CN109470154A - Value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers - Google Patents

Value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers Download PDF

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CN109470154A
CN109470154A CN201811602778.4A CN201811602778A CN109470154A CN 109470154 A CN109470154 A CN 109470154A CN 201811602778 A CN201811602778 A CN 201811602778A CN 109470154 A CN109470154 A CN 109470154A
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film thickness
zero point
spectrum
value
exemplar
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CN109470154B (en
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郭春付
夏小荣
李伟奇
张传维
李竹
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Wuhan Eoptics Technology Co Ltd
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Wuhan Eoptics Technology Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/02Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G01B11/06Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
    • G01B11/0616Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating
    • G01B11/0641Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating with measurement of polarization

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  • General Physics & Mathematics (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

The invention discloses value measurement methods at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers, including setting detection parameters, and the stokes parameter of exemplar film is obtained using ellipsometer measurement;S spectrum is decomposited to come from stokes parameter, and noise reduction process is carried out to it;It filters out the zero point in S spectrum and obtains corresponding wavelength, exemplar film thickness initial value is calculated according to the zero point of S spectrum and its corresponding wavelength.Technical solution of the present invention is detected to obtain spectrum zero point by the stokes parameter to ellipsometry for the situation of the measurement inaccuracy of film initial value in the prior art, the accurate estimation of film thickness initial value is realized using the zero point.

Description

Value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers
Technical field
The invention belongs to precision optics measuring instrument data analysis fields, and in particular to a kind of suitable for spectroscopic ellipsometers The first value measurement method of film thickness.
Background technique
Ellipsometer is a kind of for measuring the optical device of film thickness and optical constant.Usually, ellipsometer is whole A measurement process is divided into two parts:
1) oval thickness spectrometry
Its measuring principle is to generate polarised light by polarization state generator using unpolarized light source, when light is incident on sample Behind surface, reflected light occurs polarization state and changes, and is composed by the oval thickness that analyzer detects sample, it can with amplitude ratio angle Ψ and Phase angle Δ indicates, to obtain the data information of respective sample.
Certainly, oval thickness spectrum can also be indicated by Stokes parameter NCS:
N=cos2 Ψ
C=sin2 Ψ cos Δ
S=sin2 Ψ sin Δ
Since it is a kind of technology measured indirectly, the spectroscopic data information generally measured can not be converted directly into sample Film thickness and optical constant, therefore often need to establish the analysis of suitable models fitting.
Spectroscopic ellipsometers are broadly divided into rotation and are polarized type ellipsometer (P according to the difference of modulation systemRSCA), Dan Xuan Turn compensation type ellipsometer (PSCRA), dual rotary compensates type ellipsometer (PCRSCR) and phase modulation-type ellipsometer (PSMA) A. Measuring instrument range used in the present invention includes above-mentioned instrument type.
2) data are analyzed
Firstly the need of the oval thickness spectrum obtained using ellipsometer measurement, then according to known exemplar information, changed by mathematics Sample real information is solved for method, is finally reached measurement purpose.
The iterative algorithm that data analysis component uses is usually Trust Region Algorithm, is needed from given initial solution, according to Secondary iteration is continuously improved to seek optimal solution.Its rudimentary algorithm thought is to give an initial point x0And initial trusted zones Radius Δ0, start iteration, provide a trusted zones (current iteration point x in each iterationkA small neighbourhood), then solve A subproblem in the trusted zones obtains souning out step-length (trial step) sk(solution of Trust-region subproblem) recycles corresponding Evaluation function come judge the exploration step-length it is whether reasonable and determine next iteration trusted zones.Work as skRationally, then: xk+1=xk +sk, it is x if unreasonablek+1=xk.The trusted zones next time of iteration depend on souning out the quality of step-length, in short, if souning out Step-length is preferable, and in next iteration, trusted zones expand or remain unchanged, and otherwise reduces trusted zones.
