A ternary phase diagram for amorphous carbon

CARBON 94 (2015) 202–213

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CARBON journal homepage: www.elsevier.com/locate/carbon

A ternary phase diagram for amorphous carbon L. Zhang, X. Wei, Y. Lin, F. Wang ⇑ Department of Physics, Xiamen University, Xiamen, Fujian 361005, China

a r t i c l e

i n f o

Article history: Received 6 February 2015 Received in revised form 12 June 2015 Accepted 18 June 2015 Available online 23 June 2015

a b s t r a c t The sp2 phase in amorphous carbon is modeled as coexisting nc-graphite, fused aromatic ring, and olefinic chain clusters. A phenomenological linear dispersion model is derived to calculate the G peak position from weighted relative contents of the sp2 clusters and vice versa. Ternary phase diagrams based on the weighted relative contents provide quantitative predictions for G peak position, dispersion rate, sp3 content, H content, and other properties of amorphous carbon. The phase diagrams are used to classify and characterize amorphous carbon, and to track their structural changes due to modification procedures like annealing, doping, and ion irradiation. Numerous insights are drawn from patterns in the distributions or in the migration paths of the analyzed samples. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Amorphous carbon has intriguing properties and diverse applications [1–3]. Unlike other Group-IV amorphous materials, amorphous carbon has sp2 in addition to sp3 hybrid bonds, making it a much more complex system. Most growth methods use hydrocarbon gases as precursors and hence hydrogen is a natural part of amorphous carbon. Because the sp2 phase has smaller band gaps than the sp3 one, the optical and electronic properties of amorphous carbon are dominated by the content and structure of the sp2 phase [4,5]. A three-stage model is proposed by Ferrari and Robertson to describe the ‘‘amorphization trajectory’’ of the sp2 phase going from crystalline graphite to highly disordered amorphous carbon [6]. The sp2 phase is hypothesized to transform from nc-graphite (P2 nm), to fused aromatic ring (62 nm), and finally to olefinic chain nano-clusters along the ‘‘amorphization trajectory’’ [6,7] . There are many evidences for the existence of the three types of sp2 clusters. High-resolution transmission electron microscopy images of nc-graphite have been observed in amorphous carbon samples grown at high substrate temperature [8] or after annealing [9]. Robertson and O’Reilly [4] found that fused aromatic rings are the most stable configuration for the sp2 phase; Bredas and Street [10] proved that only fused aromatic rings can lead to the 2.0 eV level band gaps observed in amorphous carbon; Matsunuma [11] reproduced Raman spectra from resonant Raman scattering off fused aromatic rings; and Arenall and Liu [12] assigned the Raman peak at 867 cm1 to vibrations in the clusters of aromatic ⇑ Corresponding author. E-mail address: [email protected] (F. Wang). http://dx.doi.org/10.1016/j.carbon.2015.06.055 0008-6223/Ó 2015 Elsevier Ltd. All rights reserved.

rings. Finally, the presence of olefinic chains in amorphous carbon has been confirmed by the demonstration of Raman features from trans-polyacetylene and poly(p-phenylene vinylene) chains [13,14]. These physical evidences give strong support to the three-stage model. However, the physical picture described by this model can be further developed. One can reasonably argue that the conversion of nc-graphite to fused aromatic rings is gradual rather than abrupt, and the two types of sp2 clusters may coexist during the conversion process. The same argument may be applied to the conversion from fused aromatic rings to olefinic chains. In fact, it is not unreasonable to argue that all three types of sp2 clusters coexist through the whole process, and most amorphous carbon samples contain all three types of clusters. Changes in the proportions of different types of clusters may give the appearance of migrations from one type of clusters to another. In this work, we try to gain better understanding of amorphous carbon with a cluster-coexistence picture. A phenomenological linear dispersion model is derived to predict quantitatively the G peak position Pos(G) due to changes in the excitation wavelength or the microstructure of the sample. Weighted relative contents of the three types of sp2 clusters are calculated from multi-wavelength (MW) Raman spectra. Ternary phase diagrams are constructed from the relative contents to classify both H-free amorphous carbon (a-C) and hydrogenated amorphous carbon (a-C:H). Changes in microstructure of the sp2 phase due to modification procedures like doping, annealing, and ion irradiation are studied with these ternary phase diagrams. It will be shown that the clustercoexistence picture and the linear dispersion model based on it present a simple and direct explanation to the observed complex behaviors of Pos(G); and it will be shown that the ternary phase

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diagram along with MW Raman spectra can be a useful tool for studying amorphous carbon. The paper is structured as the following. In Sections 2 and 3, a phenomenological linear dispersion model is derived and the model parameters are estimated from amorphous carbon samples. In Section 4, ternary phase diagrams are constructed to classify amorphous carbon, and to calculate properties like Pos(G), Disp, and sp3 and H content; Migration paths due to amorphization and annealing process, and modification procedures such as doping and irradiation are analyzed in the ternary phase diagrams. Discussions and conclusions are presented in Sections 5 and 6.

