CN104677835A - Full-Mueller matrix ellipsometer calibration method - Google Patents

Abstract

The present invention discloses a full-Mueller matrix ellipsometer calibration method, and belongs to the technical field of optical measurements. According to the method, by means of an isotropic and uniform reference sample, the calibrated initial polarization angle Cs1 of a first phase compensator, the calibrated initial polarization angle Cs2 of a second phase compensator, the calibrated polarization angle Ps of a polarizer, the calibrated polarization angle As of an analyzer, the calibrated phase retardation [delta]1 of the first phase compensator, and the calibrated phase retardation [delta]2 of the second phase compensator are adopted as initial values, and through the relational expression between the theoretical Fourier coefficient and the work parameter, a least square method is used to fit by adopting (d, [theta], Ps, As, Cs1, Cs2, [delta]1, [delta]2) as the variable so as to obtain the accurate values of all the full-Mueller matrix ellipsometer work parameters (d, [theta], Ps, As, Cs1, Cs2, [delta]1, [delta]2). According to the present invention, the measured data of the full-Mueller matrix ellipsometer at the same time is completely utilized, the introduced error is relatively small, and the parameter obtained from the calibration is accurate.

Description

A kind of calibration steps of full Muller matrix ellipsometer test

Technical field

The present invention relates to optical gauge technical field, particularly a kind of calibration steps of full Muller matrix ellipsometer test.

Background technology

Ellipsometer test (abbreviation ellipsometer) is a kind of optical gauge utilizing polarisation of light characteristic to obtain testing sample information.Its corresponding principle of work is by the testing sample surface by the incidence of polarizer light, by the change (amplitude ratio and phase differential) of polarization state before and after working sample surface incident light and reflected light, thus obtains the information of testing sample.The ellipsometer of rotatable polarizer and the single compensator of rotation obtains at most 12 parameters of sample in one-shot measurement; And along with the progress of integrated circuit technology and the complicated of device architecture, need the unknown quantity measured constantly to increase, such that traditional ellipsometer is measured for the film thickness measuring of ultrathin film, anisotropic materials optical constant, in the depolarization vibration analysis of surface characteristics, integrated circuit critical size and shape characteristic measurement etc. all show certain limitation.Full Muller matrix ellipsometric measurement instrument (broad sense ellipsometer) can obtain 4 × 4 rank Muller matrixes totally 16 parameters in one-shot measurement, and the information obtaining sample than traditional ellipsometer is abundanter.It breaches the technology limitation of traditional ellipsometer, can realize quick in wide spectral range, nondestructive accurate measurement film thickness, optical constant, critical size and three-dimensional appearance etc.

Elliptic polarization spectrometer guarantees that the key link of measurement accuracy and service equipment state is the calibration of instrument.Because ellipsometer test is along with use and the passing of time, can produce system deviation gradually, especially wave plate thickness is subject to the change of temperature and pressure and the impact of environment deliquescence; Therefore, it is possible to quick and precisely revise the calibration steps of ellipsometer, it is the gordian technique guaranteeing equipment validity and production efficiency.In existing traditional ellipsometer (as Fig. 1) alignment process, when the polarization direction of polarizer being calibrated as pointed out in Chinese patent 201210375771.X, being generally the position P1 of the fixing polarizer near 0 °, rotating analyzer A, measure light intensity I ₁, obtain the I under this state ₁(t) curve; Then change the angle of polarizer P, make polarizer P be in position P2, measure light intensity I ₂, obtain I ₂(t) curve; Repeat above-mentioned steps, measure light intensity respectively when polarizer P is in different angles, obtain I (t) curve when polarizer P is in different angles.Carry out Fourier's level time to above-mentioned I (t) curve respectively to launch, acquisition polarizer P is in Fourier coefficient during different angles; Build relevant to Fourier coefficient and there is when the polarization angle of polarizer P is 0 the function of minimum value; Pass through data analysis, find the position of the polarizer P making this function minimum, can think that the angle of this position polarizer P is that 0(specifically can see Spectroscopic Ellipsometry Principles and Applications, Hiroyuki Fujiwara, 2007).Then calculated the value of polarization direction As of analyzer reference position by Fourier coefficient then.In this calibration steps, not only need to rotate analyzer, and need electronic or hand rotation polarizer P, the angle of manual or electronic adjustment polarizer is also needed after the polarization direction of polarizer is determined, in this case, due to the instability of physical construction and/or the error of manual operation, the error between the angle that actual angle and needs all can be caused to set, this inaccuracy just easily causing reference sample to be measured.Therefore, when adopting in this way, the angle calibration system precision comparison of polarizer is low, and the measuring accuracy of ellipsometer test is restricted.In ellipsometer test, angle of light degree can be obtained by manual measurement method, but due to manual measurement limited precision, and some measurement needs to measure reference sample under different incident angles, to obtain the more information of reference sample, manual measurement easily regulates mistake or error in reading because of artificial, cause the erroneous results of data analysis, Chinese patent 201010137774.0 discloses a kind of device for automatically detecting incident angle in elliptical polarization measuring system, this device can realize automatically detecting incident angle, but this device needs installation site, many places sniffer in systems in which, this just makes this system structure of device complicated, and, the calibration of positional detecting device itself is also the process of a more complicated, therefore also limit the application of this automatic detection device in ellipsometer test.