Usually, the calculated result of iterative algorithm is highly dependent on the initial value of given film thickness, and otherwise have can for pole Locally optimal solution can be fallen into, if given film thickness initial value value inaccuracy, the final result of iterative algorithm are very possible It is locally optimal solution, rather than globally optimal solution.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of suitable for the thin of spectroscopic ellipsometers The first value measurement method of film thickness, at least can partially solve the above problems.Technical solution of the present invention is for film in the prior art The situation of initial value measurement inaccuracy, is detected to obtain spectrum zero point by the stokes parameter to ellipsometry, is utilized The accurate estimation of zero point realization film thickness initial value.
To achieve the above object, according to one aspect of the present invention, a kind of film suitable for spectroscopic ellipsometers is provided The first value measurement method of thickness, which is characterized in that including,
Detection parameters are arranged in S1, and the stokes parameter of exemplar film is obtained using ellipsometer measurement;
S2 decomposites S spectrum to come from stokes parameter, and carries out noise reduction process to it;
S3 filters out the zero point in S spectrum and obtains corresponding wavelength, according to the zero point and its corresponding wavelength of S spectrum Calculate exemplar film thickness initial value.
One as technical solution of the present invention is preferred, includes in step S3,
S31 filters out the zero point in S spectrum, obtain zero point number and its corresponding wavelength;
If the number of S32 zero point is 0, the lambda1-wavelength in detection parameters is changed, S1 is entered step, otherwise enters Step S33;
If the number of S33 zero point is 1, exemplar film thickness match value corresponding to the zero point is calculated, obtains sample Part film thickness initial value, otherwise enters step S34;
If the number of S34 zero point is greater than 1, exemplar film thickness match value corresponding to each zero point is calculated, is joined The film thickness match value of vertical adjacent zeros point, obtains exemplar film thickness initial value.
One as technical solution of the present invention is preferred, the zero point in S spectrum is defined as:
S(k)*S(k+1)≤0&&S(k+1)*S(k+2)≠0;
Then λ (j)=(λ (k)+λ (k+1))/2;
Wherein, S is S spectrum in Stokes vector, and k is S spectrum zero point index number, and λ is wavelength.
One as technical solution of the present invention is preferred, and exemplar film thickness match value calculation formula is preferably as follows:
Wherein, d is film thickness, and k is S spectrum zero point index number, and λ is wavelength, N2For the refractive index of film,For Incidence angle.
Preferably as one of technical solution of the present invention, step S34 includes that calculate exemplar corresponding to each zero point thin Film thickness match value,
Wherein, d is film thickness, and k is S spectrum zero point index number, and λ is wavelength, N2For the refractive index of film,For Incidence angle;
The film thickness match value of simultaneous any two adjacent zeros point obtains the mean value of any two adjacent zeros point,
Wherein, d (i) is i-th of film thickness, niFor the refractive index under the corresponding wavelength of i-th of index, i is S spectrum zero It is worth the index of point, A is incidence angle;
Exemplar film thickness initial value is obtained according to mean value,
Wherein, d is average film thickness, and m is S spectrum zero point total number, the film thickness that d (i) is i-th point.
One as technical solution of the present invention is preferred, and detection parameters include spectral region and/or angle of incidence of light.
One as technical solution of the present invention is preferred, the preferred 380nm~1000nm of spectral region in detection parameters.
One as technical solution of the present invention is preferred, preferably 50 °~75 ° of the angle of incidence of light in detection parameters.
One as technical solution of the present invention is preferred, and noise reduction process preferably passes through Fourier filtering algorithm and/or center Filtering algorithm is completed.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, have below beneficial to effect Fruit:
1) technical solution of the present invention, in ellipsometer data analysis and solution algorithm, the initial value of film thickness ties measurement Fruit has the problem of larger impact, obtains corresponding S spectrum by carrying out optical measurement using ellipsometer, spectrally using S Zero point, which calculates, obtains immediate film thickness initial value, to reduce the mistake of measurement caused by the inaccuracy of film thickness initial value Difference.