Defining weighted relative content ni for the three types of clusters as

ni ðkÞ ¼

, Ni Ai ðkÞ X Ni Ai ðkÞ

ri ðkÞ3

i

ri ðkÞ3

;

and we will have

xG ¼

X ni xi ¼ ng xg þ nr xr þ nc xc :

Raman spectroscopy is the most common structural probe for amorphous carbon. Due to resonant enhancements from the p-electrons, Raman spectroscopy probes mostly the microstructure of the sp2 phase [1,6,7]. It is found experimentally that Pos(G) disperse linearly with the excitation wavelength, and the dispersion rate correlates strongly with the microstructure of the sample [15,16]. In this section, we will derive a phenomenological linear dispersion model that can be used to calculate Pos(G) from weighted relative contents of the sp2 clusters and vice versa. According to the cluster-coexistence picture, the intensity of the G peak IG ðxÞ can be calculated as a sum of the Raman scattering intensities from each of the three types of sp2 clusters, i.e.

IG ðx; kÞ ¼ Ig ðx; kÞ þ Ir ðx; kÞ þ Ic ðx; kÞ;

ð1Þ

where x is the Raman frequency, k is the wavelength of the excitation laser, and Ig ; Ir , and Ic represent the scattering intensities from the nc-graphite, the fused aromatic ring, and the olefinic chain clusters. Without losing generality, we can always approximate the scattering intensity from each type of the cluster with a Gaussian

Ni Ai ðkÞ  Ii ðx; kÞ ¼ pffiffiffiffiffiffiffi e 2pri ðkÞ

ðxxi ðkÞÞ2 2ri ðkÞ2

ð2Þ

where Ni is the atomic concentration, xi ðkÞ, Ai ðkÞ, and ri ðkÞ are the resonant frequency, the amplitude, and the width of the scattering peak, and i = g, r, c represents the three types of sp2 clusters. Resonant frequencies xi are sensitive to changes in k, while parameters Ai and ri should change very slowly with k [17]. The position of the G peak xG can then be calculated by finding the root of equation

@IG ðx; kÞ jxG ¼ 0: @x

ð3Þ

From Eqs. 1–3, we have

X xG  xi ðkÞ I i ð xG Þ ¼ 0; ri ðkÞ2 i

ð4Þ

and

xG ¼

X

xi

i

I i ð xG Þ

r

,

X I i ð xG Þ

2 i

i

r2i

:

ð5Þ

Eq. (5) tells us that Pos(G) = xG is a weighted average of the resonant frequencies xi from the three types of sp2 clusters. For most samples and excitation wavelengths, we expect ðxG  xi Þ2 =r2i to be a small quantity, and it can be shown (see online Supplementary data, Appendix A) that to the first order of ðxG  xi Þ2 =r2i , Eq. (5) is equivalent to

xG ¼

X

xi

i

, Ii ðxi Þ X Ii ðxi Þ

r2i

i

r2i

:

ð6Þ

ð8Þ

i

The weighted relative contents ni always satisfy normalization condition

ng þ nr þ nc ¼ 1: 2. Linear dispersion model for Raman spectra

ð7Þ

ð9Þ

Because Ai and ri are slowly varying functions of k, we expect that ni has only weak dependence on k. And since Ai and ri appears in both the numerator and the denominator in Eq. (7), the effect of k on ni is further reduced. In the online supplementary data (see Appendix A), ni are shown to be independent of k if relative changes of Ai and ri over k are identical among the different types of clusters. Experimental evidences [15] indicate that relative changes in ri are indeed approximately identical among different types of sp2 clusters. It is therefore reasonable to believe that ni does not depend or at most depend very weakly on k. Since Ai and ri themselves may be different among different types of clusters, weighted relative contents ni do not in general equal to the true relative contents of the clusters. However, we will show that the biases introduced by such differences are relatively small so that we can have meaningful and fruitful physical discussions by treating ni as the relative contents (see Section 5). Such a treatment is possible also because the three types of clusters are only loosely defined therefore accurate determination of their relative contents is neither possible nor necessary for general qualitative discussions with them. Since ni does not depend or only depend very weakly on k while xi depends sensitively on k, the derivative of xG against k or the dispersion rate of amorphous carbon can be found as

