CN109470154B - Film thickness initial value measuring method suitable for spectrum ellipsometer - Google Patents
Film thickness initial value measuring method suitable for spectrum ellipsometer Download PDFInfo
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
- G01B11/0616—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material of coating
- G01B11/0641—Measuring 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
Abstract
The invention discloses a film thickness initial value measuring method suitable for a spectroscopic ellipsometer, which comprises the steps of setting detection parameters, and obtaining a Stokes parameter of a sample film by using ellipsometer measurement; decomposing the S spectrum from the Stokes parameters, and carrying out noise reduction treatment on the S spectrum; and screening out zero points in the S spectrum, acquiring corresponding wavelengths, and calculating an initial value of the thickness of the sample film according to the zero points and the corresponding wavelengths of the S spectrum. Aiming at the condition that the initial value of the film is not accurately measured in the prior art, the technical scheme of the invention detects the Stokes parameters of the ellipsometry measurement to obtain the spectrum zero point, and realizes the accurate estimation of the initial value of the film thickness by utilizing the zero point.
Description
Technical Field
The invention belongs to the field of data analysis of precise optical measurement instruments, and particularly relates to a film thickness initial value measurement method suitable for a spectrum ellipsometer.
Background
An ellipsometer is an optical device for measuring the thickness and optical constants of a thin film. Generally, the entire measurement process of an ellipsometer is divided into two parts:
1) spectroscopic ellipsometry
The measurement principle is that a non-polarized light source is utilized to generate polarized light through a polarization state generator, after the light is incident on the surface of a sample, the polarization state of reflected light is changed, an analyzer is used for detecting an ellipsometric spectrum of the sample, and the ellipsometric spectrum can be represented by an amplitude ratio angle psi and a phase difference angle delta, so that data information of the corresponding sample is obtained.
Of course, ellipsometry can also be represented by Stokes parameter NCS:
N＝cos2Ψ
C＝sin2ΨcosΔ
S＝sin2ΨsinΔ
since it is an indirect measurement technique, the measured spectrum data information cannot be directly converted into the film thickness and optical constants of the sample, so that it is often necessary to establish a suitable model fitting analysis.
Spectroscopic ellipsometers can be roughly classified into rotating polarizer type ellipsometers (P) according to the modulation methodRSCA), single rotation compensator type ellipsometer (PSC)RA) Double rotation compensator type ellipsometer (PC)RSCRA) And a phase modulation ellipsometer (PSMA). The scope of measuring instruments used in the present invention encompasses the types of instruments described above.
2) Data analysis
Firstly, an ellipsometry spectrum obtained by measurement of an ellipsometer is required to be utilized, then, according to the known sample information, the real information of the sample is solved through a mathematical iteration method, and finally, the measurement purpose is achieved.
The iterative algorithm used by the data analysis section is typically a belief domain algorithm that needs to be iterated sequentially from a given initial solution, with constant improvement to find the optimal solution. The basic algorithm idea is to give an initial point x0And initial confidence domain radius Δ0The iteration is started, and a confidence domain is given in each iteration (current iteration point x)kA small neighborhood) and then solve a sub-problem in the trust domain to obtain a heuristic step size sk(solution of sub-problem of trust domain), then use the corresponding evaluation function to judge whether the tentative step is reasonable and determine the trust domain of the next iteration. When s iskReasonably, then: x is the number ofk+1＝xk+skIf not, xk+1＝xk. The next trust domain of an iteration depends on how good the heuristic step size is, in short, if the heuristic step size is good, the trust domain is enlarged or kept constant at the next iteration, otherwise the trust domain is reduced.
Generally speaking, the calculation result of the iterative algorithm is very dependent on the initial value of the given film thickness, otherwise, the calculation result is very likely to fall into a local optimal solution, and if the initial value of the given film thickness is inaccurate, the final result of the iterative algorithm is very likely to be the local optimal solution rather than the global optimal solution.
Disclosure of Invention
In view of the above-mentioned shortcomings or needs in the art, the present invention provides a method for measuring an initial thickness of a thin film suitable for use in a spectroscopic ellipsometer, which at least partially solves the above problems. Aiming at the condition that the initial value of the film is not accurately measured in the prior art, the technical scheme of the invention detects the Stokes parameters of the ellipsometry measurement to obtain the spectrum zero point, and realizes the accurate estimation of the initial value of the film thickness by utilizing the zero point.
In order to achieve the above object, according to one aspect of the present invention, there is provided a film thickness initial value measuring method for a spectroscopic ellipsometer, comprising,
s1, setting detection parameters, and measuring by using an ellipsometer to obtain Stokes parameters of the sample film;
s2, decomposing the S spectrum from the Stokes parameters and carrying out noise reduction processing on the S spectrum;
s3, screening out the zero point in the S spectrum and obtaining the corresponding wavelength, and calculating the initial value of the thickness of the sample film according to the zero point of the S spectrum and the corresponding wavelength.
