Method for evaluating diamond-like carbon film

Abstract

To provide a method for evaluation capable of obtaining highly accurate results that are not dependent on an analyzer, more appropriately and more rapidly than when using the Voigt function, when separation-analyzing the Raman spectrum of a diamond-like carbon (DLC) film into five peaks: N band, D band, G- band, G+ band, and D' band.SOLUTION: A Raman spectrum of a DLC film is curve-fitted using a pseudo-Voigt function represented by the following equation and is separated into the above five bands, and the characteristics of the DLC film are evaluated on the basis of at least one of the peak position, area, and intensity of each of the separated bands.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present disclosure relates to a method for evaluating diamond-like carbon films, and particularly to a method for evaluating carbon materials using Raman spectra.

Background Art

[0002] As a method for evaluating diamond-like carbon films (hereinafter referred to as "DLC films") as carbon materials using Raman spectra, Patent Document 1 below discloses a method of curve fitting the Raman spectrum of a carbon material using a Voigt function obtained by integrating the sum of a Lorentz function superimposed with a Gaussian function and a Breit-Wigner-Fano (BWF) function superimposed with a Gaussian function, separating it into a plurality of bands, and evaluating the characteristics of the carbon material based on at least one of the peak position, area, and intensity of each of the separated bands.

[0003] Specifically, the plurality of bands are five bands: the N band, the D band, the G - band, the G + band, and the D' band. The N band, the D band, the G + band, and the D' band are curve-fitted with a Lorentz function superimposed with a Gaussian function, and the G - band is curve-fitted using the BWF function superimposed with the Gaussian function.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] The Voigt function used in the technique described in Patent Document 1 requires the convolution integral of the Lorentz function and the Gaussian function, and the convolution integral of the BWF function and the Gaussian function, so the computational difficulty is high. Furthermore, the parameters in the analysis are the peak positions of each band (in other words, the wave number, unit: cm -1 ) are 5, the peak intensities of each band are 5, G - The full width at half maximum of the band (the width of the wave number at which the intensity is half of the peak intensity) is 1, the full width at half maximum of the other bands is 1, and the asymmetry parameter is 1, for a total of 13.

[0006] In the analysis, the curve obtained by inputting these parameters while adjusting them one by one to the software in which the Voigt function is programmed to the curve of the Raman spectrum obtained by measuring the actual carbon material is fitted. And as a result of that work, when the analyst determines that it is fitted, each parameter becomes the attribute value of each band, and the characteristics of the carbon material are evaluated with this. This fitting requires a huge amount of time-consuming manual work of trial and error while changing the numerical values of 12 or 13 parameters. Such work depends greatly on the experience and intuition of the operator, and it is extremely difficult to obtain an optimal solution.

[0007] An embodiment of the present disclosure aims to provide an evaluation method that can obtain highly accurate results independent of the analyst more accurately and quickly than using the Voigt function when analyzing the Raman spectrum of a DLC film by separating it into peaks of the above five bands.

Means for Solving the Problems

[0008] The evaluation method of the DLC film according to the aspect of the present disclosure curve-fits the Raman spectrum of the DLC film using the pseudo-Voigt function of Equation 1 into the N band, D band, G - band, G +The characteristics of the diamond-like carbon film are evaluated based on at least one of the peak position, area and intensity of each of the separated bands.

[0009]

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[0010]

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[0011]

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[0012]

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[0013] In the above formulas 1 to 4, j=1, j=2, j=3, j=4, and j=5 are the N band, the D band, and the G band, respectively. - Band, G + is a subscript indicating the parameters for the D band and the D′ band. In the above formula 1, G j (x) is the Gaussian function expressed by Equation 2, and L j (x) is the Lorentz function expressed by Equation 3, and B3(x) is the BWF function expressed by Equation 4. This B3(x) is G - This applies only when the band is j=3. In the above formula 1, α is a function ratio (0≦α≦1) that represents the weighting between the Gaussian function and the Lorentzian function in the first term on the right side, and β is a function ratio (0≦β≦1) that represents the weighting between the Gaussian function and the BWF function in the second term on the right side.

[0014] In the above formulas 1 to 4, μ j is the peak position of each band, and A j is the peak intensity of each band, and σ jis the full width at half maximum of the peak. In the above Equation 4, q k is the asymmetry parameter. This asymmetry parameter q k is such that the G band of the metal nanotube splits into two, namely the G + band and the G - band, and only the G - band shows an asymmetric shape, which is due to the interaction between phonons and the electron continuum. Since many DLC films are insulating, the asymmetry parameter q k becomes infinite and 1 / q k = 0. In this case, the BWF function in the above Equation 4 is reduced to the Lorentz function in the above Equation 3.

