JPH0769215B2 - Spectroscopic analysis method for thin film samples - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for spectroscopic analysis of a thin film sample by spectroscopically analyzing a thin film sample and obtaining a true spectrum, film thickness, and optical constant of the sample from observed spectral data. Regarding

Background The purpose of spectroscopic analysis is to measure the light intensity distribution modulated by the substance to be measured as a function of wavelength or wave number, that is, as a spectrum, and analyze it. A spectrum is composed of information about the wavelength / wavenumber axis such as a peak position, a half width or an absorption band, and intensity / amplitude information. Generally, peak information is used for qualitative analysis because it relates to light energy, and intensity information is used for quantitative analysis because it relates to photon number.

In order to perform accurate analysis, it is necessary to measure the sample spectrum with high accuracy. However, the observed spectrum obtained from the analytical equipment is the true spectrum of the sample multiplied by the instrumental function of the entire measurement system, and noise is added, and if the observed spectrum is directly used for qualitative / quantitative analysis, You may make mistakes. Therefore, in order to perform accurate analysis, it is important to measure the spectrum with high accuracy and extract / separate a high-quality signal from this.

In such waveform processing, processing intended for constant / quantitative analysis (for example, spectral separation processing) is called post-processing, whereas numerical processing is used to improve the performance of the spectroscopic instrument in order to obtain an accurate spectrum. A method that aims to improve indirectly is called preprocessing. Examples of the pre-processing include noise removal (improvement of SN ratio) and deconvolution processing (improvement of resolution), but the present invention is basically one of pre-processing for noise removal for spectral data. Regarding

Noise can be roughly divided into two types: random noise that is random and does not depend on signals, and systematic noise that is dependent on signals.
Both must be removed for accurate analysis. In particular, in order to remove the latter by mathematical processing, it is important to fully understand the generation mechanism and follow the reverse process precisely. In the present invention, it is a systematic noise that appears in the spectroscopic measurement of a thin film sample. The effect of multiple reflection interference is analyzed and a new elimination method is given. In the following, an infrared absorption spectrum that is frequently used as a qualitative / quantitative substance will be described as an example.

BACKGROUND OF THE INVENTION When an infrared absorption spectrum of a liquid in a thin film or a cell is measured, as shown in FIG. 1, a periodic waveform with respect to the wave number is observed in a region where the absorption is small. This waveform is called a fringe in the field of analytical chemistry, and it not only gives a periodical change to the baseline of the spectrum, but also has a non-negligible effect on the shape and height of the absorption peak that is important in the analysis. Since the change in the shape of the observed spectrum is a major obstacle to quantitative and qualitative analysis, the removal of fringes is a major issue. The cause of the fringes is the interference of the measurement light repeatedly reflected in the film or in the liquid layer narrowed by the window material of the cell, especially in the infrared measurement where the wavelength of the measurement light and the thickness of the sample are similar. In this case, the change in spectral shape is noticeable.

Conventional techniques and problems In order to eliminate the influence of this interference, methods such as roughening the sample surface and making the measurement light incident at Brewster's angle have been used early on. In that case, it is impossible to completely suppress the reflection in the film and the interference due to the reflected light, and the fringe cannot be removed. Therefore, some fringe removal methods by mathematical processing have been proposed.

T. Hirschfeld proposed a method for numerically removing the fringe frequency component from the measured spectrum. (T. Hirschfeld
and HWMantz, “Elimination of Thin Film Infrared
Channel Spectra in Fourier Transform Infrared Spe
ctroscopy ", Appl.Spectrosc.30,5, pp.552-553 (197
6)). However, this method has a single frequency fringe,
It is based on the false assumption that it is additively added to the true absorption spectrum, and this method cannot remove fringes correctly.

