JPS63241321A - Spectral analysis of membrane like specimen - Google Patents

Abstract

PURPOSE:To obtain a spectrum from which the effect of a fringe is removed and to obtain the data of a membrane thickness and refractive index dispersion with high accuracy, by utilizing the effect of the interference in a measured spectrum containing the data relating to a specimen condition such as the membrane thickness. CONSTITUTION:An infrared absorption spectrum is analyzed by a spectroscopic apparatus 20. Then, the initial value is calculated in steps 21-25 so as to smoothly converge local searching by using a non-linear optimizing technique. Further, in a step 31, in a manner so as to perfectly remove the effect of interference from the measured spectrum, refractive index dispersion n(nu) is taken in this algorithm in place of making a refractive index constant. By this method, interference is removed from the measured spectrum without using the data relating to an experimental condition such as the membrane thickness or the incident angle of light to be measured at all to make it possible to obtain a real spectrum being spectral data.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention performs spectroscopic analysis of a thin film sample and obtains the true spectrum of the sample from the observed spectrum data.

This article relates to a method for spectroscopic analysis of thin film samples to determine film thickness and optical constants.

The purpose of 1-spoon 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 and wavenumber axes, such as peak position, half-width, or absorption band, and information about intensity and amplitude. Generally, peak information is used for qualitative analysis because it is related to light energy, and intensity information is used for quantitative analysis because it is related to the number of photons.

In order to perform accurate analysis, it is necessary to measure the sample spectrum with high precision. However, the observed spectrum obtained from an analytical instrument is the true spectrum of the sample multiplied by the instrument function of the entire measurement system, and noise is added to it. There is a possibility of error in the analysis. Therefore, in order to perform accurate analysis, it is important to measure the spectrum with high precision and extract and separate high-quality signals from it.

In such waveform processing, processing for the purpose of qualitative and quantitative analysis (e.g. spectrum separation processing) is called post-processing, whereas numerical processing is used to improve the performance of spectroscopic equipment in order to obtain accurate spectra. A method aimed at indirectly improving performance is called preprocessing. Examples of preprocessing include noise removal (improving signal-to-noise ratio), deconvolution processing (improving resolution), etc., but the present invention basically uses noise removal for spectral data, which is one of the preprocessing methods. Regarding.

Noise can be roughly divided into two types: random noise that is irregular and does not depend on the signal, and systematic noise that is dependent on the signal.
Both must be removed for accurate analysis. In particular, in order to remove the latter by mathematical processing, it is necessary to completely understand the mechanism by which it occurs and trace its reverse process in detail. In the present invention, this is systematic noise that appears in spectroscopic measurements of thin film samples. We analyze the effects of multiple reflection interference and provide a new method for removing it. In the following, infrared absorption spectra, which are often used for qualitative and quantitative substances, will be explained as an example.

When measuring the infrared absorption spectrum of a thin film or a liquid in a cell, a periodic waveform with respect to the wave number is seen in the li region where absorption is small, as shown in the f:tSi diagram. This waveform is called a fringe in the field of analytical chemistry, and it not only gives periodic changes to the baseline of the spectrum, but also has a non-negligible effect on the shape and height of absorption peaks, which are important in analysis. Changes in the shape of observed spectra are a major obstacle to quantitative and qualitative analysis, so removal of 7-lino has become a major issue. The cause of fringing is the interference of the measurement light that is repeatedly reflected within the membrane or the liquid layer confined by the window material of the cell, especially in infrared measurements where the spread of the measurement light and the thickness of the sample are approximately the same. In this case, significant changes in the spectral shape can be seen.

In order to eliminate the influence of this interference on the Aiki alpha anus and skin plate, methods such as roughening the sample surface and making the measurement light incident at the Priester angle were used from early on; With the experimental method described above, it is impossible to completely suppress reflection within the film and interference caused by reflected light, and it is not possible to remove 7-phosphorus. Therefore, several methods for removing fringes using mathematical processing have been proposed.

T.rschfeld proposed a method to numerically remove the fringe frequency components from the measured spectrum (T.
1lirschfeld and Il, LMan
Elimination of Th1n Fil
m Infrared Channel 5pectr
a in Fourier Transform
Infrared 5pectroscopy'',
8pp I, 5pectrosc, 30*5tpp, 5
52-553 (1976)). However, this method is based on the erroneous assumption that the fringes are at a single frequency and addititively to the true absorption spectrum, and this method cannot correctly remove 7 rings.