[0015] In the above method for evaluating the DLC film, it is desirable to set the peak position of the curve obtained by fourth-order differentiating the Raman spectrum as the peak position μ j of each band.

Advantages of the Invention

[0016] According to the method for evaluating the DLC film of the present disclosure, when analyzing the Raman spectrum of the DLC film by separating it into peaks of five bands as described above, highly accurate results that do not depend on the analyst can be obtained more accurately and quickly than using the Voigt function.

Brief Description of the Drawings

[0017]

Figure 1

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Figure 10

Mode for Carrying Out the Invention

[0018] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings.

[0019] (1) Significance of each band obtained from the Raman spectrum of the DLC film In the evaluation method of the diamond-like carbon film (hereinafter referred to as "DLC film") of the present embodiment, the Raman spectrum of the DLC film is curve-fitted using a pseudo-Voigt function into N band, D band, G - band, G + band, and D' band, and the characteristics of the diamond-like carbon film are evaluated based on at least one of the peak position, area, and intensity of each of the separated bands.

[0020] In the present embodiment, a two-dimensional graphene sheet is used as the basic structure regarding the Raman scattering of the DLC film. The two-dimensional graphene sheet is composed of six-membered rings (benzene), which is one of the most stable structures of carbon, as basic components. The symmetry of the two-dimensional graphene sheet belongs to the D 6h point group. The D 6h point group has four Raman-active modes, each showing a corresponding unique second-order tensor. Specifically, there are two in the A 1g mode, and one each in the E 1g mode and the E 2g mode. Among these, one A 1g mode and the E 2g mode are Raman-active regarding the two-dimensional graphene sheet. The vibration coordinate of the A 1g mode is x 2 +y 2 and the vibration coordinate of the E 2g mode is x 2 -y 2 and xy. In the case of a graphene sheet, the A 1g mode is attributed to the D band, and the E 2g mode is attributed to the G band. However, the vibration of the G band is also active for bonds containing sp 3 carbon.

[0021] In the evaluation method of the DLC film of the present embodiment, as shown in Fig. 1, the Raman spectrum is, in ascending order of low wavenumber, N (Network) band, D band, G - band, G +It is divided into five active bands: the band and the D' band. These five bands are obtained by curve fitting using a pseudo-Voigt function, which is the sum of a Gaussian function and a Lorentzian function weighted at a predetermined ratio and a Gaussian function and a BWF function weighted at a predetermined ratio. In FIG. 1, each point represents the spectral intensity at each frequency, and the solid line is the fitting curve obtained by adding the above five active bands.

[0022] The N band is derived from the E 1g mode. The E 1g mode has xz and yz coordinates, and since the z-axis component contributes to both, it is not observed in a two-dimensional graphene sheet. The E 1g mode corresponds to the three-dimensional inhomogeneous stretching vibration when the three-fold degeneracy (|xy| = |yz| = |zx|) of the T 3 mode of the diamond crystal composed only of carbon belonging to the O h point group collapses. The N band not only represents the three-dimensional vibration of sp 2g carbon such as a strained aromatic ring, but is also active for the three-dimensional vibration of sp 2 carbon like the vibration of the G band. Therefore, the position and intensity of the N band can be an index for evaluating the diamond property of the DLC film. 3

[0023] The D band is derived from the A 1g mode. The A 1g mode has x 2 + y 2 coordinates and z 2 coordinates. Among these, the two-dimensional x 2 + y 2 coordinates represent a circle, and its vibration is called a breathing vibration. This is peculiar to an aromatic ring composed of equal bonds. However, in the case of an equivalent and crystalline ring, the vibrations of adjacent rings can cancel each other out, so this band is called the D (Disorder) band, which is an index representing the number of aromatic ring clusters and the size per defect.

[0024] A 1gThe mode has another tensor z 2 which belongs to the D' band. Since the D' band represents the stretching vibration between opposing aromatic ring clusters, it serves as an indicator of its density. The pair of the D band and the D' band appears when the graphene sheet is damaged in some way.