On the other hand, RNJones et al. Have proposed a method for obtaining the optical constants (absorption spectrum and refractive index spectrum) of a sample with a known film thickness (RNJones, D. Escolar, JPHawranek, PN).
eelakantan, and RPYoung, “SOME PROBLEMS IN INFRAR
ED SPECTROPHOTOMETRY ", J. Mol. Struct. 19, pp. 21-42 (1
973), JP Hawranek, P. Neelakantan, RPYoung, and R.
N. Jones, “The control of errors in irspectrophot
ometry−III.Transmission measurements using thin c
ells ", Spectrochim.Acta 32A, pp.75-84 (1976), JP
Hawranek, P. Neelakantan, RPYoung, and RNJones “Th
e control of errors in irspectrophotometry-IV.C
orrections for dispersion distortion and the evalu
ation of both optical constants ", Spectrochim.Acta
32A, pp.85-98 (1976), JPHawranek and RNJone
s, "The control of errors in irspectrophotometry
−V. Assessment of errors in the evaluation of opti
cal constants by transmission measurements on thin
films ", Spectrochim.Acta 32A, pp.99-109 (1976),
JPHawranek and RNJones, “The determination of
the optical constantds of benzene and chloroform i
n the irby thin film transmission ", Spectrochim.A
cta 32A, pp.111-123 (1976) .GK Ribbegard and RN
Jones, “The Measurement of the Optical Constants o
f Thin Solid Filme in the Infrared ", Appl.Spectros
c.34, pp.638-645 (1980)). In this method, an absorption spectrum is obtained by calculating a spectrum affected by interference using the absorption spectrum as a parameter and fitting it to the observed spectrum. However, to apply this method to the observed spectrum,
It is necessary to measure the sample film thickness with a fairly high degree of accuracy in advance, and complicated preliminary experiments are required.

In the present invention, since a sample of unknown film thickness can be targeted, stylus method, interferometry, spectroscopy, ellipsometry, etc. are mentioned as film thickness measurement methods conventionally known for film thickness. is there.

In the stylus method, the needle is brought into contact with the substrate portion and the sample portion on the substrate, and the height difference is electrically enlarged and measured. The measurement limit is about 1 nm, which requires measurement at the edges of the substrate and sample.

Similarly to the interferometry method, the height difference between the edges of the substrate and the sample is measured. A semipermeable membrane such as mica is placed on the sample with a slight inclination, and measurement light is caused to interfere between the film surface and the sample surface. Since the interference fringes shift at the edge portion according to the height difference between the substrate portion and the sample portion, the optical thickness of the sample can be measured from this shift amount. Since it is necessary to deposit a substance with high reflectance on the sample, destructive measurement is performed, and the measurement limit is about the wavelength of the measurement light (several nm).

Is calculated from the fringe frequency in the spectrum of the sample in the region without absorption. (NJ Harrick,
“Determination of Refractive Index and Film Thick
ness from Interference Fringes ", Appl.Opt.10,10, pp.
2344-2349, DJMoffatt and DGCameron, “Location
of Low Frequency Fringe Signaturse in Fourier Tra
nsforms of Spectra ", Appl.Spectrosc.37,6, p.556 (198
3), Sadako Fujimura, Atsuki Matsumura, "Film thickness measurement using spectroscopic measurement", Proceedings of the 46th JSAP Academic Conference, p.45
(1985)). However, this method can be handled only in the region where there is no absorption and no change in refractive index, and despite the use of the spectral spectrum, it does not measure the part where the physical properties of the sample are difficult to appear. As with trying to remove fringes as noise without obtaining information from them, useful material information called spectral information is discarded. This spectroscopy is a non-destructive measurement,
It is the optical thickness that is measured, and the physical thickness must be determined by another measurement of the refractive index of the sample. The measurement limit is about several nm.

In the ellipsometry method, the polarization state of the measurement light repeatedly reflected in the sample is measured to obtain the optical constant and the film thickness of the sample. The measurement limit is about 1 nm, and it is necessary to measure at a wavelength that the sample does not absorb. If the absorption coefficient of the sample is not 0,
The film thickness can be obtained by performing the measurement a plurality of times while changing the film thickness of the underlying medium or the sample and performing mathematical processing on the obtained data. It is necessary to give an accurate incident angle, and the optical constants of the underlying material must be obtained by preliminary experiments.

OBJECT OF THE INVENTION The present invention does not require any information about a measurement sample, and does not need information about measurement conditions (incident angle of measurement light), and it is possible to obtain a spectrum in which the influence of fringe is removed, The object is to resist a novel thin film spectroscopic analysis method capable of obtaining information on film thickness and refractive index dispersion with high accuracy.