And in existing full Muller matrix ellipsometric measurement instrument system calibration, as in US Patent No. 005956147 Muller ellipsometer, the light ball modulator (PEM) used is as phase compensator, when carrying out calibration phase-delay quantity to PEM, it builds in the ellipse inclined system of through type to measure, need PEM to take off above original equipment to carry out measuring its corresponding phase delay amount, again install on equipment after having calibrated, in mechanical handling process, can not ensure identical with the position of loading before, thus add systematic error, and again build through type measuring system, increase workload.At existing document (Harland G.Tompkins, Eugene A.Irene, Handbook of ellipsometry, 7.3.3.4Calibration7) in, Muller ellipsometer uses wave plate as phase compensator, its process, for build through type measuring table on experiment porch, measures the Fourier coefficient experimentally obtained, and utilizes with wherein calibrate, need two phase compensators to take off during calibration, then putting back to, increase systematic error.If do not take off when calibrating, the oblique incidence gage beam of sample both sides must be allowed to rotate, and to horizontal level, (ellipsometer of such as Woollam is as Fig. 3, during calibration, incident arm is rotated in place 3 from position 1, and outgoing arm is rotated in place 4 from position 2), add the complicacy of system.

In a word, current techniques must test the delay spectral line of phase compensator used before the fitting of equipment, and the ellipse inclined system of through type must be adopted to calibrate phase compensator phase-delay quantity.Requirement system has the design that adjustable incident angle is through type, and there is the process changing incident angle in a calibration process, these approaches increases the complexity of system, and calibration process is also more complicated.

Summary of the invention

In order to solve the problem, the present invention proposes and a kind ofly utilize isotropy and uniform reference sample intactly calibrates out the calibration steps of the full Muller matrix ellipsometer test of each systematic parameter in full Muller matrix ellipsometer test.

The calibration steps of full Muller matrix ellipsometer test provided by the invention comprises the following steps:

Build the experiment light path of full Muller matrix ellipsometer test, described experiment light path comprises light source, the polarizer, first phase compensator, analyzer, second phase compensator, spectrometer, sample stage and isotropy and uniform reference sample, described isotropy and uniform reference sample can be placed on described sample stage;

The rotating speed of described first and second phase compensators is set;

The frequency of described spectrometer measurement light intensity data is set, makes described spectrometer every T/N time measurement light intensity data, gather altogether N group light intensity data, wherein, N >=25, T is measuring period;

Gather the light intensity data that described spectrometer measurement arrives;

According to the light intensity data that described spectrometer data collecting module collected arrives, the N number of light intensity data formed by described N light intensity data-experiment Fourier coefficient relational expression, obtains each experiment Fourier coefficient α ' _2n, β ' _2n;

According to described each experiment Fourier coefficient, the initial polarization angle C of first phase compensator that calibrates _s1, second phase compensator initial polarization angle C _s2, obtain each theoretical Fourier coefficient α _2n, β _2n;

