Chemical structure and electrical characteristics of diamondlike carbon films

Accepted Manuscript Chemical structure and electrical characteristics of diamondlike carbon films

Susumu Takabayashi, Hiroyuki Hayashi, Meng Yang, Rintaro Sugimoto, Shuichi Ogawa, Yuji Takakuwa PII: DOI: Reference:

S0925-9635(17)30315-1 doi:10.1016/j.diamond.2017.11.005 DIAMAT 6967

To appear in:

Diamond & Related Materials

Received date: Revised date: Accepted date:

9 June 2017 8 November 2017 9 November 2017

Please cite this article as: Susumu Takabayashi, Hiroyuki Hayashi, Meng Yang, Rintaro Sugimoto, Shuichi Ogawa, Yuji Takakuwa , Chemical structure and electrical characteristics of diamondlike carbon films. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Diamat(2017), doi:10.1016/j.diamond.2017.11.005

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ACCEPTED MANUSCRIPT Research Paper for submission to Diamond and Related Materials (Revision A)

Chemical structure and electrical characteristics of diamondlike carbon films

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Susumu Takabayashi1†*, Hiroyuki Hayashi2, Meng Yang2, Rintaro Sugimoto2, Shuichi Ogawa2, Yuji Takakuwa2

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Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku,

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Sendai 980-8577, Japan.

Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1

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Katahira, Aoba-ku, Sendai 980-8577, Japan.

Present address: ADTEC Plasma Technology Co., Ltd., 5-6-10 Hikino-cho, Fukuyama, Hiroshima

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721-0942, Japan.

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e-mail: [email protected] (S. Takabayashi)

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†

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*corresponding author

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ACCEPTED MANUSCRIPT ABSTRACT The relationship between the chemical structure and electrical characteristics of diamondlike carbon (DLC) films has been clarified. The DLC films were formed in atmospheres with different ratios of methane to argon under the photoemission-assisted Townsend discharge. The dependence of the dielectric constant of the films on methane concentration in the synthesis was arch-like with a

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maximum. The breakdown strength was constant irrespective of the synthesis atmosphere and was approximately the same for both electrical polarizations. Raman spectra of the films were deconvoluted into five active bands. Raman analysis in conjunction with the sp2 cluster model elucidated the DLC structure. The sp2 cluster model comprises sp2 clusters floating in a dielectric

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matrix sea. The sp2 clusters were rather aliphatic for films formed in low methane concentration. The clusters grew to become aromatic with increasing methane concentration. Defects or dangling

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bonds increased similarly, but they were terminated with hydrogen for films formed in high methane concentration. The hydrogen-terminated bonds occupied large amounts of space in the

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DLC films, causing internal strain. The dielectric constant of the whole DLC film was determined by the size of sp2 clusters, dielectric constant of the matrix sea material, and space volume induced

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by the hydrogen–carbon bonds. The breakdown strength was determined by the balance between

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the size of sp2 clusters and density of dangling bonds in the matrix sea. However, because the dependences of these factors on methane concentration were opposing, the breakdown strength was

(246 words)

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approximately constant irrespective of methane concentration.

KEYWORDS: Diamondlike carbon (DLC); Photoemission-assisted plasma-enhanced chemical vapor deposition (PA-PECVD); Raman spectroscopy; The sp2 cluster model; Dielectric constant; Breakdown strength

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ACCEPTED MANUSCRIPT 1.

Introduction Diamondlike carbon (DLC) is a carbonaceous material composed of sp2 carbon, sp3 carbon,

and hydrogen with amorphous structure [1, 2]. The distinctive features of DLC, such as surface flatness, low friction, and chemical inertness, have led to it being utilized widely as a surface coating for industrial products and medical tools, and in tribology.

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We succeeded in forming a DLC film directly on a graphene sheet as a top-gate dielectric [3]. A graphene-channel field-effect transistor (GFET) with the DLC top gate exhibited clear ambipolar behavior specific to graphene, suggesting that the graphene was not damaged by DLC deposition and the DLC top gate had a low defect density. To further improve the film characteristics, for

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example, restrict defect generation, increase the breakdown strength, and control the dielectric constant, we tried to synthesize a DLC film with controlled oxygen doping [4]. DLC with precisely

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controlled structure is attractive for use in future integrated electronics. Such thin film formation was successful in the photoemission-assisted Townsend discharge

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(PATD), which is a discharge mode of the photoemission-assisted plasma-enhanced chemical vapor deposition (PA-PECVD) method [5]. PA-PECVD is a simple DC plasma system, but with the aid of

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numerous UV-excited photoelectrons emitted from a substrate. The photoelectrons function as

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initial electrons, causing electron avalanche at a low voltage. Thanks to the numerous initial electrons, PATD gives a much larger current than the conventional Townsend discharge current.

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The voltage and current in PATD can be evaluated independently, which is not the case for radiofrequency discharges. Because the discharge is restricted within the UV-irradiated area, the current density can be evaluated precisely. Thus, precise DLC synthesis is expected with PATD. In the present work, we investigate the growth and electrical characteristics of DLC films synthesized in PATD (PATD-DLC films) and clarify the relationship between the structure and electrical characteristics by Raman spectroscopy.

