Component concentration quantifying method and component concentration quantifying program

Abstract

To provide a temperature correction method capable of resolving the problems of a method for quantifying a component concentration using difference spectrum method that when a temperature of a sample fluctuates during spectrometry, absorption intensities of other components overlapping an absorption peak of a specific component of the sample increase / decrease and that absorption bands of the other components shift, thereby enabling quantification with a lower concentration of the specific component than conventional arts.SOLUTION: A component concentration quantifying method comprises: calculating a first difference spectrum between a measurement spectrum of a measurement sample and a reference spectrum of a reference sample with a lower concentration of a specific component than that of the measurement sample (S10); for a plurality of reference spectra obtained by measuring the reference sample multiple times, selecting a difference spectrum from among difference spectra between the reference spectra, which has a shape closest to the first difference spectrum (S20); calculating a second difference spectrum based on the difference spectrum and the first difference spectrum (S30); and obtaining a shape of an absorption peak of the specific component from the second difference spectrum, to quantify a concentration of the specific component (S40).SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for quantifying the component concentration of a sample by a spectroscopic measurement device such as a Fourier transform infrared spectrophotometer (FTIR).

Background Art

[0002] Conventionally, a method for quantifying the concentration of substitutional carbon atoms in a silicon crystal using FTIR has been known. For example, in the Electronic Information Technology Industries Association standard (JEITA) EM-3503 of Non-Patent Document 1, a method is shown in which a baseline is drawn at an absorption peak (near a wave number of 605 cm) specific to substitutional carbon atoms, and a carbon concentration is obtained by multiplying the peak height by a predetermined coefficient. Since the absorption peak of carbon overlaps with a broad absorption band due to the lattice vibration of silicon, in the quantification method of Non-Patent Document 1, the absorbance spectrum of the measurement sample (referred to as the "measurement spectrum") is measured, and silicon with a low concentration of substitutional carbon is used as a reference sample to measure the absorbance spectrum of the reference sample (referred to as the "reference spectrum"). By calculating the difference spectrum between the two, the absorption band due to the lattice vibration of silicon is removed, and a measurement spectrum of only the absorption peak of carbon is obtained. -1 Further, Non-Patent Document 1 shows that when calculating the difference spectrum, in order to correct the sample thickness, a difference spectrum between the measurement spectrum and the reference spectrum multiplied by "measurement sample thickness / reference sample thickness" (difference coefficient) times the reference spectrum is calculated.

[0003] The technique itself of clarifying the absorption peak of a specific component (the "difference spectrum method") by calculating the difference spectrum between the measurement spectrum and the reference spectrum is not limited to the method for quantifying the component concentration in a silicon crystal, and is applied to the measurement of the concentration of trace components in various samples, such as the method for analyzing the concentration of multiple components in Patent Document 1, and is a well-known technique.

[0004] As shown in FIG. 2 of Patent Document 1, the spectral shapes of five components belonging to perfluorocarbon are similar, and each has a wave number of 1200 to 1300 cm -1has a large absorption peak in the range. For example, from the measurement spectrum [S] of a sample containing 5 components, especially the only absorption peak of perfluoromethane (wave number 1280 cm -1 ) has a small intensity, so in the absorbance spectrum of the measurement sample in which 5 components are mixed, it is hidden by the large absorption peaks of other components. Therefore, by subtracting the spectrum of perfluorobutane whose absorbance is matched from the spectrum [S] of the measurement sample by a computer, the difference spectrum [A] of [measurement sample - perfluorobutane] is created. Similarly, by sequentially subtracting the spectra of perfluoropentane, perfluoropropane, and perfluoroethane whose absorbances are matched from the difference spectrum [A], as a result, a difference spectrum in which the absorption peak of perfluoromethane is clarified can be obtained.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Patent Document 3

Non-Patent Documents

[0006]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0007] In the method for quantifying component concentration using the above-described difference spectrum method, a factor that makes it difficult to quantify lower concentrations is that the temperature at the measurement location of the sample fluctuates during spectroscopic measurement. The inventor focused on the following phenomena as the influence of sample temperature fluctuations on the absorbance spectrum, for example, in the case of a silicon crystal. · Due to thermal expansion and thermal contraction, the thickness of silicon slightly changes, and in proportion to the thickness, the absorption intensity due to the lattice vibration of silicon increases or decreases. · The absorption band due to the lattice vibration of silicon shifts.

[0008] Due to these phenomena, with only the conventional difference spectrum method, the absorption band due to the lattice vibration of silicon cannot be completely removed from the measurement spectrum, and an appropriate baseline cannot be set for the carbon absorption peak due to the remaining absorption band, resulting in inaccurate quantification of the carbon concentration.

[0009] In order to avoid such problems, it is conceivable to strictly perform temperature adjustment of the measurement sample and the reference sample during spectrum measurement. However, for example, in the manufacturing process of silicon crystals for semiconductor manufacturing, there are also products that are too large to fit into the temperature adjuster of a general spectrum measurement device. In addition, if a temperature adjuster dedicated to measuring carbon concentration is required, it is a demerit in terms of manufacturing cost and manufacturing time.

[0010] Also, Patent Document 2 discloses a method for temperature-correcting the carbon concentration of a silicon crystal, and performs correction based on the difference in the measured temperature values of the measurement sample and the reference sample with respect to the carbon concentration in the silicon crystal measured by FTIR. However, in the method of Patent Document 2, it is necessary to measure the sample temperature for temperature correction, and in practical terms, a method that does not require measuring the sample temperature is desirable.

[0011] In addition, Patent Document 3 uses a model formula Ap(x) of a reference spectrum corrected for wavenumber shift. The model formula is represented by the model formula "Ap(x)=a1As(x - a2)+a3+a4x", and the sum of squared residuals D (D = Σ{As(x)-Ap(x)} 2 is set. The coefficients a1 to a4 in the model formula are numerically calculated so that it becomes minimal. The coefficient a2 is the shift correction amount. Using the model formula constructed numerically, the difference spectrum (As(x)-Ap(x)) from the measurement spectrum is obtained, and the concentration is quantified based on the absorption peak of a specific component appearing in this difference spectrum. However, the wavenumber shift correction in Patent Document 3 uses a model formula As(x) set mathematically, assuming that the actually occurring wavenumber shift fits the model formula. Therefore, it cannot be said to be a correction based on the spectrum data obtained by actually measuring an actual sample, and there is still room for improvement in terms of the reliability of the wavenumber shift correction.