SUMMARY OF THE INVENTION So far, much of the effect of interference on the true spectrum has been treated as noise in the analysis. However, if we change the viewpoint and consider this interference as an observation target, it means that the fringes in the measurement spectrum are generated due to the influence of the measurement system, but the information of the sample should also be included. Contemplate. As described below, for example,
The fringe frequency is inversely proportional to the product of the refractive index of the sample and the film thickness, and changes depending on the incident angle of the measurement light. Further, the fringe amplitude depends on the reflectance of the sample surface. This allows
Information about sample conditions such as film thickness is also included in the measurement spectrum, and it is possible to extract a lot of substance information from it by not only simply removing the effect of interference as noise, but also by using it in reverse. It is possible.

The present invention is based on the above idea, in which the same thin film sample is measured at least twice with a spectrophotometer while changing the angle between the sample and the optical axis of the measurement light, and the measured spectral data are not measured. In addition to linking with the absorption coefficient or extinction coefficient, which is a variable, the sum of squared errors of the absorption coefficient or extinction coefficient is set to an objective function with film thickness, refractive index, and angle as parameters, and the objective function is minimized by a nonlinear optimization method. The basic feature is that the above parameters are calculated to obtain a spectrum from which interference fringes are removed, and at the same time, the film thickness and refractive index dispersion of the sample can be obtained.

[Principle] FIG. 2 is a model diagram showing multiple reflection interference that occurs when light is projected onto a solid thin film sample. When measuring light (1) with amplitude A ₀ (ν) is incident on a thin film (2) having a film thickness d ₀ and a refractive index n at an angle θ ₀ , it is refracted by Snell's law, sin θ ₀ = nsinθ (1) , The transmission distance d in the film is d = d ₀ / cos θ (2) The refractive index n is actually a function of the wave number ν, but here it is a constant for simplicity, and the refractive index dispersion will be described later.

When the extinction coefficient of the sample (2) is a (ν), the transmittance spectrum T (ν) of the transmitted light (3) for one optical path in the film is T (ν) = exp {-nda (ν)} ... Although given by (3), in the actual absorption measurement, reflection on both surfaces of the film (2) causes multi-beam interference, and the obtained transmittance spectrum S (ν) is as follows.

Here, r is the reflectance of the sample surface, which is given by the following equation as a function of the refractive index n and the reflection angle θ of the measurement light in the film by the Fresnel equation.

In the equation (5), the upper one is S-polarized light and the lower one is P-polarized light.
This is the case of polarized light, and considering dispersion, r and n in both equations are r
It is replaced by (ν), n (ν).

In the above equation (4), the third item (the term including cos) of the denominator gives periodic modulation to the spectrum. Figure 3,
FIG. 4 shows the effect of this interference on the transmittance spectrum S (ν).

FIG. 3 shows the measured spectrum S (ν) when the film thickness d ₀ was changed to ₅ , 15, 25 μm in the same sample (corresponding to (a), (b) and (c) in the same figure, the same applies hereinafter). , Showing how the fringe changes. The refractive index n is constant at 1.6. It can be seen that the fringe frequency decreases as the film thickness increases.

FIG. 4 shows the measured spectrum S (ν) when the refractive index n is changed to 1.3, 1.6 and 2.0 in the same sample, and shows how the fringe changes. The film thickness d ₀ is constant at 15 μm. From this, it can be seen that as the refractive index increases, the fringe amplitude increases and the frequency decreases.

Further, FIG. 5 shows how the fringe changes due to the difference in transmittance. When the transmittance is constant at 100%, 60% and 30%, the film thickness d ₀ is 15 μm and the refractive index n is 1.6.
From the result of this simulation, it can be seen that the fringe amplitude increases as the transmittance increases even if the refractive index is constant.

Also, multiple reflection interference cannot be avoided when measuring the reflected light of a solid thin film. As shown in FIG. 6, when the reflected light (4) is measured, the observed spectrum S (ν) is given by the following equation.

Similar to the above, changes in the shape of the reflection spectrum by changing the film thickness and the refractive index are shown in FIGS. 7 and 8. FIG. 7 shows the change in fringe due to the difference in film thickness when the refractive index n = 2.0, and FIG. 8 shows the change in fringe due to the difference in refractive index when the film thickness d ₀ is kept constant at 15 μm.