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Experimental details DLC films were synthesized in the PATD plasma with the aid of photoelectrons. The substrate

was an arsenic-doped n-type silicon(100) wafer with a thickness of 525 μm and electrical resistivity of 0.001–0.003 Ω cm. A piece with dimensions of 10 × 10 mm was placed on the cathode stage for each synthesis. Photoelectrons were emitted from the negatively biased substrate exposed to UV

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irradiation. The UV light source was a Xe excimer lamp with an energy (wavelength) of 7.2 eV (172 nm), which exceeded the work function of the silicon substrate (~5 eV). The deposition area was restricted to 8 × 8 mm by placing a quartz cover on the substrate. The counter anode was a copper duckboard-like structure that contained spaces with definite intervals to allow passage of

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UV radiation from the overhead light source to the substrate surface. The discharge gap was 12 mm. Both the anode and chamber wall were grounded to prevent any undesired discharge between them.

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An 8-kΩ resistor was included in the circuit to limit huge current in the photoemission-assisted glow discharge (PAGD), which is another discharge mode of PA-PECVD and is explained later.

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The apparatus is described in detail in our previous report [6]. The silicon substrates were cleaned before use in piranha and 1% hydrogen fluoride solutions

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[7]. The piranha solution was composed of a 1:3 mixture of 30% hydrogen peroxide and

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concentrated sulfuric acid. Each substrate surface was passivated by oxidation in a fresh piranha solution, rinsed with pure water, and then dried under a nitrogen stream.

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The DLC synthesis was conducted in various methane/argon atmospheres under a certain current, the magnitude of which was determined according to the discharge current–bias voltage characteristics discussed later. The flow rate of the methane/argon gas source was varied from 10/50 to 55/5 sccm; i.e., from methane concentration of 17% to 92%. The total pressure and cathode stage temperature were maintained at 200 Pa and 150 °C, respectively. After growth, the capacitance and breakdown strength of the PATD-DLC films were measured in air using a two-electrode (top and bottom) system through molybdenum electrode probes 4

ACCEPTED MANUSCRIPT connected to an LCR meter (E4980A, Agilent) and semiconductor parameter analyzer (4155C, Agilent). Top electrodes consisting of Au (250 nm)/Pd (20 nm) stacked films with dimensions of 100 × 100 μm were formed on the DLC surface by conventional photolithography and electronbeam evaporation. The bottom electrode was the backside of the silicon substrate, which was common to all the top electrodes. Capacitance was measured by scanning DC bias voltage with an

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AC perturbation of 10 mV at 1 MHz. The DC bias voltage was sufficiently lower than the breakdown voltage. The breakdown strength was measured for both positive and negative polarizations by scanning the DC bias voltage from zero to each breakdown voltage. For safety, the current at breakdown was limited to ±50 mA (±500 A/cm2).

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To measure the film thickness accurately, holes with dimensions of 50 × 50 μm were formed near all the top electrodes by capacitively coupled reactive ion etching (RIE-10NR, SAMCO) with

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pure oxygen through a photoresist mask. The silicon substrate covered with a thin oxide passivation layer was not etched by oxygen, ensuring an accurate film thickness when measuring the hole depth

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with a stylus profilometer (Dektak 150, Veeco).

Time-of-flight secondary ion mass spectrometry (TOF-SIMS) of the PATD-DLC films was

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performed with a TOF spectrometer (TOF.SIMS5, ION-TOF). The primary ion source was bismuth

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ions accelerated to 50 keV. The depth profile was measured on each occasion after 1.6 s of sputtering with cesium ions accelerated to 2 keV. Charge imbalance during the measurement was

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compensated for by an electron flood gun. The pressure during the measurement was maintained at 2.0×10−7 Pa. The significant figure of the mass-to-charge ratio (m/z) was the fourth decimal place. For example, the m/z values of Si− (27.9746) and CO− (27.9921) were distinguishable from each other. Raman scattering spectra were measured in air with a micro-Raman spectrometer (Nanofinder 30, Tokyo Instruments) using the 532-nm incident line of the second harmonic generation of a Nd:YVO4 laser (JUNO J050GS-11-11-11, Showa Optronics). 5

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ACCEPTED MANUSCRIPT 3.

Results and Discussion

3.1

Photoemission-assisted plasma Figure 1 shows the current–voltage characteristics for the silicon substrates in certain

methane/argon atmospheres at different temperatures. For all conditions, the current increased monotonically with bias voltage up to the order of 10−5 A and then at a certain voltage jumped over

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ten-times in magnitude. These two discharge characteristics can be explained as follows [5]. The first monotonic increase can be attributed to PATD, which is dominated by the α regime in classical Townsend’s theory [8]. In this regime, electrons are accelerated by an electric field and then collide with argon atoms inelastically. Consider the amplification of one electron in an

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infinitesimal distance dx, which is expressed as

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where n is number of electrons, and α is the first Townsend coefficient. One electron creates (α − 1) couples of an electron and an ion in the journey of dx. When number of electrons at x = 0 (initial

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electrons) is assumed to be n0, Equation 1 is solved to

Electrons are amplified exponentially (electron avalanche). Using Equation 2, the observed current (I) is finally expressed as

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ACCEPTED MANUSCRIPT where I0 is the initial current and d is the discharge gap. Because α is a function of the electric field E(

), I is increased steeply with increasing the bias voltage. According to Eqs. 1 and 2, the current in a conventional system is negligibly small because n0

is very small (accidental electrons generated by cosmic ray). Even in the present system, the current without the aid of UV irradiation, or the conventional Townsend discharge current, is of the order of

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10−10 A, which is too weak to achieve any synthesis (not shown). Under UV radiation, the numerous photoelectrons emitted from the substrate function as initial electrons. The photoelectron count is 5 × 1011 s−1, as estimated from the current in a vacuum (photocurrent, ~8 × 10−8 A), where no electron avalanche caused by collisions with argon atoms was expected, as shown in Fig. 1. Thus,

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the discharge current becomes over ten thousand times larger, of the order of 10−6 A [5]. However, at an initial few volts, the discharge current in every atmosphere is smaller than the

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photocurrent. The discharge electrons have lower kinetic energy than the ionization energy of argon atoms. Elastic collisions between the electrons and argon atoms keep the electrons over the

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substrate cathode, preventing subsequent photoelectron emission from the substrate and giving a

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small discharge current. This phenomenon is called the space charge effect, which has been observed in vacuum tubes [9].