[0012] An object of the present invention is to provide a temperature correction method capable of eliminating these problems in a method for quantifying component concentration using the difference spectrum method. When the temperature of a sample fluctuates during spectroscopic measurement, the absorption intensity of other components overlapping the absorption peak of a specific component of the sample increases or decreases, and the absorption band of other components overlapping the absorption peak of a specific component of the sample shifts in the wavenumber direction (wavenumber shift) and the like occur, and to enable quantification of a lower concentration than before for a specific component of the sample.

Means for Solving the Problems

[0013] When the inventor measured the spectra of the same reference sample multiple times using a spectroscopic measurement device for quantification, he noticed that the shape of the measured reference spectra changed even though the measurement conditions were not changed. He considered that such a change in shape was due to a slight variation in the sample temperature. That is, in the reference spectra obtained by performing spectroscopic measurements of the reference sample multiple times, increases and decreases in the absorption intensity of other components and shifts in the absorption bands due to temperature fluctuations of the sample occurred, and these increases and decreases in absorption intensity and shifts in the absorption bands were reflected in the shape of the difference spectrum between any two reference spectra. Therefore, from among the difference spectra of two reference spectra having both increases and decreases in absorption intensity and shifts in the absorption band, a spectrum similar in shape to the difference spectrum between the measurement spectrum and the reference spectrum (the first difference spectrum) based on the difference spectrum method was selected, and by subtracting the difference spectrum between the selected reference spectra from the difference spectrum between the measurement spectrum and the reference spectrum (the second difference spectrum), it was found that the influence of fluctuations in the sample temperature could be removed from the first difference spectrum, and quantification of a specific component of the sample at a lower concentration than before became possible.

[0014] That is, the method for quantifying the component concentration of the present invention a measurement spectrum of a measurement sample showing both an absorption peak of a specific component measured by a spectrophotometer and an absorption band of another component overlapping the absorption peak, and a reference spectrum of a reference sample having a lower concentration of a specific component or a concentration of zero of the specific component than the measurement sample, measured by the spectrophotometer, and calculating the difference spectrum as the first difference spectrum; in order to correct the influence of fluctuations (increase or decrease in absorption intensity, shift in absorption band) of the absorption band of the other component due to differences in sample temperature, calculating a plurality of difference spectra between the reference spectra for the plurality of reference spectra of the reference sample measured multiple times by the spectrophotometer; selecting a spectrum similar in shape to the first difference spectrum from among the difference spectra between the reference spectra; and Calculating a difference spectrum between the first difference spectrum and a difference spectrum between the selected reference spectra as a second difference spectrum, characterized by obtaining the shape of an absorption peak of the specific component from the second difference spectrum and quantifying the concentration of the specific component.

[0015] As in the method of the present invention above, by subtracting a difference spectrum between reference spectra having similar difference spectrum shapes from the first difference spectrum (calculating the second difference spectrum), it is possible to remove the influence of sample temperature fluctuations (fluctuations in absorption bands of other components) from the first difference spectrum, enabling quantification of a lower concentration than before for a specific component of the sample.

[0016] Here, the "plurality of reference spectra" may be those measured under conditions where the sample temperatures of the reference samples are different, but it is not necessary to actually measure the sample temperature during spectroscopic measurement. For example, when the sample temperature changes due to differences in the light irradiation time, by repeatedly performing spectroscopic measurement of the reference sample multiple times, a plurality of reference spectra under different sample temperature conditions can be obtained as a result.

[0017] Also, when "selecting a reference spectrum having a shape close to that of the first difference spectrum from among the difference spectra between the reference spectra", the degree of coincidence of the shapes of the two difference spectra may be evaluated. In particular, as the evaluation range, it is advisable to specify the wavenumber range in which the influence of fluctuations in absorption bands of other components (such as increases or decreases in absorption intensity and shifts in absorption bands) due to differences in sample temperature appears in the shape of the first difference spectrum. For example, it is advisable to specify the wavenumber range obtained by removing the absorption peak of the specific component from the absorption bands of other components.

[0018] For the evaluation of the degree of coincidence of the shapes of two difference spectra, it is advisable to use the peak height or peak area of each difference spectrum. The closer the values are, the higher the degree of coincidence. Also, in the specified wavenumber range, the width (P - P) between the maximum value and the minimum value of the difference between the intensities of the two difference spectra can be evaluated, and the one with the minimum P - P can be selected. Further, for example, in the specified wavenumber range, the RMS (root mean square of the squares) of the difference between the intensities of the two difference spectra can be evaluated, and the one with the minimum RMS can be selected.

[0019] Also, in the calculation of the second difference spectrum, it is advisable to use the ratio of the peak heights or the ratio of the peak areas of the two difference spectra as the difference spectrum coefficient.

[0020] As described above, by selecting the difference spectra between the reference spectra such that the degree of coincidence of the shapes of the difference spectra in the specified wavenumber range is high and performing the calculation of the second difference spectrum, the shape of the difference spectrum in the specified wavenumber range is canceled. At the same time, in the overall absorption bands of other components, the influence of the variation of the absorption bands due to the variation of the sample temperature is reduced. Therefore, the shape of the absorption peak of the specific component in the second difference spectrum becomes clearer.

[0021] Also, when calculating the second difference spectrum, instead of selecting the difference spectrum between the reference spectra, the first derivative spectrum of the reference spectrum may be used. That is, the method for quantifying the component concentration of the present invention calculating the first derivative spectrum for each of the plurality of reference spectra of the reference sample measured a plurality of times by the spectrophotometer, selecting from among the first derivative spectra those that are close to the shape of the first difference spectrum, and calculating the difference spectrum between the first difference spectrum and the selected first derivative spectrum as the second difference spectrum. It is advisable to include this.