On the other hand, R, N. Jones et al. have proposed a method for determining the optical constants (absorption spectrum and refractive index spectrum) of a sample whose i thickness is known (R, N. Jones, D. Es
color+J,P,l1auranek,P,Nee
lakantanyanand RoP,Youngt”S
OME PROBLEMS IN INFRARED
5PECTRO1'llOTOMETRY", J, M
ol, 5truck, 19tpp, 2l-42 (197
3), J, P l1aa+ranektP, Neela
Kantan J, P, Youngtand R, N, J
onesw“TIIecontrol of erro
rs in i, r, spectrophotometer
ry-1[[,Transmission meas
urements using thin ce
llS'''tspectroehim, ^eta 32
^, pp, 75-84 (1976), J, P, tlaw
ranekyP, Neelakantan*R,P,Y
own+and R, Njone9t “The co
ntrol of errors in i, r, 5p
electrophoto.

a+etry-■, Corrections for
dispersion distortion an
d the evaluation of b
oth optical constants
spectrochim, ^eta 328, pp.
85-98 (1976), J.P.

Hawranek and R.N., Jonesw”T.
he control of errors in i
,r,spectrophotometry-V,^5
scss+aent errors in the
evaluation of optical c
instants by transmission
measureIIlents on thin fi
tis”yspeeLrochiIo, ^eta 32
^, pp, 99-109 (1976), J, P.

Hawranek and RlN, Jones*″T
he determination or the op
tical constantds of benzene
ne and chloroform in the
i, r, by thin film transmission
sion”!Spectrochim, ^eta 32
^, 1) I), 111-123 (1976), G, K
Ribbegaard and R9Njooes, “T.
be Measurement of tl+e 0
ptical Con5tants of Th
1n 5olid Films in the
Infrared″g^ppl, 5pectrosc
, 34tpp, 638-645 (1980)). This method calculates the spectrum affected by interference using the absorption spectrum as a parameter, and then fits it to the observed spectrum to obtain the absorption spectrum. However, in order to apply this method to observed spectra, it is necessary to measure the sample film thickness with considerable precision in advance, and complex preliminary experiments are required.

In the present invention, since the film 1g- is used as a sample for unknown scales, conventionally known film thickness measurement methods are as follows: (1) stylus method, (2) interferometry.

■Spectroscopy, ■Ellipsometry, etc.

In the stylus method (2), a needle is brought into contact with the substrate portion and the sample portion on the substrate, and the difference in height is electrically magnified and measured. The measurement limit is about 1 nm, and it is necessary to measure at the edge of the substrate part and the sample part.

Similar to method (2), the interferometry (2) measures the difference in height between the edges of the substrate and the sample. A semipermeable membrane such as mica is placed on the sample at a slight angle, and the measurement light is caused to interfere with the gap between the membrane and sample surfaces. Since the interference fringes shift at the edges according to the difference in height between the substrate section and the sample section, the optical thickness of the sample can be measured from this amount of shift. Since it is necessary to deposit a highly reflective substance on the sample, this is a destructive measurement, and the measurement limit is approximately the wavelength (several nanometers) of the measurement light.

The spectroscopy method (2) is calculated from the frequency of fringes in the spectroscopic spectrum of the sample in the region where there is no absorption.

(N.J., Harrick, Determinatio.
n of Refractive Index anc
l Film Th1ckness from Int
erference Fringes'', Δpp1.O
pt, 1(Ll(Lpp, 2344-2349, DJ,
Moffatt and D.G., Cameron, L.
Occasion of Lou+ Frequency
Fringe Signatures in F
ourier Transform LIls ofS
pectra", ^pp1.5pectrosc, 37
,6. p, 556 (1983), Sadako Fujimura, Atsuki Matsumura, “Measurement of film thickness using spectrometry”.

, Proceedings of the 46th Japan Society of Applied Physics Academic Conference +p.

45 (1985)). However, this method can only be used in areas where there is no absorption and no change in the refractive index, and even though it uses a spectroscopic spectrum, it measures areas where the physical properties of the sample are difficult to express. , 7. Similar to trying to eliminate phosphorus as noise without obtaining information from it, we are also throwing away useful material information called spectral information. Although this spectroscopy is a non-destructive measurement, what is measured is the optical thickness, and the physical thickness must be determined by a separate measurement of the refractive index of the sample. The measurement limit is about several n111.

