Mueller matrix ellipsometer, which belongs to the technical field of optical measurements. The optical measurement method comprises: constructing an experimental optical path of a full Mueller matrix ellipsometer; conducting complete regression calibration on the full Mueller matrix ellipsometer; placing a sample to be measured on a sample platform, and obtaining an experimental Fourier coefficient of the sample to be measured; and according to the experimental Fourier coefficient of the sample to be measured, obtaining information about the sample to be measured. Since a calibration method for the full Mueller matrix ellipsometer is not only simple in operation process, but also makes full use of data of the full Mueller matrix ellipsometer measured at the same time, the introduced error is relatively small and the parameter obtained by calibration is more accurate, so that the measurement result is more accurate when the sample to be measured is measured. Thus, the process of the optical measurement method is simplified.
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7 Claims
 1. A method for conducting optical measurement with a full Mueller matrix ellipsometer, comprising the following steps:
constructing an experimental optical path of the full Mueller matrix ellipsometer, the experimental optical path of the full Mueller matrix ellipsometer including a light source, a polarizer, a first phase compensator, an analyzer, a second phase compensator, a spectrometer, and a sample stage; performing a total regression calibration on operating parameters of the full Mueller matrix ellipsometer; placing a sample to be tested on the sample stage, and obtaining experimental Fourier coefficients of the sample to be tested with the full Mueller matrix ellipsometer; obtaining information of the sample to be tested based on the experimental Fourier coefficients of the sample to be tested; wherein a method for calibrating the full Mueller matrix ellipsometer comprises the following steps; setting rotational speeds of the first phase compensator and the second phase compensator; setting a frequency of the spectrometer for measuring light intensity data, so that the spectrometer measures the light intensity data every T/N time, wherein a total of N sets of light intensity data are acquired, where N≥
25, and T is a period of measurement;acquiring the light intensity data measured by the spectrometer; obtaining respective experimental Fourier coefficients α
′
_{2n}, β
′
_{2n }from N relation formulas between the light intensity data and experimental Fourier coefficients formed by the N sets of light intensity data, based on the light intensity data acquired by a data acquisition module of the spectrometer;obtaining respective theoretical Fourier coefficients α
_{2n}, β
_{2n }based on the respective experimental Fourier coefficients, an initial polarization angle C_{s1 }of the first phase compensator and an initial polarization angle C_{s2 }of the second phase compensator which have been calibrated;obtaining, by a phase retardation calculation module for the first phase compensator, a phase retardation δ
_{1 }of the first phase compensator based on the respective theoretical Fourier coefficients, a polarization angle P_{s }of the polarizer and a polarization angle A_{s }of the analyzer which have been calibrated, on the basis that a reference sample is isotropic and uniform;obtaining, by a phase retardation calculation module for the second phase compensator, a phase retardation δ
_{2 }of the second phase compensator, based on the respective theoretical Fourier coefficients, the polarization angle P_{s }of the polarizer and the polarization angle A_{s }of the analyzer which have been calibrated, on the basis that the reference sample is isotropic and uniform;obtaining accurate values of all operating parameters (d, θ
, P_{s}, A_{s}, C_{s1}, C_{s2}, δ
_{1}, δ
_{2}) of the full Mueller matrix ellipsometer through least square fitting according to the relation formulas between the theoretical Fourier coefficients and the operating parameters, with (d, θ
, P_{s}, A_{s}, C_{s1}, C_{s2}, δ
_{1}, δ
_{2}) being as variables, and with the initial polarization angle C_{s1 }of the first phase compensator, the initial polarization angle C_{s2 }of the second phase compensator, the polarization angle P_{s }of the polarizer, the polarization angle A_{s }of the analyzer, the phase retardation δ
_{1 }of the first phase compensator and the phase retardation δ
_{2 }of the second phase compensator, which have been calibrated, being as initial values, where d is a thickness of the reference sample, and θ
is an angle at which light is incident on the reference sample. View Dependent Claims (2, 3, 4, 5, 6, 7)
1 Specification
The present disclosure relates to the field of optical measurement technology, and more particularly to a method for conducting optical measurement with a full Mueller matrix ellipsometer.