[0022] Since the difference spectrum between reference spectra and the first derivative spectrum of a reference spectrum have similar spectral shapes, similar to the method of the present invention described above, even if the first derivative spectrum of the reference spectrum is used instead of the difference spectrum between reference spectra, the influence of fluctuations in the sample temperature (fluctuations in the absorption bands of other components) can be removed from the first difference spectrum in the same manner.

[0023] The component concentration quantification program of the present invention causes a computer to a measurement spectrum of a measurement sample showing both an absorption peak of a specific component measured by a spectrophotometer and a broad absorption band of another component overlapping the absorption peak, and a reference spectrum of a reference sample measured by the spectrophotometer, in which the concentration of the specific component is lower than that of the measurement sample or the concentration of the specific component is zero, and calculate, as a first difference spectrum, a difference spectrum therebetween; in order to correct the influence of fluctuations in the broad absorption band caused by differences in sample temperature, calculate a plurality of difference spectra between reference spectra for a plurality of reference spectra of the reference sample measured a plurality of times by the spectrophotometer; select, from among the difference spectra between reference spectra, one that is close to the shape of the first difference spectrum; calculate, as a second difference spectrum, a difference spectrum between the first difference spectrum and the selected difference spectrum between reference spectra; is a program for realizing the above, characterized by obtaining the shape of the absorption peak of the specific component from the second difference spectrum and quantifying the concentration of the specific component. Here, when calculating the second difference spectrum, instead of selecting the difference spectrum between reference spectra, the first derivative spectrum of the reference spectrum may be used.

Advantages of the Invention

[0024] Among the multiple reference spectra obtained by measuring the reference sample multiple times, fluctuations in the absorption bands of other components (such as increases or decreases in absorption intensity and shifts in absorption bands) corresponding to temperature fluctuations of the sample during each measurement are included. The method of the present invention utilizes such characteristics of the reference spectra to remove the influence of temperature fluctuations of the sample included in the difference spectrum obtained by the conventional difference spectrum method. That is, in order to temperature-correct the first difference spectrum, multiple difference spectra between the reference spectra are calculated, and among these, the one closest in shape to the difference spectrum between the measurement spectrum and the reference spectrum is selected. Based on the difference spectrum between the selected reference spectra and the difference spectrum between the measurement spectrum and the reference spectrum, the second difference spectrum is calculated. In the thus temperature-corrected difference spectrum (the second difference spectrum), the absorption peak of the specific component appears clearly, so that quantification of the specific component at a lower concentration than before becomes possible.

Brief Description of the Drawings

[0025]

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Mode for Carrying Out the Invention

[0026] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the method for quantifying the substitutional carbon concentration in silicon according to this embodiment, an FTIR apparatus with a general configuration is used. On the sample stage of the FTIR apparatus, a silicon wafer to be quantified (measurement silicon) or a reference sample (reference silicon) is installed. Here, the reference silicon is a silicon wafer in which the substitutional carbon concentration is lower than the detection limit (about 40 ppba) of the differential spectrum method according to the JEITA standard of Non-Patent Document 1. In the sample chamber and the spectroscopic instrument chamber, a purge device for introducing a purge gas such as nitrogen gas is provided to remove carbon dioxide, water vapor, etc. in the atmosphere that absorb infrared light.

[0027] In addition, the FTIR apparatus is provided with an arithmetic unit that performs arithmetic processing such as Fourier transform on the interferogram that is the output from the detector, and a recording unit that records infrared absorbance spectra (measurement spectrum, reference spectrum, etc.) obtained by measuring the measurement silicon and the reference silicon respectively. In the FTIR apparatus, the movable mirror of the interferometer is stroked a plurality of times within a predetermined integration time, and the integrated value of a plurality of detection data is output as an infrared spectrum. The recording unit also stores other measurement conditions necessary for quantification, quantification programs, etc.

[0028] The arithmetic unit reads and executes the quantification program stored in the recording unit. FIG. 1 shows the execution flow of the quantification program for the substitutional carbon concentration in silicon. When the program starts, the arithmetic unit reads the measurement spectrum and the reference spectrum measured by the FTIR apparatus from the recording unit, and calculates the difference as the "first difference spectrum" (step S10).

[0029] FIG. 2 shows the read measurement spectrum S1 and reference spectrum R1 superimposed. The shapes of the two spectra are almost the same, and there is a broad absorption band in the wavenumber range around 650 - 580 cm -1 Nearby. This absorption band consists of a plurality of absorption bands derived from the lattice vibration of the silicon single crystal, and overlaps with the absorption peak of the substitutional carbon atom. Note that the absorption peak of the substitutional carbon atom is 605 cm at room temperature. -1and at a temperature condition of 80 K or lower, it is 607 cm -1 (see Non-Patent Document 2).

[0030] Figure 3 shows the difference spectrum S1 - R1 of the two spectra in Figure 2. This difference spectrum S1 - R1 is the simple difference between the two spectra (the difference spectrum coefficient is 1). It has a portion that changes from a region with relatively large difference spectrum intensity (high frequency side) to a region with relatively small difference spectrum intensity (low frequency side). The portion is enclosed by the dashed line in Figure 3. This phenomenon is due to the temperature difference between the sample silicon and the reference silicon, and can be said to be the result of the occurrence of the following (1) and (2). (1) Due to the thermal expansion or contraction of silicon, the thickness of silicon slightly changes, and proportionally, the absorption intensity due to the lattice vibration of silicon fluctuates. (2) The absorption band due to the lattice vibration of silicon shifts in the wave number direction. The silicon temperature depends not only on the installation environment of the FTIR (room temperature) but also varies when infrared light is irradiated on the silicon. Therefore, it can be said that the temperature of the silicon is changing even during the spectrum measurement (integration) with the FTIR apparatus. The region of the dashed line in Figure 3 is the remainder of the absorption band due to the lattice vibration of silicon, which affects the setting of the baseline when calculating the height or area of the absorption peak (605 cm -1 ) of the substitutional carbon that is the quantification target, resulting in an error in the quantification result of the substitutional carbon.