In the ellipsometry method (2), the optical constants and film thickness of the sample are determined by measuring the polarization state of measurement light that is repeatedly reflected within 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 multiple measurements while changing the underlying medium and the film thickness of the sample, and performing mathematical processing on the obtained data. It is necessary to provide an accurate angle of incidence, and the optical constants of the underlying material must be determined through preliminary experiments.

Purpose of the Invention The present invention is capable of obtaining a spectrum from which the influence of 7-lino has been removed without requiring all information regarding the measurement sample and without requiring information regarding the measurement conditions (incident angle of measurement light). Another object of the present invention is to provide a novel spectroscopic analysis method for thin film samples that can obtain information on S thickness and refractive index dispersion with high precision.

Until now, we have treated the effects of interference on the true spectrum as noise in the analysis.

However, if we change our perspective and consider this interference as the object of observation, we can see that the fringes in the measured spectrum are caused by the influence of the measurement system, but they must also contain information about the sample. come to mind. As will be described later, the frequency of, for example, 7-lino 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. Furthermore, the amplitude of the fringe depends on the reflectance of the sample surface.

This means that the measured spectrum also contains information about the film thickness and sample conditions, and by using the influence of interference instead of simply removing it as noise, we can obtain a lot of material information from it. It is possible to extract.

The present invention is based on the above idea, and involves measuring the same thin-film sample at least twice using a spectrophotometer while changing the angle between the sample and the optical axis of the measurement light, and comparing the measured spectral data with respect to each other. It is linked by a variable absorption coefficient or extinction coefficient, and the sum of squared errors of the absorption coefficient or extinction coefficient is set as an objective function with film thickness, refractive index, and angle as parameters, and a nonlinear optimization method is used to minimize the objective function. The basic feature is that the above-mentioned parameters are calculated to obtain a spectrum with interference fringes removed, and the film thickness and refractive index dispersion of the sample can be obtained simultaneously.

[Principle] FIG. 2 is a model diagram showing the multiple reflection interference that occurs when light is projected onto a solid thin film sample. Furi'l'lii A
.

The measurement light (1) of (ν) has a film thickness d. , a thin film with refractive index n (
2) angle θ. When the incidence is , Skill's law, sin θ
. = n sin θ ... Refracted at (1),
The transmission distance d within the membrane is d=d,/cosθ-(2).

Although the refractive index n is actually a function of the wave number ν, it is assumed to be a constant here for simplicity, and the refractive index dispersion will be described later.

Letting the extinction coefficient of sample (2) be a(ν), the transmittance spectrum T(ν) of transmitted light (3) for one optical path in the film is T(
ν) = exp(-nda(ν)l - (3) However, in actual absorption measurements, multi-beam interference occurs due to reflection on both sides of the film (2), and the resulting transmittance spectrum S(ν ) is the following formula.

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

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

In the above equation (4), the third term in the denominator (the term including cos) gives periodic modulation to the spectrum.

Figures 3 and 4 show the influence of this interference on the transmittance spectrum S(v).

Figure 3 shows that the film thickness d0 is 5.15.25μ for the same sample.
If it changes to a pond (the same figure (a L (b) t (c
), the same applies hereinafter) is shown, and the state of change in the fringe is shown. The refractive index n is 1.
It is constant at 6. It can be seen that the thicker the film, the lower the frequency of the 7-rinno.

Figure 4 shows the same sample with refractive index n of 1.3, 1, 6,
The measured spectrum S(ν) when the temperature is changed to 2°O is shown, and the change in the fringe is shown. The film thickness d is constant at 15μ. It can be seen from this that as the refractive index increases, the amplitude of the fringe increases and the frequency decreases.

Moreover, FIG. 5 shows how the 7-lino changes due to the difference in transmittance. When the transmittance is constant at 100%, 80%, and 30%, the film thickness d. is 15 μm, refractive index n
is 1.6. From the results of this Schemilehessian, it can be seen that even if the refractive index is constant, the higher the transmittance, the thicker the amplitude of the 7-lino.