On the other hand, when the sample is a liquid, the absorption spectroscopic measurement is performed by enclosing the sample in a liquid cell. FIG. 9 shows a cross section of the liquid cell in which the liquid is enclosed. In the figure, the first and fifth layers are air. The thickness d ₂ of the third layer (liquid layer) is usually 1
Since the thickness is about 100 μm to 100 μm, multiple reflection interference occurs in the layer as in the case of the solid sample. The window materials of the second and fourth layers do not have an absorption peak in the measurement wavelength range, and their thickness d ₁ is several
Since it is about mm, which is sufficiently thick compared to the liquid layer, the multiple reflection interference in the window material does not actually pose a problem.

[Principle of Fringe Removal] FIG. 10 shows the basic concept of the present invention and the method of removing interference components, taking the case of the transmitted light measurement of a solid sample shown in FIG. 2 as an example.

Spectrum S obtained by absorption measurement with a spectroscope (10)
(Ν) is given by the above equation (4). This equation (4) is
When modified, it becomes a quadratic equation regarding the target true fringe-free spectrum T (ν) as in the following equation.

r ⁴ S (ν) T ² (ν)-[2S (ν) r ² cos (4πnd ₀ cos θ · ν) -1] T (ν) + S (ν) = 0 ... (7) (7) Equation In addition to the unknown T (ν), the film thickness d _{0 of} the sample, the refractive index n, and the reflection angle θ of the measurement light in the film are unknown. It will exceed, and equation (7) cannot be solved.

Therefore, in order to solve this equation, the same sample is measured at least twice by the spectroscopic device (10). The incident point of the measurement light on the sample is kept constant, and the angle formed by the optical axis of the incident light and the sample, that is, the incident angle is changed, and the measurement is performed at incident angles θ ₀₁ and θ ₀₂ . When the incident angle is changed, the absorption length d (= d ₀ / cos
θ ₁ ) and the reflectance r change, and the measured spectrum S (ν) existing therein changes to S ₁ (ν), S ₂ (ν) in the same sample.
You can get two of them. The absorption length d in each measurement is d ₁ , d
₂ (d = d ₀ / cos θ ₁ , d = d ₀ / cos θ ₂ , θ ₁ and θ ₂ are reflection angles in the film with respect to incident angles θ ₀₁ and θ ₀₂ , respectively), S ₁
Each true spectrum T corresponding to (ν), S ₂ (ν)
₁ (ν) and T ₂ (ν) are linked as follows by the absorption coefficient a (ν) which is an invariant.

The equation (7) is established for each of the two measurement spectra S ₁ (ν) and S ₂ (ν), and the equation (8) is added to this, so that the number of equations is known as an unknown number. Therefore, by solving this simultaneous equation, the true spectrum T ₁ (ν), T
₂ (ν), the film thickness d ₀ , the refractive index n, and the reflection angles θ ₁ and θ ₂ can be obtained.

However, it is virtually impossible to solve this simultaneous equation analytically. Furthermore, there is a problem that the number of expressions is larger than the number of unknowns. That is, if the observed spectrum contains noise, it is impossible to find a unique solution. Therefore, in order to solve this problem, attention is paid to the equation (8), and the least squares method is applied to this.

In the equation (8), the standard that minimizes the sum of squared errors between the left side and the right side is used. Then, an optimal solution is obtained here by using a non-linear optimization method. This criterion is expressed by equation (9).

The criterion is that the absorbance per unit length, that is, the absorption coefficient a
₁ (ν), a ₂ (ν) is calculated and the parameters are calculated so that the sum of squared errors is minimized. By substituting the finally calculated parameters into Eq. (7), , The true spectrum with interference fringes removed T ₁ (ν), T
₂ (ν) is obtained (steps (13) to (16) in Fig. 10). In each iteration of changing the parameter in the nonlinear optimization method, the measured spectrum S ₁ (ν), S
By solving equation (7) from ₂ (ν) and the parameters (n, d ₀ , θ ₁ , θ ₂ ), T ₁ (ν) and T ₂ (ν) are obtained, and these are substituted into the above equation (9). Then, the objective function Q is calculated.

Example FIG. 11 shows a process chart of an example. This example relates to analysis of an infrared absorption spectrum using a two-beam infrared spectrophotometer for the spectroscopic device (20).

The simplex method is used as the nonlinear optimization method.
Then, the initial value is calculated so that the local search by this simplex method can be smoothly converged (step (21)
~(twenty five)).