With described reference sample isotropy and evenly for foundation, described first phase compensator phase-delay quantity computing module is according to described each theoretical Fourier coefficient, the polarization angle P of the polarizer that calibrates _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of first phase compensator ₁;

With described reference sample isotropy and evenly for foundation, described second phase compensator phase-delay quantity computing module is according to described each theoretical Fourier coefficient, the polarization angle P of the polarizer that calibrates _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of second phase compensator ₂;

To calibrate the initial polarization angle C of the first phase compensator obtained _s1, second phase compensator initial polarization angle C _s2, the polarizer polarization angle P _s, analyzer polarization angle A _s, first phase compensator phase-delay quantity δ ₁with the phase-delay quantity δ of second phase compensator ₂as initial value, by the relational expression between described theoretical Fourier coefficient and running parameter, with (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) be variable, use least square fitting to obtain described full Muller matrix ellipsometer test whole running parameter (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) exact value, wherein, d is the thickness of described reference sample, and θ is the angle that light incides described reference sample.

The calibration steps of full Muller matrix ellipsometer test provided by the invention utilizes isotropy and uniform reference sample, according to light intensity data-experiment Fourier coefficient relational expression and the polarization angle P of the polarizer that calibrated _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of first phase compensator ₁with the phase-delay quantity δ of second phase compensator ₂, then will calibrate the initial polarization angle C of the first phase compensator obtained _s1, second phase compensator initial polarization angle C _s2, the polarizer polarization angle P _s, analyzer polarization angle A _s, first phase compensator phase-delay quantity δ ₁with the phase-delay quantity δ of second phase compensator ₂as initial value, by the relational expression between theoretical Fourier coefficient and running parameter, with (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) be variable, use least square fitting to obtain described full Muller matrix ellipsometer test whole running parameter (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) exact value.This calibration steps can make full use of homogeneous measurement data, the error introduced is relatively little, and the parameter that calibration obtains is more accurate, and then, apply method provided by the invention to when measuring testing sample after full Muller matrix ellipsometer test, measurement result is more accurate again.

Accompanying drawing explanation

The experiment index path of the full Muller matrix ellipsometer test built in the calibration steps of the full Muller matrix ellipsometer test that Fig. 1 provides for the embodiment of the present invention;

The logic diagram of the calibration steps of the full Muller matrix ellipsometer test that Fig. 2 provides for the embodiment of the present invention one;

The logic diagram of the calibration steps of the full Muller matrix ellipsometer test that Fig. 3 provides for the embodiment of the present invention two.

Embodiment

In order to understand the present invention in depth, below in conjunction with drawings and the specific embodiments, the present invention is described in detail.

Embodiment one

See accompanying drawing 1, the calibration steps of full Muller matrix ellipsometer test provided by the invention comprises the following steps:

1st step: the experiment light path of building full Muller matrix ellipsometer test comprises light source 1, annular mirror 2, pin hole 3, first off-axis paraboloidal mirror 4, the polarizer 5, first phase compensator 6, first plane mirror 7, sample stage 8, second off-axis paraboloidal mirror 9, the 3rd off-axis paraboloidal mirror 10, second plane mirror 11, second phase compensator 12, analyzer 13, the 4th off-axis paraboloidal mirror 14, spectrometer 15 and terminal 16, sample stage 8 carries isotropy and uniform reference sample; This can the two-phonon process of experiment light path of self-alignment full Muller matrix ellipsometer test be

S _out=M _AR(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 _pR(P)S _in

That is:

