Residual stress measurement in DLC films deposited by PBIID method using Raman microprobe spectroscopy

    Residual stress measurement in DLC films deposited by PBIID method using Raman microprobe spectroscopy Yasuhiro Miki, Akio Nishimoto, Takumi Sone, Yoshiji Araki PII: DOI: Reference:

S0257-8972(15)30343-1 doi: 10.1016/j.surfcoat.2015.10.048 SCT 20667

To appear in:

Surface & Coatings Technology

Received date: Revised date: Accepted date:

28 May 2015 20 October 2015 22 October 2015

Please cite this article as: Yasuhiro Miki, Akio Nishimoto, Takumi Sone, Yoshiji Araki, Residual stress measurement in DLC films deposited by PBIID method using Raman microprobe spectroscopy, Surface & Coatings Technology (2015), doi: 10.1016/j.surfcoat.2015.10.048

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ACCEPTED MANUSCRIPT Residual Stress Measurement in DLC Films Deposited by PBIID Method Using Raman Microprobe Spectroscopy

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Yasuhiro Mikia, Akio Nishimotob, Takumi Sonec, Yoshiji Arakid

Corresponding Author: Industrial Technology and Application Research Department,

Nara Prefecture Institute of Industrial Development 129-1, Kashiwagi-cho, Nara,

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630-8031, Japan. E-mail: [email protected], Phone No: +81

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0742-31-9096 (direct)

Department of Chemistry and Materials Engineering, Kansai University 3-3-35,

Yamate-cho, Suita-shi, Osaka, 564-8680, Japan. E-mail: [email protected],

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Phone No: +81 06-6368-1121

ASAHI HEAT TREATMENT Corporation, Japan 2-9-1, kuzuhara, Neyagawa-shi,

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Osaka, 572-0075, Japan. E-mail: [email protected], Phone No: +81 072-827-1139

KAIBARA Corporation, Japan. [email protected] 1216-3, Nukatabekita-machi,

Yamotokouriyama-shi, Nara, 639-1037, Japan. E-mail: [email protected], Phone No: +81

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0743-56-6371

ACCEPTED MANUSCRIPT Abstract Diamond-like carbon (DLC) films were prepared and their residual stresses were measured nondestructively using Raman microprobe spectroscopy. The plasma-based ion implantation

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and deposition (PBIID) method was used to coat the DLC films on thin glass substrates using

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acetylene, a mixture of acetylene and toluene, or only toluene gas at 1.0 Pa. Peaks in the Raman

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spectra of the DLC films were assigned as the D′(disordered) or C–C bonding peaks at 1,150 cm−1. The phonon deformation potentials (a′) of the films were estimated from data for the

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phonon deformation potentials for pure graphite and diamond and calculated using the sp3/sp2 bonding ratio and the hydrogen content of the films. Thus, a relation was observed between the

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Raman shift of the G peak (ωG) and the residual stress (σc) in each film. The Raman shifts (ω0) of the G peak for the films with no deformation were 1,554, 1,556, and 1,562 cm−1 for the films

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deposited using acetylene, a mixture gas and toluene gas. Moreover, only toluene and had stress

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constants of −0.378, −0.384, and −0.391 GPa/cm−1. The residual stresses constant in each film using (8.2 × 10−4·a′)−1ω0−1 were estimated as −0.379, −0.384, and −0.391 GPa/cm−1. The

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Raman shift of the D peak remained stationary as the compressive σc in the films increased but changed when the deposition gas was varied. The distance the D peak moved from 1,420 cm−1

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corresponded to that of the G peak from 1,560 cm−1 in the Raman spectra of the films in the stress-free state. In addition, compressive residual stress of the DLC film has had a major impact on the hardness.

ACCEPTED MANUSCRIPT 1. Introduction Diamond-like carbon (DLC) films are excellent surface lubricants, even though it is difficult to fabricate good lubricants from natural diamond. Moreover, due to their high hardness and

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excellent abrasion resistance, DLC films are widely used on various mechanical and metal

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molding parts [1, 2]. The residual stress in a DLC film is related to the properties of the film and

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the adhesion properties between the film and the substrate. Therefore, determination of the residual stress in films is very important. Unfortunately, due to the amorphous structure of DLC

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films, it is not possible to perform X-ray residual-stress analyses. However, based on the method reported by Stoney and Hoffman [3, 4], it is possible to calculate the residual stress in

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DLC films from the deformation of the coated substrate. A nondestructive Raman microprobe spectroscopic technique has also been shown to be a

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good alternative for calculating the residual stress in diamond films [5–8]. To the best of our

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knowledge, however, there is no available report on the use of the Raman microprobe

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spectroscopic technique for evaluation of the residual stress in DLC films. The purpose of this study, therefore, was to use this technique to obtain the residual stress in DLC films. The plasma-based ion implantation and deposition (PBIID) method was used to coat the DLC films

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on thin glass substrates using acetylene (C2H2) gas, toluene (C7H8) gas, or a mixture of the two gases at 1.0 Pa. The relationship between the residual stresses and Raman shifts of the graphite peaks (G peaks) for the graphitized structures in the DLC films was investigated.

