Method for determining a component concentration and program for determining a component concentration

Abstract

A first difference spectrum between a sample spectrum of a sample to be tested and a reference spectrum of a reference sample in which the concentration of a component under consideration is lower than in the sample to be tested is calculated (S10); using a plurality of reference spectra obtained by multiple measurements of the reference sample, a difference spectrum having a similar shape to the first difference spectrum is selected from among a plurality of difference spectra between two reference spectra (S20); a second difference spectrum is calculated from the selected difference spectrum and the first difference spectrum (S30); and the shape of an absorption band of the component under consideration is determined from the second difference spectrum to determine the concentration of the component under consideration (S40).

Description

RELATED REGISTRATION

[0001] This application claims priority from Japanese Patent Application No. 2024-2536, filed on January 11, 2024, the specification of which is incorporated herein by reference in its entirety. FIELD OF EXPERTISE

[0002] The present invention relates to a method for determining a component concentration in a sample to be tested by a spectroscopic analysis device such as a Fourier transform infrared spectrometer (FTIR). TECHNICAL BACKGROUND

[0003] A method for determining the concentration of substituted atomic carbon in single-crystal silicon using FTIR is known. For example, EM-3503, a standard of the Japan Electronics and Information Technology Industries Association (JEITA), Non-Patent Literature 1, describes a method by drawing a baseline in an absorption band (near the wavenumber 605 cm-). -1) specific to substituted atomic carbon, and the band height is multiplied by a predetermined factor to obtain the carbon concentration. The absorption band of carbon overlaps with a broad absorption band of the silicon lattice; therefore, in the determination method of Non-Patent Literature 1, the absorption spectrum of the sample to be tested (referred to as "sample spectrum") is measured, silicon with a low concentration of substituted carbon is used as a reference sample to measure the absorption spectrum of the reference sample (referred to as "reference spectrum"), the difference spectrum of the two spectra is calculated to remove the lattice absorption band of silicon, and the sample spectrum of only the absorption band of carbon is obtained.

[0004] In addition, Non-Patent Literature 1 describes that when calculating the difference spectrum for correcting the sample thickness, the difference spectrum is calculated from the reference spectrum multiplied by [thickness of the sample / thickness of the reference sample] (ie, the difference coefficient) and the sample spectrum.

[0005] The method of clarifying the absorption band of a component of interest by calculating the difference spectrum from the sample spectrum and the reference spectrum (i.e., the "difference spectrum method") is applied not only to the method for determining the concentration of a component in single-crystal silicon, but also in the concentration analysis of small amounts of components in different samples, such as the method for analyzing concentrations of multiple components in Patent Literature 1, and is a well-known method.

[0006] As in Fig. 2 of Patent Literature 1, the spectra shapes of five components belonging to perfluorocarbon are similar, and each has a broad absorption band in the wavenumber range of 1200 to 1300 cm -1 For example, in the sample spectrum [S] of the sample to be tested, which contains five components, due to the fact that the only absorption spectrum of perfluoromethane (at wavenumber 1280 cm -1) has low intensity, the peak of perfluoromethane is obscured by the broad absorption peaks of the other components in the absorption spectrum of the test sample in which five components are mixed. Therefore, a computer calculates the difference spectrum [A] from [Sample spectrum - Perfluorobutane spectrum] by subtracting the spectrum of perfluorobutane with matching absorption from the spectrum [S] of the test sample. Similarly, by successively subtracting the spectra of perfluoropentane, perfluoropropane, and perfluoroethane with matching absorption from the difference spectrum [A], a difference spectrum can be obtained in which the absorption band of perfluoromethane is clearly defined. PREVIOUS TECHNOLOGY Patent Literature 1: Unexamined Japanese Patent Application Publication No. 2009-236565 A Patent Literature 2: Unexamined Japanese Patent Application Publication No. 2020-012772 A Patent Literature 3: Unexamined Japanese Patent Application Publication No. 2009-162667 A Non-patent literature 1: JEITA Standard EM-3503 “Standard test method for the content of substituted atomic carbon in silicon by infrared absorption” Non-patent literature 2: SEMI standard MF-1391-1107 “Test method for the proportion of substituted atomic carbon in silicon by infrared absorption” OBJECT AND SUMMARY OF THE INVENTION

[0007] According to the method for determining the concentration of components using the difference spectrum method described above, the factor that makes it difficult to determine low concentrations is the fluctuation of the sample temperature at the measurement point during spectroscopic measurement. The inventors focused on the following phenomena as the influence of sample temperature fluctuations on the absorption spectrum during single-crystal silicon measurement.

[0008] - The thickness of the silicon varies slightly due to thermal expansion / contraction and the absorption intensity due to lattice vibrations of the silicon increases / decreases proportionally to the thickness.

[0009] - The absorption band of the silicon lattice shifts.

[0010] Due to these phenomena, the absorption band of the silicon lattice cannot be completely removed from the sample spectrum by the conventional difference spectrum method alone, and a baseline suitable for the absorption band of carbon cannot be established by the remaining absorption band, thus making the determination of carbon concentration imprecise.

[0011] To avoid such problems, strict temperature control of the sample under test and the reference sample can be implemented during spectral measurement. For example, during the production of single-crystal silicon for semiconductor manufacturing, some samples may be too large to fit into the temperature regulator of a conventional spectrometer. Furthermore, requiring a temperature regulator specifically for measuring carbon concentration is a disadvantage in terms of production costs and time.

[0012] Patent Literature 2 also describes a method for temperature correction of the carbon concentration of single-crystal silicon. Temperature correction based on the difference between the temperature measurement values of the sample under test and the reference sample is applied to the carbon concentration in single-crystal silicon measured by FTIR. However, in the method of Patent Literature 2, the temperature of the sample under test must be measured for temperature correction, and a method that does not require temperature measurement of the sample under test is desirable in practice.

[0013] In addition, Patent Literature 3 uses a model function Ap(x) of the reference spectrum on which the wavenumber shift correction is performed. The model function is expressed as a model function "Ap(x) = a1As(x-a2) + a3 + a4x", and the factors a1 to a4 in the model function are numerically calculated such that the sum of squares of the deviations D (D = Σ{As(x) - Ap(x)} 2) between the model function Ap(x) and the sample spectrum As(x) becomes minimal. The factor a2 is a shift correction value. The difference spectrum between the model function and the sample spectrum (As(x) - Ap(x)) is obtained by applying the model function constructed by numerical calculation to determine the concentration based on the absorption band of the component under consideration that appears in this difference spectrum. However, the wavenumber shift correction according to Patent Literature 3 uses the model function As(x) that is mathematically determined and is based on the premise that the wavenumber shift that actually occurs satisfies the model function. Therefore, it cannot be regarded as a correction based on spectral data obtained by actual measurement of the sample under test, and there remains room for improvement in the reliability of the wavenumber shift correction.