[0031] Therefore, in this embodiment, in step S10, first, correction for fluctuations in absorption intensity due to lattice vibrations of silicon is automatically performed. That is, when calculating the difference spectrum between the measurement spectrum S1 and the reference spectrum R1, a coefficient corresponding to the shape of the spectrum (generally called the difference spectrum coefficient, but here called the thickness correction coefficient) is set, and the reference spectrum R1 multiplied by the thickness correction coefficient is subtracted from the measurement spectrum S1 (or the measurement spectrum S1 multiplied by the thickness correction coefficient is subtracted from the reference spectrum R1), thereby automatically calculating the difference spectrum. In this document, this is called the "first difference spectrum". The method for deriving the thickness correction coefficient will be described with reference to FIG. 4. First, the setting range of the baseline is determined so as to include the absorption band due to lattice vibrations of silicon (here, it is 650~580 cm -1 is used). Next, using this baseline, the absorption band height (spectrum intensity) of silicon in each of the measurement spectrum and the reference spectrum is read. For example, the band height at 620 cm -1 (the length of the upward arrow in FIG. 4) is read. Then, the thickness correction coefficient is set so that the difference between the two band heights becomes zero. The ratio of the band heights may be set as the thickness correction coefficient. Here, the absorption peak height of silicon is read at a wavenumber outside the absorption peak of substitutional carbon in the baseline setting range, rather than near the absorption peak of substitutional carbon.

[0032] Note that instead of the band height, the band area may be calculated and the thickness correction coefficient may be set so that the difference between the two band areas becomes zero, or the ratio of the band areas may be set as the thickness correction coefficient. When using the band area, in the example of the two spectra S1 and R1 in FIG. 4, the spectral area may be calculated based on the wavenumber range excluding the vicinity of the absorption peak of substitutional carbon (605 cm -1 ) from the baseline setting range (650~580 cm -1 ).

[0033] Figure 5 shows the first difference spectrum obtained by the calculation formula of "S1 - (thickness correction coefficient) × R1" using the thickness correction coefficient (0.996 in the example of Figure 4). The difference spectrum in the dashed-line region of Figure 5 shows that the remaining absorption band of silicon is improved compared to Figure 3, and the baseline set for the absorption peak of the substitutional carbon to be quantified approaches a horizontal state. That is, the influence of the fluctuation of the absorption intensity due to the lattice vibration of silicon is suppressed.

[0034] Next, the arithmetic unit reads the information of a plurality of reference spectra from the recording device and calculates their difference spectra (step S20 in FIG. 1). In the storage device, a plurality of reference spectra of the same reference silicon measured a plurality of times in advance by the FTIR device are stored. These plurality of reference spectra are represented by R2, R3, R4, ···. The plurality of reference spectra may include the reference spectrum R1 used in step S10. Here, the plurality of reference spectra R2, R3, R4, ··· are preferably measured under conditions where the temperatures of the reference silicon are different, but it is not necessary to actually measure the silicon temperature during the spectrum measurement by the FTIR device. For example, by utilizing the fact that the silicon temperature gradually increases due to the difference in the irradiation time of infrared light on silicon, the spectrum measurement of the reference silicon is repeatedly executed a plurality of times, and as a result, a plurality of reference spectra R2, R3, R4, ··· under conditions where the silicon temperatures are different can be obtained.

[0035] In step S20, the arithmetic unit further extracts any two reference spectra from the plurality of reference spectra R2, R3, R4, ··· and calculates the difference spectra between the plurality of reference spectra.

[0036] Alternatively, the memory device stores information on the difference spectra between a plurality of reference spectra calculated based on the plurality of reference spectra R2, R3, R4, ··· measured as described above, and the arithmetic unit may read out the difference spectra between these plurality of reference spectra. As a data set of the difference spectra between the reference spectra, a data set of the difference spectra between a certain reference spectrum (for example, R2) and the remaining reference spectra R3, R4, ··· may be used with the certain reference spectrum (for example, R2) as a reference. Alternatively, it may be a data set of difference spectra calculated by extracting all combinations of two reference spectra for the plurality of reference spectra R2, R3, R4, ···.

[0037] Also in the calculation of the difference spectrum in step S20, the thickness correction coefficient according to the setting method shown in FIG. 4 above is used. In the example of the two reference spectra R2 and R3 in FIG. 6, using the baseline set in the range of 580 to 650 cm -1 the band heights at 620 cm -1 are read respectively, and a thickness correction coefficient is set such that the difference between the two band heights becomes zero. Then, using this thickness correction coefficient, the difference spectrum between the two reference spectra is calculated. Similar to FIG. 4, instead of the band height, the band area may be used to derive the thickness correction coefficient. Also, the ratio of the band heights or the ratio of the band areas may be set as the thickness correction coefficient.

[0038] FIG. 7 shows an example of the difference spectrum between reference spectra obtained by the calculation formula of "R3 - (thickness correction coefficient) × R2" using the thickness correction coefficient. In the shape of the difference spectrum between the reference spectra in FIG. 7, there is a relatively deep valley (negative peak) around 635 to 620 cm -1 within the range of the absorption band (650 to 580 cm -1 ) due to the lattice vibration of silicon, and a relatively shallow valley (negative peak) around 615 to 610 cm -1 , and a peak (positive peak) around 610 to 580 cm -1 .

[0039] The positive and negative shapes such as those in Fig. 7 that appear in the difference spectrum between the reference spectra are phenomena that occur when the silicon absorption band of the reference spectrum R3 measured at a later time is slightly shifted "toward the low wavenumber side" with respect to the silicon absorption band of the reference spectrum R2. Such a phenomenon occurs when the silicon temperature at the time of measurement of the reference spectrum R3 is higher than the silicon temperature at the time of measurement of the reference spectrum R2.

[0040] In addition, when obtaining the difference spectrum between the reference spectra using the same calculation formula, if the silicon absorption band of the reference spectrum R3 is slightly shifted "toward the high wavenumber side" with respect to the silicon absorption band of the reference spectrum R2, a difference spectrum with the positive and negative shapes in Fig. 7 inverted will occur.