2. Experimental 2.1 Preparation of the DLC films and measurement of the film thickness Thin sheets of alkali borate glass (50 × 15 × 0.22 mm3) were used as substrates. A PBIID apparatus (KURITA Seisakusho Co Ltd.) was used to coat the substrates with approximately 1.0-μm-thick DLC films. The plasma was generated using radio-frequency pulses at 13.56 MHz and 300 W, and a pulse voltage between −20 and −5 kV was applied to the substrates.

ACCEPTED MANUSCRIPT Acetylene and toluene (both of 99.0% purity) were used as the deposition gases. Table 1 lists the experimental conditions. A 3-mm-wide section of the edge of the substrate was attached to a coating holder with Kapton® tape. A Calotest apparatus (CSM Instrument Co., Ltd.) was used

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time to be 1.0 μm under each set of film-forming conditions.

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to measure the thickness of the DLC films. Film thickness was controlled via the deposition

2.2 Determination of the residual stresses in the DLC films from the deformation of the

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coated substrates and their sp3/sp2 bonding ratios, hydrogen contents, Young’s modulus and hardness

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Figure 1 illustrates the warp and other geometric parameters for the coated substrates. If the deformation of a DLC film is known, the residual stress (σc) in the film can be calculated as

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follows:

(1)

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σc = (Ebd2δ)/{3(1 − νb)tl2},

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where Eb is the Young’s modulus for the substrate (= 70 GPa), νb is the Poisson’s ratio for the substrate (= 0.22), t is the thickness of the substrate (= 0.22 mm), d is the thickness of the DLC film (=0.001 mm), l is the length of the coated substrate (= 47 mm), and δ is the amount of

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displacement of the free-edge deformation (mm). The variations of residual stress calculated from equation (1) for the deformation of the coated substrate were ±40 MPa at the maximum. An X-ray photoelectron spectroscopy apparatus (Shimadzu Co Ltd.) was used to obtain the sp3/sp2 bonding ratio of the DLC films. After balancing the base strength, the C1s spectrum was divided into the sp2-bond (284.5 eV) and sp3-bond (285.3 eV) spectra. The sp3/sp2 bonding ratio of the DLC film was then obtained from these sp2- and sp3-bond spectra [9]. Rutherford backscattering spectroscopy (Ion Technology Center Co Ltd.) and elastic recoil detection analysis were used to determine the hydrogen content of the DLC films. Helium ions were irradiated onto each DLC film; the recoils of atoms other than hydrogen (carbon and helium) were removed using a polyester film.

ACCEPTED MANUSCRIPT A nano-indentation tester (ELIONIX Co., Ltd.) was used to measure the Young’s modulus and hardness of the DLC films. The indentation load was 3 mN.

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2.3 Raman analysis of the DLC films and determination of their G-peak shifts

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A laser Raman microprobe spectroscopic device (JASCO Corporation) was used to obtain

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Raman spectra of the DLC films. The wavelength and power of the laser were 532 nm and approximately 3 mW, respectively. The laser light was irradiated vertically onto the surface of

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the DLC films, and Raman spectra were obtained over the range ω = 900–1,900 cm−1 using the backscattering method. Each run involved accumulation of data from five 10 s exposures. The

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analysis was repeated at nine different points on each DLC film (the space resolution was φ2 μm, and the aperture size was 50 μm).

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Figure 2 shows the Raman spectra obtained from the DLC films with large compressive

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residual stress and very small compressive residual stress. In general, the Raman spectra of the DLC films consisted of a D (disordered) peak at approximately 1,360 cm−1 and a G (graphite)

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peak at approximately 1,580 cm−1 [10]. The Raman scattered strength, after balancing the base strength, was normalized by the maximum strength. Normalized Raman spectra were then

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obtained. In the Raman spectrum of the resulting DLC film in the present study, deconvolution into the D and the G peaks will cause a mismatch in the 900–1,300 cm−1 region. As shown in Fig. 2, the waveforms were divided into three Raman peaks: (a) the D′ or C-C bonding peak at 1,150 cm−1, which was assumed to originate from the high-density phonons of graphite [11,12] or from the C-C bonding of polyacetylene [13]; (b) a D peak; and (c) a G peak. As evident in the figures, all three peaks are represented by Gaussian functions. Moreover, the Raman shifts of the G peaks were obtained. Variations in the Raman shift of the G peak for the same DLC film were approximately ±1 cm−1; therefore, the mean value of the nine measurements for each sample was used for the Raman shift of the G peak.