An ellipsometer is an optical measuring instrument that takes advantage of the polarization characteristics of light to acquire information of a sample to be tested. The working principle of the ellipsometer is as below: letting light passing through a polarizer be incident on a sample to be tested; obtaining the information of the sample to be tested by measuring a change of polarization state (amplitude ratio and phase difference) of an incident light and a reflected light on a surface of the sample to be tested. The ellipsometer with rotatory polarizer or single rotatory compensator can obtain up to 12 parameters of the sample in one measurement. With the advancement of the integrated circuit technology and the complexity of device structure, unknown variables to be measured are continuously increased, and traditional ellipsometers present certain limitations in various aspects, such as film thickness measurement of ultrathin films, measurement of optical constants for anisotropic materials, depolarization analysis of surface features, and measurement of critical dimensions and topography in integrated circuits. A full Mueller matrix ellipsometer (ellipsometer in a broad sense) can acquire 16 parameters of 4×4 order Mueller matrix in one measurement, obtaining more abundant information as compared with a traditional ellipsometer. It breaks through technical limitations of traditional ellipsometers and enables accurate, fast, nondestructive measurement of film thickness, optical constants, critical dimensions and threedimensional topography in a wide spectral range.
The key to ensure measurement accuracy and maintain device status for a spectroscopic ellipsometer is the calibration of the device. The ellipsometer may generate system deviation gradually during use as time goes on, especially a thickness of a wave plate is susceptible to changes in temperature and pressure as well as environmental deliquescence. Therefore, a calibration method enabling quick and accurate correction of the ellipsometer is a key technique to ensure device effectiveness and production efficiency. With a calibration process of an existing conventional ellipsometer (
In a systematic calibration of an existing full Mueller matrix ellipsometer, such as the Mueller ellipsometer in US Patent US005956147, a photoelastic modulator (PEM) is used as a phase compensator. When a phase retardation of the PEM is calibrated, it is built in a straightthrough ellipsometry system for measurement, and the PEM needs to be taken off the original equipment to measure its corresponding phase retardation. After the calibration is completed, the PEM is reloaded onto the equipment. During the mechanical loading and unloading processes, it cannot be guaranteed that loading position is the same as the previous loading position, which increases systematic error, and reconstruction of the straightthrough measuring system will increase workload. In the existing literature (Harland G. Tompkins, Eugene A. Irene, Handbook of ellipsometry, 7.3.3.4 Calibration 7), a Mueller ellipsometer uses a wave plate as a phase compensator, the process of which is to build a straightthrough measuring platform on an experimental table to measure Fourier coefficients obtained experimentally and use δ_{1}=
where B′_{B}=√{square root over ((α′_{2n})^{2}+(β′_{2n})^{2})} for calibration. It is required to remove two phase compensators during calibration and then put back, which increases systematic error. If the calibration is carried out without removing the phase compensators, obliquelyincident measuring arms on both sides of the sample must be rotated to a horizontal position (eg. Woollam'"'"'s ellipsometer as shown in
In summary, with current techniques, delay spectral lines of all phase compensators being used must be tested prior to device assembly, and a phase retardation of the phase compensator must be calibrated using a straightthrough ellipsometry system. The system is required to have a design to adjust an angle of incidence to a straightthrough type, and there is a process of changing the angle of incidence during the calibration process. These methods increase the complexity of the system and the calibration process is more complicated.
Since a method for conducting optical measurement with a full Mueller matrix ellipsometer is performed after the calibration of the full Mueller matrix ellipsometer, the complexity in the calibration process of the full Mueller matrix ellipsometer must result in the complexity of the method for conducting optical measurement with a full Mueller matrix ellipsometer.
In order to solve the above problems, the present disclosure proposes a simplified method for conducting optical measurement with a full Mueller matrix ellipsometer whose calibration process is simplified.