[0041] Thus, even when the same reference silicon is measured with the same FTIR apparatus, since the influence of the shift of the silicon absorption band due to the variation in the sample temperature appears in the difference spectrum between the two reference silicons R2 and R3 in Fig. 7, it can be said that the influence of the shift of the silicon absorption band due to the variation in the sample temperature also remains in the first difference spectrum between the measurement spectrum S1 obtained using the thickness correction coefficient in Fig. 5 and the reference spectrum R1. And, since the absorption peak (605 cm -1 ) of the substitutional carbon, which is a specific component, overlaps in the range where such an influence of the shift of the silicon absorption band occurs, when the substitutional carbon is quantified based on the first difference spectrum in Fig. 5, errors will be included in the quantification result.

[0042] Therefore, in step S30, the arithmetic unit selects, from among the difference spectra between the plurality of reference spectra calculated in step S20, those that are close to the shape of the first difference spectrum. Further, in step S40, the arithmetic unit calculates the difference spectrum (second difference spectrum) between the first difference spectrum calculated in step S10 and the difference spectrum between the reference spectra selected in step S30.

[0043] In the selection in step S30, it is preferable to compare the shapes of the two difference spectra and select the one that most closely matches. In particular, in the wavenumber range excluding the vicinity of the absorption band of silicon (650 to 580 cm -1 ) to the absorption band of substitutional carbon (605 cm -1 ) in the first difference spectrum of FIG. 5, it is preferable to compare the shapes with the difference spectrum between the reference spectra. Specifically, for example, it is preferable to compare the shapes of the valleys (negative peaks) in the vicinity of 635 to 620 cm -1 common to the two difference spectra shown in FIG. 7.

[0044] In comparing the shapes of the two difference spectra in step S30, compare the peak height (or peak area) of the first difference spectrum in the specified wavenumber range with the peak height (or peak area) of the difference spectrum between the reference spectra in the specified wavenumber range, and select the difference spectrum between the reference spectra with the closest value.

[0045] Here, the comparison of the shapes of the difference spectra in step S30 will be described using the two difference spectra (the first difference spectrum and the difference spectrum between the reference spectra) shown in FIG. 9. In FIG. 9, the two difference spectra are shown superimposed. The upper side of FIG. 9 is the first difference spectrum calculated in step S10, represented by "S1 - (thickness correction coefficient) × R1". The lower side of FIG. 9 is the difference spectrum between the reference spectra selected in step S30, represented by "R3 - (thickness correction coefficient) × R2". When using the peak height (or peak area), set the baseline in accordance with the valley (negative peak) of the spectrum that occurs relatively largely in the range of 635 to 620 cm -1 , and read and compare the peak height (or peak area) at 626 cm -1 from each difference spectrum.

[0046] Alternatively, in comparing the shapes of the two difference spectra in step S30, within the specified wavenumber range, the width (P-P) between the maximum and minimum values of the difference in the intensities of the two difference spectra may be evaluated, and the difference spectrum between the reference spectra that minimizes P-P may be selected. Or, within the specified wavenumber range, the RMS (root mean square of the squares) of the difference in the intensities of the two difference spectra may be evaluated, and the difference spectrum between the reference spectra that minimizes RMS may be selected.

[0047] Note that by incorporating known spectrum shape comparison software, the shapes of the difference spectra can be efficiently compared.

[0048] When measuring the reference silicon at regular time intervals (also called interval measurement), the multiple reference spectra obtained are those measured under discrete temperature conditions. For example, if the change in the silicon temperature is steep, there may be cases where an appropriate difference spectrum between the reference spectra cannot be found. In such cases, the time interval for acquiring the spectra may be changed and the measurement may be performed again, or an appropriate reference spectrum may be created by taking the average of two reference spectra that are temporally before and after, or by taking a virtual spectrum by interpolation or extrapolation of the two reference spectra.

[0049] The specified wavenumber range is the wavenumber range in which the influence of the variation in the absorption band of silicon (increase or decrease in absorption intensity, shift of the absorption band) due to the difference in sample temperature strongly appears in the shape of the first difference spectrum, and is also outside the absorption peak of the substituted carbon (605 cm -1 )). In step S30, for example, 635 to 620 cm -1In the wavenumber range, select the difference spectrum between reference spectra that most closely matches the shape of the first difference spectrum. In the following step S40, by calculating the second difference spectrum based on both of them, the influence of the variation of the absorption band of silicon remaining in the calculation of the first difference spectrum can be efficiently reduced. As a result, the shape of the absorption peak of substitutional carbon in the second difference spectrum obtained in step S40 becomes more clearly represented. And the quantitative error of the substitutional carbon concentration based on the second difference spectrum in step S50 becomes smaller.

[0050] Here, in step S30, assume that the difference spectrum between the two reference spectra R2 and R3 shown in FIG. 9 is selected as the one that most closely matches the shape of the first difference spectrum. In step S40, when calculating the second difference spectrum, using the method described with reference to FIG. 9, read the peak height (or peak area) of the first difference spectrum in the specified wavenumber range and the peak height (or peak area) of the difference spectrum between the reference spectra in the specified wavenumber range, respectively, and set the ratio of the two peak heights (or the ratio of the peak areas) as the temperature correction coefficient. Then, using this temperature correction coefficient, calculate the difference between the two difference spectra as the "second difference spectrum".

[0051] FIG. 8 shows the first derivative spectrum of the reference spectrum. The first derivative spectrum indicates the rate of change of the reference spectrum. For example, at the wavenumber where the absorption of the reference spectrum reaches a maximum, the spectrum value of the first derivative spectrum becomes zero. The difference spectrum between the two reference spectra in FIG. 7 is similar in spectrum shape to the first derivative spectrum of the reference spectrum in FIG. 8. For example, the difference spectrum between the reference spectra in FIG. 7 and the first derivative spectrum of the reference silicon in FIG. 8 have a relatively deep valley (negative peak) near 635 - 620 cm -1 and a relatively shallow valley (negative peak) near 615 - 610 cm -1 and there are relatively shallow valleys (negative peaks) near 610 - 580 cm -1They are common in that there is a mountainous area (positive peak) nearby. Therefore, the difference spectra between the reference spectra in steps S20 to S40 can be replaced with the first-order differential spectra of the reference spectra.