[0014] In the method for determining the concentration of a component using the difference spectrum method, when the temperature of the sample to be tested fluctuates during spectroscopic measurement, the absorption intensity of another component that overlaps with the absorption band of the component in question of the sample to be tested increases / decreases, and the absorption band of another component that overlaps with the absorption band of the component in question of the sample to be tested shifts (that is, wavenumber shifts); therefore, the object of the present invention is to provide a temperature correction method that can solve these problems and enable determinations of lower concentrations than heretofore with respect to a component in question of a sample to be tested. Solution to the problem

[0015] The inventors focused on the fact that when the spectrum of the same reference sample is measured multiple times using a spectroscopic quantitative measurement device, the shape of the measured reference spectrum changes even though the measurement conditions remain unchanged. They considered that such a change in shape is due to a slight temperature fluctuation of the sample under test. This means that in the reference spectra obtained by repeatedly performing spectroscopic measurements of the reference sample, increases / decreases in the absorption intensities of other components and a shift in the absorption band occur due to the fluctuations in the sample temperature. This increase / decrease in the absorption intensities and shift in the absorption band are reflected in the form of the difference spectrum between any two reference spectra.They found that by selecting the difference spectrum having a similar shape to the difference spectrum between the sample spectrum and the reference spectrum (the first difference spectrum) according to the difference spectrum method, among the difference spectra between two reference spectra, which show both increase / decrease in absorption intensity and shift in absorption band, and subtracting the selected difference spectrum between reference spectra from the difference spectrum between the sample spectrum and the reference spectrum to derive the second difference spectrum, the influence due to the fluctuations in sample temperature could be eliminated from the first difference spectrum and a lower concentration of the component in question of the sample to be tested could be determined than previously.

[0016] This means that a method for determining the concentration of a component according to the present invention comprises the following steps: Calculation of a difference spectrum as the first difference spectrum between: a sample spectrum of a sample to be tested, measured with a spectrometer, which shows both an absorption band of a component under consideration and an absorption band of another component that overlaps with the absorption band of the component under consideration, and a reference spectrum of a reference sample measured with the spectrometer in which the concentration of the component in question is lower than in the sample to be tested, or the concentration of the component in question is zero, Calculating a difference spectrum between any two reference spectra selected from among several reference spectra of the reference sample measured multiple times with the spectrometer, and repeating the process of calculating several difference spectra to correct the influence of a change in the absorption band of the other components caused by a difference in sample temperature (e.g., increase / decrease in absorption intensity, shift in absorption band), Selecting a difference spectrum having a shape similar to that of the first difference spectrum from among the plurality of difference spectra between two reference spectra, and Calculating a difference spectrum between the first difference spectrum and the selected difference spectrum between two reference spectra as a second difference spectrum, wherein a shape of the absorption band of the component under consideration is determined from the second difference spectrum in order to determine the concentration of the component under consideration.

[0017] In the manner of the method of the present invention described above, by subtracting the difference spectrum between two reference spectra having a shape similar to the shape of the first difference spectrum (ie, by calculating the second difference spectrum), the influence due to the fluctuations of the sample temperature (change in the absorption band of the other component) can be eliminated from the first difference spectrum and lower concentrations of the considered component of the sample to be tested can be determined than before.

[0018] Here, "multiple reference spectra" preferably refers to those measured under conditions where the sample temperature of the reference sample is different, but the sample temperature during the spectroscopic measurement itself does not need to be measured. For example, if the sample temperature changes due to different light irradiation times, multiple reference spectra at different sample temperatures can be obtained as a result by performing spectroscopic measurements of the reference sample multiple times.

[0019] In addition, "selection of a difference spectrum having a shape similar to that of the first difference spectrum among the plurality of difference spectra between two reference spectra" can be performed based on the result of evaluating the similarity of the shapes of the two difference spectra. Specifically, a wavenumber range in which the influence of the change in the absorption band of the other component due to the temperature difference of the sample under test (e.g., increase / decrease in absorption intensity, shift of the absorption band) is evident in the shape of the first difference spectrum can be set as the subject range to be evaluated. For example, the absorption band of the other component excluding the absorption band of the component under consideration can be set as the wavenumber range for evaluating the similarity of the shapes of the two difference spectra.

[0020] A band height or band area of the respective difference spectra can be used to evaluate the similarity of the shapes of the two difference spectra. The closer two values are, the greater the similarity. Furthermore, in the considered wavenumber range, a distance between a maximum value and a minimum value (peak-to-peak) of an intensity difference between the two spectra can be evaluated, and the one whose peak-to-peak is minimal can be selected. Furthermore, for example, in the considered wavenumber range, the root mean square deviation (RMS) of the intensity difference between the two spectra can be evaluated, and the one whose RMS is minimal can be selected.

[0021] In addition, a ratio of band heights or a ratio of band areas of the two difference spectra can be used as a difference spectrum factor in the calculation of the second difference spectrum.

[0022] As described above, by selecting the difference spectrum from two reference spectra in such a way that the shape similarity of the difference spectra in the considered wavenumber range increases, and calculating the second difference spectrum, the shape of the difference spectrum in the considered wavenumber range is suppressed. At the same time, the influence of changes in the absorption band due to fluctuations in the sample temperature is reduced across the entire absorption band of the other component. Accordingly, the shape of the absorption band of the considered component appears more clearly in the second difference spectrum.

[0023] Furthermore, when calculating the second difference spectrum, a first derivative spectrum of the reference spectrum may be used instead of selecting the difference spectrum between two reference spectra. This means that the method for determining a component concentration of the present invention may comprise the following steps: Calculation of a first derived spectrum for several reference spectra of the reference sample, which was measured several times by the spectrometer, selecting a first derived spectrum having a shape similar to the first difference spectrum from among the plurality of first derived spectra, and Calculating the difference spectrum between the first difference spectrum and the selected first derived spectrum as a second difference spectrum.