Further, in order to completely eliminate the influence of interference from the measured spectrum, the refractive index dispersion n (ν) is incorporated into this algorithm instead of keeping the refractive index constant (step (31)). That is, in the above description, the refractive index is treated as constant within the measurement wave number range, but in reality, the refractive index is a function related to the wave number, and changes greatly in the vicinity of the absorption peak.
FIG. 12 (a) is an infrared absorption spectrum of myra measured twice by changing the incident angle, and FIG. 12 (b) shows the result of removing fringes from this spectrum while keeping the refractive index constant. It can be seen that the fringe removal has failed on the high frequency side. The refractive index affects both the frequency and the amplitude of the fringe, and the refractive index dispersion is incorporated in order to completely eliminate the influence of interference from the measured spectrum. On the contrary, this suggests that the refractive index dispersion of the sample can be known from the spectrum affected by the interference. By taking the refractive index dispersion into consideration in this way, the accuracy of the absorption spectrum can be further improved.

FIG. 13 is a block diagram of the device system of this embodiment. The thin film sample is model 98 manufactured by Perkin Elmer.
The absorption spectrum is measured by the infrared spectrophotometer (3) (3). This spectrophotometer (20) is controlled by the company's model 3600 data station (20C),
The measured spectrum data is used as a communication interface.
Transferred to the computer (35) by RS-232C. The computer (35) is specifically PC-9801 manufactured by NEC Corporation.
F is a personal computer. Computers (35)
The spectrum data is stored in the floppy disk set in. Arithmetic processing is performed on this PC-9801F, and the result is displayed on the CRT display (36), and / or
Or record with a plotter or printer (37).

The arithmetic processing on the computer (35) is performed by a program in BASIC language. The programs include a simplex method program, a least squares method program, a golden section method program for obtaining an initial value, and the like.

First, the measured spectral data S ₁ (ν), S ₂ (ν)
Determine the initial value from. The objective function Q as shown by the above equation (9) has a large number of local minimum points near its minimum point. Therefore, when performing a local search by the simplex method, it is confirmed that the search will not be successful unless initial values of the film thickness d ₀ and the refractive index n of the parameters are about ± 10% of the optimum values. There is. Therefore, the initial value of the parameter for each measured spectrum is set to a value that satisfies the following criteria.

Here, T ″ (ν) represents the second derivative with respect to the wave number ν of T (ν). This criterion gives a parameter such that the peak of the spectrum after fringe removal is localized.
In other words, it is an operation similar to searching for a parameter by which humans can remove fringes as visually as possible. The golden section method was used to find the optimal solution of Eq. (10).

Using the parameters thus obtained as initial values, the optimum solution is estimated by the simplex method. A flowchart of the simplex method program (package program) is shown in FIG.

The parameters of the iteration in the simplex method of steps (25) to (33) are the following four.

d ₀ : Film thickness of thin film sample θ ₁ : Reflection angle in the film at incident angle θ ₀₁ θ ₂ : Reflection angle in the film at incident angle θ ₀₂ : Average value of refractive index within the measured wave number range d ₀ , θ Refractive index dispersion n obtained by using ₁ , θ ₂ and
Using (ν), the true spectra T ₁ (ν) and T ₂ (ν) are obtained from the measured spectra S ₁ (ν) and S ₂ (ν), respectively. T
The following relational expression is established between (ν) and S (ν), as in the above equation (4).

However, r _i (ν) is the reflectance on the surface of the sample, which is n by the Fresnel formula as shown in equation (5).
It is given as a function of (ν) and θ _i .

Since the equation (11) is a quadratic equation regarding T (ν) as described above, if four parameters and S (ν) are known, T (ν) can be obtained from this.

However, C (ν) = r _i ² (ν) S _i (ν) cos (4π νn (ν) d ₀ cosθ _i ) −1/2 The spectrum T (ν) not affected by interference and the extinction coefficient of the sample k (ν) is connected by the following relation.

Since i = 1,2 and S ₁ (ν) and S ₂ (ν) are spectra of the same sample, the absorption coefficients a ₁ (ν), a obtained from each are
₂ (ν) or extinction coefficients k ₁ (ν) and k ₂ (ν) are equal. Therefore, an extinction coefficient spectrum obtained from the two spectra is calculated, the sum of squared errors is calculated, and four parameters d ₀ , θ ₁ , θ ₂ that minimize the objective function Q are calculated.