A method for conducting optical measurement with a full Mueller matrix ellipsometer provided by the present disclosure may comprise the following steps:
constructing an experimental optical path of the full Mueller matrix ellipsometer, and wherein the experimental optical path of the full Mueller matrix ellipsometer includes a light source, a polarizer, a first phase compensator, an analyzer, a second phase compensator, a spectrometer, and a sample stage;
performing a total regression calibration on the full Mueller matrix ellipsometer;
placing a sample to be tested on the sample stage, and obtaining experimental Fourier coefficients of the sample to be tested with the full Mueller matrix ellipsometer;
obtaining information of the sample to be tested based on the experimental Fourier coefficients of the sample to be tested.
In addition, a method for calibrating the full Mueller matrix ellipsometer may comprise the following steps:
setting rotational speeds of the first phase compensator and the second phase compensator;
setting a frequency of the spectrometer for measuring light intensity data, so that the spectrometer measures the light intensity data every T/N time, wherein a total of N sets of light intensity data are acquired, where N≥25, and T is a period of measurement;
acquiring the light intensity data measured by the spectrometer;
obtaining respective experimental Fourier coefficients α′_{2n}, β′_{2n }from N relation formulas between the light intensity data and experimental Fourier coefficients formed by the N sets of light intensity data, based on the light intensity data acquired by a data acquisition module of the spectrometer;
obtaining respective theoretical Fourier coefficients α_{2n}, β_{2n }based on the respective experimental Fourier coefficients, an initial polarization angle C_{s1 }of the first phase compensator and an initial polarization angle C_{s2 }of the second phase compensator which have been calibrated;
obtaining, by a phase retardation calculation module for the first phase compensator, a phase retardation δ_{1 }of the first phase compensator based on the respective theoretical Fourier coefficients, a polarization angle P_{s }of the polarizer and a polarization angle A_{s }of the analyzer which have been calibrated, on the basis that a reference sample is isotropic and uniform;
obtaining, by a phase retardation calculation module for the second phase compensator, a phase retardation δ_{2 }of the second phase compensator, based on the respective theoretical Fourier coefficients, the polarization angle P_{s }of the polarizer and the polarization angle A_{s }of the analyzer which have been calibrated, on the basis that the reference sample is isotropic and uniform;
obtaining accurate values of all operating parameters (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) of the full Mueller matrix ellipsometer through least square fitting according to the relation formulas between the theoretical Fourier coefficients and the operating parameters, with (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) being as variables, and with the initial polarization angle C_{s1 }of the first phase compensator, the initial polarization angle C_{s2 }of the second phase compensator, the polarization angle P_{s }of the polarizer, the polarization angle A_{s }of the analyzer, the phase retardation δ_{1 }of the first phase compensator and the phase retardation δ_{2 }of the second phase compensator, which have been calibrated, being as initial values, where d is a thickness of the reference sample, and θ is an angle at which light is incident on the reference sample.
The method for conducting optical measurement with a full Mueller matrix ellipsometer according to the present disclosure may utilize a reference sample which is isotropic and uniform, and obtain the phase retardation δ_{1 }of the first phase compensator and the phase retardation δ_{2 }of the second phase compensator based on the relation formulas between the light intensity data and the experimental Fourier coefficients as well as the polarization angle P_{s }of the polarizer and the polarization angle A_{s }of the analyzer which have been calibrated; and then obtains accurate values of all operating parameters (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) of the full Mueller matrix ellipsometer by least square fitting according to the relation formulas between the theoretical Fourier coefficients and the operating parameters, with (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) being as variables, and with the initial polarization angle C_{s1 }of the first phase compensator, the initial polarization angle C_{s2 }of the second phase compensator, the polarization angle P_{s }of the polarizer, the polarization angle As of the analyzer, the phase retardation δ_{1 }of the first phase compensator, the phase retardation δ_{2 }of the second phase compensator, which have been calibrated, being as initial values. The calibration method can take full advantages of measurement data obtained at a same time, which introduces relatively small error and obtains more accurate parameters after calibration. Thus, the result of measurement is more accurate when a sample to be tested is measured using the method of the present disclosure.
The present invention will be described in detail below in conjunction with the drawings and specific embodiments for the indepth understanding of the invention.