As a preferable aspect of the present invention, step S3 includes,
s31, screening out zero-value points in the S spectrum, and acquiring the number of the zero-value points and the corresponding wavelengths thereof;
s32, if the number of zero point is 0, changing the wavelength of incident light in the detection parameter, entering step S1, otherwise entering step S33;
s33, if the number of the zero value points is 1, calculating the fitting value of the thickness of the sample film corresponding to the zero value points to obtain the initial value of the thickness of the sample film, otherwise, entering the step S34;
s34, if the number of the zero value points is larger than 1, calculating the film thickness fitting value of the sample corresponding to each zero value point, and combining the film thickness fitting values of adjacent zero value points to obtain the initial film thickness value of the sample.
As a preferred embodiment of the present invention, the definition of the zero point in the S spectrum is:
S(k)*S(k+1)≤0&&S(k+1)*S(k+2)≠0；
λ (j) ═ 2 (λ (k) + λ (k + 1))/2;
wherein S is the S spectrum in the Stokes vector, k is the zero index number of the S spectrum, and lambda is the wavelength.
As a preferred embodiment of the present invention, the calculation formula of the film thickness fitting value of the sample is preferably as follows:
wherein d is the film thickness, k is the S spectrum zero index number, lambda is the wavelength, N2Is the refractive index of the thin film,
is the angle of incidence.
As a preferred embodiment of the present invention, step S34 includes calculating a fitting value of the film thickness of the sample corresponding to each zero point,
wherein d is the film thickness, k is the S spectrum zero index number, lambda is the wavelength, N2Is the refractive index of the thin film,
is the angle of incidence;
combining the film thickness fitting values of any two adjacent zero points to obtain the mean value of any two adjacent zero points,
wherein d (i) is the thickness of the ith film, niThe index is the refractive index under the wavelength corresponding to the ith index, i is the index of the S spectrum zero value point, and A is the incident angle;
obtaining an initial value of the thickness of the film of the sample piece according to the average value,
wherein d is the average film thickness, m is the total number of S spectrum zero points, and d (i) is the film thickness of the ith point.
As a preferred embodiment of the present invention, the detection parameter includes a spectral range and/or a light incidence angle.
As a preferable mode of the present invention, the spectral range in the detection parameter is preferably 380nm to 1000 nm.
As one preferable aspect of the present invention, the incident angle of the light in the detection parameter is preferably 50 ° to 75 °.
As a preferred embodiment of the present invention, the noise reduction processing is preferably performed by a fourier filter algorithm and/or a center filter algorithm.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
1) according to the technical scheme, aiming at the problem that the initial value of the film thickness has great influence on the measurement result in the data analysis and solving algorithm of the ellipsometer, the ellipsometer is used for carrying out optical measurement to obtain the corresponding S spectrum, and the zero point on the S spectrum is used for calculating to obtain the closest initial value of the film thickness, so that the measurement error caused by inaccuracy of the initial value of the film thickness is reduced.
2) According to the technical scheme, the thickness order of the used film can reach the nanometer order of magnitude, the zero value of the S spectrum corresponding to the zero value can be effectively found by changing the wavelength range of incident light, meanwhile, the zero value is subjected to quantity classification in the technical scheme, different zero values correspond to different film calculation modes, and the obtained result is more accurate.
Drawings
FIG. 1 is a flow chart of the initial measurement of the film thickness according to an embodiment of the present invention;
FIG. 2 is an NCS diagram obtained by measuring a silicon substrate silicon dioxide transparent thin film using an ellipsometer according to an embodiment of the present invention;
FIG. 3 is a spectrum diagram of a sample S obtained after noise reduction by using a center filtering algorithm in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. The present invention will be described in further detail with reference to specific embodiments.
The embodiment of the technical scheme of the invention provides a method for calculating the initial value of the thickness of a single-layer transparent film before the numerical analysis of a spectroscopic ellipsometer, and the method can realize that the ellipsometer does not depend on the given initial value of the thickness of the film in the data analysis process, thereby achieving the effect of a quick and accurate fitting algorithm.