ACCEPTED MANUSCRIPT 3. Results and Discussion 3.1 Raman shift of the G peak in the stress-free state Figure 3 shows the relation between the shifts (ωG) of the G peaks in the Raman spectra of

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the DLC films and the calculated residual stresses (σc), which were obtained from the

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deformations of the substrates coated with the films. The damage to the DLC films at a laser

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power of 3mW could not be confirmed. The differences between the Raman shifts of the G and D peaks in the spectra of the DLC films deposited using C2H2 gas and a C2H2/C7H8 gas mixture

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are certainly negligible. However, slight differences can be confirmed using the average values for the Raman shifts obtained for each gas species. The shift of the G peak moved to higher

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wavenumbers in the Raman spectra as the compressive residual stress in the DLC film increased. Although, the variations in the measurement of the Raman shift of the G peak for the

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same DLC film were approximately ±1 cm−1, a direct linear relationship between the residual

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stress and the Raman shift of the G peak can be seen in the figure. It is assumed that the

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half-widths of the G peaks contribute to the error in the Raman shift values. In addition, different direct linear relationships were obtained for films prepared using different deposition gases at the same pressure. When the deposition gas was acetylene, a mixture of acetylene and

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toluene, and toluene, the shifts (ω0) of the G peaks in the Raman spectra for the obtained DLC films with zero stress were estimated to be 1,554, 1,556, and 1,562 cm−1, respectively. Clearly, the Raman shifts (ω0) of the G peaks of the films with zero stress moved to higher wavenumbers when the deposition gas was changed from acetylene to a mixture of acetylene and toluene to pure toluene. This shift is thought to be due to the formation of clusters of carbon networks in the DLC films. This phenomenon corresponds to the results reported by J. Robertson [14]. In addition, the stress constants (GPa/cm−1) for the DLC films were calculated from the reciprocal slopes of the approximate straight lines in Fig. 3 to be −0.378, −0.384, and −0.391 GPa/cm−1, respectively.

ACCEPTED MANUSCRIPT 3.2 Relationship between the residual stresses in the DLC films and the shifts of the G peaks in their Raman spectra Residual stress analysis for silicon wafers or silicon films using Raman spectroscopy [15,16]

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and the behavior of the residual stress with respect to the G peaks of the DLC films [17] have

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been previously reported. The G peak is actually the stretching vibration of any pair of sp2 sites,

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whether in the C=C chains or the aromatic rings [14]. Moreover, the Raman shifts of the G peaks and the macroscopic residual stresses of the DLC films exhibited a linear relationship, as

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shown in Fig. 3. And the X-ray diffraction analysis revealed that the DLC films had amorphous structures. Therefore, we assumed that the DLC films were in stressed states without any shear

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stress, and that the sp2 and sp3 bonding states of the carbon atoms remained constant. Based on these assumptions, a direct relationship could be drawn between the residual stresses in the

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films and the shifts of the G peaks in their Raman spectra, as shown in Fig. 3. This relationship

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was attributed to the graphitized carbon in the DLC films, and consequently, planar residual

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stresses in the DLC films were examined. Raman excitation of the optical phonons of graphite results in the doubly degenerate E2g optical phonon mode. It is thought that this peak in the Raman spectrum moves from its position for the stress-free state to a new position for the

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stressed state. Moreover, the interatomic distances decrease when a compressive residual stress exists in a film. As a result, the spring constant K due to sp3- and sp2-bonding and the phonon frequency both increase. Therefore, when a compressive residual stress exists in a film, it is predicted that the E2g peak in the Raman spectrum of the stressed film will appear at a higher wavenumber than the peak in the spectrum for the stress-free film. The equation of motion for the linear relationship between a doubly-degenerate phonon and the strain in a graphitized structure can be expressed as follows: ω2Ｕi ＝ ΣKijＵi,

(2)

where ω is the Raman shift with strain, Kij is the spring constant tensor, and Ｕ i is the eigenvector in the crystal coordinate system. The tensor Kij is related to the strain by:

ACCEPTED MANUSCRIPT Kij = K0 + aΣεij,

(3)

where a is the phonon deformation potential constant of graphite (the total of the phonon deformation potential constant components p and q) [18], K0 is the spring constant tensor without

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strain, and εij is the strain for the graphitized structure. It was assumed that the Raman

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excitation mode for graphite without shear stress is mode 2; therefore, a simplified relationship

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was obtained:

ωG2 − ωG02 = a(ε11 + ε22)  2ωG0(ωG − ωG0),

(4)

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where ε11 and ε12 are the strains for graphite, ωG is the Raman shift of the G peak for the DLC film, and ωG0 is the Raman shift of the G peak for the DLC film without stress. The stress tensor

as follows:

(5)

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ε11 = ε22 = (S11 + S12)σ,

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is related to the plane strain tensor in a symmetric linear elastic solid of hexagonal-like graphite

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where S11 and S12 are the elastic compliance constants of graphite. Combining equations (4) and (5) gives an expression for the stress:

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σ = {a (S11 + S12)}−1 ω0 (ωG–ωG0).

(6)

The numerical values for aG/ω02, aD/ω02, S11, and S12 were −1.32 [18], 2.84 [19], 0.98 ×

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10−3/GPa [20], and −0.16 × 10−3/GPa [20], respectively. As a result, the relationship between the shift ωG of the G peak in the Raman spectrum of a DLC film and its residual stress σr is given by:

σr (GPa) = (8.2 × 10−4·a)−1ω0−1(ωG − ωG0).

(7)

In DLC films, the diamond structure has a constant sp3/sp2 bonding ratio. The phonon deformation potential of graphite can thus be calculated as follows: a = (1 − γD)aG + γDaD,

(8)

where γD is the sp3/sp2 ratio in the DLC film, aG is the phonon deformation potential constant for graphite, and aD is the phonon deformation potential constant for diamond. The sp3/sp2 bonding ratios (γD) for the DLC films prepared using the PBIID method were determined using

ACCEPTED MANUSCRIPT X-ray photoelectron spectroscopy. As shown in Table 2, the sp3/sp2 bonding ratios (γD) for typical DLC films deposited via PBIID ranged from 0.47 to 0.53. The sp 3/sp2 bonding ratios (γD) for the films prepared using the same deposition gas were averaged, and the phonon

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deformation potential for graphite was calculated for each type of film. Thus, by having an

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accurate value for the sp3/sp2 bonding ratio in DLC films, it was possible to calculate the

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residual stresses using equation (7). In other words, the residual stress distributions in minute areas on the surfaces of DLC films can be determined nondestructively using laser Raman

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microprobe spectroscopy. To determine the residual stress in a DLC film using equation (7), the Raman shift of the G peak in the spectrum of the film in the stress-free state (ωG0) must be

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known. As shown in Fig. 3, for the DLC films prepared using acetylene gas, an acetylene/toluene mixture, and toluene gas, ωG0 = 1,554, 1,556, and 1,562 cm−1, respectively.

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The average sp3/sp2 bonding ratios for each deposition gas were respectively 0.52, 0.50, and

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0.48 (Table 2). Therefore, expression (7) becomes: (9-1)

for the acetylene/toluene mixture, σr = −0.377(ωG − 1,556) GPa,

(9-2)

for toluene gas, σr = −0.383(ωG − 1,562) GPa.

(9-3)

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for acetylene gas, σr = −0.372(ωG − 1,554) GPa,

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Table 3 shows the residual stress constants (GPa/cm−1) estimated using the values for σc (residual stresses in the DLC films determined from the deformations of coated substrates) and σr (residual stresses in the DLC films calculated using equations (7) and (8)). As can be seen in the table, the residual stress constants estimated using the σc values were smaller than those estimated using the σr values for each type of deposition gas. It is therefore thought that the phonon deformation potential of graphite in DLC films cannot be described using only the sp3/sp2 bonding ratio, as indicated in expression (8). All DLC films in this study were a-C:H films in which carbon atoms are terminated by hydrogen bonds. For this reason, it is assumed that an increase in the hydrogen content relaxes the residual stress in DLC films, and therefore the hydrogen content of a DLC film influences

ACCEPTED MANUSCRIPT the phonon deformation potential of the graphite in the film. As shown in Table 2, the hydrogen content in the DLC films prepared in the present study varied depending on the type of deposition gas, and increased when acetylene was replaced with toluene. The phonon

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deformation potentials (a) for acetylene gas, the mixture of acetylene and toluene, and toluene

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alone determined from the residual stress constants σr were respectively −2.13–−2.10 (average

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2.11), −2.10–−2.06 (average 2.08), and −2.03–−1.99 (average 2.02). Conversely, the phonon deformation potentials (a) for acetylene gas, the mixture of acetylene and toluene, and toluene

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alone obtained using the residual stress constants σc were respectively −2.08, 2.05, and −1.99. The differences a obtained using the different residual stress constants are attributed to the

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different hydrogen contents in the DLC films.