A method for conducting optical measurement with a full Mueller matrix ellipsometer according to Embodiment 1 of the present invention may comprise the following steps:
step 1: referring to
S_{out}=M_{A}R(A′)R(−C_{2})M_{c2}(δ_{2})R(C′_{2})×M_{s}×R(−C′_{1})M_{c1}(δ_{1})R(C′_{1})R(−P′)M_{p}R(P)S_{in }
that is,
Step 2 of the method may comprise: performing a total regression calibration on the full Mueller matrix ellipsometer.
Step 3 of the method may comprise: placing the sample to be tested on the sample stage, and obtaining experimental Fourier coefficients of the sample to be tested with the full Mueller matrix ellipsometer.
Step 4 of the method may comprise: obtaining information of the sample to be tested based on the experimental Fourier coefficients of the sample to be tested.
The experimental Fourier coefficients have relation to Mueller elements of the sample, an azimuth angle P_{s }of the polarizer, an azimuth angle A_{s }of the analyzer, azimuth angles C_{s1 }and C_{s2 }of the two phase compensators, and phase retardations δ_{1 }and δ_{2 }(refer to Harland G. Tompkins, Eugene A. Irene, Handbook of ellipsometry, 7.3.3 Dual Rotating Compensator 7). However, the Mueller elements of the sample are related to optical constants n, k of a material of the sample, a thickness d, an angle θ at which light beams are incident on the sample, and a wavelength λ of the light beams. Therefore, after the experimental Fourier coefficients of the sample are measured, the Mueller elements of the sample can be obtained according to the above relationships, and then the information of the sample can be obtained.
In an embodiment, the process of performing a total regression calibration on the full Mueller matrix ellipsometer comprises the following steps:
step 21: setting rotational speeds of the first and second phase compensators;
step 22: setting a frequency of a spectrometer for measuring light intensity data, so that the spectrometer may measure the light intensity data every T/N time, and a total of N sets of light intensity data are acquired, wherein N≥25, and T is a period of measurement;
step 23: acquiring the light intensity data measured by the spectrometer;
step 24: obtaining respective experimental Fourier coefficients α′_{2n}/β′_{2n }from N relation formulas between the light intensity data and the experimental Fourier coefficients formed by the N sets of light intensity data, based on the light intensity data acquired by a data acquisition module of the spectrometer;
step 25: obtaining respective theoretical Fourier coefficients α_{2n}, β_{2n }according to the respective experimental Fourier coefficients, an initial polarization angle C_{s1 }of the first phase compensator and the initial polarization angle C_{s2 }of the second phase compensator which have been calibrated;
step 26: obtaining, on the basis that a reference sample is isotropic and uniform, by a phase retardation calculation module for the first phase compensator, phase retardation δ_{1 }of the first phase compensator based on the respective theoretical Fourier coefficients, a polarization angle P_{s }of the polarizer and a polarization angle A_{s }of the analyzer which have been calibrated; and
obtaining, on the basis that the reference sample is isotropic and uniform, by a phase retardation calculation module for the second phase compensator, phase retardation δ_{2 }of the second phase compensator based on the respective theoretical Fourier coefficients, a polarization angle P_{s }of the polarizer and a polarization angle A_{s }of the analyzer which have been calibrated;
step 27: obtaining accurate values of all operating parameters (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) of the full Mueller matrix ellipsometer through least square fitting according to the relation formulas between the theoretical Fourier coefficients and the operating parameters, with (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) being as variables, and with the initial polarization angle C_{s1 }of the first phase compensator, the initial polarization angle C_{s2 }of the second phase compensator, the polarization angle P_{s }of the polarizer, the polarization angle A_{s }of the analyzer, the phase retardation δ_{1 }of the first phase compensator, the phase retardation δ_{2 }of the second phase compensator, which have been calibrated, being as initial values, where d is a thickness of the reference sample, and θ is an angle at which light is incident on the reference sample.