For a single-layer film, the reflection coefficient expressions of P light and S light obtained by orthogonal decomposition of incident light according to Fresnel' S law are as follows:
the calculation formula of the phase delay amount is as follows:
therefore, the ellipsometry parameters in this embodiment can be expressed as:
in particular, the thickness of the monolayer film mainly affects the ellipsometric parametersThe initial film thickness calculation is performed by considering the phase difference Δ. The invention is applicable to a single-layer transparent film, so that the refractive index N of a sample film can be obtained2＝n2-ik2(k here)2Is the extinction coefficient of the material, which is different from k in the natural number k) shown below20, whereby only n is considered2. As can be seen from equation (3), when the imaginary parts of Rp and Rs are 0, Δ ═ 0 or pi. In this case, as can be seen from formula (1), 2 β ═ 0, pi, 2 pi, …, that is:
namely, it is
S ═ sin (2 Ψ) sin (Δ) ═ 0 in Stokes parameter NCS. Also, since the amplitude ratio angle tan Ψ is a ratio of the amplitudes of the two polarized light components, and thus cannot be equal to 0 or π/2, S-0 may be equivalent to Δ -0 or π. To summarize: when the single-layer film thickness d and the wavelength λ satisfy formula (5), the stokes parameter S is 0.
That is, the method for measuring the initial value of the single film thickness in the present embodiment is based on the principle that "when the single film thickness d and the wavelength λ satisfy the formula (5), the stokes parameter S is 0", and the method for calculating the initial value of the single film thickness in the present embodiment will be further described based on this.
As shown in fig. 1, the method for calculating the initial thickness of the single-layer transparent film in the present embodiment includes the steps of:
the first step is as follows: and measuring the sample to obtain the Stokes parameters (i.e. the ellipsometry spectrum or the S spectrum) of the sample.
In this embodiment, a silicon substrate silicon dioxide film is preferably used, the thickness value is preferably about 500nm, the measurement incident angle is preferably 50 to 75 °, and 65 ° is preferred in this embodiment. Further, the spectral range used in this embodiment is 380nm to 1000nm (preferably including a near ultraviolet band, a visible light band, and a near infrared band), the above parameters may be adjusted according to measurement requirements, and the above specific parameters are not considered to be specific limitations on the technical solution of the present invention. The process of obtaining the Stokes parameter of the sample is prior art for those skilled in the art, and is not described in detail in this embodiment.
The second step is that: and analyzing the S spectrum of the given waveband, and reducing noise by using a filtering algorithm.
In the process of measuring by an instrument, noise inevitably affects the S spectrum obtained by measuring the sample, so that a filtering algorithm is required to perform noise reduction processing on the S spectrum obtained by measuring. In particular, when the ellipsometry spectrum of the sample is obtained through simulation, the influence of noise needs to be added in the sample simulation, and then the noise reduction processing is performed on the sample simulation through a filtering algorithm. The spectral noise processing is important, but the position of the wavelength point must be ensured not to have large translation when the noise is reduced so as not to influence the precision of the initial value of the thickness of the single-layer transparent film.
In fact, the processing of spectral noise is very important in the algorithm, and it must be ensured that the position of the wavelength point does not shift greatly when the noise is reduced, so as not to affect the precision of the initial value of the thickness of the single-layer transparent film. Specifically, a fourier filter algorithm or a center filter algorithm may be selected to perform noise reduction filtering processing on the signal, in this embodiment, it is preferable to perform noise reduction processing by using the center filter algorithm, that is, a point near each S value is selected, and an average value of the points is calculated to achieve the purpose of noise reduction, in this embodiment, the calculation formula is preferably as follows:
as shown in fig. 2, the spectrum of the sample S obtained after denoising using the center filtering algorithm is shown.
The third step: finding out all the wavelength points with S equal to 0 in the S spectrum, judging the number of 0 value points, and calculating the initial value of the film thickness.
The definition of the 0 point of the S spectrum is (the product of the k point and the k +1 point is less than 0 represents that the two values are opposite in sign, so there must be a 0 point between k and k + 1.):
S(k)*S(k+1)≤0&&S(k+1)≠0 (7)
λ(j)＝(λ(k)+λ(k+1))/2 (8)
s is the S spectrum in the Stokes vector, k is the zero index number of the S spectrum, and lambda is the wavelength.
Specifically, the number of 0-value points of the wavelength of the S spectrum is determined, and if the number of zero-value points is 0, the waveband range of incident light is adjusted;
if the number of the zero-point points is 1, calculating all values d (k) according to the following formula, and then respectively using the values d (k) as initial values of an ellipsometric numerical fitting algorithm to obtain the value d (k) of the minimum MSE (mean square error), namely the initial value of the film thickness:
wherein: k index of the zero point of the whole band (the index in the band is unknown and needs to be traversed), d (k) is the film thickness of the k point, λ is the wavelength corresponding to the zero point,
is an angle of incidence, N2Is the refractive index of the film.
If the number of the zero points is more than 1, directly calculating the initial value of the film thickness by combining a formula (9) corresponding to the zero points of two adjacent S:
wherein: n represents a refractive index at a wavelength corresponding to S equal to 0, a represents an incident angle, and λ represents a wavelength corresponding to S equal to 0.