2) technical solution of the present invention passes through change since the used film thickness order of magnitude is up to nanometer scale Wavelength change can be effectively utilized to find the zero point value of the S spectrum corresponding to it, while this hair in the wave-length coverage of incident light Quantitative classification is carried out to zero point value in bright technical solution, different zero point values correspond to different film calculations, knot obtained Fruit is more accurate.
Detailed description of the invention
Fig. 1 is the flow chart that film thickness initial value measures in the embodiment of technical solution of the present invention;
Fig. 2 is to be obtained in the embodiment of technical solution of the present invention using ellipsometer measurement silicon base silica transparent membrane NCS figure;
Fig. 3 is in the embodiment of technical solution of the present invention using gained sample S spectrogram after center filtering algorithm noise reduction.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below Not constituting a conflict with each other can be combined with each other.The present invention is described in more detail With reference to embodiment.
Single-layer and transparent film is thick before providing a kind of spectroscopic ellipsometers numerical analysis in the embodiment of technical solution of the present invention The initial value carculation method of degree, this method may be implemented at the beginning of being no longer dependent on given film thickness in ellipsometer data analysis process Value, to achieve the effect that quickly accurate fitting algorithm.
To single thin film, can be obtained according to Fresnel law, P light that incident light obtains after Orthogonal Decomposition and S light it is anti- It is as follows to penetrate coefficient expressions:
Wherein, the calculation formula of phase-delay quantity are as follows:
Therefore, ellipsometric parameter may be expressed as: in the present embodiment
Specifically, monolayer film thickness mainly influences the phase angle Δ in ellipsometric parameter, therefore considers to pass through phase Poor Δ carries out the calculating of film thickness initial value.Applicable object of the present invention is single-layer and transparent film, therefore sample thin film refraction can be obtained Rate N2=n2-ik2(k herein2For the extinction coefficient of material, be different from it is following shown in k in natural number k)2=0, thus only use Consider n2.By formula (3) it is found that when the imaginary part of Rp and Rs is 0, Δ=0 or π.At this point, by formula (1) it is found that 2 β=0, π, 2 π ..., that is:
I.e.
S=sin (2 Ψ) sin (Δ)=0 in Stokes parameter NCS.Also, since amplitude ratio angle tan ψ is two polarizations The ratio of the amplitude of light component, therefore 0 or pi/2 can not be equal to, so S=0 can be equivalent to Δ=0 or π.In summary: when When monofilm thickness d and wavelength X meet formula (5), stokes parameter S=0.
That is, the method for measuring monofilm thickness initial value in the present embodiment, is based on " when monofilm thickness d and wavelength X When meeting formula (5), this principle of stokes parameter S=0 ", below accordingly to the monofilm thickness initial value in the present embodiment Calculation method is further detailed.
As shown in Figure 1, the single-layer and transparent film thickness initial value carculation method in the present embodiment, step include:
Step 1: measurement exemplar, obtains the Stokes parameter (i.e. oval thickness spectrum or S spectrum) of exemplar.
The present embodiment, it is preferred to use silicon base silica membrane, thickness value preferably in 500nm or so, measure incidence angle It is preferred that 50~75 °, preferably 65 ° in the present embodiment.Further, in this embodiment used spectral region 380nm~ 1000nm (preferably includes black light wave band, visible light wave range, near infrared light wave band), and above-mentioned parameter can be according to measurement demand It is adjusted, above-mentioned design parameter is not intended as the concrete restriction to technical solution of the present invention.Wherein, exemplar Stokes parameter is obtained Process be the prior art to those skilled in the art, repeated in the present embodiment not to this.
Step 2: the S spectrum to given wave band is analyzed, filtering algorithm noise reduction is used.