[0024] Since the difference spectrum between two reference spectra and the first derivative spectrum of the reference spectrum have a similar spectral shape, as in the method of the present invention described above, the influence due to the fluctuations in sample temperature (change in the absorption band of the other component) can be removed from the first difference spectrum in a similar manner by using the first derivative spectrum of the reference spectrum instead of the difference spectrum between two reference spectra.

[0025] A program for determining a component concentration of the present invention is a program configured to achieve the following: a function to calculate a difference spectrum as the first difference spectrum between: a sample spectrum of a sample to be tested, measured with a spectrometer, which shows both an absorption band of a component under consideration and an absorption band of another component that overlaps with the absorption band of the component under consideration, and a reference spectrum of a reference sample measured with the spectrometer in which the concentration of the component in question is lower than in the sample to be tested, or the concentration of the component in question is zero, a function for calculating a difference spectrum between any two reference spectra selected from among several reference spectra of the reference sample measured several times with the spectrometer, and repeating the process of calculating several difference spectra to correct the influence of a change in the broad absorption band caused by a difference in the sample temperature, a function for selecting a difference spectrum having a shape similar to that of the first difference spectrum from among the plurality of difference spectra between two reference spectra, and a function for calculating a difference spectrum between the first difference spectrum and the selected difference spectrum between two reference spectra as a second difference spectrum, wherein a shape of the absorption band of the component under consideration is determined from the second difference spectrum in order to determine the concentration of the component under consideration.

[0026] Here, when calculating the second difference spectrum, a first derived spectrum of the reference spectrum can be used instead of selecting the difference spectrum between two reference spectra. Advantageous effects of the invention

[0027] The multiple reference spectra obtained by multiple measurements of the reference sample include the change in the absorption band of the other component corresponding to the sample temperature fluctuations in each measurement (e.g., increase / decrease in absorption intensity or shift in the absorption band). The method of the present invention utilizes such characteristics of the reference spectrum to remove the influence of sample temperature fluctuations on the difference spectrum in the conventional difference spectrum method.in that, in order to perform a temperature correction on the first difference spectrum, the difference spectrum between any two reference spectra selected from among a plurality of reference spectra of the reference sample measured a plurality of times by the spectrometer is calculated, the process is repeated to calculate a plurality of difference spectra, the difference spectrum whose shape is similar to that of the difference spectrum between the sample spectrum and the reference spectrum is selected from among the plurality of difference spectra, and the second difference spectrum is calculated on the basis of the selected difference spectrum between two reference spectra and the difference spectrum between the sample spectrum and the reference spectrum.In the difference spectrum (second difference spectrum), to which a temperature correction was made in this way, the absorption band of the component under consideration appears clearly, so that lower concentrations than previously can be determined with regard to the component under consideration. SHORT DESCRIPTION OF THE CHARACTERS Fig. 1 is a flowchart of a program for determining carbon concentration in a silicon wafer according to a present embodiment. Fig. 2 shows an overlay of a sample spectrum S1 and a reference spectrum R1. Fig. 3 is a curve showing a difference spectrum S1-R1 between both spectra of the Fig. 2 shows. Fig. 4 is a graph illustrating a method for deriving a difference spectrum factor of the two spectra of the Fig. 2. Fig. 5 shows a difference spectrum S1-0.996R1 between both spectra of the Fig. 2. Fig. Figure 6 shows an overlay of two reference spectra R2, R3, where the reference spectra were selected from several reference spectra determined by multiple measurements of a reference silicon. Fig. 7 is a curve showing a difference spectrum between the reference spectra of the Fig. 6 shows. Fig. Figure 8 is a curve showing a first derived spectrum of the reference spectrum. Fig. 9 shows a difference spectrum between the first difference spectrum and the reference spectrum with shift in the direction of the vertical axis. Fig. 10 is a curve showing a second difference spectrum based on the two difference spectra of the Fig. 9 shows. Fig. 11 a spectral curve showing a method for deriving a thickness correction factor when calculating a difference spectrum between a sample spectrum S_144min and a reference spectrum, R_144min as a test example. Fig. 12 is a spectrum image showing that a wavenumber shift, which cannot be removed by thickness correction, exists between the two spectra of the Fig. 11 exists. Fig. Figure 13 (A) shows the first difference spectra of the sample spectra at each measurement duration (S_0min, S_50min, S_100min, S_144min) and (B) shows a time-dependent change in an absorption band intensity of carbon based on the first difference spectrum of the sample spectrum at measurement durations from 0 min to 144 min. Fig. Figure 14 shows a method for selecting a combination of the reference spectra (R_0min, R_144min) for temperature correction of a first difference spectrum (S_0min - thickness correction factor x R_100min). Fig. 15 (A) shows the second difference spectra of the sample spectra at each measurement duration (S_0min, S_50min, S_100min, S_144min) and (B) shows a time-dependent change in an absorption band intensity of carbon based on the second difference spectrum of the sample spectrum at measurement durations from 0 min to 144 min. BEST MODE FOR CARRYING OUT THE INVENTION

[0028] An embodiment of the present invention will be described below with reference to the drawings. In the method for determining the concentration of substituted carbon in silicon according to the present embodiment, an FTIR device of a conventional configuration is used. A silicon wafer (silicon sample) that is the target of the determination or a reference sample (reference silicon) is placed on the sample plate of the FTIR device. Here, the reference silicon is a silicon wafer with a concentration of substituted carbon lower than a lower detection limit (approximately 40 ppba) of the difference spectrum method according to the JEITA standard of Non-Patent Literature 1. To remove carbon dioxide or water vapor in the atmosphere that absorbs infrared light, a purification device is provided that introduces a purified gas, such as nitrogen, into a sample chamber and a spectroscope instrument chamber.

[0029] The FTIR instrument also includes a computing unit that performs calculations such as Fourier transforms on an interferogram, which is the output of a detector, and a recording unit that records infrared absorption spectra (sample spectrum, reference spectrum) obtained by measuring the silicon sample or reference silicon. In the FTIR instrument, a movable mirror of an interferometer beats multiple times within a specified accumulation time, and the accumulated values of multiple detected data are output as an infrared spectrum. The recording unit stores the measurement conditions required for the determination and the determination programs.

[0030] The arithmetic unit reads the destination program stored in the registration unit in order to execute it.

[0031] Fig. Figure 1 is the execution flowchart of the program for determining the concentration of substituted carbon in silicon. When the program is started, the computing unit reads the sample spectrum and the reference spectrum, each measured by the FTIR device, from the recording unit to calculate their difference as the "first difference spectrum" (step S10).