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Up to 70 V, the current in low methane (high argon) concentration is small because electrons still have insufficient kinetic energy to ionize numerous argon atoms. Over 70 V, electrons are

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accelerated enough, and large current is observed. In high methane concentration, electrons collide with methane molecules rather than argon atoms. Because the electron energy is consumed in rotational and vibrational excitations of the methane molecules prior to their ionization [10-12], the electron amplification is restricted in high methane concentration. The discharge after the current jump when the bias voltage increased further is PAGD. PAGD is a glow discharge dominated by the γ regime in the Townsend’s theory, but is different from the conventional glow discharge because photoelectrons contribute to the discharge. In the γ regime, 8

ACCEPTED MANUSCRIPT ions are accelerated in the ion sheath to reach the cathode, where they create secondary electrons [13]. One ion creates γ secondary electrons. The coefficient γ is called the second Townsend coefficient (note that the regime name and number share the same character γ). If one ion creates more than one secondary electron at the cathode, continuous electron amplification is accomplished,

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which is expressed as

Equation 4 is called the Townsend’s breakdown criterion and is satisfied at the current-jump voltage.

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For safety, the current in PAGD was regulated by a series resistor (8 kΩ here). The current-jump voltage or starting voltage of PAGD increases with increasing methane concentration. This is

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because the electron energy is consumed in rotational and vibrational excitations of methane molecules, as described above.

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In PAGD, excited argon atoms themselves emit strong UV photoluminescence. This photoluminescence can compensate for the UV radiation from the lamp. Thus, as demonstrated in

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our previous report [5], once started, PAGD continues by itself without external UV irradiation.

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Because of the spontaneous UV photoluminescence, PAGD survives even at much lower voltages than the starting voltage. As a result, the current–voltage characteristics show hysteresis. In contrast,

voltage.

3.2

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because PATD lacks distinct UV photoluminescence, the discharge is regularly controlled by bias

DLC growth by PATD To make the growth as fast as possible, the PATD-DLC growth was conducted under a current

regulation of 20 μA, which is indicated by a dashed line close to the region of PAGD in Fig. 1. Figure 2(a) shows the chronopotentiograms during the growth. We previously analyzed the growth 9

ACCEPTED MANUSCRIPT of DLC films synthesized by PA-PECVD quasi-electrochemically [14]. Because the number of radicals created, which form films, is a function of the discharge current, the constant charge syntheses in different atmospheres facilitate the comparison between the films synthesized. To obtain sufficient thick films for evaluation of the electrical characteristics, the total charge in all of the syntheses was fixed at 100 mC, taking 5000 s. Corresponding to the results in Fig. 1, the

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chronopotentiogram shifted to higher voltage with increasing methane concentration. However, it accompanied oscillation. The voltage oscillation is probably determined by the surface work function or band bending of the growing film [15, 16]. In other words, the photoemission activity of the growing surface may contribute to the voltage oscillation. Further investigation of this topic will

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be discussed in the future, but the voltage oscillation suggests that constant-voltage synthesis may suddenly transition to PAGD or vice versa. Thus, constant-current synthesis can be an appropriate

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technique to synthesize well-defined DLC films.

Figure 2(b) shows the film thickness as a function of methane concentration during the

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synthesis. The left axis also indicates the result in terms of growth efficiency in nm/mC. Both the film thickness and growth efficiency increased with increasing methane concentration. These

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factors changed steeply over 67% methane and saturated in higher methane concentration. These

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results suggest that methyl radicals and the fragmented radicals increased with increasing methane concentration and saturated in very high methane concentration. Our previous DLC synthesis by

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PAGD used a current of approximately 80 μA/(8 × 8) mm2 (~4 mA/φ20 mm2), which was four times larger than the present magnitude in PATD. Although the discharge modes are different, the growth efficiency results of the present and previous syntheses are similar. This interesting result suggests that the dissociation efficiency of methane molecules per charge is similar for the two discharge modes, even though the ion energy is quite different: ~0.1 eV in PATD and ~10 eV in PAGD, as estimated previously by a Langmuir probe technique [14]. However, because ions in

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ACCEPTED MANUSCRIPT PAGD are accelerated by the ion sheath and contribute to the film formation (the ion assist), the

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film quality depends on the discharge mode.

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ACCEPTED MANUSCRIPT 3.3

Film characteristics Figure 3(a) shows the dielectric constant of the PATD-DLC films as a function of methane

concentration. The measured capacitance of every film was constant irrespective of the bias voltage scan (not shown), demonstrating that every film was sufficiently thick such that variation of the capacitance of the space charge layer of the silicon substrate did not affect the measurement [17].

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The dielectric constant reached a maximum value of 5.2 in 50% methane, decreasing in both high and low methane concentrations. However, all of the values were higher than the dielectric constants of DLC films synthesized in PAGD (PAGD-DLC films), which were less than 4.0 [6]. Figure 3(b) shows the breakdown strengths for both positive and negative polarizations.