An increase in the hydrogen content of a DLC film is thought to result in a decrease in the

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phonon deformation potential of diamond. Thus, the hydrogen contents (γH) of the DLC films

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prepared using the same deposition gas were averaged, and the phonon deformation potential of

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graphite was calculated for each type of DLC film using equation (10), which takes into account the hydrogen content: a′ = (1 − γD)·aG + γD·aD·{ (1 − (γH)2},

(10)

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where γH is the hydrogen content of the DLC film. As shown in Table 2, the average hydrogen contents for each deposition gas were respectively 15.8, 16.4, and 17.3. Therefore, when the phonon deformation potentials (a′) in expression (10) are substituted in expression (7), expression (7) becomes: for acetylene gas, σr = −0.379(ωG − 1,554) GPa,

(11-1)

for the acetylene/toluene mixture, σr = −0.384(ωG − 1,556) GPa,

(11-2)

for toluene gas, σr = −0.391(ωG − 1,562) GPa.

(11-3)

Table 4 lists the residual stress constants (GPa/cm−1) estimated using the values for σc (residual stresses in the DLC films determined from the warps of the substrates) and σr (residual stresses in the DLC films determined using equations (7) and (10)). As can be seen in the table,

ACCEPTED MANUSCRIPT the residual stress constants estimated using the σc values agreed well with the residual stress constants estimated using the σr values for the DLC films prepared using the different types of deposition gases. These results demonstrate that if both the sp3/sp2 bonding ratio and the

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hydrogen content of a DLC film can be determined, then the phonon deformation potential for

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graphite in the DLC film can be estimated.

3.3 Relationship between the residual stress (σc) in the DLC films and the shifts of the D

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peaks in their Raman spectra, and between the residual stress (σr) and their hardness Figure 4 shows the relationship between the shifts (ωD) of the D peaks in the Raman spectra

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of the DLC films prepared in the present study and their calculated residual stress (σc) values, which were obtained from the deformations of the substrates coated with the DLC films. The

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variation in the measurement of the Raman shifts of the D peaks is approximately ±1.5 cm−1. As

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evident in Figure 2, the half-width of the separated D peak is large, such that the half-width of

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the G peak is smaller than the half-width of the D peak. It was thought that the half-widths of these peaks contributed significantly to the measured Raman shift. However, the shift of the D peak in the Raman spectrum did not tend to move to higher or lower wavenumbers as the

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compressive residual stress in the DLC films increased. The D peak is the breathing mode for those sp2 sites only in the ring, not in chains [14]. Therefore, the absence of any change in the Raman shift of the D peak has little significance. The shift of the D peak varied for the films prepared using different deposition gases at the same pressure. As can be seen in Fig.4, the D peak shifted to higher wavenumbers in the spectra of the DLC films prepared using acetylene gas, the acetylene/toluene mixture, and toluene gas (1,414, 1,416, and 1,422 cm−1, respectively). In addition, the values of the shifts of the D peaks from 1,420 cm−1 corresponded with the values of the shifts of the G peaks from 1,560 cm−1 in the same DLC films in the stress-free state. Therefore, it may be possible to use the shift of the D peak in the Raman spectrum of a DLC film to estimate the Raman shift of the G peak in the

ACCEPTED MANUSCRIPT same DLC film in the stress-free state. Thus, the residual stresses in the DLC films deposited using the PBIID method were estimated using expression (12): σr (GPa) = (8.2 × 10−4·a′)−1(ωD + 140)−1(ωG − ωD − 140).

(12)

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Figure 5 shows the relationship between the Young’s modulus and the G peak or the D peak.

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With each film deposition gas, as the Young’s modulus of the DLC film increases, the position

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of the G peak tends to shift to the higher-wavenumber side. In contrast, the Raman shift of the D peak is not expected to be dependent on the Young’s modulus of the DLC films. We have

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previously reported that, in the case of the DLC film formed under 1.0 Pa pressure using acetylene gas [21], the G peak is shifted to the lower-wavenumber side when the bias voltage

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and repetition frequency are set to be large in the PBIID method [21]. An increase of the hydrogen content of the graphite of the DLC in the film is hypothesized to shift the G peak to

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the lower-wavenumber side. Conversely, as noted by Ferrari and J. Robertson [22], the G peak

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associated with a cluster of graphite structures should be shifted to the higher-wavenumber side.