During apparatus measures, have an impact inevitable that noise measures resulting S spectrum to sample, therefore It needs to carry out noise reduction process to the S spectrum that measurement obtains using filtering algorithm.Particularly, the ellipse inclined of exemplar is being obtained by emulation It when spectrum, while being also required to that the influence of noise is added in sample emulation, then it is carried out at noise reduction by filtering algorithm Reason.Spectral noise processing is particularly significant, but it must be ensured that big translation will not occur for the position of wavelength points in noise reduction, in order to avoid Influence the precision of single-layer and transparent film thickness initial value.
In fact, the processing of spectral noise is very important in the algorithm, it is necessary to assure the position of wavelength points in noise reduction Big translation will not be occurred by setting, in order to avoid influence the precision of single-layer and transparent film thickness initial value.Specifically, it can choose Fourier Filtering algorithm or center filtering algorithm carry out noise reduction filtering processing to it, in the present embodiment preferably by center filtering algorithm into Row noise reduction process chooses the point near each S value, the average value of these points is calculated, to achieve the purpose that noise reduction, this implementation Calculation formula is preferably as follows in example:
As shown in Fig. 2, for using sample S spectrum obtained after the filtering algorithm noise reduction of center.
Step 3: finding out the wavelength points that all S are equal to 0 in S spectrum, the number of 0 value point is judged, at the beginning of calculating film thickness Value.
The definition of 0 value point of S spectrum is (product of and+1 point of kth represents two value symbols on the contrary, institute less than 0 at k-th point Necessarily to there is 0 value point between k and k+1.):
S(k)*S(k+1)≤0&&S(k+1)≠0 (7)
λ (j)=/ 2 (8) (λ (k)+λ (k+1))
S is S spectrum in Stokes vector, and k is S spectrum zero point index number, and λ is wavelength.
Specifically, it is first determined the number of the 0 value point of wavelength of S spectrum adjusts incidence if zero point number is 0 The wavelength band of light;
If zero point number is 1, all d (k) values are calculated according to the following equation out, then respectively as ellipse inclined The initial value of numerical fitting algorithm is analyzed, d (k) value of obtained minimum MSE (mean-square value error) is film thickness initial value:
Wherein: the index (index in this wave band is unknown, so needing to be traversed for) of k all band zero point, d (k) is Refer to that k-th point of film thickness, λ are the corresponding wavelength of zero point,For incidence angle, N2For film refractive index.
If zero point number is greater than 1, formula (9) corresponding to the zero point of two adjacent S of simultaneous directly calculates film thickness Spend initial value:
Wherein: n indicates that S is equal to refractive index when 0 under corresponding wavelength, and A indicates incidence angle, and λ indicates corresponding when S=0 Wavelength.
Above-mentioned classification in the present embodiment, respectively for ultrathin film (be lower than 10 nanometers), 10~200nm and The film of 200nm or more thickness has accurate calculated result.
As shown in figure 3, in a preferred embodiment, the number n value of the 0 value point of wavelength of sample S spectrum is 4, then root Film thickness initial value is directly calculated according to formula (7), (8) and (10), if it is desired to obtain the initial value d of measurement exemplar, it would be desirable to First shift to an earlier date known refractive index n2, it can be obtained from exemplar database or by dispersive model, finally by calculating, wavelength value Value of the S close to zero point when is taken, is taken as λ respectively1=422.23nm, λ2=498.41nm, λ3=614.57nm, λ4= 809.69nm (value according to n=4), the average value of d is calculated in conjunction with formula (10), transparent membrane thickness value d=is calculated 501.14nm (given sample clear film thickness true value is 500nm).The result shows that we are used to calculate substrate by the invention Upper single-layer and transparent film thickness initial value can obtain the initial value close to film thickness true value, guarantee the accuracy of subsequent fitting, shorten Fit time.