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Considering the error bars, the breakdown strengths for both polarizations were constant independent of methane concentration; the strengths were approximately symmetric (±5 MV/cm).

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Figure 4(a) shows the Raman spectrum of the PATD-DLC film synthesized in 50% methane. Such a large background was observed for all spectra. This is attributed to photoluminescence from

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the film. When the hydrogen content in a DLC film increases, hydrogen atoms terminate trap sites or tail states of the optical gap, which enhances the photoluminescence [18, 19]. Adamopoulos et al.

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reported a positive correlation between the hydrogen content in DLC films and the slope of the

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background line of the Raman spectrum [20]. Figure 4(b) shows the background slope of the Raman spectra as a function of methane concentration. The slope increased with increasing methane

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concentration. Thus, large amounts of hydrogen should be incorporated into the films synthesized in high methane concentration. Figures 5(a) and (b) show the TOF-SIMS depth profiles of the PATD-DLC films synthesized in 17% and 83% methane, respectively. The profiles show the atomic ratios of hydrogen (m/z = 1.0081) and silicon (27.9746) to carbon (11.9994), which are designated as H/C and Si/C, respectively. Because the silicon intensity is derived from the substrate, the starting point of steep increase of the differential coefficient corresponds to the substrate surface. Although the cesium ion 12

ACCEPTED MANUSCRIPT energy for sputtering was the same 2 keV in both measurements, the resultant sputtering rates were quite different: 14.1 and 36.5 nm/min for the films synthesized in 17% and 83% methane, respectively. The depth resolutions were approximately 0.4 and 1.0 nm, respectively. Very large H/C values were observed at both surfaces, suggesting that numerous surface dangling bonds were terminated with hydrogen. The H/C values of both films decreased steeply at the sub-surfaces,

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where dangling bonds should not only be terminated with hydrogen, but also form carbon-bond networks. The H/C values increased again inside the films. However, the present H/C values were much lower than unity, implying that the PATD-DLC films have three-dimensional complex structure with polyaromatic rings. The hydrogen–carbon bonds take up a large amount of space to

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produce internal strain. A larger H/C value was observed for the film synthesized in 83% methane. The space taken up by the hydrogen–carbon bonds should contribute to the increase of apparent

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film thickness shown in Fig. 2(b).

As shown in Fig. 3(a), the dielectric constant of the films as a function of methane

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concentration presented an arch-like shape with a maximum. This result suggests that the PATDDLC films have at least two constituents: one is affected by hydrogen and the other is not. However,

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although the balance between these constituents was obviously different, the two films synthesized

Raman analysis

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in 17% and 83% methane possessed similar dielectric constants.

To clarify the relationship between the chemical structure and electrical characteristics of the PATD-DLC films, their Raman spectra were analyzed. Figure 6 shows the Raman spectra with fitting curves. In Raman spectra of carbonaceous materials, two bands, which are called the D (disorder) and G (graphite) bands, are representative of the material characteristics [21]. The vibration coordinates of these bands are x2 + y2 and (xy, x2 – y2), respectively. They belong to the

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ACCEPTED MANUSCRIPT A1g and E2g modes of the D6h point group, respectively, and the group represents the symmetry of a graphene sheet [22]. However, generally, the Raman spectra of DLC exhibit fused peaks [23, 24]. Thus, peak separation or curve-fitting analysis with a defined formula is necessary to properly characterize the material, although the spectra can be treated as fingerprints [25]. Because the curve-fitting

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technique is generally arbitrary, the error increases with increasing number of parameters unless some cue is found. In fact, many Raman analyses of DLC have been reported, but they vary depending on the researchers [26, 27]. Consequently, because the present spectra have more than two obvious peaks, they have been deconvoluted into five active bands (N, D, G−, G+, and D′) using

and

indicate the Lorentzian function for the j band and the Breit–Wigner–Fano

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where

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Equation 5, a function of Raman shift ( ) [6, 14], as

(BWF) function for the k band, respectively.

is a Gaussian function, which contributes to all

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the bands evenly. These functions include specific parameters. ΓLj is the full-width at halfmaximum (FWHM) of the Lorentzian curve for the j band. The qk is a negative parameter of the BWF curve for the k band, and its reciprocal is a measure of the interaction between the k band phonon and an electronic continuum. ΓBk is the FWHM of the BWF curve for the k band at 1/qk = 0, where the BWF function is reduced to the Lorentzian. ΓG is the FWHM of the common Gaussian. For the present analysis, the ΓLj values except for that of the D band (ΓLD) are assumed to be 16 cm−1 [14]. This value was obtained from the experimental G band width of highly oriented pyrolytic 14

ACCEPTED MANUSCRIPT graphite (HOPG), and the spectrum was completely represented by a single Lorentzian curve. Variation of the experimental G band width is regarded as the extent of crystallinity of the graphite structure or as an index for the degree of aromatic growth. A perfect graphene sheet or graphite without strain produces a single sharp G band peak [21, 28], where the two coordinates (xy, x2 − y2) are degenerate. The separation of the two coordinates is

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difficult. However, Eklund and Subbaswamy have reported [29] that intercalation of an alkali metal into graphite resulted in an asymmetric G band, implying that the degeneracy was lost or the band was influenced by a secondary effect. Brown et al. have reported [30] that the G band of a metallic nanotube showing a similar asymmetric lineshape was split into two bands. The band at higher

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Raman shift was attributed to the G band along the nanotube axis (G+ band), and the lower band was attributed to the G band in the circumferential direction (G− band). Brown et al. demonstrated