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The shift of the G peak to the higher-wavenumber side because of the use of different gas species is considered to correspond to this cluster of graphite structures. In the present work, the increase in the growth of sp2 bonds and the increase in the hydrogen content in the DLC film

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changes the phonon deformation potential, causing a decrease in the Young’s modulus and hardness. We believe that the position of the G peak is shifted to the lower-wavenumber side as a consequence of these effects. Since residual stress in the films affects the hardness, relationships between the residual stress in the DLC films estimated from expression (12) and the hardness of the films was evaluated. Figure 6 shows these relationships, which were determined using the nano-indentation method. As can be seen in the figure, the hardness of the DLC films increased as the compressive residual stress increased. The influence of the residual stress on the nano-indentation hardness of the DLC films may be related to changes in the contact areas because of residual stresses. During the nano-indentation test, the increase in the compressive

ACCEPTED MANUSCRIPT residual stress in the film causes a decrease in the contact area and the indentation depth of the indenter [23]. Also in the present study, it is thought that increases in the compressive residual stresses in the DLC film caused decreases in the contact areas and the indentation depths of the

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indenter, which appeared to cause increases in the Young’s modulus and hardness of the DLC

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films. The compressive residual stress of the DLC film has had a major impact on the hardness.

relaxed the residual stress in the DLC films.

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It is thought that a decrease in the sp3/sp2 bonding ratio and an increase in the hydrogen content

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Based on the aforementioned considerations, the reduction of the hydrogen content and the increase of the sp3/sp2 bonding ratio in the DLC film are believed to reduce the Raman shift of

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the G peak and the increase of the compressive residual stress in the DLC film is believed to increase the Raman shift of the G peak. Two phenomena result in a variation of the Raman shift

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of the G peak.

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hydrogen content.

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Further experiments are required to investigate the behavior of DLC films with very low

4. Conclusions

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The purpose of this study was to evaluate the residual stresses in DLC films using Raman microprobe spectroscopy. The DLC films were deposited on glass substrates via PBIID at 1.0 Pa using acetylene gas, a mixture of acetylene and toluene, and toluene gas. The phonon deformation potentials and residual stress constants and the relationship between the shift of the G peak in the Raman spectra, which belongs to a graphitized structure in DLC films, and the residual stress in the DLC films were examined. The main results are as follows. 1) The Raman shifts of G peaks and the macroscopic residual stresses of the DLC films exhibited a linear relationship. The shifts (ω0) of the G peaks in the Raman spectra of the DLC films without residual stress with increasing the Carbon content of the using deposition gas were shift from approximately 1,554 cm-1 to 1,562 cm−1.

ACCEPTED MANUSCRIPT 2) The phonon deformation potential constants of the DLC films, represented by the symbol a′, were estimated using the sp3/sp2 bonding ratio (γD) and the hydrogen content (γH) in the DLC films. The expression for the phonon deformation potential for the DLC films using the

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phonon deformation potentials for graphite and diamond is a′ = (1 − γD)·aG + γD·aD·{ (1 −

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(γH)2}.

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3) Using a′ to represent the phonon deformation potential of the DLC films, the residual stresses (σr) in the DLC films were estimated from the shifts (ωG) of the G peaks in their

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Raman spectra using the expression σr ＝(8.2 × 10−4·a′)−1ω0−1 (ωG − ω0) GPa. 4) The values of the stress constants for the films were determined using two methods. From the

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warps of the substrates, the values with increasing the Carbon content of the using deposition gas were changed from −0.378 GPa/cm−1 to −0.391 GPa/cm−1. From the shifts of the G

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peaks in the Raman spectra of the DLC films, the values with increasing the Carbon content

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of the using deposition gas were changed from −0.379 GPa/cm−1 to −0.391 GPa/cm−1.

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Notably, the values obtained using the two methods were in good agreement. 5) The shift (ωD) of the D peak in the Raman spectra of the DLC films hardly changed as the compressive residual stress in the DLC films increased. However, as the deposition gas was

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changed from acetylene to a mixture of acetylene and toluene to only toluene, the D peak did shift away from 1,420 cm−1, and the distance in wavenumbers from 1,420 cm−1 corresponded to the difference in wavenumbers that the G peak shifted from 1,560 cm−1 for the DLC films in the stress-free state. 6) The hardness of the DLC films determined using the nano-indentation method increased as the compressive residual stress increased. The compressive residual stress of the DLC film has had a major impact on the hardness.