[0052] That is, in step S20, for a plurality of reference spectra R2, R3, R4,... of the reference silicon measured in advance by FTIR a plurality of times, the arithmetic unit calculates the first-order differential spectrum of each, or reads out the first-order differential spectra of the plurality of reference spectra R2, R3, R4,... calculated in advance from the storage device. In step S30, the arithmetic unit selects, from among the plurality of first-order differential spectra, one that is close to the shape of the first difference spectrum. In step S40, the second difference spectrum based on the first difference spectrum and the selected first-order differential spectrum may be calculated.

[0053] As described above, in step S10, when calculating the first difference spectrum based on the spectra of the measurement silicon and the reference silicon, using the optimal thickness correction coefficient (difference spectrum coefficient), correction is performed for the variation in the absorption intensity due to the lattice vibration of silicon (also referred to as the vertical variation). Further, in steps S20 to S40, correction for the shift of the absorption band due to the lattice vibration of silicon (also referred to as the horizontal variation) is automatically performed.

[0054] FIG. 10 is the "second difference spectrum" based on the two difference spectra calculated in step S40, and is represented by "(first difference spectrum) - (temperature correction coefficient) × (difference spectrum between reference spectra)". As a result of the two-stage calculation of the difference spectrum, the influence of the shift in the wavenumber direction of the absorption band due to the lattice vibration of silicon is also corrected. As shown in FIG. 10, the shape of the absorption peak of the substitutional carbon at 605 cm -1 clearly appears in the second difference spectrum.

[0055] Finally, the arithmetic unit quantifies the carbon concentration based on the absorption peak of substitutional carbon in the second difference spectrum calculated in step S30 (step S50), and the flow of the quantification program of the present embodiment ends.

[0056] According to the method for quantifying substitutional carbon in silicon of the present embodiment, (1) It is possible to obtain a difference spectrum (second difference spectrum) with reduced influence of the variation in silicon temperature (variation in the wave number of the absorption band due to the lattice vibration of silicon) remaining in the difference spectrum (first difference spectrum) between the measurement spectrum and the reference spectrum of silicon. As a result, the absorption peak of substitutional carbon clearly appears in the second difference spectrum, and by performing quantification of the substitutional carbon concentration based on the absorption peak, quantification of a lower concentration than before becomes possible.

[0057] (2) Since the numerical value of the silicon temperature is not used for calculating the quantification value, it is not always necessary to measure the silicon temperature of the measurement target, and it is not necessary to provide a measuring means such as a thermometer.

[0058] (3) In order to measure the reference spectrum at different silicon temperatures, a method of measuring the reference silicon multiple times over time can be adopted. Therefore, it is not always necessary to perform temperature adjustment of silicon during measurement, and it can also be applied to an FTIR apparatus with a standard configuration, resulting in a highly versatile quantification method. Even when there is no temperature control of silicon without using a temperature controller, quantification is possible. For example, it becomes possible to quantify large-sized silicon that does not fit into a temperature controller. Also, since it can be applied to the quantification operation of carbon concentration at normal temperature, it is easy to introduce into the manufacturing process of silicon crystals. On the other hand, in order to shorten the measurement time, a method of measuring the reference silicon multiple times after temperature adjustment (after confirming that the temperature has changed) can also be adopted.

[0059] (4) In the quantification method of Patent Document 2, the shape of the absorption spectrum of carbon after temperature correction is not calculated. However, in the quantification method of the present embodiment, since the shape of the absorption spectrum of carbon after correcting the influence of the variation of the absorption band of the lattice vibration of silicon due to the variation of the silicon temperature can be obtained, there is an advantage that the user can easily visually confirm whether the temperature correction has been appropriately performed based on the peak shape.

[0060] (5) Also, since the absorption band due to the lattice vibration of silicon is proportional to the thickness of the sample, if the thickness of the reference silicon is known, the thickness of the measurement silicon can also be calculated using the thickness correction coefficient or the temperature correction coefficient calculated in the present embodiment.

[0061] (6) Even if the second difference spectrum is calculated according to the procedure of the present embodiment, when a good absorption peak of a specific component does not appear (for example, when the temperature change is very large), the measured spectrum data can be regarded as abnormal data and excluded. Also, as a condition for determining abnormal data, for example, the second difference spectrum may include a differential waveform (a peak shape of upward and downward connected adjacent to each other). The computer can automatically determine whether such conditions are satisfied, and when it is determined as abnormal data, it is also possible to prompt the user to re-measure the spectrum.

[0062] Note that the method for quantifying the substitutional carbon concentration in silicon of the present embodiment is only an example, and the quantification method of the present invention is widely applicable to the method for quantifying the component concentration by the difference spectrum method using a spectrophotometer. In particular, in a measurement sample where the absorption band of another component overlaps with the absorption peak of a specific component, even when affected by the variation of the absorption band of another component due to the difference in the sample temperature, it is suitable for quantifying the concentration of the specific component in terms of being able to appropriately quantify the concentration of the specific component.

[0063] Hereinafter, the effects of the present invention will be further described based on the results of a quantitative test example of the carbon concentration in silicon using an FTIR apparatus. Note that the measurement conditions are an example, and the present invention is not limited thereto.

[0064] <Measurement conditions> Detector: MCT Measurement range: 700~500 cm -1 Resolution: 2 cm -1 Sample temperature: Room temperature Number of integrations: 110 times / 2 minutes

[0065] Here, a plurality of spectra of silicon are acquired using the interval measurement function of the FTIR apparatus. Specifically, after the start of measurement, integrated data for 2 minutes is repeatedly acquired until 146 minutes have elapsed. For example, the spectrum at "0 min" is the integrated data from 0 min to 2 min, and the spectrum at "144 min" is the integrated data from 144 min to 146 min.

[0066] As samples, two pieces of silicon from a silicon wafer with a thickness of 2 mm were used. In both cases, the carbon concentration is below the detection limit (40 ppba) of the JEITA standard in Non-Patent Document 1. Although the specific numerical values are unknown, the one estimated to have a lower carbon concentration based on the spectrum comparison is taken as the reference silicon R, and the one estimated to have a higher carbon concentration is treated as the measurement silicon S.