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

Similarly to the above, FIGS. 7 and 8 show changes in the shape of the reflection spectrum due to changes in film thickness and refractive index. Figure 7 shows the change in fringe due to the difference in film thickness when the refractive index n=2.0, and Figure 8 shows the film thickness d. This is a change of 7 linos due to the difference in refractive index when the refractive index is kept constant at 15 μm.

On the other hand, when the sample is a liquid, absorption spectrometry is performed by enclosing the sample in a liquid cell. FIG. 9 shows a cross section of a liquid cell filled with liquid. In the figure, the 11th and 5th layers are air. Since the thickness d2 of the third layer (liquid layer) is usually about 1 to 100 μm, multiple reflection interference occurs within the layer as in the case of a solid sample. Second. The fourth layer window material does not have an absorption peak in the measurement wavelength range, and its thickness d is approximately several DII+, which is sufficiently thick compared to the liquid layer, so multiple reflection interference within the window village is actually Not a problem.

[7 Principle 1 of Phosphorus Removal] Taking the case of measuring transmitted light of a solid sample shown in FIG. 2 as an example, FIG. 10 shows the basic concept of the present invention and a method for removing interference components.

The spectrum S(ν) obtained by absorption measurement using the spectrometer (10) is given by the above equation (4). When this equation (4) is transformed, it becomes a quadratic equation regarding the target true spectrum T(v) without the 7-lino as shown in the following equation.

r's(L')T2(L')-[23(ν)r2cos
(4yn, docosθ, ν)−1]T(1/)+S(
ν)=0...
......(7) In equation (7), unknown T
In addition to (ν), if we assume that the film thickness dot of the sample, the refractive index n, and the reflection angle θ of the measurement light within the film are unknown, the number of these unknowns exceeds the number of equations, and the equation (7) cannot be solved.

Therefore, in order to be able to solve this equation, the same sample is measured at least twice using the spectrometer (10). By keeping the point of incidence of the measurement light on the sample constant and changing the angle between the optical axis of the incident light and the sample, that is, the angle of incidence, the angle of incidence θ can be calculated. 1. θo2
Measure with. When the angle of incidence is changed, the absorption length d (=d,
/cos θ1) and the reflectance r change, and the measured spectrum S(ν) that depends on this changes from S+(ν) in the same sample.
, S2(ν) are obtained.

If the absorption fgd in each measurement is d, d2, then (
d=d, )/cosθ1. d=d(,/cosθ2,θ
1. θ2 is the incident angle θ. 1tθ. 2), S, (ν).

Each true spectrum T1(
ν) and T2(ν) are connected by the absorption coefficient a(ν), which is an invariant, as follows.

ndl nd2 Equation (7) holds true for each of the two measured spectra S+(v)-32(v), and by adding equation (8) to this, the number of equations exceeds the number of unknowns.

Therefore, by solving this simultaneous equation, the true spectrum 'r
+(ν), T2(ν), film thickness dos refractive index n, and angle of incidence θ1. It becomes possible to obtain θ2.

However, it is virtually impossible to solve this simultaneous equation analytically. Furthermore, there is a problem that the number of equations is greater 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, we focus on equation (8) and apply the least squares method to it.

In equation (8), the norm is used to minimize the sum of quadratic errors between the left and right sides. Then, an optimal solution is found here using a nonlinear optimization method. This norm is represented by equation (9).

→ll1in, --(9) This norm calculates the absorbance per unit length, that is, the absorption coefficient at(νL
aw(ν), and then find the parameters so that the sum of errors is minimized. By substituting the finally found parameters into equation (7), the interference fringe Removed true spectrum T+(ν), T
2(v) (Steps (13) to (16) in Figure 10)
). Note that in each iteration of changing parameters in the nonlinear optimization method, the measured spectrum S, (ν)
, S2(ν) and parameters (ntdotθ1.θ2) to obtain TI(ν) and T2(ν), which are then substituted into the above equation (9) to calculate the objective function Q.

Fire pan ■ Fig. 11 shows a process diagram of one embodiment. This example relates to analysis of an infrared absorption spectrum using a two-beam infrared spectrophotometer as a spectrometer (20).

The simplex method is used as a nonlinear optimization method.

Then, initial values are determined so that the local search using the simplex method converges smoothly (step (21)
) to (25)).