$1\begin{array}{c}\left[\begin{array}{c}{S}_A\\ S_B\\ 0\\ 0\end{array}\right]=\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos 2A& \sin 2A& 0\\ 0& -\sin 2A& \cos 2A& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos C_2^{\′}& -\sin C_2^{\′}& 0\\ 0& \sin C_2^{\′}& \cos {2C}_2^{\′}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos {\mathrm{\δ}}_2& \sin {\mathrm{\δ}}_2\\ 0& 0& -\sin {\mathrm{\δ}}_2& \cos {\mathrm{\δ}}_2\end{array}\right]\\ \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos C_2^{\′}& \sin C_2^{\′}& 0\\ 0& -\sin C_2^{\′}& \cos 2C_2^{\′}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}{M}_{11}& M_{12}& M_{13}& M_{14}\\ M_{21}& M_{22}& M_{23}& M_{24}\\ M_{31}& M_{32}& M_{33}& M_{34}\\ M_{41}& M_{42}& M_{43}& M_{44}\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos C_1^{\′}& -\sin C_1^{\′}& 0\\ 0& \sin C_1^{\′}& \cos 2C_1^{\′}& 0\\ 0& 0& 0& 0\end{array}\right]\\ \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos {\mathrm{\δ}}_1& \sin {\mathrm{\δ}}_1\\ 0& 0& -\sin {\mathrm{\δ}}_1& \cos {\mathrm{\δ}}_1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos C_1^{\′}& \sin C_1^{\′}& 0\\ 0& -\sin C_1^{\′}& \cos 2C_1^{\′}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos 2P& -\sin 2P& 0\\ 0& \sin 2P& \cos 2P& 0\\ 0& 0& 0& 1\end{array}\right]\\ \left[\begin{array}{cccc}1& 1& 0& 0\\ 1& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos 2P& \sin 2P& 0\\ 0& -\sin 2P& \cos 2P& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right]\end{array}---2.0$

2nd step: the rotating speed of the first and second phase compensators is set;

3rd step: set the frequency of spectrometer measurement light intensity data, makes spectrometer every T/N time measurement light intensity data, gathers altogether N group light intensity data, wherein, N >=25, T is measuring period;

4th step: gather the light intensity data that spectrometer measurement arrives;

5th step: the light intensity data arrived according to spectrometer data collecting module collected, the N number of light intensity data-experiment Fourier coefficient relational expression formed by N light intensity data, obtains each experiment Fourier coefficient α ' _2n, β ' _2n;

6th step: according to each experiment Fourier coefficient, the initial polarization angle C of first phase compensator that calibrates _s1, second phase compensator initial polarization angle C _s2, obtain each theoretical Fourier coefficient α _2n, β _2n;

7th step: with reference sample isotropy and be evenly foundation, first phase compensator phase-delay quantity computing module is according to each theoretical Fourier coefficient, the polarization angle P of the polarizer that calibrates _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of first phase compensator ₁;

With reference sample isotropy and be evenly foundation, second phase compensator phase-delay quantity computing module is according to each theoretical Fourier coefficient, the polarization angle P of the polarizer that calibrates _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of second phase compensator ₂;

8th step: will calibrate the initial polarization angle C of the first phase compensator obtained _s1, second phase compensator initial polarization angle C _s2, the polarizer polarization angle P _s, analyzer polarization angle A _s, first phase compensator phase-delay quantity δ ₁with the phase-delay quantity δ of second phase compensator ₂as initial value, by the relational expression between theoretical Fourier coefficient and running parameter, with (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) be variable, use least square fitting to obtain full Muller matrix ellipsometer test whole running parameter (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) exact value, wherein, d is the thickness of reference sample, and θ is the angle that light incides reference sample.

Isotropy and the uniform corresponding Mueller matrix of reference sample are:

$M_s=\left[\begin{array}{cccc}{M}_{11}& M_{12}& 0& 0\\ M_{21}& M_{22}& 0& 0\\ 0& 0& M_{33}& M_{34}\\ 0& 0& M_{43}& M_{44}\end{array}\right]$

With N=36, the rotating speed of first phase compensator 6: rotating speed=5 of second phase compensator 12: 3 is example, now, first phase compensator 6 and second phase compensator 12 are in rotation status respectively, the rotating speed of first phase compensator 6: rotating speed=5 of second phase compensator 12: 3, now, C ' ₁=5 (C-C _s1), C ' ₂=3 (C-C _s2), the time of first phase compensator 6 turn of 5 circle or second phase compensator 12 turn of 3 circle is one-period T,

Wherein,

The angle of-Cs1, t=0 moment first phase compensator 5 fast axis,

The angle of-Cs2, t=0 moment second phase compensator 12 fast axis,

C=ω t, the angle that the first compensator 5 and the second compensator 12 rotate under basic physical frequencies ω.