Acknowledgements We wish to express our gratitude to Prof. Hirohisa Kimachi (Department of Mechanical

ACCEPTED MANUSCRIPT Engineering, Faculty of Science and Technology, Meijo University, Japan) for his valuable advice.

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The authors would like to thank Enago ( www.enago.jp ) for the English language review.

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[1] S. Miyake, Tribological Improvement of Carbon Films by Material Additions, J. Jpn. Soc. Tribologis. 41, (9) (1996) 754–759.

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[2] M. Kano, DLC Coating Technology Applied to Sliding Parts of Automotive Engine, New Diam. Front. Carbon Technol., 16 (2006) 201–210.

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[3] G. G. Stoney, The Tension of Metallic Films Deposited by Electrolysis, Proc. R. Soc. A 82, (1909) 172–175. [4] R. W. Hoffman, Physics of Thin Films, Phys. Thin Films, 3, Academic Press, New York, (1966) 219–253.

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[5] T. Itou, H. Higashi, M. Noda, Stress Analysis in Micro Areas of LSIs Using Raman Microprobe, R&D Review of Toyota CRDL, 29, (4) (1994) 43–52.

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[6] F. Cerdeira, C. J. Bachenauer, F. H. Pollak M. Cardona, Stress-Induced Shifts of First-Order Raman Frequencies of Diamond- and Zinc-Blende-Type Semiconductors, Phys. Rev., 5, (2) (1972) 580–589. [7] M. H. Grimsditch, E. Anastassakis, M.Cardona, Effect of uniaxial stress on the zone-center optical phonon of diamond, Phys. Rev. 18 (1978) 901–904.

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[8] F. Ahmed, M. Krottenthaler, C. Schmid, K. Durst, Surf. Assesment of stress relaxation experiments on diamond coatings analyzed by digital image correction and micro-Raman spectroscopy, Coat. Tech. 237 (2013) 255–260. [9] S. R. P. Silva, S. Xu, B. K. Tay, H. S. Tan, H. J. Scheibe, M. Chhowalla, W. I. Milne, The structure of tetrahedral amorphous carbon thin films, Thin Solid Films 290–291 (1996) 317–322. [10] B. S. Elman, M. S. Dresselhaus, G. Dresselhaus, E. W. Maby, H. Mazurek, Raman Scattering from ion-implanted graphite, Phys. Rev., B 24 (1981) 1027–1034. [11] B. Oral, R. Hauert, U. Muller, K. H. Errunst, Structural changes in doped a-C:H films during annealing, Diamond Relat. Mater. 4, (4) (1995) 482–487. [12] M. Iwaki, H. Watanabe, Analysis of Raman spectra for Na-ion implanted polyacetylene, Nuclear Instrument Method in Physics Research Section B, B 141 (1998) 206-210. [13] B. S. Elman, M. Shayegan, M. S. Dresselhaus, H. Mazurek, G. Dresselhaus, Structural characterization of ion-implanted graphite, Phys. Rev., B 25 (1982) 4142–4156. [14] J. Robertson, Diamond-like amorphous carbon, Mater. Sci. Eng., R 37, (2002) 129–281.

ACCEPTED MANUSCRIPT [15] S. Narayanan, Surya R. Kalidindi, Linda S. Schadler, Determination of unknown stress in silicon wafers using microlaser Raman spectroscopy, J. Appl. Phys. 82, (5) (1997) 2595-2602.

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[16] Th. Englert, G. Abstreiter, J. Pontcharra, Determination of Existing Stress in Silicon Films on Sapphire Substrate Using Raman Spectroscopy, Solid State Electron., 23, (1) (1980) 31-33.

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[17] Y. Miki, T. Taniguchi and T. Sone, Measurement of Residual Stress in DLC Films Using Raman Spectroscopy, Proceeding of the 49th JSMS Annual Meeting, (2000) 275-276.

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[18] C. Thomsen, S. Reich, Ab initio determination of the phonon deformation potentials of graphite, Phys. Rev. B65 (2002) 403–405.

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[19] J. M. Calleja, J. Kuhl, M. Cardona, Resonant Raman scattering in diamond, Phys. Rev. B 17 (1978) 876–883. [20] B. T. Kelly, Physics of Graphite, Appl. Sci. Publ., London, (1981) 43–50.

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[21] Y. Miki, H. Adachi, Y. Nishimura, M. Sugihara, Y. Horino, Rsidual Stress Measurement in DLC Films Prepared by Plasma-based Ion Implantation and Deposition (PBIID) Method, Report of Nara Prefectural Institute of Industrial Technology, 31 (2005) 10-15.