Furthermore, in order to completely eliminate the influence of interference from the measured spectrum, instead of keeping the refractive index constant, refractive index dispersion n(ν) is incorporated into this algorithm (step (31)). That is, in the above description, the refractive index has been treated as being constant within the measurement wavenumber range, but in reality, the refractive index is a function of the wavenumber, and changes particularly in the vicinity of the absorption peak. Figure 12 (a) shows the infrared absorption spectrum of Mylar measured twice with different incident angles, and the result of removing 7 phosphorus from this spectrum while keeping the refractive index constant is the same figure (b).
).

It can be seen that fringe removal fails on the high frequency side. The refractive index affects both the frequency and amplitude of the 7-ring beam, and in order to completely eliminate the influence of interference from the measurement spectrum, refractive index dispersion is incorporated. On the contrary, this suggests that the refractive index dispersion of the sample can be determined from the spectrum affected by interference. By taking 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 apparatus system of this embodiment. The thin film sample was manufactured by Perkin Elmer Model 9.
The absorption spectrum is measured by an infrared spectrophotometer (20) at 83. This spectrophotometer (20) is controlled by a model 3600 data station (20C) manufactured by the same company, and the measured spectral data is transmitted to a computer (35C) through a communication interface R8-232C.
) will be forwarded to. The computer (35) is specifically a PC-9801F personal computer manufactured by NEC Corporation. The spectrum data is stored on a floppy disk set in the computer (35). Arithmetic processing is performed on this PC-9801F, and the results are displayed on a CRT display (36) and/or recorded on a plotter or printer (37).

Arithmetic processing on the computer (35) is BASIC
This is done using a language program. The program includes
Includes simplex method programs, least squares method programs, and golden section method programs for finding initial values.

First, the measured spectrum data St(')=S, (
ν) to determine the initial value. The objective function Q as shown in equation (9) above has many minimum points in the vicinity of its minimum point. Therefore, when performing a local search using the simplex method, it is necessary to use values within ±10% of the optimal values as the initial values of the film thickness -〇 and refractive index n among the parameters, or the search will not be successful. There is. For this reason, the initial values of parameters for each measured spectrum are adopted as values that satisfy the following criteria.

E(n, θ=do)=-ΣP (vt) ・logI
P (vt)]→min, -・・・・・・(10) However, P(ν)=IT′ し)17 光い′(plug) 1Here, T゛(ν) is T(ν) represents the second derivative with respect to the wave number ν. This criterion gives parameters such that the peaks of the spectrum after removing fringes are localized. In other words, this process is similar to how humans visually search for parameters that will remove as many fringes as possible. (1
The golden section method was used to find the optimal solution to equation 0).

Using the parameters thus obtained as initial values, the optimal solution is then estimated using the simplex method. 70 simplex method programs (package programs)
-The chart is shown in Figure 14.

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

do: Film thickness of thin film sample θ1: Incident angle θ. Reflection angle θ2 in the film at , incident angle θ. Reflection angle i in the film at dot θ1.2: Average value of refractive index within the measurement wavenumber range. Using θ2 and the refractive index dispersion n(ν) obtained using a stone, the observed spectrum St(
ν)−82(ν) to the true spectrum T+(ν
Obtain L T 2(ν). Similar to the above equation (4), the following relational expression holds between T(v) and S(v).

As shown in equation (5), this is calculated according to the 7-Renel formula.
(ν) and θi.

...(5゛) As mentioned above, equation (11) is a quadratic equation regarding T(ν), so if the four parameters and S(ν) are known,
From this, T(1/) can be found.

However, C(ν) = r, 2 (ν)S, (ν)cos(4π
νn(ν) d, cos θ1) The spectrum T(ν) which is not affected by interference and the extinction coefficient k(ν) of the sample are related by the following relationship.

i ” 1, 2, S, (ν), S2 (ν) are spectra of the same sample, so the absorption coefficient at(ν), a2(ν) or extinction coefficient obtained from each is (ν), 2(ν) is equal to.

Therefore, the extinction coefficient spectrum obtained from the two spectra is calculated, and the sum of squared errors is calculated to obtain four parameters d that minimize the inter-objective IQ. , θ1°θ2,11
seek.

The refractive index spectrum n(v) is Kramere −Kr
Onig's relational expression is given by the following equation.

Note that P represents the reproductive integral.