[0032] In Fig. 2, the sample spectrum S1 and the reference spectrum R1 are shown together. The shapes of the two spectra are almost the same, and there is a broad absorption band in a wavenumber range near 650 to 580 cm -1 This absorption band consists of several absorption bands resulting from lattice vibrations of the silicon single crystal and overlaps with the absorption band of substituted atomic carbon. The absorption band of substituted atomic carbon is 605 cm at room temperature. -1and at low temperatures (below 80K) 607 cm -1 (see Non-Patent Literature 2).

[0033] Fig. 3 shows a difference spectrum S1-R1 between the two spectra of the Fig. 2. This difference spectrum S1-R1 is a simple difference between the two spectra (the difference spectrum factor is 1). There is a region where the difference spectrum intensity transitions from a relatively high region (high wavenumber side) to a relatively low region (low wavenumber side). This region is in Fig. 3 is outlined with a dashed line. This phenomenon is due to a temperature difference between the silicon sample and the reference silicon and can be considered as a result of (1) and (2) below. (1) The thickness of silicon is slightly changed by expansion or contraction of silicon by heat and the absorption intensity changes proportionally due to lattice vibrations of silicon. (2) The lattice absorption band of silicon shifts in the direction of the wavenumbers.

[0034] The temperature of the silicon not only depends on the operating temperature at which the FTIR is performed, but also changes when infrared light is irradiated onto the silicon. Therefore, it can be said that the temperature of the silicon changes during the spectral measurement (during accumulation) in the FTIR device. This is indicated by the dashed line in Fig. The area outlined in 3 is a remnant of the absorption band of the silicon lattice. It influences the definition of a baseline when calculating a height or area of the absorption band (605 cm -1) of the substituted carbon, the target of the determination, and an error may occur in the result of the determination of the substituted carbon.

[0035] Therefore, in the present embodiment, in step S10, correction of the change in absorption intensity due to lattice vibrations of silicon is automatically performed. That is, when calculating the difference spectrum between the sample spectrum S1 and the reference spectrum R1, a factor (generally referred to as a difference spectrum factor, but here referred to as a thickness correction factor) is set according to the shape of the spectrum, and the reference spectrum R1 is multiplied by the thickness correction factor and subtracted from the sample spectrum S1 (or the sample spectrum S1 is multiplied by the thickness factor and subtracted from the reference spectrum) to automatically calculate the difference spectrum. This is referred to herein as a “first difference spectrum.” A method for deriving the thickness correction factor will be described with reference to Fig. 4. First, a baseline region is defined to include the absorption band of the silicon lattice (here it is defined as 650 to 580 cm -1 This baseline is then used to read the absorption band heights (spectrum intensity) of the sample spectrum and the reference spectrum of each silicon. The thickness correction factor is then set such that the difference between the two band heights becomes zero. A ratio of the band heights can be set as the thickness correction factor. Here, the absorption band height of silicon is read at a wavenumber not close to the absorption band of the substituted carbon, but outside the absorption band of the substituted carbon in the range of the baseline setting.

[0036] Instead of the band height, a band area can be calculated to set the thickness correction factor such that the difference between the band areas becomes zero, and a ratio of the band areas can be set as the thickness correction factor. When the band area is used, the spectrum area can be calculated based on a wavenumber range that includes the region near the absorption band of the substituted carbon (605 cm -1 ) from the area for establishing the baseline (650 to 580 cm -1 ) in the example of the two spectra S1, R1 of the Fig. 4 excludes.

[0037] Fig. 5 shows the first difference spectrum, which was calculated according to the equation “S1 - thickness correction factor x R1” using the thickness correction factor (0.996 in the example of Fig. 4). In the difference spectrum, the Fig. 5 The area surrounded by the broken line is the rest of the silicon absorption band opposite the Fig. 3, and the baseline established for the absorption band of substituted carbon, the target of the determination, more closely approximates a horizontal state. This means that the influence of changes in absorption intensity due to lattice vibrations of silicon is suppressed.

[0038] Next, the arithmetic unit reads data of several reference spectra from the registration unit to calculate their difference (step S20 in Fig. 1). In the registration unit, a plurality of reference spectra of the same reference silicon, which have been measured multiple times in advance by the FTIR device, are stored. These multiple reference spectra are referred to as R2, R3, R4, etc. The multiple reference spectra may include the reference spectrum R1 used in step S10. Here, the multiple reference spectra R2, R3, R4, etc. may be those measured under conditions where the temperature of the reference silicon is different, but the temperature of the silicon itself does not need to be measured during the spectral measurement performed by the FTIR device. Taking advantage of, for example, the fact that the temperature of the silicon gradually rises due to the difference in the irradiation time of the silicon with infrared light, a spectral measurement of the reference silicon is repeatedly performed multiple times, so that the multiple reference spectra R2, R3, R4, etc.can be determined as a result under conditions where the temperature of the silicon is different.

[0039] In step S20, the arithmetic unit further selects any two reference spectra among the plurality of reference spectra R2, R3, R4, etc. to calculate the difference spectra between the plurality of reference spectra.

[0040] However, data on the difference spectra between the multiple reference spectra calculated based on the multiple reference spectra R2, R3, R4, etc. measured as mentioned above are stored in the registration unit, and the arithmetic unit can read out these difference spectra between the multiple reference spectra. With a specific reference spectrum (for example, R2) as the standard, a data set of difference spectra may be a data set of difference spectra between the reference spectrum R2 and the remaining reference spectra R3, R4, etc. Or it may be a data set of difference spectra calculated by selecting all combinations of two reference spectra among the multiple reference spectra R2, R3, R4, etc.

[0041] The thickness correction factor according to the setting method of Fig. 4 is also used to calculate the difference spectra in step S20. In the example of two reference spectra R2, R3 of the Fig. 6 is within the range of 580 to 650 cm -1 fixed baseline used to set each band height at 620 cm -1 and the thickness correction factor is set so that the difference between the two band heights is zero. This thickness correction factor is used to calculate the difference spectrum between two reference spectra. As in Fig. 4, the strip area can be used instead of the strip height to derive the thickness correction factor. Furthermore, a ratio of the strip heights or a ratio of the strip areas can be set as the thickness correction factor.