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[22] A. C. Ferrari, J. Robertson, Interpretation of Raman spectra of disordered and amorphous carbon, Phys. Rev., B 61, (20) (2000) 14095-14107.

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[23] TY Tsui, WC Oliver, GM Pharr, Influence of stress on the measurement of mechanical properties using nanoindentation:Part I Experimantal studies in a aluminum alloy, J. Mater. Res., 11 (1996) 752-759.

ACCEPTED MANUSCRIPT Figure Captions

Fig. 1 Schematic showing the deformation of the substrate coated with a DLC film.

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Fig. 2 Typical Raman spectra of a DLC film prepared using the PBIID method. The spectrum is

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divided into the D′, D, and G peaks. The spectrum labeled (a) is the Raman spectrum for the

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DLC film with the large residual stress, σc (σc = −0.95 GPa for acetylene gas). The spectrum labeled (b) is the Raman spectrum for the DLC film with small residual stress (σc = −0.03 GPa

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for toluene gas).

Fig. 3 Relationship between the residual stress σC obtained from the deformation of the

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substrate and the shift of G band, ωG, in the Raman spectrum of a DLC film. Fig. 4 Relationship between the residual stress, σc, obtained from the deformation of the

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substrate and the shift of the D peak, ωD, in the Raman spectrum of a DLC film.

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Fig. 5 Relationship between the Young’s modulus and the Raman shifts of the G peaks and the

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Raman shifts of the D peaks of the DLC films. Figure (a) figure shows the relationship between the Young’s modulus and the Raman shifts of the G peaks. Figure (b) figure shows the relationship between the Young’s modulus and the Raman shifts of the D peaks.

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Fig. 6 Relationship between the hardness and residual stresses, σr, obtained from the Raman shifts of the G peaks in the Raman spectra of the DLC films.

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Fig. 1

DLC film

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Fig. 2

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Fig. 3

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Fig. 4

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Fig. 6

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Width (x10−6s) 10 5 5 5 5

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Pulsed voltage (kV) −10 −20 −20,−15,−10,−5 −20,−15,−10,−5 −20,−15,−10,−5

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Pressure (Pa) 0.5 0.5 1.0 1.0 1.0

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Ar CH4/C2H2 C2H2 C2H2/C7H8 C7H8

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Step 1 Step 2 Step 3

Flow (cc/min) 50 25/25 50 25/25 50

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Frequency (kHz) 2 1 1,2,3,4 1,2,3,4 1,2,3,4

ACCEPTED MANUSCRIPT Table 2 The thickness of the DLC films, the sp3/sp2 bonding ratio and hydrogen content for the DLC films deposited using the PBIID method. Film thickness (μm)

sp3/sp2 bonding ratio

Hydrogen content (at %)

C2H2

0.98–1.05 (Average 1.02) 0.97–1.10 (Average 1.04) 0.98–1.08 (Average 1.03)

0.51–0.53 (Average 0.52) 0.49–0.51 (Average 0.50) 0.47–0.50 (Average 0.48)

15.4–16.2 (Average 15.8) 16.0–16.7 (Average 16.4) 17.0–17.6 (Average 17.3)

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ACCEPTED MANUSCRIPT Table 3 Residual stress constants estimated from σc or σr for the DLC films deposited using the PBIID method.* Residual stress constant estimated Residual stress constant estimated from σc (GPa/cm−1) from σr (GPa/cm−1) C2H2 −0.378 −0.372 C2H2/C7H8 −0.384 −0.377 C7H8 −0.391 −0.383 *The phonon deformation potential was calculated only from the sp3/sp2 bonding ratio.

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ACCEPTED MANUSCRIPT Table 4 Residual stress constants estimated from σc or σr for the DLC films deposited using the PBIID method.* Residual stress constant estimated Residual stress constant estimated from σc (GPa/cm−1) from σr (GPa/cm−1) C2H2 −0.378 −0.379 C2H2/C7H8 −0.384 −0.384 C7H8 −0.391 −0.391 *The phonon deformation potential was calculated from both the sp3/sp2 bonding ratio and the hydrogen content.

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ACCEPTED MANUSCRIPT Highlights ・Raman microprobe spectroscopy was used for residual stress constant in the DLC film.

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・The Raman shift of the G peak and the residual stress exhibit a linear relationship.

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・The phonon deformation potentials were estimated from bonding ratio and H content.

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・Estimation of the residual stress in DLC films is proposed using G and D peak shifts.

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・The methods allow the estimation of the residual stress in DLC films nondestructively.