Disp ¼

@ xG ðkÞ X @ xi ðkÞ ¼ ni : @k @k i

ð10Þ

Extensive MW Raman data have shown that amorphous carbon disperses linearly with the excitation wavelength k [15]. In addition, there are also experimental and theoretical evidences of linearly dispersive xg and xc . A very small linear dispersion effect has been observed for nc-graphite from the annealed a-C:H samples [15] and from pitch coke carbonized at 1700° [18], indicating linear dispersive xg . Linear dispersion is also observed in amorphous carbon with high sp3 content (close to 90%) [15], which contain mostly olefinic chain sp2 clusters. This indicates that xc disperses linearly with k. Ab initio simulation confirms that xc from olefinic chain clusters disperses linearly with k in a-C samples [19]. Since xg ; xc , and xG all have linear dispersion, xr is required by Eq. (10) to have linear dispersion as well. Therefore, experimental and theoretical evidences suggest that resonant frequencies xi from all three types of sp2 clusters disperse linearly with k. We can now write xi as a linear function of k

xi ðkÞ ¼ ki k þ bi ;

ð11Þ

where ki and bi are constants and i = g, r, c is the type index. Eq. (10) now becomes

Disp ¼ ng kg þ nr kr þ nc kc :

ð12Þ

Based on these results, equations will be developed in the next section so that one can obtain the weighted relative contents ni from multiple Pos(G)s (at least two) or calculate properties like Pos(G), sp3 content, and H content from ni .

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In summary, we propose a linear dispersion model by asserting that (1) three types of sp2 clusters coexist in amorphous carbon and the position of the G peak is a weighted average of the resonant frequencies (xi ) of the sp2 clusters; (2) the weights (ni ) do not depend or only weakly depend on excitation wavelength k, and the weights (ni ) equal approximately to the relative contents of the sp2 clusters; (3) the resonant frequencies (xi ) disperse linearly with k. Assertion (1) and (3) are directly supported by the existing experimental evidences while assertion (2) will have to be validated by the correctness of the predictions from the model.

nr ¼

Disp  kc þ ng ðkc  kg Þ ; kr  kc

ð14bÞ

nc ¼

Disp  kr þ ng ðkr  kg Þ ; kc  kr

ð14cÞ

where Disp and b are the slope and the intercept of a linear regression to the MW data as xG ðkÞ ¼ Disp  k þ b. Note also that ng can be calculated without the knowledge of kr and kc . Defining Dk = kc  kr , Eqs. (14b) and (14c) can be changed into the following form

3. Parameters in the linear dispersion model We now try to estimate model parameters ki and bi from MW Raman data of amorphous carbon samples. Amorphous carbon annealed at high temperature [15] and graphitic carbon materials with small crystalline sizes [18] contain almost pure nc-graphite type of sp2 clusters, and can be used to measure parameters kg and bg . It is rather difficult to find samples with pure fused aromatic ring or olefinic chain type of sp2 cluster. However, it can be shown with Eqs. (8), (9) and (11) that samples with no nc-graphite type of sp2 clusters (ng = 0) have a fixed point at k0 = ðbc  br Þ=ðkc  kr Þ and x0 = kr k0 þ br for arbitrary nr and nc . Since samples with high sp3 content have very little nc-graphite clusters, and we can use these types of samples to locate the fixed point. MW Raman data of tetragonal a-C (ta-C) and tetragonal a-C:H (ta-C:H) from [15] are used to find the fixed point. In Fig. 1, Pos(G)s of the ta-C and the ta-C:H samples are plotted together with their linear regression lines. The fixed point is located at the cross point of the lines. We obtain the following estimation of k0 = 750 nm and x0 = 1455 cm1. To demonstrate the validity of the fixed point, MW Pos(G) data of polymeric-like a-C:H (PLCH) [15] are fitted with a straight line that goes through the fixed point, and reasonable accuracy is obtained. With kg , bg , k0 , and x0 , we can convert Eq. (11) into

xi ðkÞ ¼ ki ðk  k0 Þ þ Xi ;

ð13Þ

where Xg ¼ kg k0 þ bg , and Xr = Xc = x0 . Now the only undetermined model parameters are kr and kc . Combining Eqs. (8), (9), (12) and (13), we can have the following expressions for ni :