The above classification in this embodiment has more accurate calculation results for ultra-thin films (less than 10 nm), films with thicknesses of 10-200 nm and films with thicknesses of more than 200 nm.
In a preferred embodiment, as shown in FIG. 3, the number n of 0-point wavelength points of the S spectrum is 4, and the initial value of the film thickness is directly calculated according to the formulas (7), (8) and (10), and if the initial value d of the measurement sample is to be obtained, we need to know the refractive index n in advance2It can be obtained from a sample database or by a dispersion model, and finally, by calculation, the wavelength value is the value when S is close to a zero value point, and is respectively taken as lambda1＝422.23nm、λ2＝498.41nm、λ3＝614.57nm、λ4The average value of d was calculated by using formula (10) at 809.69nm (a value corresponding to n being 4), and the transparent film thickness value d was calculated at 501.14nm (the true value of the transparent film thickness of the sample was 500 nm). The result shows that the initial value close to the true value of the film thickness can be obtained by calculating the initial value of the thickness of the single-layer transparent film on the substrate through the method, the accuracy of subsequent fitting is ensured, and the fitting time is shortened.
It should be noted that the initial value of the film thickness calculation method in the present embodiment is preferably applied to the case where the S spectrum has a zero point. If the obtained S spectrum has no zero point, the wavelength band of the incident light wave needs to be adjusted. The reason for this is that the zero point on the S spectrum has a direct relationship with the wavelength of the incident light. Meanwhile, when the initial value of the film thickness is calculated by using the embodiment, the higher the wavelength resolution precision is, the better the spectral noise processing quality is, and the more accurate the calculation of the initial value of the thickness of the obtained single-layer transparent film is.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A method for measuring the initial thickness of a film suitable for a spectroscopic ellipsometer comprises,
step S1, setting detection parameters, and obtaining the Stokes parameters of the sample film by using ellipsometry;
step S2 decomposes the S spectrum from the Stokes parameters and carries out noise reduction processing on the S spectrum;
s3, screening out a zero value point in the S spectrum and acquiring a corresponding wavelength, and calculating an initial value of the thickness of the sample film according to the zero value point of the S spectrum and the corresponding wavelength; the step S3 includes the steps of,
step S31, screening out zero-value points in the S spectrum, and acquiring the number of the zero-value points and the corresponding wavelengths thereof;
step S32, if the number of zero value points is 0, changing the wavelength of incident light in the detection parameters, and entering step S1, otherwise entering step S33;
step S33, if the number of the zero value points is 1, calculating the fitting value of the thickness of the sample film corresponding to the zero value points to obtain the initial value of the thickness of the sample film, otherwise, entering the step S34;
the sample piece film thickness fitting value calculation formula is as follows:
wherein d is a film thickness fitting value, k is an S spectrum zero-point index number, lambda is a wavelength, and N is2Is the refractive index of the thin film,
is the angle of incidence;
step S34, if the number of the zero value points is more than 1, calculating the film thickness fitting value of the sample corresponding to each zero value point, and combining the film thickness fitting values of adjacent zero value points to obtain the initial film thickness value of the sample; combining the film thickness fitting values of any two adjacent zero points to obtain the mean value of any two adjacent zero points,
whereinD (i) is the thickness of the film at the point i, niThe index of the refractive index at the wavelength corresponding to the ith point index is shown, i is the index of the S spectrum zero point, and A is the incident angle;
obtaining an initial value of the thickness of the film of the sample piece according to the average value,
wherein d' is the average film thickness, m is the total number of S spectrum zero points, and d (i) is the film thickness of the ith point.
2. The method of claim 1, wherein the zero point in the S spectrum is defined as:
S(k)*S(k+1)≤0&&S(k+1)*S(k+2)≠0；
λ (i) ═ λ (k) + λ (k + 1))/2;
wherein S is the S spectrum in the Stokes vector, k is the index number of the zero value point of the S spectrum, lambda is the wavelength, and i is the index of the zero value point of the S spectrum.
3. The method of claim 1 or 2, wherein the detection parameters include a spectral range and/or an incident angle of light.
4. The method for measuring initial thickness of thin film according to claim 1 or 2, wherein the spectrum range of the detection parameter is 380 nm-1000 nm.
5. The method of claim 1 or 2, wherein the incident angle of the light in the detection parameter is 50 ° to 75 °.
6. The method of claim 1 or 2, wherein the noise reduction process is performed by a fourier filter algorithm and/or a central filter algorithm.
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| CN112629421B (en) * | 2020-12-31 | 2022-09-23 | 武汉颐光科技有限公司 | Film thickness measuring method based on fast Fourier transform |
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