Here, the integration range is O-■, but since the spectrum can actually be measured only in a finite range, the following approximate formula is used.

tatashi, i is the measurement wave number range ['1ever t "1lf
Fe? ' ] is the average value of n(ν). This five is given as a parameter in the iteration. In addition, k(ν) is 2 obtained from the two observed spectra S+(ν) and 82(ν) in that iteration.
This is the average value of +(ν) and 2(ν) for one extinction coefficient spectrum, and is the estimated value of the extinction coefficient in the repeating direction.

k (ν) = most likely Ω (16) In this way, the average value k (ν) of the extinction coefficient obtained when calculating the optimization objective function and the parameter n to n (ν ) is calculated (step (31)).

It is said that the error caused by using equation (14) instead of equation (13) will hardly be a problem if multiple absorption peaks or bands are isolated within the measurement wavenumber range and the sampling is sufficiently fine. Therefore, when applying the method according to the present invention, the spectrum is measured so as to satisfy the above conditions.

Absorption coefficient a(ν
) is given by the following equation from the extinction coefficient k(ν).

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

n(')=n(,v)+ik(+'),
- (18) After completing the iterative calculation, these can be calculated and displayed together with the film thickness, extinction coefficient spectrum, refractive index spectrum, and reflectance spectrum, or printed out on a printer (37).

The effectiveness of the above embodiment in infrared absorption spectrum measurement was verified through simulation experiments.

Assuming a material with the optical constants shown in Figure 15 (aL(b)), the film thickness of the sample is 25.000 μm, JI constant likelihood, total incidence angle, ooo', and the infrared absorption spectrum of this material. is observed as shown in Figure 16(a) due to the influence of interference.Next, the incident angle of the measurement light is set to 10.000°.
16(b), the absorption spectrum is observed as shown in FIG. 16(b) (however, noise is not included). FIG. 17 shows a rough transmittance spectrum obtained by applying this method to these two spectra.

FIG. 17(a) shows T1(v) and 72(v) superimposed in a spectrum based on the optimal initial solution obtained by the golden section method. Figure (b) shows 70- of the f511 diagram.
This is the spectrum of the optimal solution obtained using all of them.

Although T, (v) and T2 (v) are shown at the same time, they completely overlap. The film thickness value of the sample obtained at this time was 25
The angle of incidence of the measurement light was 0.01° and 10.00°, respectively. Also, the extinction coefficient spectrum and refractive index spectrum that were simultaneously etched are shown in Figure @18. The error from the true value of the obtained spectrum is 2.9334X10-' for the i11 optical coefficient spectrum and 2.9334X10-' for the refractive index spectrum.
．． It was 7337X10-4. For spectral data of 250 points, the time required for calculation was approximately 2 minutes to obtain the initial solution and approximately 10 minutes to obtain the optimal solution.

Specific example 1 This method was applied to infrared absorption measurements of actual solid samples.

Figure fjS19 shows the observed infrared absorption spectrum of polyvinyl chloride with a thickness of 15 μm. Measurements were taken at 340 sampling points and at different angles of incidence and are shown superimposed.

Figure 20 shows the results of applying this method. The figure (,) shows the absorption spectrum with the influence of interference completely removed, and the figure (b) shows the obtained refractive index spectrum.
The obtained film thickness was 14.947 μm, and the incident angles of the measurement light (θ.1.θ.2) were 3.05" and 13.12", respectively.
It was °.

Specific Example 2 This is an example in which PET (polyethylene terephthalate) with a film thickness of 25 μm was used as a sample. FIG. 21 shows this infrared absorption spectrum (175 points).

Figure 22 shows the results of applying this method. The absorption spectrum is shown in (,) of the same figure, and the refractive index spectrum is shown in (b) of the same figure. The determined film thickness was 26,974 microns, and the measured light incident angle was 9,83 x 10-'° and 5.90''.

Confocality This is an example of applying this method to an actual liquid sample.

The liquid is benzene. This infrared absorption spectrum is
Sl(v) and S2(v) shown in FIG. 3 are shown superimposed. Sampling is 200 points. Cell thickness is 2
KRS-5 was used for the window material of the liquid cell, and a 25-μm spacer was used to determine the thickness of the liquid layer.