[0025] The G band is derived from the E 2g mode. The E 2g mode has x 2 -y 2 coordinates and xy coordinates. The function x 2 -y 2 =r 2 is a hyperbola, but the variation of r represents the stretching and contraction of the bond. Therefore, the x 2 -y 2 coordinates of the G band correspond to the stretching vibrations of both the sp 2 carbon and the sp 3 carbon carbon-carbon bonds. The coordinates of the G band coincide with another xy coordinate by a rotation of π / 4 with respect to the coordinate origin. Therefore, generally, these coordinates cannot be distinguished.

[0026] A perfect graphene sheet or strain-free graphite composed only of sp 2 carbon shows a single and sharp G-band peak. On the other hand, in metallic carbon nanotubes, the G band is known to split into a G + band on the high-frequency side and a G - band on the low-frequency side. The former shows the vibration in the tube axis direction, and the latter shows the circumferential vibration with a large strain. Also, by forcibly applying strain to the graphene sheet, the G band similarly splits into two bands of G + band and G - band, and as the strain increases, the band splitting becomes larger. Therefore, the ratio of the G - band to the G + band serves as an indicator of the strain of sp 2 carbon and thus the magnitude of the strain of the entire DLC film.

[0027] (2) Pseudo-Fokker function The pseudo-Fokker function used in this embodiment is as shown in the following Equation 5. Here, G j (x) in the following Equation 5 is the Gaussian function shown in the following Equation 6, and L j (x) is the Lorentz function shown in the following Equation 7. Also, B3(x) in the following Equation 5 is the BWF function represented by the following Equation 8, and it is applied only to the G - band.

[0028]

Equation

[0029]

Equation

[0030]

Equation

[0031]

Equation

[0032] Note that μ j in the above Equations 5 to 8 is the peak position of each band, A j is the peak intensity of each band, σ j is the full width at half maximum of the peak, α is the function ratio representing the weighting between the Gaussian function and the Lorentz function, and β is the function ratio representing the weighting between the Gaussian function and the BWF function. Also, the subscript j attached to each parameter takes integer values from 1 to 5. When j = 1, it indicates the parameters of the N band. When j = 2, it indicates the parameters of the D band. When j = 3, it indicates the parameters of the G - band. When j = 4, it indicates the parameters of the G + band. When j = 5, it indicates the parameters of the D' band. Also, the BWF function shown in Equation 8 has the asymmetry parameter q k and is for the G -It is applicable only in the case of the band (j = 3). Since many DLC films exhibit insulating properties, the asymmetric parameter q k becomes infinite, and 1 / q k = 0. Therefore, in this case, the BWF function in Equation 8 above is reduced to the Lorentz function in Equation 7 above.

[0033] The peak position μ j represents the wave number (unit: cm -1 ) at the peak shown by each band. The peak intensity A j refers to the intensity of the peak of each measured band. It is desirable to use the relative value normalized with respect to the maximum intensity value of the measured data group for the peak intensity A j , but the value measured by the measuring instrument may be used as it is.

[0034] In this embodiment, the peak position μ j is obtained as follows. That is, each point of the Raman spectrum shown in FIG. 2 is smoothed using a moving average, a boxcar integrator, or the Savitzky-Golay or Hites-Biemann algorithm. Then, when this smoothed curve is differentiated four times, a curve having five peaks as shown in FIG. 2 is obtained. These five peaks are respectively compared with the N band having a peak around 1200 cm -1 , the D band having a peak around 1330 cm -1 , the G -1 band having a peak around 1420 cm, the G - band having a peak around 1540 cm -1 , and the D′ band having a peak around 1640 cm + . That is, in this embodiment, the wave numbers at which these peaks are located are used as the peak position μ -1 . j

[0035] The full width at half maximum σ j refers to the width of the wave number (unit: cm -1 ) at which the intensity becomes half of the peak intensity. For example, the peak intensity at the peak position μ x is A xWhen the full width at half maximum is σ x at the position of μ x ±σ x separated from the peak position by the full width at half maximum, the peak intensity becomes A x / 2. That is, the full width at half maximum σ j is a value indicating the degree of spread from the peak of each band. Here, when the DLC film does not contain hydrogen, the full width at half maximum σ j of each band may be a common value. Also, when the DLC film contains hydrogen, the full width at half maximum σ j of the bands other than the D band may be a common value, but the full width at half maximum of the D band needs to be a value different from these values (σ D ).