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further that only the G− band exhibited an asymmetric lineshape, which was enhanced by coupling with plasmons exhibiting collective electron excitations. Such enhancement suggests that the G−

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band intensity increased through an interaction between the phonon and a strain-induced electronic continuum in the circumferential direction. Later, Mohiuddin et al. observed similar band splitting

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for a graphene sheet [31]. Imposing forced strain on the graphene sheet also split the G band into

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two bands, and the band splitting increased with increasing strain. Strain inside DLC is also known to be considerable, reaching the order of 10 GPa [32, 33]. This is because, unlike amorphous silicon,

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DLC consists of two independent bonding types of carbon (sp2 carbon and sp3 carbon). The BWF function has been applied only to the G− band [6, 14]. In the present Raman curvefitting analysis, however, the BWF curve for the G− band was reduced to the Lorentzian by setting . Because qk is related to the interaction between the phonon and an electronic continuum, it should not take a meaningful value when the film is an insulator. Adding a new band N around 1220 cm−1 and the D′ band around 1620 cm−1 completed the curve fitting. Regarding the N band, consider the E1g mode of the D6h point group, which is not 15

ACCEPTED MANUSCRIPT observed for a two-dimensional graphene sheet. This mode contains xz and yz coordinates, to both of which the z-axis component contributes. A diamond crystal shows its only Raman peak at 1332 cm−1, which belongs to the T2g mode of the Oh group [34, 35]. The coordinate is triply degenerate (xy, yz, zx) at the Γ point. Deduced from this fact, the N band is assigned to sp3-bonded tetrahedral carbon. However, the structures in DLC films are disordered and heterogeneous, different from the

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ordered diamond crystal. Because this tetrahedral carbon forms a three-dimensional network structure, we designate this band as the N band. The D′ band is attributed to another tensor of the A1g mode, z2, but which is also out of consideration for the two-dimensional graphene sheet. The D′ band is regarded as a longitudinal optical phonon process with intravalley double resonance,

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whereas the D band is regarded as an in-plane transverse optical phonon process with intervalley double resonance [36]. This couple appears when some damage is introduced into a graphene sheet

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[37, 38]. The z2 vibration suggests that the aromatic ring is affected by another ring facing it. Figure 7(a) summarizes the relative areas of the Raman bands as functions of methane

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concentration during film synthesis. The present analysis is based on comparison of the areas of Raman bands, not the intensities, because the former is a more general index for comparison of

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bands with different FWHM values [14]. The areas of both the G+ and G− bands decrease with

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increasing methane concentration. The area ratio of the G−/G+ bands presented in Figure 7(b) is related to the quantity of strained constituents [31]. The G−/G+ ratio is approximately constant and

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independent of methane concentration. The area of the D band increases with increasing methane concentration, rising rapidly over 67% methane. At the same time, the film thickness and growth efficiency increase steeply, as shown in Fig. 2(b). The D band originates from the loss of aromatic crystallinity (imbalance between adjacent rings), which is triggered by a defect [21]. However, a defect or dangling bond must not be the final form, at least in the PATD-DLC films, because our previous report demonstrated that the film worked well as a top-gate dielectric for a GFET [3]. Dangling bonds 16

ACCEPTED MANUSCRIPT impede electrostatic induction. Considering the TOF-SIMS results in Fig. 5, defects must be terminated with hydrogen, which is the smallest atom. In high methane concentration, the hydrogen-terminated constituents occupy a large volume to form a thick film (Fig. 2(b)). Accordingly, the incompleteness or disorder of aromatic constituents is required for the D band, but defects are not the only possible origin of such disorder (the hydrogen-terminated bond is also a

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candidate). That is, the D band represents disorder, but does not always indicate defects or dangling bonds. The area of the D′ band increases slightly with methane concentration. This result suggests that the density of disordered aromatic constituents increases with increasing methane concentration. The N band area is small and remains approximately constant. Thus, the number of sp3-bonded

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tetrahedral carbon constituents does not depend on the present synthesis atmosphere. Figure 7(c) shows ΓLD. Like the D band area, the ΓLD also increases rapidly over 67% methane.

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Because the reciprocal of ΓLD corresponds to the phonon lifetime [39], the disorder of aromatic constituents prevents the phonon propagation. However, the present ΓLD values are much smaller

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than those of PAGD-DLC films (140–150 cm−1) [14]. Very slow PATD synthesis without ionassisted bond rearrangement should allow steady film formation with relatively low disorder. As

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discussed in Fig. 2(b), the PATD-DLC films grow rapidly when methane concentration exceeds

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67%. Thus, the disorder is determined by the balance between the ion-assist energy and the growth rate. A rapidly growing film requires a larger ion-assist energy to dissolve the disorder.

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Figure 7(c) also shows ΓG. In contrast to ΓLD, the ΓG decreases monotonically with increasing methane concentration. The large ΓG of the films synthesized in low methane concentration means that the internal constituents are sufficiently dispersed. In other words, the constituents grow heterogeneously and form various chemical structures. The constituents tend to become disordered but homogeneous aromatic in high methane concentration. Like ΓLD, however, all the values are much smaller than those of PAGD-DLC films (160–170 cm−1) [14]. The ion assist causes bond

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ACCEPTED MANUSCRIPT rearrangement to provide various molecular or cluster structures. Because the ion assist is weak in PATD, the present small ΓG resolves the fused Raman peak. Figure 8(a) shows the G+ band position as a function of methane concentration. The position is related to the degree of graphitization or aromatic growth in the film, and the blueshift estimates the extent of its change [40]. The graphitization inside the PATD-DLC film proceeds up to a methane

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concentration of 67% and starts to degrade slightly thereafter. However, because these positions are much lower than that of graphite (experimentally 1586 cm−1), the aromatic growth of the present films is insufficient. As discussed in Fig. 7(c), the small ΓG in high methane concentration suggests that the constituents grow homogeneously. The redshift of the G+ band position in higher methane

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concentration corresponds to the rapid increase in the D band area in Fig. 7(a). Although

disorder caused by hydrogen termination.