It is important to note that the film thickness initial value carculation method in the present embodiment, is preferably useful in S and spectrally has There is the case where zero point.If S spectrum obtained does not have zero point, need to be adjusted the wave band of incident light wave.Its reason It is, spectrally the wavelength of zero point and incident light has direct relation to S.Meanwhile using the present embodiment to film thickness initial value into When row calculates, wavelength resolution precision is higher, spectral noise processing quality is better, and single-layer and transparent film obtained is thick It is more accurate to spend initial value calculating.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include Within protection scope of the present invention.

Claims (9)

1. value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers, which is characterized in that including,
Detection parameters are arranged in S1, and the stokes parameter of exemplar film is obtained using ellipsometer measurement;
S2 decomposites S spectrum to come from stokes parameter, and carries out noise reduction process to it;
S3 filters out the zero point in S spectrum and obtains corresponding wavelength, is calculated according to the zero point of S spectrum and its corresponding wavelength Exemplar film thickness initial value.
2. value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers according to claim 1, wherein described Include in step S3,
S31 filters out the zero point in S spectrum, obtain zero point number and its corresponding wavelength;
If the number of S32 zero point is 0, the lambda1-wavelength in detection parameters is changed, S1 is entered step, otherwise enters step S33;
If the number of S33 zero point is 1, exemplar film thickness match value corresponding to the zero point is calculated, it is thin to obtain exemplar Film thickness initial value, otherwise enters step S34;
If the number of S34 zero point is greater than 1, exemplar film thickness match value corresponding to each zero point, simultaneous phase are calculated The film thickness match value of adjacent zero point obtains exemplar film thickness initial value.
3. value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers according to claim 2, wherein described Zero point in S spectrum is defined as:
S(k)*S(k+1)≤0&&S(k+1)*S(k+2)≠0;
Then λ (j)=(λ (k)+λ (k+1))/2;
Wherein, S is S spectrum in Stokes vector, and k is S spectrum zero point index number, and λ is wavelength.
4. value measurement method at the beginning of a kind of film thickness suitable for spectroscopic ellipsometers according to claim 2 or 3, wherein The exemplar film thickness match value calculation formula is preferably as follows:
Wherein, d is film thickness, and k is S spectrum zero point index number, and λ is wavelength, N2For the refractive index of film,For incidence Angle.
5. according to value measurement method at the beginning of a kind of described in any item film thicknesses suitable for spectroscopic ellipsometers of claim 2~4, Wherein, the step S34 includes calculating exemplar film thickness match value corresponding to each zero point,
Wherein, d is film thickness, and k is S spectrum zero point index number, and λ is wavelength, N2For the refractive index of film,For incidence Angle;
The film thickness match value of simultaneous any two adjacent zeros point obtains the mean value of any two adjacent zeros point,
Wherein, d (i) is i-th of film thickness, niFor the refractive index under the corresponding wavelength of i-th of index, i is S spectrum zero point Index, A is incidence angle;
Exemplar film thickness initial value is obtained according to mean value,
Wherein, d is average film thickness, and m is S spectrum zero point total number, the film thickness that d (i) is i-th point.
6. value measurement method at the beginning of a kind of described in any item film thicknesses suitable for spectroscopic ellipsometers according to claim 1~5, Wherein, the detection parameters include spectral region and/or angle of incidence of light.
7. value measurement method at the beginning of a kind of described in any item film thicknesses suitable for spectroscopic ellipsometers according to claim 1~6, Wherein, the preferred 380nm~1000nm of spectral region in the detection parameters.
8. value measurement method at the beginning of a kind of described in any item film thicknesses suitable for spectroscopic ellipsometers according to claim 1~7, Wherein, preferably 50 °~75 ° of the angle of incidence of light in the detection parameters.
9. value measurement method at the beginning of a kind of described in any item film thicknesses suitable for spectroscopic ellipsometers according to claim 1~8, Wherein, the noise reduction process preferably passes through Fourier filtering algorithm and/or center filtering algorithm is completed.
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