[0042] Fig. Figure 7 shows an example of a difference spectrum between the reference spectra, which was determined according to the calculation equation "R3 - thickness correction factor x R2" using the thickness correction factor. In the form of the difference spectrum between the reference spectra of the Fig. 7 there is a relatively deep valley (negative band) at about 635 to 620 cm -1 , a relatively shallow valley (negative band) at approximately 615 to 610 cm -1 , and a peak (positive band) at approximately 610 to 580 cm -1 within the range of the lattice absorption band of silicon (650 to 580 cm -1 ).

[0043] The positive / negative forms, as in Fig. 7, which appear in the difference spectrum between the reference spectra, represent a phenomenon that occurs when the silicon absorption band of the reference spectrum R3, which was measured at a later time than the silicon absorption band of the reference spectrum R2, is slightly shifted toward the lower wavenumber side relative to the silicon absorption spectrum of the reference spectrum R2. This phenomenon occurs when the temperature of the silicon during the measurement of the spectrum R3 is higher than the temperature of the silicon during the measurement of the spectrum R2.

[0044] When the difference spectrum between the reference spectra is determined using the same calculation equation, assuming that the absorption band of silicon of the reference spectrum R3 is slightly shifted to the high wavenumber side compared to the absorption band of silicon of the reference spectrum R2, a difference spectrum is generated in which the positive and negative forms of the Fig. 7 are reversed.

[0045] Since, as described above, the shift of the absorption band of the silicon caused by the change in sample temperature affects the difference spectrum between two reference spectra R2, R3 of the Fig. 7, even if the same reference silicon was measured with the same FTIR device, it can be said that an influence of a shift in the absorption band of the silicon caused by the change in sample temperature in the first difference spectrum between the sample spectrum S1 and the reference spectrum R1, prepared using the thickness correction factor of the Fig. 5, remains. Since the absorption band (605 cm -1 ) substituted carbon, which is the component under consideration, is superimposed in the area where this influence of a shift in the absorption band of silicon occurs, an error may be included in the result of the determination if the determination of the substituted carbon is based on the first difference spectrum of the Fig. 5 is carried out.

[0046] Therefore, in step S30, the calculation unit selects a difference spectrum among the difference spectra between a plurality of reference spectra calculated in step S20, which has a similar shape to the first difference spectrum, and then calculates a difference spectrum (second difference spectrum) in step S40 between the first difference spectrum calculated in step S10 and the difference spectrum between the reference spectra selected in step S30.

[0047] During the selection in step S30, the shapes of two difference spectra can be compared to select the one that best fits. In particular, in the wavenumber range where the vicinity of the absorption band of substituted carbon (605 cm -1 ) from the silicon absorption band (650 to 580 cm -1 ) in the first difference spectrum of the Fig. 5, the shapes of the difference spectra between reference spectra can be compared. In particular, for example, the shapes of the valley (negative band) around 635 to 620 cm -1 , which represents both difference spectra in Fig. 7 is common.

[0048] When comparing the shapes of two difference spectra in step S30, the band height (or the band area) of the first difference spectrum in said wavenumber range is compared with the band height (or the band area) of the difference spectrum between reference spectra in said wavenumber range to select the difference spectrum between reference spectra with the closest value.

[0049] Hereinafter, the comparison of the shapes of the difference spectrum in step S30 will be explained with reference to two difference spectra (the first difference spectrum, the difference spectrum between the reference spectra) shown in Fig. 9 are shown. In Fig. 9 two difference spectra are superimposed. The upper spectrum of the Fig. 9 is the first difference spectrum calculated in step S10 and is labeled “S1 - (thickness correction factor) x R1”. The lower spectrum of the Fig. Figure 9 is the difference spectrum between reference spectra selected in step S30 and is denoted by "R3 - (thickness correction factor) x R2". When using the band height (or band area), the baseline can be set to coincide with the valley (negative band) of the spectrum, which is relatively large in the range of 635 to 620 cm -1 occurs, and the band height (or band area) in 626 cm -1 can be read out from the respective difference spectra for comparison.

[0050] Or, in step S30, in the wavenumber range under consideration, a distance (peak-to-peak) between the maximum and minimum values of the difference between two difference spectra can be evaluated in order to select the difference spectrum between the reference spectra such that the peak-to-peak value is minimized. Or, in the wavenumber range under consideration, the root mean square deviation (RMS) of the difference between two difference spectra can be evaluated in order to select the difference spectrum between the reference spectra such that the RMS is minimized.

[0051] By implementing software to compare known spectral shapes, the shapes of the difference spectra can be compared efficiently.

[0052] If the reference silicon is measured at regular time intervals (which can be referred to as an interval measurement), the multiple reference spectra to be created are those measured at a discrete temperature state. For example, if the temperature change of the silicon occurs rapidly, it may be the case that a suitable difference spectrum between the reference spectra cannot be found. In this case, the time interval for generating the spectra can be changed to repeat the measurement, or the reference spectrum deemed suitable can be generated by averaging a preceding and succeeding reference spectrum, or by creating a virtual spectrum by interpolating or extrapolating two reference spectra.

[0053] The considered wavenumber range is a wavenumber range in which the change (increase / decrease of absorption intensity, shift of absorption band) of the silicon absorption band caused by a difference in sample temperature is strongly pronounced, and which lies outside the absorption band (605 cm -1 ) of the substituted carbon. In step S30, by selecting the difference spectrum between reference spectra that matches the shape of the first difference spectrum in a wavenumber range of, for example, 635 to 620 cm -1and calculating the second difference spectrum based on two reference spectra in the next step S40, the influence of the change in the absorption band of silicon that remained in the calculation of the first difference spectrum can be effectively reduced. As a result, the shape of the absorption band of the substituted carbon appears clearer in the second difference spectrum obtained in step S40. This makes an error in the determination of the substituted carbon concentration based on the second difference spectrum in step S50 small.

[0054] Here, in step S30, it is assumed that the difference spectrum between the two Fig. 9, the difference spectrum was selected as the one that most closely matches the shape of the first difference spectrum.

[0055] When calculating the second difference spectrum in step S40, the band height (or band area) of the first difference spectrum in the considered wavenumber range and the band height (or band area) of the difference spectrum between the reference spectra in the considered wavenumber range can each be read out according to the method which is described with respect to Fig. 9 to set a ratio of two band heights (or band areas) as a temperature correction factor. This temperature correction factor is then used to calculate the difference between two difference spectra as a "second difference spectrum."