[0036] The function ratio α is a value that contributes to the weighting of the Gaussian function component and the Lorentzian function component in the first term on the right side of the pseudo-Voigt function, and is a value in the range of 0 ≦ α ≦ 1. This function ratio α can be determined, for example, as the value of α that gives the highest degree of fit with the pseudo-Voigt function for a known approximate curve using curve fitting with the Voigt function described later. For example, in FIG. 3, the curve obtained with the pseudo-Voigt function when α = 0.9 is shown by a broken line. The coefficient of determination (R 2 ) of this broken line with the curve obtained with the Voigt function shown by a solid line is 0.971513. On the other hand, FIG. 4 shows the curve obtained with the pseudo-Voigt function when α = 0.1 by a broken line. The coefficient of determination (R 2 ) of this broken line with the curve obtained with the Voigt function shown by a solid line is 0.99994. The coefficients of determination (R 2 ) for other values of α are shown in Table 1 below. It is presumed that when the value of α is about 0.1, the coefficient of determination (R 2 ) approaches 1 and the compatibility with the Voigt function becomes high. Furthermore, by examining the value of α in the vicinity of α = 0.1, the coefficient of determination (R 2As a result of obtaining the α value at which [[ID=]] is the highest, 0.12 was obtained as the optimal value of α. The function ratio β is a value that contributes to the weighting of the Gaussian function component and the BWF function component in the second term on the right side of the pseudo-Fokt function, and is a value in the range of 0 ≤ β ≤ 1. The optimal value of β can be obtained in the same manner as α.

[0037]

Table 1

[0038] From the above, among the parameters of the pseudo-Fokt function of the present embodiment, since the peak position μ of each band j is determined as described above, the parameters that require optimization are the peak intensity (A j ) of 5 for each band and, for the hydrogen-free DLC film, 1 half-width (σ j ) or, for the hydrogen-containing DLC film, 2 half-widths (σ j and σ D ), a total of 6 or 7.

[0039] Here, the Fokt function that has been conventionally used for curve fitting is as shown in the following mathematical formula 9 for the Raman spectrum of the insulating DLC film.

[0040]

Equation

[0041] Among the two functions multiplied in the above mathematical formula 9, the first function is the Lorentz function shown in the following mathematical formula 10, and the second function is the Gaussian function shown in the following mathematical formula 11.

[0042]

Equation

[0043]

Equation

[0044] And the parameters involved in the calculation of the above formula (9) are the peak positions (ν j ) of each band, with 5 of them, the peak intensities (I Lj ) of each band, with 5 of them, and the full-width at half-maximum (Γ Lj and Γ G ), with 2 of them, for a total of 12.

[0045] As described above, the Voigt function shown in formula (9) requires a convolution integral of a Lorentz function and a Gaussian function, while the pseudo-Voigt function of the present embodiment shown in formula (5) is merely the sum of a Gaussian function and a Lorentz function and the sum of a Gaussian function and a BWF function. Therefore, the calculation is extremely easy.

[0046] Furthermore, the number of parameters required for the calculation of the Voigt function shown in formula (9) is 12, while the number of parameters required for the calculation of the pseudo-Voigt function of the present embodiment shown in formula (5) is 6 or 7, and the number of parameters to be adjusted is approximately half.

[0047] As described above, the curve fitting of the Raman spectrum using the pseudo-Voigt function of the present embodiment is extremely easy compared to the case of using the Voigt function shown in formula (9), and the time required to obtain an optimal curve can be dramatically shortened.

[0048] (3) Curve fitting procedure Next, with reference to the flowchart of FIG. 5, an example of the curve fitting procedure in the evaluation method of the DLC film of the present embodiment will be described. Each procedure in the flowchart of FIG. 5 is actually stored in a storage device such as a ROM (Read-Only Memory) or an external storage of a computer as a program incorporating the pseudo-Voigt function shown in formula (4), and the central processing unit (CPU) of the computer expands the data into the RAM (Random Access Memory) and executes the program to automate the process.

[0049] First, in the step shown as S10, after reading the Raman spectrum data of the already measured DLC film, in the step shown as S20, the fitting range and the initial conditions for fitting (for example, A j or σ j ) are set. Next, the Raman spectrum data is fourth-order differentiated (see Figure 2), and five peak positions (μ j ) are determined

[0050] Next, in the step shown as S30, for the Raman spectrum data at each individual wave number, the data values are corrected using the linear method, and the individual data is normalized using the maximum intensity value of the measurement data group.