The refractive index of KRS-5 is given in the literature (J, ^, Jemleso
n, R, H, Mcfee, G, N, Plass, R, H
oGrube, and R,G, Ricl+ards,
INFRARED PI (YSICS AND ENG)
INEERING”9M8 to R8 to old LL.

2 in the measurement wavenumber range from New York (1963)).
It was set at 392.

The thickness of the liquid layer determined is 26.573μi''Chff
The angle of incidence of il constant light is 3.48X10-'° and 7.12
It was °. The obtained transmittance spectrum is shown in Figure 24.
The extinction coefficient spectrum is shown in FIG. 25(a), and the refractive index spectrum is shown in FIG. 25(b).

Co-calyx I This is a verification of the results obtained in Specific Example 3. That is, the same measurement was performed using benzene while changing the thickness of the liquid layer. A spacer with a thickness of 50 μm was used. Sampling is also 200 points. The two measured infrared absorption spectra are shown in FIG. 26 superimposed. The results obtained from this spectral data are shown in Figure 27, and the extinction coefficient spectrum is expressed as fjS
FIG. 28(a) shows the refractive index spectrum, and FIG. 28(b) shows the refractive index spectrum. The extinction coefficient spectrum and refractive index spectrum shown in FIG. 25 match extremely well.

Also, the thickness of the liquid layer found is 50.777μ+n,
The incident angle of the measurement light is 3.49X10-'° and 4.55°
Met.

The optical constants obtained can be found in reliable literature (Appl, 5pe
ctrosc, 34,6. pp, 657-691 (19
80)). This is shown in Table 1°. According to this method, the obtained film thickness and refractive index have an accuracy of 4 to 5 digits.

Table 1 In the above embodiments, a dispersion type spectrophotometer was used, but of course a 7-Lier transform type spectrophotometer may also be used.

It is preferable that the angle of incidence of the measurement light on the sample be close to 0° because it can eliminate the influence of polarization, and the angular difference in the angle of incidence should be 5°.
The angle of incidence is preferably ~10°, but there is no particular limitation.To change the angle of incidence, the optical axis of the measurement light may be changed, or the optical axis may be kept constant and the sample may be tilted.However, the angle of incidence, α is unchanged.

In the above embodiment, the measurement is performed twice by changing the incident angle, but the measurement is performed twice or more, and the spectral data SI(ν), S
2(ν), S3(ν), etc. are obtained, and the optimal parameters are determined using the same method as in the example by connecting these using absorption coefficients or extinction coefficients, and more accurate spectra and optical constants are obtained. data can be obtained.

Moreover, it can be applied to multilayer film samples. Multilayer film materials such as antireflection films and interference filters have various uses, and applying this method to multilayer film samples may be extremely effective in controlling their spectral characteristics and film thickness.

Although the method according to the present invention uses a software program, this program can be converted into a ROM and combined with a microcomputer to configure it as firmware or hardware. In addition, in such a device, when measuring the absorption or reflection spectrum of a semiconductor material, for example, the measurement light is guided using an optical fiber and the sensor head is scanned over the sample to obtain the sample spectrum and film thickness. , 2 of refractive index dispersion
Dimensional measurement is also possible. Furthermore, it can also be applied to absorption data from a microspectroscopy device.

Although the above embodiments were related to infrared absorption spectra, the present invention is not limited to the infrared region. In order to utilize 1° interference, the target is an organic thin film sample with a thickness of several to several tens of microliters. In this case, spectral measurement in the infrared region is suitable; however, when the target is a sample with a thickness of about 1 μm or less, such as a coating film, measurement in the visible to ultraviolet region is more suitable. FIG. 29 shows the fringe appearance of samples with thicknesses 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 visible spectrum.If a wavelength region with no absorption is selected according to the sample, it can be used to measure film materials such as film materials without prior information such as refractive index. Since thickness can be measured with high precision and in a short time, it is possible to inspect film thickness directly on the production line. Specific examples include functional glands and protective films formed on semiconductor surfaces, single-layer or multi-layer films forming the recording layer of optical memory, and any organic or inorganic thin films formed by sputtering, vapor deposition, plasma polymerization, etc. Applicable to

As mentioned above, the present invention reversely utilizes the multiple reflection interference that occurs in spectral analysis, and does not use any information regarding the experimental conditions such as the sample film thickness or the incident angle of the measurement light. At the same time, it is possible to remove interference from the measured spectrum and obtain the true spectrum, which is spectral information, and at the same time, it is possible to obtain the refractive index spectrum and information about the experimental conditions, such as the sample film thickness and measurement light incident angle, from the measured spectrum with high accuracy. can be analyzed.