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homogeneous aromatic growth proceeds with increasing methane concentration, it is limited by

Figure 8(b) shows the G− band position. The position redshifts as methane concentration

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increases except for the lowest concentration of 17%. Figure 8(c) shows the difference between the positions of the G+ and G− bands (G+ − G−). This difference is related to the quality or strength of

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internal strain [31] and becomes larger as methane concentration increases. Internal strain becomes

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greater in the PATD-DLC films synthesized in higher methane concentration, although the quantity related to G+/G− does not vary, as discussed in Fig. 7(b). The increase in ΓLD (Fig. 7(c)) that

concentration.

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demonstrates the enhancement of disorder agrees with the intensifying strain with rising methane

Figure 8(d) shows the D′ band position. The blueshift of this band means that the z2 vibration energy increases with increasing methane concentration. The three-dimensional interaction between disordered aromatic constituents becomes intense in high methane concentration; in other words, the aromatic constituents are concentrated. The D and N band positions are fixed at 1322 and 1223 cm−1, respectively, and independent of methane concentration in the synthesis. (not shown). The 18

ACCEPTED MANUSCRIPT size of aromatic aggregate constituents or clusters per defect is evaluated by the D band position [41]. A higher (lower) position of the band indicates larger (smaller) aromatic cluster size. The position in the present experiments is lower than other DLC films [42], suggesting that the cluster size is smaller. The small ΓG values observed for the films synthesized in high methane concentrations demonstrate that numerous small and relatively homogeneous graphite nanosheets

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are formed. This is in harmony with relatively high G+ band positions shown in Fig. 8(a). Such nanosheets increase the total area of the D band and blueshift the D′ band position. Similarly, the N band position is related to the size of clusters of sp3-bonded tetrahedral carbon. Compared with the peak position of the diamond crystal (1332 cm−1), the redshift of the N band position means that the

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cluster size of sp3 carbon is smaller than that of the ordered ones. The fixed position in the present experiments demonstrates that the size is independent of the synthesis atmosphere investigated. The

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result for G+ − G−, as shown in Fig. 8(c), demonstrate that the DLC films synthesized in high methane concentration, where aromatic growth is encouraged, have high internal strain. Thus, a

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certain number of the sp3-bonded tetrahedral carbon constituents should contribute to the internal

The sp2 cluster model

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3.5

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strain of the film.

Consequently, each DLC structure can be elucidated by the sp2 cluster model [14], as shown in

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Figures 9(a)–(c). This model comprises clusters of sp2 carbon (sp2 clusters) floating in or surrounded by a dielectric matrix of sp2 carbon, sp3 carbon, and hydrogen (the matrix sea). The sp2 cluster is regarded as a conductive material composed of not only aromatic rings like nanographites but also π-conjugated aliphatic chains. The sp2 cluster is not necessarily composed of a single nanographite but rather has a chemical structure similar to coal [43, 44]. Although the matrix sea also contains sp2-carbon atoms, such molecules or clusters are so small that they do not exhibit conductivity (i.e., they are isolated or non-conjugated). 19

ACCEPTED MANUSCRIPT The DLC material has been traditionally recognized as an amorphous structure composed of sp2 carbon and sp3 carbon [2]. However, details of the structure remain unclear. Considering sp2 carbon and sp3 carbon as simple solid materials should lead to observations of grain boundaries; however, such results have never been reported. For example, the Raman spectra of DLC films definitely do not coincide with the spectrum of graphite composed of pure sp2 carbon or the

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spectrum of diamond composed of pure sp3 carbon [45]. Our previous analysis using X-ray photoelectron spectroscopy led to similar conclusions [46, 47]. DLC is an independent material. Rather, as previously mentioned, it is natural to consider the structure from a viewpoint of the extent of the growth of π-conjugation of carbon–carbon bonds. The sp2 cluster model is a simple but

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essential model of the π-conjugation growth. Each present film structure can be elucidated with this model as follows.

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For DLC films synthesized in low methane concentration (Fig. 9(a)), sp2 clusters form various structures in the dielectric matrix sea, giving a large Γ G (Fig. 7(c)). The low G+ band position (Fig.

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8(a)) demonstrates that the clusters are aliphatic rather than aromatic. The combination of the small D band area and small ΓLD (Fig. 7(a) and (c)) indicates that the number of the clusters is small and

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the clusters are weakly disordered. The weakly disordered structure is caused by a small number of

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hydrogen-terminated bonds (Fig. 5).

Because DLC is amorphous and does not exhibit anisotropy, its electrical characteristics can be

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considered one-dimensionally. The dielectric constant of the whole DLC film (κDLC) is expressed as

where κm is the dielectric constant of the matrix sea itself (> 1) (see Appendix). The d is the film thickness. The dsp2 is the sum of the sp2-cluster diameters along the axis of the applied electric field; 20

ACCEPTED MANUSCRIPT ds is the sum of diameters of spaces induced by hydrogen–carbon bonds (CH spaces). The electric field is applied to the dielectric matrix sea and and CH spaces, not to the conductive sp2 clusters. Because dsp2 is small for films synthesized in low methane concentration, κDLC is small and the actual electric field applied to the dielectric matrix is weak. The breakdown strength should become high in consequence.