[0056] Fig. Figure 8 shows a first derivative spectrum of the reference spectrum. A first derivative spectrum is one that shows a rate of change in the reference spectrum, and a spectrum value of the first derivative spectrum is taken at a wavenumber equal to zero, at which the absorption of the reference spectrum becomes maximum, for example. The difference spectrum between two reference spectra of the Fig. 7 has a spectral shape similar to that of the first derived spectrum of the reference spectrum of the Fig. 8. For example, the difference spectrum between the reference spectra of the Fig. 7 and the first derived spectrum of the reference silicon of the Fig. 8 agree that they have a relatively deep valley (negative band) around 615 to 610 cm -1 and a peak (positive band) around 610 to 580 cm -1. Therefore, the difference spectrum between the reference spectra in steps S20 to S40 can be replaced by the first derived spectrum of the reference spectrum.

[0057] This means that in step S20, the computing unit calculates first derived spectra of the plurality of reference spectra R2, R3, R4, etc. of the reference silicon, which were measured multiple times in advance using FTIR, or reads the first derived spectra of the plurality of reference spectra R2, R3, R4, etc. from the registration unit that were calculated in advance. In step S30, the computing unit selects the first derived spectrum that has a similar shape to the first difference spectrum from the plurality of first derived spectra. In step S40, the second difference spectrum between the first difference spectrum and the selected first derived spectrum is calculated.

[0058] As described above, when calculating the first difference spectrum based on the respective spectra of the silicon sample and the reference silicon in step S10, the optimal thickness correction factor (difference spectrum factor) is used to correct the change in absorption intensity due to lattice vibrations of the silicon (also referred to as a change in the vertical direction). Furthermore, in steps S20 to S40, correction of the shift of the absorption band of the silicon lattice (also referred to as a change in the horizontal direction) is automatically performed.

[0059] Fig. Figure 10 is a "second difference spectrum" based on two difference spectra calculated in step S40, and is denoted by "(first difference spectrum) - (temperature correction factor) x (difference spectrum between reference spectra)". As a result of calculating the difference spectrum in two phases, the influence of the shift in a wavenumber direction of the absorption band of the silicon lattice is also corrected, and the shape of the absorption band of the substituted carbon at 605 cm -1 in the second difference spectrum appears clearly, as in Fig. 10 shown.

[0060] Finally, the calculation unit determines the carbon concentration from the absorption band of the substituted carbon of the second difference spectrum calculated in step S30 (step S50), and the flow of the determination program of the present embodiment ends.

[0061] According to the method for determining substituted carbon in silicon of the present embodiment: (1) A difference spectrum (second difference spectrum) can be obtained with less influence of temperature changes in silicon (changes in the wavenumber of the absorption band of the silicon lattice), which remains in the difference spectrum (first difference spectrum) between the sample spectrum and the reference silicon spectrum. As a result, the absorption band of substituted carbon appears clearly in the second difference spectrum, and by performing a concentration determination based on its absorption band, a lower concentration can be determined than previously. (2) Since the numerical value of the temperature of silicon is not used in the calculation of a determination value, it is not necessary to measure the temperature of the silicon which is the object of measurement and a measuring apparatus such as a thermometer need not be provided. (3) To measure the reference spectrum at different silicon temperatures, a method of repeatedly measuring the reference silicon over time can be used. Accordingly, temperature control of the silicon is not necessarily required during the measurement, so it can be applied to a standard-configuration FTIR instrument, becoming a highly flexible determination method. Since the determination can be performed without a temperature controller and temperature control of the silicon, it can be used to determine a large piece of silicon that cannot be placed in a temperature controller. Furthermore, since it can be applied to the determination of carbon concentration at room temperature, it can be easily incorporated into the single-crystal silicon manufacturing process.

[0062] On the other hand, to shorten the measurement time, a method of temperature control of the reference silicon (and after confirming that the temperature has changed) and repeating the measurement several times can be used. (4) In the determination method of Patent Literature 2, the shape of the absorption spectrum of carbon is not calculated after temperature correction; however, in the determination method of the present embodiment, the FTIR device can calculate the shape of the absorption spectrum of carbon after correcting the influence of the change in the absorption band of the silicon lattice caused by the change in the temperature of the silicon, so that the user can visually and easily confirm whether temperature correction has been appropriately performed based on the shape of the absorption band. (5) In addition, since the absorption band of the silicon lattice is proportional to the thickness of the sample to be tested, in the present embodiment, if the thickness of the reference silicon is known, the thickness of the sample silicon can be calculated using the thickness correction factor or the temperature correction factor. (6) When a good absorption band of the component under consideration does not appear by calculating the second difference spectrum by applying the steps of the present embodiment (for example, when the temperature change is exceptionally large), the measured spectrum data may be deleted as exceptional data.

[0063] Additionally, as a condition for determining exceptional data, the second difference spectrum, for example, may have a differential waveform (upward and downward band shapes connected side by side). The computer automatically determines whether such a condition is met, and if it is determined to be exceptional data, it can suggest the user to repeat the spectrum measurement.

[0064] The method for determining the concentration of substituted carbon in silicon of the present embodiment is only one example, and the determination method of the present invention is widely applied to methods for determining the concentration of components by the difference spectrum method using spectrometers. Particularly, in a sample to be tested in which the absorption band of another component overlaps with the absorption band of a component of interest, the concentration of the component of interest can be appropriately determined even if it is affected by a change in the absorption band of another component caused by a difference in sample temperature; therefore, it is preferable for determining a component concentration in such samples.

[0065] The effect of the present invention will be described in more detail below based on the result of a test example for determining the carbon concentration in silicon using an FTIR device. The measurement conditions are an example, and the present invention is not limited thereto. <messbedingungen>

[0066] Detector: MCT Measuring range: 700 to 500 cm -1 Resolution: 2 cm -1 Sample temperature: room temperature Repetitions for accumulation: 110 times / 2 minutes

[0067] Here, an interval measurement function of the FTIR instrument is used to create multiple spectra of silicon. Specifically, data accumulation is repeatedly determined for 2 minutes until 146 minutes have passed since the start of the measurements. For example, the spectrum from "0 min" represents data accumulation from 0 min to 2 min, and the spectrum from "144 min" represents data accumulation from 144 min to 146 min.

[0068] Two silicon pieces from a 2 mm thick silicon wafer were used as samples. The carbon concentrations were lower than the detection limit (40 ppba) according to the JEITA standard of Non-Patent Literature 1. Although the specific numerical value is unknown, one assumed to have a lower carbon concentration by spectra comparison is treated as reference silicon R, and one assumed to have a higher carbon concentration is treated as silicon sample S.