A corresponding Mueller matrix of the reference sample that is isotropic and uniform is:
Taking N=36, the ratio of the rotation speed of the first phase compensator 6 to the rotation speed of the second phase compensator 12 equaling 5:3 as an example, at this time, the first phase compensator 6 and the second phase compensator 12 are respectively in a rotating state, and the ratio of the rotation speed of the first phase compensator 6 to the rotation speed of the second phase compensator 12 equals 5:3. At this time, C′_{1}=5(C−C_{s1}), C′_{2}=3(C−C_{s2}), and the time during which the first phase compensator 6 rotates 5 turns or the second phase compensator 12 rotates 3 turns is a period T, and where:
−C_{s1}, an angle of a fast optical axis of the first phase compensator 6 at a time t=0,
−C_{s2}, an angle of a fast optical axis of the second phase compensator 12 at a time t=0,
C=ωt, a rotation angle by which the first phase compensator 6 and the second phase compensator 12 rotate at a fundamental physical frequency ω.
where ω=π/T.
With the acquired S1, S2, S3 . . . S36, 36 equations containing 25 unknowns can be obtained through the above formula (n=9, 12, 14, 15, the primed Fourier coefficients α′_{2n}=0 and β′_{2n}=0). Through a nonlinear least square method, a total of 24 primed Fourier coefficients α′_{2n }and β′_{2n }can be obtained.
The transformation relationship between the theoretical Fourier coefficients α_{2n }and β_{2n }and the experimental Fourier coefficients α′_{2n }and β′_{2n }is expressed in formulas 2.7 and 2.8:
α_{2n}=α′_{2n }cos ϕ_{2n}+β′_{2n }sin ϕ_{2n} 2.7
β_{2n}=−α′_{2n }sin ϕ_{2n}+β′_{2n }cos ϕ_{2n} 2.8
where:
ϕ_{2}=12C_{s2}−10C_{s1}; ϕ_{4}=10C_{s1}−6C_{s2};
ϕ_{6}=6C_{s2}; ϕ_{8}=20C_{s1}−12C_{s2};
ϕ_{10}=10C_{s1}; ϕ_{12}=12C_{s2};
ϕ_{14}=20C_{s1}−6C_{s2}; ϕ_{16}=10C_{s1}+6C_{s2};
ϕ_{20}=20C_{s1}; ϕ_{22}=10C_{s1}+12C_{s2};
ϕ_{26}=20C_{s1}+6C_{s2}; ϕ_{32}=20C_{s1}+12C_{s2 }
The theoretical Fourier coefficients α_{2n }and β_{2n }can be obtained from the formulas 2.7 and 2.8.
For a sample which is isotropic and uniform, M_{13}=M_{31}=M_{14}=M_{41}=M_{23}=M_{32}=M_{24}=M_{42}=0. Further, according to theoretical principles of the Mueller ellipsometer, the following theoretical expressions for the theoretical Fourier coefficients α_{2}, β_{2}, α_{10}, β_{10}, α_{6}, β_{6}, α_{14}, β_{14}, α_{22}, β_{22}, α_{26}, β_{26 }can be obtained:
From formulas 2.10 and 2.12, it can be obtained:
(n is an integer) (the Fourier coefficients must be guaranteed to be nonzero)
Similarly, the phase retardation δ_{1 }of the compensator can also be calculated through formulas 2.9 and 2.12, formulas 2.9 and 2.11, formulas 2.10 and 2.11, formulas 2.9 and 2.13, formulas 2.9 and 2.14, formulas 2.10 and 2.13, formulas 2.10 and 2.14.
The phase retardation δ_{2 }of the second compensator is calibrated below.
From formulas 2.16 and 2.18, it can be obtained:
(n is an integer) (the Fourier coefficients must be guaranteed to be nonzero)
Similarly, the phase retardation δ_{2 }of the compensator can also be calibrated through formulas 2.16 and 2.19, formulas 2.17 and 2.18, formulas 2.17 and 2.19, formulas 2.18 and 2.20, formulas 2.18 and 2.21, formulas 2.19 and 2.20, formulas 2.19 and 2.21.