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For DLC films synthesized in intermediate methane concentration (Fig. 9(b)), sp2 clusters grow and become more aromatic than aliphatic (Fig. 8(a)). Because the increase of the D band area indicates the increase of dsp2 (Fig. 7(a)), κDLC becomes high. The electric field applied to the matrix sea becomes stronger. Thus, in the present experiments, a maximum dielectric constant 5.2 was

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obtained in the synthesis with 50 % methane concentration.

For DLC films synthesized in high methane concentration (Fig. 9(c)), both the D band area and

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ΓLD increase steeply. The sp2 clusters formed here are relatively aromatic and homogeneous, but highly disordered with a large number of hydrogen-terminated bonds (Figs. 5(b) and 7(c)). The

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numerous hydrogen-terminated bonds take up a large amount of CH space in the dielectric matrix, giving a coarse matrix. Thus, the sputtering rate in the TOF-SIMS measurement shown in Fig. 5 is

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different for the PATD-DLC films containing different amounts of hydrogen. The sputtering rate of

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a film containing a large amount of hydrogen is high. The conductivity of sp2 clusters is not related to the hydrogen content of the film. Regarding the electrical characteristics, the matrix sea is the

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constituent affected by hydrogen, while the sp2 clusters are not, as discussed in Figs. 3 and 5. The high D′ band position (Fig. 8(d)) indicates that the concentration of sp2 clusters is high, giving a large dsp2. Similarly, because the well-grown CH spaces gives a large ds with κm > 1, κDLC becomes small in consequence. The breakdown strength is expected to be low. However, the measured breakdown strength results of all the DLC films were approximately constant. This is inconsistent with the arch-like shape of the dielectric constant characteristics

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ACCEPTED MANUSCRIPT shown in Fig. 3(a). We must reconsider our previous conclusion that the breakdown strength of DLC films is a function of the reciprocal of dsp2 (dsp2−1) [14]. We consider the chemical structure of the matrix sea. The TOF-SIMS results in Fig. 5 indicate that the number of hydrogen-terminated bonds in the matrix sea is different for PATD-DLC films synthesized in different methane concentrations. A dangling bond with an active electron in the

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matrix sea will trigger breakdown of the film, whereas a hydrogen-terminated bond will not. The matrix sea of a film formed in low methane concentration contains a large number of dangling bonds. Although dsp2 is small there, the dangling bonds present should promote breakdown. In contrast, because hydrogen-terminated bonds are dominant in the matrix sea of films formed in high

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methane concentration, the degradation of the breakdown strength should be suppressed. Consequently, the breakdown strength of the DLC film (EBD) is improved as a function of dsp2−1 and

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the reciprocal of the density of dangling bonds in the matrix sea (ρDm−1).

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While dsp2−1 enhances the breakdown strength of films synthesized in low methane concentration

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and degrades it for those synthesized in high methane concentration, ρDm−1 works oppositely. As a result, the breakdown strength is constant irrespective of methane concentration. The very high

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breakdown strength of oxygen box-doped DLC films in our previous report [4] may be caused by the decrease of dangling bonds by oxygen termination.

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Conclusion DLC films were synthesized in PATD under current regulation. The dependence of the

dielectric constant of the films on the methane concentration in the synthesis was arch-like with a maximum. The breakdown strength was approximately constant irrespective of methane concentration and was symmetric for both polarizations.

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On the basis of the Raman analysis with five active bands (N, D, G−, G+, and D′), the film structure was elucidated using the sp2 cluster model. Aliphatic sp2 clusters were dominant in films synthesized in low methane concentration. The clusters grew to become aromatic with increasing methane concentration; however, the growth was prevented by disorder in the films produced in

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very high methane concentration. The disorder was induced not only by defects or dangling bonds, but also hydrogen-terminated bonds. Hydrogen-terminated bonds were dominant in the films

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synthesized in high methane concentration.

The sp2 cluster model indicated that the dielectric constant of the PATD-DLC films should be

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determined by the sp2-cluster diameter, dielectric constant of the matrix sea, and space volume induced hydrogen–carbon bonds in the films. These constituents became concerted in the film

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synthesized in 50% methane and gives a maximum dielectric constant of the whole film. The

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breakdown strength of the films was functions of the reciprocal of the sum of sp2-cluster diameters and the reciprocal of the density of dangling bonds in the matrix sea. These factors were opposing

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with regard to methane concentration and gave an approximately constant breakdown strength for the films synthesized in different methane concentrations.

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Appendix For Eq. 6, we consider a DLC tube structure with a cross section ΔS that is a small part of a

DLC film. Figure 10(a) shows the model. The tube consists of conductive sp2 clusters, dielectric matrix materials, and CH spaces; their widths (diameters) are dsp2x, dmy, and dsz (x, y, z = 1, 2, 3, …), respectively. The order of the elements is random. The tube is sandwiched between the top and

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bottom (silicon substrate) electrode; a voltage V is applied to the tube horizontally. Figure 10(b) shows an equivalent circuit of the DLC tube. Rsp2x, Rmy, and Rsz are resistances of a sp2 cluster, dielectric matrix material, and CH space, respectively. Cmy and Csz are capacitances of the dielectric matrix material and CH space, respectively. Assuming that Rsp2x is very low, and Rmy and Rsz are

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very high, the equivalent circuit can be reduced to the one shown in Figure 10(c). Cmy and Csz are

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expressed by

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where κm and κs are the dielectric constants of the dielectric matrix material and CH space, respectively. The ε0 is the vacuum permittivity.