The refractive index spectrum n (ν) is given by the following equation based on the Kramere-Kronig relational expression.

In addition, P represents the integral of the principal value.

Here, the integration range is 0 to ∞, but since the spectrum can be actually measured only in the finite region, the following approximate expression is used.

Where is n in the measured wave number range [ν _lower , ν _upper ].
The average value of (ν), Is. This is given as a parameter in the iteration. K (ν) is the average of the _two extinction coefficient spectra k ₁ (ν), k ₂ (ν) obtained from the _two observed spectra S ₁ (ν) and S ₂ (ν) in that iteration. The value is the estimated value of the extinction coefficient in the repeated times.

In this way, the average value k (ν) of the extinction coefficients obtained when calculating the optimization objective function and the parameters n to n (ν)
Is calculated (step (31)).

The error caused by using Eq. (14) instead of Eq. (13) is said to be of little concern if multiple absorption peaks or bands are isolated within the measured wavenumber range and the sampling is sufficiently fine. Therefore, when the method according to the present invention is applied, the spectrum is measured so as to satisfy the above conditions.

Absorption coefficient a which is actually often used in spectroscopic analysis
(Ν) is given by the following equation from the extinction coefficient k (ν).

a (ν) = 4πν · k (ν) (17) The complex refractive index n (ν) is given by the following equation from n (ν) and k (ν).

(Ν) = n (ν) + ik (ν) (18) These are calculated and displayed together with the film thickness, the extinction coefficient spectrum, the refractive index spectrum, and the reflectance spectrum after completion of the iterative calculation, or by the printer (37). You can launch.

The effectiveness of the above examples in the infrared absorption spectrum measurement was verified by a simulation experiment. Figure 15 (a),
A substance having an optical constant shown in (b) was assumed. When the film thickness of the sample is 25.000 μm and the incident angle of the measurement light is 0.000 °, the infrared absorption spectrum of this substance is observed as shown in FIG. 16 (a) under the influence of interference. Next, when the incident angle of the measuring light is changed to 10.000 °, the absorption spectrum is observed as shown in Fig. 16 (b) (however, noise is not included). Figure 17 shows the transmittance spectra obtained by applying this method to these two spectra.

FIG. 17 (a) shows a spectrum based on the optimum initial solution obtained by the golden section method, in which T ₁ (ν) and T ₂ (ν) are superimposed. FIG. 11B is the spectrum of the optimum solution obtained by using the entire flow of FIG. T ₁ (ν), T
₂ (ν) are shown at the same time, but they are completely overlapping. The film thickness of the sample obtained at this time was 25.003 μm, and the incident angles of the measurement light were 0.01 ° and 10.00 °, respectively. Also,
The extinction coefficient spectrum and refractive index spectrum obtained at the same time are shown in FIG. The error from the true value of the obtained spectrum was 2.9334 × 10 ⁻⁶ in the extinction coefficient spectrum and 2.7337 × 10 ⁻⁴ in the refractive index spectrum. With respect to the spectrum data of 250 points, the time required for calculation was about 2 minutes for obtaining the initial solution and about 10 minutes for the optimum solution.

Example 1 This method was applied to the actual infrared absorption measurement of a solid sample.

FIG. 19 shows the observed infrared absorption spectrum of polyvinyl chloride with a thickness of 15 μm. Sampling is 340
The points and the incident angles are changed, and the measurements are shown in an overlapping manner.

Figure 20 shows the result of applying this method. The figure (a) shows the absorption spectrum in which the influence of interference is completely removed, and the figure (b) shows the obtained refractive index spectrum. Also,
The obtained film thickness was 14.947 μm, and the incident angles (θ ₀₁ , θ ₀₂ ) of the measurement light were 3.05 ° and 13.12 °, respectively.

Specific Example 2 This is an example in which PET (polyethylene selephthalate) having a film thickness of 25 μm is used as a sample. Figure 21 shows the infrared absorption spectrum (175 points).

Figure 22 shows the result of applying this method. The absorption spectrum is shown in (a) and the refractive index spectrum is shown in (b). The calculated film thickness is 26.974 μm, and the measurement light incident angle is 9.83.
It was × 10 ^-3 ° and 5.90 °.

Concrete Example 3 This is an example in which this method is applied to an actual liquid sample.