[0067] First, the absorbance spectra of the measurement silicon S and the reference silicon R are respectively acquired and recorded by interval measurement. Here, the measurement spectra and reference spectra at each time of 0 min, 50 min, 100 min, and 144 min are shown as in Table 1.

[0068]

Table 1

[0069] In this test example, the carbon concentration of the measured silicon S is quantified using a plurality of reference spectra obtained by measuring the reference silicon R. To clarify the effect of the present invention, a plurality of measurement spectra with different measurement times are also obtained for the measured silicon S, the carbon concentration is quantified based on each measurement spectrum, and the variation in the quantification results is examined.

[0070] For the first difference spectrum, the thickness correction coefficient derived by the method shown in FIG. 11 is used. In FIG. 11, the measurement spectrum S_144min and the reference spectrum R_144min are shown superimposed. A baseline (650~580 cm -1 ) is set in the same range as the absorption band due to the lattice vibration of silicon in the two spectra, and from the ratio of the peak heights at 620 cm -1 , the thickness correction coefficient becomes 0.998. This thickness correction coefficient is used for calculating the difference spectrum between the measurement spectrum S_144min and the reference spectrum R_144min in FIG. 11. Note that the thickness correction coefficient is calculated for each combination of the measurement spectrum and the reference spectrum, and the difference spectrum is calculated using each thickness correction coefficient.

[0071] In FIG. 12, the measurement spectrum S_144min in FIG. 11 and the reference spectrum R_144min multiplied by the thickness correction coefficient (0.998) are shown superimposed. Also, the overlapping condition of the spectra around 626 cm -1 and around 599 cm -1 is shown enlarged. From these enlarged views, it can be seen that due to the difference in silicon temperature, the band of the measurement spectrum S_144min is shifted to the lower wavenumber side than the band of the reference spectrum R_144min. That is, there is a wavenumber shift that cannot be removed only by thickness correction between the two spectra.

[0072] Figure 13(A) is an image showing the superposition of the first difference spectra of the measurement spectra (S_0min, S_50min, S_100min, S_144min) at each measurement time with the reference spectrum fixed at R_0min. As shown in Figure 12, these first difference spectra are based on the measurement spectra of the same measured silicon S. However, due to a slight variation in the silicon temperature during measurement, the absorption band (630~580 cm -1 ) caused by the lattice vibration of the silicon single crystal is shifted, so that just thickness correction cannot completely remove the absorption band of silicon, and the shape of the difference spectrum changes significantly. Since infrared light continues to irradiate the silicon for measurement, it is expected that the silicon temperature at the measurement time of 0 min is the lowest, and the silicon temperature increases as the measurement time progresses. The change in the shape of the difference spectrum as shown in Figure 13(A) is due to the shift of the absorption band of silicon.

[0073] Figure 13(B) shows the change over time of the carbon absorption peak intensity at 605 cm -1 based on the first difference spectrum of the measurement spectra at the measurement times from 0 min to 144 min. It can be seen that the moving average of the carbon absorption peak intensity gradually increases as the measurement time elapses. Thus, it is necessary to correct the influence of the variation in the silicon temperature on the first difference spectrum.

[0074] Next, a method for selecting a combination of reference spectra for temperature correction of the first difference spectrum will be described with reference to FIG. 14. Above the image in FIG. 14, the first difference spectrum (S_0min - (thickness correction coefficient) × R_100min) to be temperature-corrected is shown. Here, using the reference spectra R_0min to R_144min of the reference silicon measured between the measurement times of 0 min and 146 min, a combination of reference spectra for temperature correction is selected. Specifically, using these reference spectra R_0min to R_144min, difference spectra between multiple reference spectra are calculated, and the one that most closely matches the shape of the first difference spectrum is selected from them. For example, below the image in FIG. 14, a difference spectrum (R_144min - (thickness correction coefficient) × R_0min) considering thickness correction based on two reference spectra R_0min and R_144min is displayed. -1 ) Using the baseline drawn in the specified wave number range (635 to 620 cm -1 , the peak heights at 626 cm

[0075] are read respectively, and the ratio of the peak heights is calculated. Based on this ratio of the peak heights, the degree of coincidence of the shapes of the two difference spectra shown in FIG. 14 is evaluated.

[0076] For the difference spectra between various combinations of reference spectra based on the reference spectra R_0min to R_144min, the ratio of the peak heights is calculated in the same way as in FIG. 14 respectively, and the difference spectrum between the reference spectra with the smallest ratio of the peak heights is selected. Here, the difference spectrum between the reference spectra (R_144min - (thickness correction coefficient) × R_0min) shown in FIG. 14 is selected for temperature correction. Then, the ratio of the peak heights (0.406) calculated for this difference spectrum between the reference spectra is set as the temperature correction coefficient, and the second difference spectrum is calculated using this temperature correction coefficient.

[0076] In Fig. 15(A), for the case where the reference spectrum is fixed at R_100min and the first difference spectra of the measurement spectra (S_0min, S_50min, S_100min, S_144min) at each measurement time are calculated, further, the second difference spectra at each measurement time (S_0min, S_50min, S_100min, S_144min) calculated using the difference spectra between the selected reference spectra are superimposed and shown. For example, the second difference spectrum for the measurement time S_0min is expressed as "S_0min - (thickness correction coefficient) × R_100min - 0.406 × {R_144min - (thickness correction coefficient) × R_0min}" using the above temperature correction coefficient (0.406).

[0077] The second difference spectrum in Fig. 15(A) shows that the shape of the absorption peak (605 cm -1 ) of substitutional carbon is improved by temperature correction, and it can be seen that for any measurement time, the shape becomes more reasonable compared to Fig. 13(A). Also, for the second difference spectrum in Fig. 15(A), using the baseline drawn in the specified wavenumber range (616~598 cm -1 ), the peak height of the absorption peak (605 cm -1 ) of substitutional carbon is read respectively. Fig. 15(B) shows the change over time of the carbon absorption peak intensity based on the second difference spectra of the measurement spectra at the measurement times from 0 min to 144 min.