[0051] Then, in the step shown as S40, for the pseudo-Voigt function shown in Equation 4, first, the values of the five peak positions (μ j ) determined in the step shown as S20 are substituted, and then the above-mentioned six or seven parameters are appropriately substituted to perform fitting. This fitting is automated by a program that repeatedly performs calculations by changing the values of the parameters until the degree of deviation between the values (f(x)) at each individual wave number obtained by the pseudo-Voigt function and the actual Raman spectrum data is below a predetermined threshold.

[0052] Next, in the step shown as S50, it is determined whether the fitting curve obtained by fitting converges within a certain range with respect to the original Raman spectrum data. If it is determined that it has converged, in the step shown as S60, the values of each parameter substituted into the pseudo-Voigt function during the final fitting are saved, and the obtained fitting curve is saved as an image and / or displayed on the screen.

[0053] When the curve fitting is completed, in the step shown as S70, it is determined whether there is Raman spectrum data to be curve-fitted next. If there is, the steps shown as S10 and later are repeated with the new Raman spectrum data. On the other hand, if not, the process ends.

[0054] On the other hand, in the stage shown in S50 above, if it is determined that the fitting result has not converged, in other words, it is diverging, it is considered that there is some error (for example, incorrect sample preparation or incorrect measurement method) in the original Raman spectrum data. Therefore, in the stage shown in S80, it is determined whether to replace the Raman spectrum data. If replacement is made, the stages shown in S10 and later are repeated with new Raman spectrum data. If replacement is not made, the process ends.

Example

[0055] (1) Preparation of samples As samples for measuring Raman spectra, a hydrogen-free DLC film and a hydrogen-containing DLC film were each formed in a substrate shape using a 3-inch diameter graphite target as follows.

[0056] (1-1) Hydrogen-free DLC film The hydrogen-free DLC film was formed using the high-frequency - high-power pulse sputtering (HF-HiPIMS: high-frequency inclusion high-power impulse magnetron sputtering) method. The film formation conditions were as follows: the distance between the graphite target and the substrate was 100 mm, the rotation speed of the substrate was 5 rpm, the ultimate vacuum was 5×10 -4 Pa, the operating pressure was 0.5 Pa, the film formation time was 2 hours, and argon was flowed as the sputtering gas at a flow rate of 5 sccm. As for the pulse conditions, the negative applied voltage was 810 V, the frequency was 200 Hz, T1 of the HF pulse shown in FIG. 6 was 20 μsec, T2 was 5 μsec, T3 was 50 μsec, T4 was 36 μsec, T5 was 3 μsec, and T6 was 3 μsec.

[0057] (1-2) Hydrogen-containing DLC film The hydrogen-containing DLC film was formed using the alternating current high voltage burst plasma chemical vapor deposition (AC-HV-CVD) method. The film formation conditions were as follows: the alternating voltage was 5 kV, the offset voltage was 2 kV, the frequency was 10 kHz, and methane gas was flowed as the film formation gas at a flow rate of 5 sccm. The pulse conditions were 10 pulses per second, the film formation time was 1 hour, and the operating pressure was 39 Pa.

[0058] (2) Measurement of Raman spectrum The Raman spectrum was measured using a laser Raman microscope (Raman-11, manufactured by Nanophoton) at an excitation wavelength of 532 nm, a laser output of 0.5 mW, and a laser spot diameter of 2.55 μm. The exposure time was 90 seconds for the hydrogen-free DLC film and 30 seconds for the hydrogen-containing DLC film.

[0059] (3) Curve fitting Examples of curve fitting using a pseudo-Voigt function based on the Raman spectra obtained by measuring the above-mentioned hydrogen-free DLC film and hydrogen-containing DLC film are shown below in comparison with an example using the Voigt function.

[0060] (3-1) Hydrogen-free DLC film Figure 7 shows an example of curve fitting using the Voigt function for the Raman spectrum of the hydrogen-free DLC film. In this curve fitting, the above-mentioned 12 parameters were input while manually adjusting them to achieve a high degree of fitness. The fitting curve at the point where the degree of fitness was highest is shown in the upper part of Figure 7. The lower part of Figure 7 shows the degree of deviation ((r - f) / r × 100 (%)) defined as the ratio of the difference between the value (f) indicated by the fitting curve and the value (r) of the raw data of the Raman spectrum indicated by black dots in the upper graph. It took several hours to obtain this fitting curve. The chi-square value (χ 2 ) representing the degree of fitness of this fitting curve is 3.12, and the coefficient of determination (r 2) was 0.98874.