The liquid is benzene. This infrared absorption spectrum is shown as 23rd
Shown in the figure. S ₁ (ν) and S ₂ (ν) are shown superimposed. Sampling is 200 points. The cell thickness is 25 μm,
KRS-5 was used as the window material of the liquid cell, and 25 μm spacers were used to determine the thickness of the liquid layer. The refractive index of KRS-5 is shown in the literature (JAJemleson, RHMcfee, GNPlass, RHG).
rube, and RGRichards, “INFRARED PHYSICS AND ENGIN
EERING ", MAGRAW-HILL, New York (1963)) and set it to 2.392 in the measurement wave number range.

The thickness of the obtained liquid layer was 26.573 μm, and the incident angles of the measurement light were 3.48 × 10 ⁻⁴ ° and 7.12 °. The obtained transmittance spectrum is shown in FIG. 24, the extinction coefficient spectrum is shown in FIG. 25 (a), and the refractive index spectrum is shown in FIG. 25 (b).

Concrete Example 4 This is a verification of the results obtained in Concrete Example 3. That is, the thickness of the liquid layer was changed and the measurement was similarly performed with benzene. A spacer having a thickness of 50 μm was used. Sampling is the same
200 points. The two infrared absorption spectra measured are shown in FIG. The results obtained from this spectrum data are shown in Fig. 27, and the extinction coefficient spectrum is shown in Fig. 28 (a).
FIG. 28 (b) shows the refractive index spectrum. It is in very good agreement with the extinction coefficient spectrum and refractive index spectrum shown in Fig. 25.

The thickness of the obtained liquid layer was 50.777 μm, and the incident angles of the measuring light were 3.49 × 10 ⁻⁴ ° and 4.55 °. The obtained optical constants can be used as a reliable reference (Appl.Spectrosc.34,6, pp.657
-691 (1980)). This is shown in Table 1.
According to this method, the obtained film thickness and refractive index have accuracy of 4 to 5 digits.

Although the dispersion type spectrophotometer is used in the above embodiment, it is of course possible to use the Fourier transform type.

It is preferable that the incident angle of the measurement light on the sample is close to 0 ° because the influence of polarization can be eliminated. Moreover, the angle difference of the incident angle is 5
It is preferably ~ 10 °, but is not particularly limited. The incident angle may be changed by changing the optical axis of the measuring light or by tilting the sample while keeping the optical axis constant. However,
The incident point is unchanged.

In the above-described embodiment, the incident angle is changed and the measurement is performed twice, but the measurement is performed twice or more to obtain the spectral data S ₁ (ν), S.
₂ (ν), S ₃ (ν) ... Is obtained, and the optimum parameters are obtained by linking them with the absorption coefficient or the extinction coefficient by the same method as in the embodiment, and more accurate spectrum and optical constant data can be obtained. it can. It can also be applied to multilayer film samples. There are various uses for multilayer film materials such as antireflection films and interference filters, but application of this method to multilayer film samples may be extremely effective in controlling their spectral characteristics and film thickness.

The method according to the present invention uses a software program, but the program can be made into a ROM and combined with a micro computer to be configured as firmware or as hardware. Further, in such an apparatus, for example, when measuring an absorption or reflection spectrum for a semiconductor material, the measurement light is guided using an optical fiber, and the sensor head is scanned on the sample to measure the sample spectrum and the film thickness. Two-dimensional measurement of refractive index dispersion is also possible. Furthermore, it can be applied to absorption data from a microspectroscope.

Although the above examples relate to the infrared absorption spectrum, the present invention is not limited to the infrared region. In order to utilize interference, when an organic thin film sample with a thickness of several to several tens of μm is targeted, infrared spectrum measurement is suitable, but when a sample with a thickness of 1 μm or less such as a coating film is targeted. Is more suitable for measurement in the visible or ultraviolet range. Fig. 29 shows the fringe state of the samples with a thickness of 1 µm and 0.2 µm.

The method of the present invention does not limit the wavelength of the measurement light and can also be used for the spectrum in the visible range. Since the thickness can be measured with high accuracy and in a short time, it is possible to directly inspect the film thickness on the production line. Specific examples include a functional film and a protective film formed on the surface of a semiconductor, a single-layer or multi-layer film that forms a recording layer of an optical memory, and any organic or inorganic thin film formed by sputtering, vapor deposition, plasma polymerization, or the like. Is applicable to.