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The DLC film thickness d is given by

where

. The charge accumulated in a capacitor Q is common to every capacitor and

is expressed by 24

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where Vmy and Vsz are partial applied voltages for Cmy and Csz, respectively. V is expressed as

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. Thus,

Meanwhile, we consider the capacitance of the whole DLC film C and the dielectric constant

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κDLC. The relationship between these factors is expressed by

From Eqs. A4 and A5, we obtain

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and κs is regarded as

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.

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where

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Using Eq. A2, we finally obtain

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ACCEPTED MANUSCRIPT Acknowledgments This research was partly performed at the Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University. A constant current source suitable for photoemission-assisted discharge experiments was fabricated by Mr. Minaji Furudate and Mr. Tadahiko Goto, Institute of Multidisciplinary Research for Advanced Materials, Tohoku

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University. The TOF-SIMS measurements were supported by Ms. Rie Shishido, Institute of Multidisciplinary Research for Advanced Materials, Tohoku University. The Raman measurements were supported by Dr. Tadao Tanabe and Mr. Masaya Hino, Center for Fusion Research of NanoInterface Devices, Tohoku University of Low-Carbon Research Network. Valuable comments were

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provided by Dr. Yasunori Niiyama, DENSO Corporation.

This work was financially supported by the Japan Society for the Promotion of Science:

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Grants-in-Aid (KAKENHI) for Young Scientists (B) and (A), JP24760247 and JP26709017 (S. T.), and Grants-in-Aid for challenging Exploratory Research, JP15K13938 (S. T.) and JP16K14124 (S.

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O.).

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ACCEPTED MANUSCRIPT Figure captions Figure 1. (free color online) Discharge current–bias voltage curves for the silicon substrate under UV irradiation in different methane concentrations. The dashed line indicates the current magnitude (20 μA) used in the following constant-current syntheses. The curve in a vacuum is also shown as a

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reference.

Figure 2. (free color online) (a) Chronopotentiograms under a current regulation of 20 μA during PATD-DLC growth in different methane concentrations. (b) Thickness of the synthesized PATDDLC films as a function of methane concentration. The left axis also indicates the result in terms of

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growth efficiency in nm/mC.

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Figure 3. (free color online) (a) Dielectric constant and (b) breakdown strengths in positive and

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negative electrical polarizations of the PATD-DLC films as functions of methane concentration.

Figure 4. (free color online) (a) Raman spectrum of the PATD-DLC film synthesized in 50%

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methane. The dashed line indicates the background line. (b) Slope of the background line as a

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Figure 5. (free color online) TOF-SIMS depth profiles of the PATD-DLC films synthesized in (a) 17% and (b) 83% methane. The profiles show the atomic ratios of hydrogen (m/z =1.0081) and silicon (27.9746) to carbon (11.9994), designated as H/C and Si/C, respectively. Each dashed line indicates the silicon substrate surface.

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ACCEPTED MANUSCRIPT Figure 6. (free color online) Raman spectra of the PATD-DLC films synthesized in (a) 17%, (b) 50%, and (c) 83% methane. Each spectrum is overlaid by fitting curves. The black and red curves indicate the experimental result and total fitting curve, respectively. The brown, green, purple, blue, and yellow-green curves indicate the curves of the N, D, G−, G+, and D′ bands, respectively. Each

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dashed curve in the same color indicates the Lorentzian component of the band.

Figure 7. (free color online) (a) Relative areas of the Raman bands of the PATD-DLC films as functions of methane concentration during film synthesis. The plots indicate the G+ band (blue circles), G− band (purple hexagons), D band (green triangles), N band (ocher squares), and D′ band

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(yellow-green inverted triangles). (b) Area ratio of the G− band to the G+ band (G−/G+) as a function of methane concentration. (c) ΓLD (red diamonds) and ΓG (orange crosses) as functions of methane

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concentration.

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Figure 8. (free color online) (a) G+ band position, (b) G− band position, (c) difference between

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methane concentration.

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these two positions (G− − G+), and (d) D′ band position of the PATD-DLC films as a function of

Figure 9. (free color online) The sp2 cluster models for the PATD-DLC structures. The sp2 clusters

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are represented by exaggerated blocks: aliphatic clusters (white), grown and partly aromatic clusters (gray), and well-grown clusters with highly disordered structure (black). The matrix sea is dense with dangling bonds in (a) and (b) and coarse with hydrogen-terminated bonds in (c).

Figure 10. (free color online) (a) DLC tube model with a cross section ΔS consisting of conductive sp2 clusters, dielectric matrix materials, and CH spaces. The widths (diameters) of the elements are dsp2x, dmy, and dsz (x, y, z = 1, 2, 3, …), respectively. The tube is sandwiched between the top and 34

ACCEPTED MANUSCRIPT bottom (silicon substrate) electrode. A voltage V is applied to the tube horizontally. (b) Equivalent circuit of the DLC tube. Rsp2x, Rmy, and Rsz are resistances of a sp2 cluster, dielectric matrix material, and CH space, respectively. Cmy and Csz are capacitances of the dielectric matrix material and CH

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ACCEPTED MANUSCRIPT Highlights for “Chemical structure and electrical characteristics of diamondlike carbon films”

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・Raman spectra of diamondlike carbon (DLC) films were analyzed with five bands.

・The sp2 cluster model with the Raman analysis clarified the DLC structure.

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・Electrical characteristics of the films can be elucidated by the sp2 cluster model.

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