[0069] First, absorption spectra of the silicon sample S and the reference silicon R are determined and recorded by an interval measurement. Here, the sample spectra and the reference spectra for each of the time points 0 min, 50 min, 100 min, and 144 min are labeled as shown in Table 1. Table 1 Messzeitpunkt Siliziumprobe S Referenzsilizium R 0 min Probenspektrum S-0min Referenzspektrum R-0min 50 min Probenspektrum S-50min Referenzspektrum R-50min 100 min Probenspektrum S-100min Referenzspektrum R-100min 144 min Probenspektrum S-144min Referenzspektrum R-144min

[0070] In the present test example, the multiple reference spectra obtained by measuring the reference silicon R are used to determine the carbon concentration of the silicon sample S. In order to clarify the effect of the present invention, multiple sample spectra of the silicon sample S are obtained at different measurement times, and the carbon concentration is determined based on the respective sample spectra to investigate deviations in the determination results.

[0071] The first difference spectrum uses a thickness correction factor calculated according to the Fig. 11. In Fig. 11, the sample spectrum S_144min and the reference spectrum R_144min are superimposed. A baseline is set in the same range as the absorption band of the silicon grating of the two spectra (650 to 580 cm -1 ), and the thickness correction factor was 0.998 from the ratio of the strip heights in 620 cm -1 This thickness correction factor is used to calculate the difference spectrum between the sample spectrum S_144min and the reference spectrum R_144min of the Fig. 11. The thickness correction factor is calculated for each combination of sample spectrum and reference spectrum, and each thickness correction factor is used to calculate the difference spectrum.

[0072] Fig. 12 shows the superimposed spectra of the sample spectrum S_144min in Fig. 11 and the reference spectrum R_144min in Fig. 11, multiplied by the thickness correction factor (0.998). Also shown are enlarged views of the degree of spectral overlap around 626 cm -1 and by 599 cm -1 These enlarged views show that the band of the sample spectrum S_144min is shifted toward the low frequency side due to the difference in silicon temperature compared to the band of the reference spectrum R_144min. This indicates a wavenumber shift between the two spectra that cannot be removed by thickness correction alone.

[0073] Fig. Figure 13 (A) is a plot in which the reference spectrum for the calculation is set to R_0min and the calculated first difference spectra of the sample spectra at each measurement time point (S_0min, S_50min, S_100min, S_144min) are superimposed. As in Fig. 12, these first difference spectra are based on Fig. 13 (A) on the sample spectra of the same silicon S; nevertheless, the absorption band of silicon cannot be completely removed by the thickness correction alone, since the lattice absorption band of single crystal silicon (630 to 580 cm -1 ) was shifted by the small change in the temperature of the silicon during the measurement, and the shapes of the difference spectra have changed significantly. Since infrared light is continuously irradiated onto the silicon for the measurement, it is predictable that the temperature of the silicon is at its lowest at the measurement time 0 min and that the temperature of the silicon increases with the passage of time. The changes in difference spectral shapes as in Fig. 13 (A) are caused by the shift of the absorption band of silicon.

[0074] Fig. Figure 13 (B) shows a time-dependent change in the absorption band intensity of carbon at 605 cm -1 Based on the first difference spectrum between the sample spectrum at measurement times from 0 min to 144 min, it can be seen that the changing mean value of the absorption band intensity of carbon increases with time. Accordingly, as with the first difference spectrum, the influence of the temperature change of the silicon must be corrected.

[0075] Next, with reference to Fig. 14 describes a method for selecting a combination of reference spectra to perform the temperature correction of the first difference spectrum. At the top of the illustration of the Fig. Figure 14 shows the first difference spectrum (S_0min - (thickness correction factor) x R_100min) that must be subjected to temperature correction. Here, the reference spectra R_0min to R_144min of the reference silicon, measured with measurement times from 0 min to 146 min, are used to select the combination of reference spectra for temperature correction. Specifically, these reference spectra R_0min to R_144min are used to calculate the difference spectra between several reference spectra, and one that most closely matches the shape of the first difference spectrum is selected. For example, in the illustration below, Fig. 14 shows the difference spectrum (R_144min - (thickness correction factor) x R_0min), whose thickness correction is considered based on two reference spectra R_0min and R_144min. For the two Fig. 14 difference spectra, the respective band height is given in 626 cm -1 using the baseline which is in the considered wavenumber range (635 to 620 cm -1 ) to calculate the ratio of the band heights. The similarity of the shapes of the two in Fig. The difference spectra shown in Figure 14 are evaluated by this ratio of the band heights.

[0076] As for the difference spectra between different combinations of the reference spectra based on the reference spectra R_0min to R_144min, the ratio of the band heights is determined as in Fig. 14 to select the difference spectrum between reference spectra whose band height ratio is the smallest. Here, the Fig. The difference spectrum between reference spectra (R_144min - (thickness correction factor) x R_0min) shown in Figure 14 is selected for temperature correction. Then, the band height ratio (0.406) calculated from the difference spectrum between the reference spectra and the first difference spectrum is set as the temperature correction factor, and the second difference spectrum is calculated using this temperature correction factor.

[0077] In Fig. 15 (A) superimposes the second difference spectra of each measurement time point (S_0min, S_50min, S_100min, S_144min). Here, the second difference spectra are calculated using (A) the first difference spectra between the sample spectra (S_0min, S_50min, S_100min, S_144min) of each measurement time point and the set reference spectrum R_100min, and (B) the difference spectra between reference spectra selected for each first difference spectrum. For example, using the temperature correction factor (0.406) described above, the second difference spectrum for the measurement time point S_0min is expressed as "S_0min - Thickness Correction Factor × R_100min - 0.406 × {R_144min - Thickness Correction Factor × R_0min}".

[0078] It can be seen that in the second difference spectrum of the Fig. 15 (A) the shape of the absorption band (605 cm -1 ) of substituted carbon is improved by the temperature correction and the shapes of all measurement times compared to Fig. 13 (A) are plausible.

[0079] In addition, the second difference spectrum of the Fig. 15 (A) in the considered wavenumber range (616 to 598 cm -1 ) was applied to determine the band heights of the absorption band of substituted carbon (605 cm -1 ) to read out. Fig. Figure 15 (B) shows the time-dependent course of the absorption band intensity of carbon based on the second difference spectrum between the sample spectrum at the measurement times from 0 min to 144 min.