$\begin{array}{c}{S}_j={\∫}_{\frac{(j-1)T}{36}}^{\frac{\mathrm{jT}}{36}}{I}_0^{\′}[1+\underset{n=1}{\overset{16}{\mathrm{\Σ}}}({\mathrm{\α}}_{2n}^{\′}\cos 2\mathrm{n\ωt}+{\mathrm{\β}}_{2n}^{\′}\sin 2\mathrm{n\ωt})]\mathrm{dt}\\ =\frac{\mathrm{\π}{I}_0^{\′}}{36\mathrm{\ω}}+\underset{n=1}{\overset{16}{\mathrm{\Σ}}}\frac{I_0^{\′}}{\mathrm{n\ω}}\left(\sin \frac{\mathrm{n\π}}{36}\right)[{\mathrm{\α}}_{2n}^{\′}\cos (2j-1)\mathrm{n\π}+{\mathrm{\β}}_{2n}^{\′}\sin \frac{(2j-1)\mathrm{n\π}}{36}]\\ (j=\mathrm{1,2}...36)\end{array}...2.1$

Wherein ω=π/T.Utilize S1, S2, S3 of collecting ... S36, therefore, by above formula can obtain comprising 25 unknown numbers 36 equations (n=9,12,14,15 time, experiment Fourier coefficient α ' _2n=0 and β ' _2n=0), by nonlinear least square method, experiment Fourier coefficient α ' can be solved _2nwith β ' _2n, totally 24.

Theoretical Fourier coefficient α _2nand β _2nthe Fourier coefficient α ' obtained with experiment _2nwith β ' _2ntransformational relation (formula 2.7 and 2.8)

α _2n=α′ _2ncosφ _2n+β′ _2nsinφ _2n…2.7

β _2n=-α′ _2nsinφ _2n+β′ _2ncosφ _2n…2.8

Wherein:

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

Therefore, Fourier coefficient α in theory can be obtained by formula (formula 2.7 and 2.8) _2nand β _2n.

Due to isotropy and uniform sample, M ₁₃=M ₃₁=M ₁₄=M ₄₁=M ₂₃=M ₃₂=M ₂₄=M ₄₂=0, then according to the theoretical principle of Mueller ellipsometer test, theoretical Fourier coefficient α can be known ₂, β ₂, α ₁₀, β ₁₀, α ₆, β ₆, α ₁₄, β ₁₄, α ₂₂, β ₂₂, α ₂₆, β ₂₆theoretical expression:

${\mathrm{\α}}_6=M_{43}{\cos }^2\frac{{\mathrm{\δ}}_1}{2}\sin {\mathrm{\δ}}_2\sin 2P_s\sin 2A_s...2.9$

${\mathrm{\β}}_6=-M_{43}{\cos }^2\frac{{\mathrm{\δ}}_1}{2}\sin {\mathrm{\δ}}_2\sin 2P_s\cos 2A_s...2.10$

${\mathrm{\α}}_{14}=-0.5M_{43}{\sin }^2\frac{{\mathrm{\δ}}_1}{2}\sin {\mathrm{\δ}}_2\cos 2(P_s-A_s)...2.11$

${\mathrm{\β}}_{14}=-0.5M_{43}{\sin }^2\frac{{\mathrm{\δ}}_1}{2}\sin {\mathrm{\δ}}_2\sin 2(P_s-A_s)...2.12$

${\mathrm{\α}}_{26}=0.5M_{43}{\sin }^2\frac{{\mathrm{\δ}}_1}{2}\sin {\mathrm{\δ}}_2\cos 2(P_s+A_s)...2.13$

${\mathrm{\β}}_{26}=0.5M_{43}{\sin }^2\frac{{\mathrm{\δ}}_1}{2}\sin {\mathrm{\δ}}_2\cos 2(P_s+A_s)...2.14$