[0061] Figure 8 shows an example of curve fitting using a pseudo-Voigt function for the same Raman spectrum as in Figure 7. In this curve fitting, the six parameters described above are automatically adjusted using the automation program of the flowchart shown in Figure 5, and the fitting curve at the point of the highest degree of fit is shown in the upper part of Figure 8. The degree of deviation shown in the lower part of Figure 8 is the same as that in the lower part of Figure 7. The time required to obtain this fitting curve was 2 to 3 seconds. Also, the chi-square value (χ 2 ) was 1.974, and the coefficient of determination (r 2 ) was 0.99486. Here, since the smaller the chi-square value (χ 2 ), the better the degree of fit, and the closer the coefficient of determination is to 1, the better the degree of fit. It was found that curve fitting using the pseudo-Voigt function can obtain a fitting curve with higher accuracy in an extremely short time from any index.

[0062] (3-2) Hydrogen-containing DLC film Figure 9 shows an example of curve fitting using a Voigt function for the Raman spectrum of a hydrogen-containing DLC film. The fitting curve shown in the upper part of Figure 9 and the degree of deviation shown in the lower part of Figure 9 are the same as those in the upper and lower parts of Figure 7 described above, respectively. The work required to obtain this fitting curve took several hours. The chi-square value (χ 2 ), which is an index representing the degree of fit of this fitting curve, was 3.925, and the coefficient of determination (r 2 ) was 0.97583.

[0063] Figure 10 shows an example of curve fitting using a pseudo-Voigt function for the same Raman spectrum as in Figure 9. The fitting curve shown in the upper part of Figure 10 and the degree of deviation shown in the lower part of Figure 10 are the same as those in the upper and lower parts of Figure 8 described above, respectively. The time required to obtain this fitting curve was 2 to 3 seconds. Also, the chi-square value (χ 2 ) was 3.458, and the coefficient of determination (r 2) was 0.97624. From any of the indices, it was found that, similar to the case of the hydrogen-free DLC film, for the hydrogen-containing DLC film as well, curve fitting using the pseudo-Voigt function can obtain a fitting curve with higher accuracy in an extremely short time.

[0064] In addition, when comparing the fitting curve shown in the upper part of Fig. 8 and the fitting curve shown in the upper part of Fig. 10, for the hydrogen-containing DLC film, since the G - band is lower, it can be seen that the vicinity around 1420 cm -1 is flattened.

[0065] (3-3) Summary In any case, by using the pseudo-Voigt function, fitting with a higher degree of conformity than the result obtained with the Voigt function could be realized in a much shorter time.

Industrial Applicability

[0066] The embodiments of the present disclosure can be used as a method for evaluating DLC films.

Claims

1. The Raman spectrum of the diamond-like carbon film is curve-fitted using the pseudo-Voigt function of Equation 1 into five bands, namely the N band, D band, G － band, G ＋ band, G band, and D' band. Based on at least one of the peak position, area, and intensity of each of the separated bands, a method for evaluating the characteristics of the diamond-like carbon film is provided to evaluate the characteristics of the diamond-like carbon film. 【Number 1】 [Number 2] 【Number 3】 【Number 4】 (In Mathematical Expressions 1 to 4, j = 1, j = 2, j = 3, j = 4, and j = 5 are subscripts indicating parameters for the N band, D band, G － band, G ＋ band, and D' band, respectively, In Equation 1, G ｊ (x) is a Gaussian function represented by Equation 2, and L ｊ (x) is a Lorentz function represented by Equation 3, and B ３ (x) is a BWF function represented by Equation 4, α is a function ratio (0 ≦ α ≦ 1) representing the weighting of the Gaussian function and the Lorentz function in the first term on the right side, and β is a function ratio (0 ≦ β ≦ 1) representing the weighting of the Gaussian function and the BWF function in the second term on the right side. In Mathematical Formulas 1 to 4, μ ｊ is the peak position of each band, A ｊ is the peak intensity of each band, σ ｊ is the full width at half maximum of the peak, In Equation 4, q ｋ is an asymmetry parameter.)

2. The peak position μ of each band ｊ is the peak position of the curve obtained by fourth-differentiating the Raman spectrum, and is the method for evaluating a diamond-like carbon film according to claim 1.

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