By using this method, the reflection of thin film samples.

The influence of multiple reflection interference included in the absorption spectrum can be eliminated, and a spectrum shape with minute reflections and absorption peaks can be provided with high precision, dramatically improving the accuracy and precision of analysis in qualitative and quantitative analysis. be able to.

Furthermore, this method does not require information such as the refractive index or the incident angle of measurement light, and can determine the sample film thickness regardless of the presence or absence of reflection or absorption of the sample. In other words, the absolute film thickness can be measured with high precision even on arbitrary or unknown samples without changing parameters for each sample or using any information from measurement in other systems, and it can also be used as a film thickness measurement method. Extremely useful.

Note that, in contrast to the prior art, this method does not cause any problem even if an absorption band exists in the spectral region for film thickness measurement, and therefore, highly accurate film thickness measurement is possible using a wide spectral region.

[Brief explanation of drawings]

Figure f: 141 is a diagram showing the infrared absorption spectrum of PET with a film thickness of 1!125μ, where the horizontal axis shows VENUMBER (wave number) and the vertical axis shows TRANSM ITTANNCE (transmittance, unit %) (the same applies below). Figure 2 is a model diagram of repeated reflection interference in a solid sample thin film, Figure 3 is a diagram showing changes in fringe due to differences in film thickness, Figure 4 is a diagram showing changes in fringe due to differences in refractive index, Figure 5 Figure 6 shows the change in 7L due to the difference in transmittance. Figure 6 is a model diagram showing multiple reflection interference in measuring the reflection spectrum of a solid thin film. Figure 7 shows the change in 7L due to the difference in the thickness of the solid thin film. Figure 8 is a diagram showing the change in 7L due to the difference in refractive index of solid thin films, Figure 9 is a model diagram showing multiple reflection interference in measuring the reflection spectrum of solid thin films, and Figure 110 is a diagram showing the variation of 7L due to differences in the refractive index of solid thin films. Figure 11 is a flowchart showing the basic concept, Figure 11 is a diagram showing an embodiment of the present invention, Figure 12 is a diagram showing the infrared absorption spectrum of Mylar, and (a) is before 7-phosphorus removal (b). ) shows the processing results with a constant refractive index. FIG. 13 is a block diagram showing an apparatus system according to an embodiment of the present invention, FIG. 14 is a 70-chart of an example of the simplex method, FIG. 15 is a spectrum diagram showing optical constants of a substance for simulation, and FIG. 16 The figure shows its infrared absorption spectrum, ff51
Figure 7 shows the spectrum of the processing results; a) is the initial solution; (b) is the spectrum of the optimal solution; Figure 18 is the spectrum of optical constants resulting from data processing; Figure 19 is the red color of polyvinyl chloride. Figure 20 is a spectrum diagram of the processing result, Figure t521 is a diagram showing the infrared absorption spectrum of PET, Figure 22 is a spectrum diagram of the treatment result, fjS23 is the infrared absorption spectrum of benzene. Figures 24 and 25 are spectrum diagrams showing the processing results, Figure 26 is a diagram showing the infrared absorption spectrum of benzene when the cell thickness is changed, and Figures 127 and 28 are spectrum diagrams showing the processing results. The spectrum diagram shown and the tj&29 diagram are diagrams showing fringes appearing in the spectrum of the visible T: outer region of a thin film with a thickness of 1 μm or less.

Claims (1)

[Claims] (1) Measure the same thin film sample at least twice using a spectrophotometer while changing the angle between the sample and the optical axis of the measurement light, and calculate the absorption coefficient or extinction coefficient of each measured spectrum data, which is an invariant. In addition, the sum of squared errors of the absorption coefficient or extinction coefficient is determined by the film thickness, refractive index,
The angle is set as an objective function as a parameter, and the parameters that minimize the objective function are calculated using a nonlinear optimization method to obtain a spectrum with interference fringes removed, as well as the film thickness and refractive index dispersion of the sample. A method for spectroscopic analysis of a thin film sample, characterized in that it is possible to simultaneously obtain the following.