Obtained by formula 2.10 and 2.12

$\frac{{\mathrm{\β}}_{14}}{{\mathrm{\β}}_6}=\frac{0.5\sin 2(P_s-A_s)}{\sin 2P_s\cos 2A_s}\×{\tan }^2\frac{{\mathrm{\δ}}_1}{2}$

${\mathrm{\δ}}_1={\cos }^{-1}\left[\frac{1-\frac{2{\mathrm{\β}}_{14}\sin 2P_s\cos 2A_s}{{\mathrm{\β}}_6\sin 2(P_s+A_s)}}{1+\frac{2{\mathrm{\β}}_{14}\sin 2P_s\cos 2A_s}{{\mathrm{\β}}_6\sin 2(P_s+A_s)}}\right]...2.15$

Wherein and and (n is integer) (must ensure that Fourier coefficient is non-vanishing)

In like manner by formula 2.9 and 2.12, formula 2.9 and 2.11, formula 2.10 and 2.11, formula 2.9 and 2.13,2.9 and 2.14, formula 2.10 and 2.13, formula 2.10 and 2.14 also can calculate the phase-delay quantity δ of compensator ₁.

Calibrate the phase-delay quantity δ of second compensator below ₂.

${\mathrm{\α}}_2=0.5M_{34}\sin {\mathrm{\δ}}_1{\sin }^2\frac{{\mathrm{\δ}}_2}{2}\cos 2(P_s-A_s)...2.16$

${\mathrm{\β}}_2=-0.5M_{34}\sin {\mathrm{\δ}}_1{\sin }^2\frac{{\mathrm{\δ}}_2}{2}\sin 2(P_s-A_s)...2.17$

${\mathrm{\α}}_{10}=-M_{34}\sin {\mathrm{\δ}}_1{\cos }^2\frac{{\mathrm{\δ}}_2}{2}\sin 2P_s\sin 2A_s...2.18$

${\mathrm{\β}}_{10}=M_{34}\sin {\mathrm{\δ}}_1{\cos }^2\frac{{\mathrm{\δ}}_2}{2}\sin 2P_s\cos 2A_s...2.19$

${\mathrm{\α}}_{22}=-0.5M_{34}\sin {\mathrm{\δ}}_1{\sin }^2\frac{{\mathrm{\δ}}_2}{2}\cos 2(P_s+A_s)...2.20$

${\mathrm{\β}}_{22}=-0.5M_{34}\sin {\mathrm{\δ}}_1{\sin }^2\frac{{\mathrm{\δ}}_2}{2}\sin 2(P_s+A_s)...2.21$

Obtained by formula 2.16 and 2.18:

$\frac{{\mathrm{\α}}_2}{{\mathrm{\α}}_{10}}=-\frac{0.5\cos 2(P_s-A_s)}{\sin 2P_s\sin 2A_s}\×{\tan }^2\frac{{\mathrm{\δ}}_2}{2}$

${\mathrm{\δ}}_2={\cos }^{-1}\left[\frac{1+\frac{2{\mathrm{\α}}_2\sin 2P_s\sin 2A_s}{{\mathrm{\α}}_{10}\cos 2(P_s-A_s)}}{1-\frac{2{\mathrm{\α}}_2\sin 2P_s\sin 2A_s}{{\mathrm{\α}}_{10}\cos 2(P_s-A_s)}}\right]...2.22$

Wherein and and (n is integer) (must ensure that Fourier coefficient is non-vanishing)

In like manner by formula 2.16 and 2.19, formula 2.17 and 2.18, formula 2.17 and 2.19, formula 2.18 and 2.20,2.18 and 2.21, formula 2.19 and 2.20, formula 2.19 and 2.21 also can calibrate out the phase-delay quantity δ of compensator ₂.