[0080] As with the first difference spectrum of the Fig. 13 (B), the change in band intensity was large, and the moving average of the band intensity was not constant and gradually increased. The determination value (mean) based on this band was 13.00 ppba, and the standard deviation (SD) was 0.906 ppba.

[0081] On the other hand, in the second difference spectrum of the Fig. 15 (B), the change in band intensity became relatively small, and the moving average value of the band intensity became almost constant. The determination value (average value) based on this band was 10.11 ppba, and the standard deviation was 0.670 ppba. That is, the detection limit according to the 3σ method is 0.67 x 3 = 2 ppba = 0.002 ppma, which is almost one-twentieth of the detection limit of 0.04 ppma in the JEITA standard of Non-Patent Literature 1, and is a numerical value that sufficiently demonstrates the applicability of the present invention. According to the determination method of the present invention, an extremely low carbon concentration of about 10 ppba can be stably determined.

[0082] From the above results, it can be said that by performing not only thickness correction but also correction of the absorption band shift of silicon, the shape of the difference spectrum is improved, and the carbon concentration can be determined in a steady state. It should also be noted that a carbon concentration value close to the correct value is obtained. LIST OF REFERENCE SYMBOLS S10 to S50 Step S10 to Step S50 S1 sample spectrum R1, R2, R3 reference spectrum QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] JP 2024-2536

[0001] JP 2009-236565 A

[0006] JP 2020-012772 A

[0006] JP 2009-162667 A

[0006] < / messbedingungen>

Claims

[1] Method for determining the concentration of a component, comprising the following steps: Calculation of a difference spectrum as the first difference spectrum between: a sample spectrum of a sample to be tested, measured with a spectrometer, which shows both an absorption band of a component under consideration and an absorption band of another component that overlaps with the absorption band of the component under consideration, and a reference spectrum of a reference sample measured with the spectrometer in which the concentration of the component in question is lower than in the sample to be tested, or the concentration of the component in question is zero, calculating a difference spectrum between any two reference spectra selected from among several reference spectra of the reference sample measured several times with the spectrometer, and repeating the process of calculating several difference spectra in order to correct the influence of a change in the absorption band of the other component caused by a difference in the sample temperature (e.g., increase / decrease in absorption intensity, shift in an absorption band), Selecting a difference spectrum having a shape similar to that of the first difference spectrum from among the plurality of difference spectra between two reference spectra, and Calculating a difference spectrum between the first difference spectrum and the selected difference spectrum between two reference spectra as a second difference spectrum, wherein a shape of the absorption band of the component under consideration is determined from the second difference spectrum in order to determine the concentration of the component under consideration. [2] A method for determining the concentration of a component according to claim 1, wherein, when a difference spectrum having a shape similar to that of the first difference spectrum is selected from among the plurality of difference spectra between two reference spectra, the absorption band of the other component excluding the absorption band of the component in question is set as the wavenumber range for evaluating the similarity of the shapes of the two difference spectra. [3] A method for determining the concentration of a component according to claim 2, in which a band height or a band area of corresponding difference spectra or a distance between a maximum value and a minimum value (PEAK-TO-PEAK) of an intensity difference between the two spectra or the root mean square deviation (RMS) of the intensity difference between the two spectra is used to evaluate the similarity of the shapes of the two difference spectra. [4] Method for determining the concentration of a component according to claim 3, in which a ratio of band heights or a ratio of band areas is used as a difference spectrum factor in the calculation of the second difference spectrum. [5] Method for determining the concentration of a component, comprising the following steps: Calculation of a difference spectrum as the first difference spectrum between: a sample spectrum of a sample to be tested measured with a spectrometer, which includes both an absorption band of a component under consideration, as well as an absorption band of another component that overlaps with the absorption band of the component under consideration, and a reference spectrum of a reference sample measured with the spectrometer in which the concentration of the component in question is lower than in the sample to be tested, or the concentration of the component in question is zero, calculating a first derived spectrum for several reference spectra of the reference sample measured several times with the spectrometer in order to correct the influence of a change in the absorption band of the other component caused by a difference in the sample temperature, selecting a first derived spectrum from among the several first derived spectra that has a shape similar to that of the first difference spectrum, and Calculating a difference spectrum between the first difference spectrum and the selected first derived spectrum as a second difference spectrum, wherein a shape of the absorption band of the component under consideration is determined from the second difference spectrum in order to determine the concentration of the component under consideration. [6] Program for determining the concentration of substituted carbon in silicon, configured to achieve the following: a function to calculate a difference spectrum as the first difference spectrum between: a sample spectrum of a sample to be tested, measured with a spectrometer, which shows both an absorption band of a component under consideration and a broad absorption band of another component that overlaps with the absorption band of the component under consideration, and a reference spectrum of a reference sample measured with the spectrometer in which the concentration of the component in question is lower than in the sample to be tested, or the concentration of the component in question is zero, a function for calculating a difference spectrum between any two reference spectra selected from among several reference spectra of the reference sample measured several times with the spectrometer, and repeating the process of calculating several difference spectra to correct the influence of a change in the broad absorption band caused by a difference in the sample temperature, a function for selecting a difference spectrum having a shape similar to that of the first difference spectrum from among the plurality of difference spectra between two reference spectra, and a function for calculating a difference spectrum between the first difference spectrum and the selected difference spectrum between two reference spectra as a second difference spectrum, whereby a shape of the absorption band of the component under consideration is determined from the second difference spectrum, to determine the concentration of the component in question. [7] Program for determining the concentration of substituted carbon in silicon, configured to achieve the following: a function to calculate a difference spectrum as the first difference spectrum between: a sample spectrum of a sample to be tested, measured with a spectrometer, which shows both an absorption band of a component under consideration and a broad absorption band of another component that overlaps with the absorption band of the component under consideration, and a reference spectrum of a reference sample measured with the spectrometer in which the concentration of the component in question is lower than in the sample to be tested, or the concentration of the component in question is zero, a function for calculating a first derived spectrum for several reference spectra of the reference sample, which were measured several times with the spectrometer, in order to correct the influence of a change in the broad absorption band caused by a difference in the sample temperature, a function for selecting a first derived spectrum having a shape similar to that of the first difference spectrum from among the plurality of first derived spectra, and a function for calculating a difference spectrum between the first difference spectrum and the selected first derived spectrum as a second difference spectrum, wherein a shape of the absorption band of the component under consideration is determined from the second difference spectrum in order to determine the concentration of the component under consideration.

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