Effect of the Invention As described above, the present invention reversely utilizes the multiple reflection interference generated in the spectrum analysis, without using any information about the experimental conditions such as the film thickness of the sample and the incident angle of the measurement light, Interference can be removed from the measured spectrum to obtain a true spectrum that is spectral information.At the same time, the refractive index spectrum and information related to experimental conditions, such as the sample film thickness and the incident angle of light to be measured, can be accurately measured from the measured spectrum. Can be analyzed.

By using this method, the influence of multiple reflection interference contained in the reflection and absorption spectra of the thin film sample can be eliminated, and the spectral shape with minute reflection and absorption peaks can be given with high accuracy. In analysis, the accuracy and precision of analysis can be significantly improved.

In addition, this method does not require information such as the refractive index and the incident angle of the measurement light, and the sample film thickness can be obtained regardless of whether the sample is reflected or absorbed. That is, the absolute film thickness can be measured with high accuracy even on an arbitrary sample or an unknown sample without changing the parameters for each sample or using the measurement information of other systems at all. Extremely useful.
It should be noted that in contrast to the conventional technique, this method has no problem even if there is an absorption band in the spectral region of film thickness measurement, and therefore, highly accurate film thickness measurement is possible using a wide spectral region.

[Brief description of drawings]

Figure 1 shows the infrared absorption spectrum of PET with a film thickness of 25 μm. The horizontal axis is WAVE NUMBER and the vertical axis is TRANSMITTENNCE.
(Transmittance, unit%) is shown (same below). FIG. 2 is a model diagram of repeated reflection interference in a solid sample thin film, FIG. 3 is a diagram showing changes in fringe due to difference in film thickness, FIG. 4 is a diagram showing changes in fringe due to difference in refractive index, and FIG. Is a diagram showing a change in fringe due to a difference in transmittance, FIG. 6 is a model diagram showing multiple reflection interference in the measurement of a reflection spectrum of a solid thin film, and FIG. 7 is a fringe change due to a difference in film thickness of a solid thin film. Fig. 8 is a diagram showing the change in fringe due to the difference in the refractive index of the solid thin film, Fig. 9 is a model diagram showing multiple reflection interference in the measurement of the reflection spectrum of the solid thin film, and Fig. 10 is the basic of the present invention. 11 is a flow chart showing an embodiment of the present invention, and FIG. 12 is a view showing an infrared absorption spectrum of Myra (a).
Shows the processing result before the fringe removal (b) with the refractive index kept constant. FIG. 13 is a block diagram showing an apparatus system of an embodiment according to the present invention, FIG. 14 is a flowchart of an example of the simplex method, FIG. 15 is a spectrum diagram showing optical constants of a substance for simulation, and FIG. 16 is Fig. 17 shows the infrared absorption spectrum, Fig. 17 shows the spectrum of the processing result, (a) shows the initial solution, (b) shows the spectrum of the optimum solution, and Fig. 18 shows the spectrum of the optical constants by data processing. , Fig. 19 is a diagram showing an infrared absorption spectrum of polyvinyl chloride, Fig. 20 is a spectrum diagram of a treatment result, Fig. 21 is a diagram showing an infrared absorption spectrum of PET, and Fig. 22 is a spectrum diagram of a treatment result. Fig. 23 shows the infrared absorption spectrum of benzene. Fig. 24 and Fig. 25 show the spectrum results of the treatment. Fig. 26 shows the infrared absorption spectrum of benzene when the cell thickness is changed. , Fig. 27, FIG. 28 is a spectrum diagram showing the processing result, and FIG. 29 is a diagram showing fringes appearing in the visible and ultraviolet spectrum of a thin film having a thickness of 1 μm or less.

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Claims (1)

[Claims] 1. The same thin film sample is analyzed by a spectrophotometer.
The angle between the sample and the optical axis of the measuring light is changed at least twice, and the measured spectral data are linked by the invariant absorption coefficient or extinction coefficient, and the sum of squared error of the absorption coefficient or extinction coefficient is calculated. Film thickness, refractive index,
Set the objective function with the angle as a parameter, and calculate the parameter that minimizes the objective function by a non-linear optimization method to obtain a spectrum from which interference fringes are removed. A method for spectroscopic analysis of a thin film sample, characterized in that