[0078] Regarding the first difference spectrum in Fig. 13(B), the fluctuation of the peak intensity was large, the moving average of the peak intensity did not become constant, and it gradually increased. The quantitative value (average value) based on this peak was 13.00 ppba, and the standard deviation SD was 0.906 ppba. On the other hand, regarding the second difference spectrum in Fig. 15(B), the fluctuation of the peak intensity became relatively small, and the moving average of the peak intensity became almost a constant value. The quantitative value (average value) based on this peak was 10.11 ppba, and the standard deviation SD was 0.670 ppba. That is, the detection limit from the 3σ method is 0.67×3 = 2 ppba = 0.002 ppma, which is about 1 / 20 of the detection limit of 0.04 ppma according to the JEITA standard of Non-Patent Document 1, and it is a numerical value that sufficiently shows the usefulness of the present invention. According to the quantitative method of the present invention, a very low carbon concentration of about 10 ppba can be stably quantified.

[0079] From the above results, it can be said that by correcting not only the thickness but also the shift of the absorption band of silicon, the shape of the difference spectrum is improved, and it becomes possible to quantify the carbon concentration in a stable state. Also, it is considered that a carbon concentration value close to the true value is obtained.

Explanation of Signs

[0080] S10~S50 Procedure S10~Procedure S50 S1 Measurement spectrum R1, R2, R3 Reference spectra

Claims

1. The measurement spectrum of a measurement sample showing both the absorption peak of a specific component and the absorption band of another component overlapping the absorption peak, measured by a spectrophotometer, and The reference spectrum of a reference sample measured by the spectrophotometer, in which the concentration of the specific component is lower than that of the measurement sample or the concentration of the specific component is zero, and Calculating the difference spectrum as the first difference spectrum; In order to correct the influence of the variation of the absorption band of the other component due to the difference in sample temperature, Calculating a plurality of difference spectra between the reference spectra for a plurality of reference spectra of the reference sample measured a plurality of times by the spectrophotometer; Selecting, from among the difference spectra between the reference spectra, one that is close to the shape of the first difference spectrum; and Calculating a difference spectrum between the first difference spectrum and the difference spectrum between the selected reference spectra as the second difference spectrum, including Obtaining the shape of the absorption peak of the specific component from the second difference spectrum and quantifying the concentration of the specific component. A method for quantifying component concentration, characterized by

2. In the method for quantifying component concentration according to Claim 1, When selecting, from among the difference spectra between the reference spectra, one that is close to the shape of the first difference spectrum, a range obtained by excluding the absorption peak of the specific component from the absorption band of the other component is specified as the wavenumber range for evaluating the degree of coincidence of the shapes of the two difference spectra. A method for quantifying component concentration, characterized by

3. In the method for quantifying component concentration according to Claim 2, In the evaluation of the degree of coincidence of the shapes of the two difference spectra, the peak height or peak area of each difference spectrum is used, or the width (P - P) of the maximum value and the minimum value of the difference between the intensities of the two difference spectra, or the RMS of the difference between the intensities of the two difference spectra is used. A method for quantifying component concentration, characterized by

4. In the method for quantifying component concentration according to Claim 3, In the calculation of the second difference spectrum, the ratio of the peak heights or the ratio of the peak areas is used as the difference spectrum coefficient. A method for quantifying component concentration, characterized by

5. The measurement spectrum of a measurement sample showing both the absorption peak of a specific component and the absorption band of another component overlapping the absorption peak, measured by a spectrophotometer, and The reference spectrum of a reference sample, which has a lower concentration of a specific component or a zero concentration of the specific component than the measurement sample, measured by the spectrophotometer, and calculating the difference spectrum as the first difference spectrum; To correct the influence of the variation of the absorption band of the other component caused by the difference in sample temperature, calculating the first derivative spectra of a plurality of reference spectra of the reference sample measured a plurality of times by the spectrophotometer; selecting, from among the first derivative spectra, one that is close to the shape of the first difference spectrum; and calculating the difference spectrum between the first difference spectrum and the selected first derivative spectrum as the second difference spectrum, including obtaining the shape of the absorption peak of the specific component from the second difference spectrum and quantifying the concentration of the specific component. A method for quantifying component concentration characterized by this.

6. A quantification program for quantifying the substitutional carbon concentration in silicon, to a computer, the measurement spectrum of a measurement sample measured by a spectrophotometer, showing both the absorption peak of a specific component and the broad absorption band of another component overlapping the absorption peak, and the reference spectrum of a reference sample, which has a lower concentration of a specific component or a zero concentration of the specific component than the measurement sample, measured by the spectrophotometer, and a function of calculating the difference spectrum as the first difference spectrum; To correct the influence of the variation of the broad absorption band caused by the difference in sample temperature, a function of calculating a plurality of difference spectra between the reference spectra for a plurality of reference spectra of the reference sample measured a plurality of times by the spectrophotometer; a function of selecting, from among the difference spectra between the reference spectra, one that is close to the shape of the first difference spectrum; a function of calculating the difference spectrum between the first difference spectrum and the selected difference spectrum between the reference spectra as the second difference spectrum; A program for realizing obtaining the shape of the absorption peak of the specific component from the second difference spectrum and quantifying the concentration of the specific component. A component concentration quantification program characterized by this.

7. A quantification program for quantifying the substitutional carbon concentration in silicon, to a computer, the measurement spectrum of a measurement sample measured by a spectrophotometer, showing both the absorption peak of a specific component and the broad absorption band of another component overlapping the absorption peak, and The reference spectrum of a reference sample, which has a lower concentration of a specific component than the measurement sample or a concentration of the specific component of zero, measured by the spectrophotometer, and a function of calculating the difference spectrum as the first difference spectrum; To correct the influence of the variation of the broad absorption band caused by the difference in sample temperature, a function of calculating the first derivative spectrum of each of the plurality of reference spectra of the reference sample measured a plurality of times by the spectrophotometer; a function of selecting, from among the first derivative spectra, one that is close to the shape of the first difference spectrum; a function of calculating the difference spectrum between the first difference spectrum and the selected first derivative spectrum as the second difference spectrum; a program for realizing the above; a component concentration quantification program, characterized by obtaining the shape of the absorption peak of the specific component from the second difference spectrum and quantifying the concentration of the specific component.

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