By formula 2.7 and 2.8, the conversion of testing Fourier coefficient and theoretical Fourier coefficient can be realized, and the position angle P of the Muller element of theoretical Fourier coefficient and sample, the polarizer _s, analyzer position angle A _s, two phase compensators position angle C _s1and C _s2and phase-delay quantity δ ₁and δ ₂all there is relation (with reference to Harland G.Tompkins, Eugene A.Irene, Handbook of ellipsometry, 7.3.3Dual Rotating Compensator7).And optical constant n, k, the thickness d of the Muller element of sample and specimen material, light beam incides sample angle θ and wavelength X is relevant.Therefore Fourier coefficient α ' is tested _2nwith β ' _2nwith (n, k, d, θ, λ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) relevant.For under a wavelength, the reference sample of known optical constant n, k, measures the α ' obtained in experiment _2nwith β ' _2n, totally 24,24 corresponding equations can be obtained, only with (d, θ, λ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) relevant.By calibrating the P obtained above _s, A _s, C _s1, C _s2, δ ₁, δ ₂as initial value, and to measure corresponding wavelength in experiment be known, experimentally 24 equations obtaining of Fourier coefficient, with (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) relevant, utilize least square fitting to go out all Muller ellipsometer running parameter (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂).Wherein, reference sample can be take silicon as the silica membrane sample of substrate, and its optical constant n, k can from Literature Consults, and for the wavelength of 632.8nm, its optical constant is n=1.457, k=0.

Work as N=25, experiment Fourier counts coefficient and calculates N number of light intensity data-experiment Fourier coefficient relational expression that module formed according to N light intensity data, directly obtains each experiment Fourier coefficient α ' _2n, β ' _2n.

As N > 25, N light intensity data-experiment Fourier coefficient relational expression that experiment Fourier coefficient computing module is formed according to N light intensity data, obtains each experiment Fourier coefficient α ' by least square method _2n, β ' _2n.

Light source can be broad spectrum light source, the number of the wavelength of the light that light source can produce is N ', the corresponding 24 groups of experiment Fourier coefficients of each wavelength, therefore, when calculating the running parameter of Muller matrix ellipsometer, the number participating in the relational expression between the theoretical Fourier coefficient of least square fitting and running parameter is 24 × N '.

In like manner, it is individual that isotropy and uniform reference sample can be m, and the number of the relational expression between theoretical Fourier coefficient and running parameter is 24 × N ' × m.

Embodiment two

See accompanying drawing 3, what the embodiment of the present invention two provided can the difference of self-alignment full Muller matrix ellipsometer test calibration steps being of providing of self-alignment full Muller matrix ellipsometer test calibration steps and the embodiment of the present invention one, the embodiment of the present invention two provide can the method for self-calibrating of self-alignment full Muller matrix ellipsometer test further comprising the steps of:

According to each experiment Fourier coefficient α ' _2n, β ' _2nobtain each θ _2n, herein, θ _2nit is the intermediate parameters defined for ease of computing;

According to each θ _2nobtain the initial polarization angle C of first phase compensator _s1;

According to each θ _2nobtain the initial polarization angle C of second phase compensator _s2;

According to each θ _2nobtain the polarization angle P of the polarizer _s;

According to each θ _2nobtain the polarization angle A of analyzer _s.

Wherein,

θ _2n=tan ^-1(β′ _2n/α′ _2n)···2.2

Utilize (the R.W.Collins and JoohyunKoh Dual rotating-compensator multichannel ellipsometer:instrument design for real-time Mueller matrix spectroscopy of surfaces andfilms Vol.16 of existing method in document, No.8/August1999/J.Opt.Soc.Am.A1997 ~ 2006), corresponding formula 2.3 ~ 2.6, can calibrate out the initial polarization angle C of compensator _s1and C _s2, and the polarization angle P of the polarizer and analyzer _sand A _s.

$C_{s1}=\frac{{\mathrm{\θ}}_{14}-{\mathrm{\θ}}_4}{10}...2.3$

$C_{s2}=\frac{{\mathrm{\θ}}_2+{\mathrm{\θ}}_4}{6}...2.4$

$P_s=\left(\frac{{\mathrm{\θ}}_4+{\mathrm{\θ}}_6}{4}\right)-5C_{s1}...2.5$

$\mathrm{As}=\left(\frac{{\mathrm{\θ}}_{16}-{\mathrm{\θ}}_4}{4}\right)-3C_{s2}...2.6$

Calibrating P _s, A _s, C _s1and C _s2basis on, when not compensator from experiment table or equipment remove carry out independent measurement, we propose a kind of method, once can test and all calibrate out two compensators phase-delay quantity at different wavelengths, calibration process accurately, simple.