The transformation of the experimental Fourier coefficients and the theoretical Fourier coefficients can be realized by the formulas 2.7 and 2.8. Meanwhile, the theoretical Fourier coefficients have relation to Mueller elements of the sample, an azimuth angle P_{s }of the polarizer, an azimuth angle A_{s }of the analyzer, azimuth angles C_{s1 }and C_{s2 }of the two phase compensators, and the phase retardations δ_{1 }and δ_{2 }(refer to Harland G. Tompkins, Eugene A. Irene, Handbook of ellipsometry, 7.3.3 Dual Rotating Compensator 7). Mueller elements of the sample are related to optical constants n, k of a material of the sample, thickness d, an angle θ at which light beams are incident on the sample, and a wavelength λ of the light beams. The experimental Fourier coefficients α′_{2n }and β′_{2n }are related to (n, k, d, θ, λ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}), θ is an angle at which light beams are incident on the sample. For a reference sample with known optical constants n, k under a single wavelength, there are 24 α′_{2n }and β′_{2n }in total obtained by measurement in an experiment, and correspondingly 24 equations can be obtained, which are related only to (d, θ, λ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}). The P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2 }obtained above by calibration can be used as initial values, and the wavelength corresponding to the measurement in the experiment are known; 24 equations obtained according to experimental Fourier coefficients have relation to (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}). Thus, the remaining operating parameters (d, θ, P_{s}, A_{s}, C_{s1}, C_{s2}, δ_{1}, δ_{2}) of the Mueller ellipsometer can be obtained by the least square fitting. The reference sample may be a silicon dioxide film sample with silicon as the substrate, the optical constants n and k of which can be consulted in the literatures. Taking the wavelength of 632.8 nm as an example, the optical constants of the reference sample are n=1.457, and k=0.
When N=25, an experimental Fourier coefficient calculation module directly obtains the respective experimental Fourier coefficients α′_{2n}, β′_{2n }based on N relation formulas between light intensity data and experimental Fourier coefficients formed by the N sets of light intensity data.
When N>25, the experimental Fourier coefficient calculation module obtains the respective experimental Fourier coefficients α′_{2n}, β′_{2n }by the least square method according to N relation formulas between light intensity data and experimental Fourier coefficients formed by the N sets of light intensity data.
The light source may be a broad spectrum light source. The number of wavelengths of light which can be generated by the light source is N′, and the number of relation formulas between theoretical Fourier coefficients and operating parameters may be 24×N′.
The number of the reference samples which are isotropic and uniform may be m, and the number of relation formulas between theoretical Fourier coefficients and operating parameters may be 24×N′×m.
Referring to
obtaining respective θ_{2n }based on respective experimental Fourier coefficients α′_{2n}, β′_{2n}, where θ_{2n }is an intermediate parameter defined for the convenience of calculation;
obtaining an initial polarization angle C_{s1 }of a first phase compensator based on the respective θ_{2n};
obtaining an initial polarization angle C_{s2 }of a second phase compensator based on the respective θ_{2n};
obtaining a polarization angle P_{s }of a polarizer based on the respective θ_{2n};
obtaining a polarization angle A_{s }of an analyzer based on the respective θ_{2n};
where
θ_{2n}=tan^{−1}(β′_{2n}/α′_{2n}) 2.2
Using the method available in the literature (R. W. Collins and JoohyunKoh Dual rotatingcompensator multichannel ellipsometer: instrument design for realtime Mueller matrix spectroscopy of surfaces and films Vol. 16, No. 8/August 1999/J. Opt. Soc. Am. A 1997 to 2006), which corresponds to the following formulas 2.3 to 2.6, the initial polarization angles Cs1 and Cs2 of the compensators, as well as the polarization angles P_{s }and A_{s }of the polarizer and the analyzer can be calibrated.
On the basis of calibrated P_{s}, A_{s}, C_{s1}, and C_{s2}, in the case that the compensators are not disassembled from the experimental stage or equipment for separate measurement, the method we proposed can calibrate phase retardations of both compensators under different wavelengths in one experiment. The calibration process is accurate and simple.
The above embodiments describe the objects, the technical solutions and advantages of the present invention in detail. However, it should be appreciated that the foregoing is only specific embodiments of the present invention rather than limiting the invention. Therefore, any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.