Above embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; these are only the specific embodiment of the present invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. a calibration steps for full Muller matrix ellipsometer test, is characterized in that, comprise the following steps:

Build the experiment light path of full Muller matrix ellipsometer test, described experiment light path light source, the polarizer, first phase compensator, analyzer, second phase compensator, spectrometer, sample stage and isotropy and uniform reference sample, described isotropy and uniform reference sample can be placed on described sample stage;

The rotating speed of described first and second phase compensators is set;

The frequency of described spectrometer measurement light intensity data is set, makes described spectrometer every T/N time measurement light intensity data, gather altogether N group light intensity data, wherein, N >=25, T is measuring period;

Gather the light intensity data that described spectrometer measurement arrives;

According to the light intensity data that described spectrometer data collecting module collected arrives, the N number of light intensity data formed by described N light intensity data-experiment Fourier coefficient relational expression, obtains each experiment Fourier coefficient α ' _2n, β ' _2n;

According to described each experiment Fourier coefficient, the initial polarization angle C of first phase compensator that calibrates _s1, second phase compensator initial polarization angle C _s2, obtain each theoretical Fourier coefficient α _2n, β _2n;

With described reference sample isotropy and evenly for foundation, described first phase compensator phase-delay quantity computing module is according to described each theoretical Fourier coefficient, the polarization angle P of the polarizer that calibrates _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of first phase compensator ₁;

With described reference sample isotropy and evenly for foundation, described second phase compensator phase-delay quantity computing module is according to described each theoretical Fourier coefficient, the polarization angle P of the polarizer that calibrates _s, analyzer polarization angle A _s, obtain the phase-delay quantity δ of second phase compensator ₂;

To calibrate the initial polarization angle C of the first phase compensator obtained _s1, second phase compensator initial polarization angle C _s2, the polarizer polarization angle P _s, analyzer polarization angle A _s, first phase compensator phase-delay quantity δ ₁with the phase-delay quantity δ of second phase compensator ₂as initial value, by the relational expression between described theoretical Fourier coefficient and running parameter, with (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) be variable, use least square fitting to obtain described full Muller matrix ellipsometer test whole running parameter (d, θ, P _s, A _s, C _s1, C _s2, δ ₁, δ ₂) exact value, wherein, d is the thickness of described reference sample, and θ is the angle that light incides described reference sample.

2. method according to claim 1, is characterized in that, further comprising the steps of:

According to described each experiment Fourier coefficient α ' _2n, β ' _2nobtain each θ _2n=tan ^-1(β ' _2n/ α ' _2n);

According to described each θ _2nobtain the initial polarization angle C of first phase compensator _s1;

According to described each θ _2nobtain the initial polarization angle C of second phase compensator _s2;

Described each θ _2nobtain the polarization angle P of the polarizer _s;

According to described each θ _2nobtain the polarization angle A of analyzer _s.

3. method according to claim 1, is characterized in that, described N=25, N number of light intensity data-experiment Fourier coefficient relational expression that described experiment Fourier coefficient computing module is formed according to described N light intensity data, directly obtains each experiment Fourier coefficient α ' _2n, β ' _2n.

4. method according to claim 1, it is characterized in that, described N > 25, N light intensity data-experiment Fourier coefficient relational expression that described experiment Fourier coefficient computing module is formed according to described N light intensity data, obtains each experiment Fourier coefficient α ' by least square method _2n, β ' _2n.

5. full Muller matrix ellipsometer test according to claim 1, it is characterized in that, described light source is broad spectrum light source, and the number of the wavelength of the light that described light source can produce is N ', and the number of the relational expression between described theoretical Fourier coefficient and running parameter is 24 × N '.

6. full Muller matrix ellipsometer test according to claim 5, is characterized in that, described isotropy and uniform reference sample is m, and the number of the relational expression between described theoretical Fourier coefficient and running parameter is 24 × N ' × m.

7. full Muller matrix ellipsometer test according to claim 1, is characterized in that, described reference sample is the silica membrane of silicon substrate.