ng ¼

Disp  k0  x0 þ b ; Xg  x0

ð14aÞ

kr ¼

Disp  nc Dk  ng kg ; 1  ng

ð15aÞ

kc ¼

Disp þ nr Dk  ng kg ; 1  ng

ð15bÞ

and used to estimate parameters kr and kc . For amorphous carbon samples with small nc or nr content, the nc Dk or nr Dk terms in Eq. (15) is very small compare to the other two terms, so that one can set nc Dk or nr Dk equal to zero and calculate kr or kc without much errors. With kr and kc , one can calculate nr and nc of the samples with Eqs. (14b) and (14c). And with the obtained nr , nc , and Dk, one can repeat the calculation with Eq. (15) to get better estimates of kr and kc . This process can be repeated until stable evaluations of kr and kc are achieved. Parameters including kr and kc for a-C and a-C:H samples are estimated from MW Raman data [15] using this procedure, and are shown in Table 1. The errors in kr and kc shown in Table 1 are estimated from variations of  0.05 in the minority content nc or nr during the calculation. The introduction of H atoms affects Raman response from the fused aromatic ring and olefinic chain clusters significantly, which is reflected by the different kr and kc values listed for a-C and a-C:H samples in Table 1. The nc-graphite clusters are not affected so that identical value for the kg parameter is obtained. This is understandable as the local structure of nc-graphite is dominated by the C–C bonds. Using the corresponding a-C or a-C:H model parameters listed in Table 1, one can calculate Pos(G) at arbitrary excitation wavelength from the weighted relative contents ni with Eqs. (8) and (13). To calculate the relative contents ni from MW Raman data, one needs Pos(G)s from at least two different excitation wavelengths (more wavelengths will give better accuracy). First, one need to obtain the slope Disp and the intercept b of the MW Pos(G) data using linear equation xG ðkÞ ¼ Disp  k þ b; then one can use Eq. (14) with the corresponding a-C or a-C:H parameters listed in Table 1 to calculate ni . A MATLAB program is provided in the online Supplementary data (see Appendix A) to carryout these calculations automatically. As an example, we show in Fig. 2 the G peaks of an a-C:H sample at 244 and 514 nm with 1590 and 1533 cm1 Pos(G)s respectively [20]. The slope Disp and the intercept b of dispersive Pos(G) data are 0.211 cm1/nm and 1642 cm1 respectively. Plug these values into Eq. (14) with model parameters for a-C:H in Table 1, and we have the weighted relative contents ng = 0.19, nr = 0.68, and nc = 0.13. We can see that this sample has primarily fused

Table 1 Parameters in the linear dispersion model. Type

Fig. 1. A fixed point at 750 nm and 1455 cm1 for a-C and a-C:H samples with no nc-graphite clusters (ng  0). (A color version of this figure can be viewed online.)

a-C a-C:H

kg (cm1/nm)

kr (cm1/nm)

kc (cm1/nm)

k0 (nm)

x0

Xg

(cm1)

(cm1)

0.04 0.04

0.26(1) 0.25(1)

0.52(1) 0.39(1)

750 750

1455 1455

1600 1600

L. Zhang et al. / CARBON 94 (2015) 202–213

205

Fig. 2. G peaks in Raman spectra (circles) of an a-C:H sample collected at 514 nm (a) and at 244 nm (b) are fitted with superposed scattering intensities (solid lines) from the nc-graphite (dotted lines), fused aromatic rings (dashed lines) and olefinic chains (long dashed lines). (A color version of this figure can be viewed online.)

aromatic ring type of sp2 clusters. With the obtained relative contents ni , we can predict the Pos(G) of the sample at arbitrary excitation wavelength including 244 and 514 nm. Given an excitation wavelength k, we can calculate the resonant frequencies xi with Eq. (13), and plug the results into Eq. (8) to obtain xG or Pos(G). We can even reproduce the full G peak spectra at arbitrary excitation wavelength with Eqs. (1) and (2) if parameters Ai and ri are known or can be guessed. We now try to use the obtained relative contents ni to reproduce the G peak spectra shown in Fig. 2(a) and (b). Parameters Ai and ri at 244 and 514 nm are obtained by fitting Eq. (1) to the experimental data. To reduce the number of fitting parameters, identical parameters A and r are used for all types of clusters. The G peak spectra (solid lines) and the scattering intensities from each type of sp2 clusters (broken lines) are plotted with the experimental G peak spectra (circles) in Fig. 2. We can see that the reproduced G peak spectra fit the experimental spectra very well. 4. sp2 ternary phase diagrams Weighted relative content ni correspond uniquely to the microstructure of the sp2 phase. One can construct from ni a ternary phase diagram similar to the sp2–sp3–H ternary phase diagram widely used to categorize amorphous carbon [6,16]. As discussed in Section 2, we can qualitatively discuss the microstructure of the sp2 phase by regarding ni as the relative contents of the three types of sp2 clusters. We will prove the validity of such an approach by predicting structural distributions and structural changes coincide with the existing data, and will demonstrate the effectiveness of the method by adding many new insights about this material. MW Raman data of a-C and a-C:H samples from this and other studies are analyzed with the linear dispersion model and studied with ternary phase diagrams. The preparation and measurement of the samples used in this study are reported elsewhere [20–22]. We will show in the following subsections that this new way of characterizing amorphous carbon can provide new perspectives and new insights which are difficult to infer directly from the Raman spectra. 4.1. Classification of amorphous carbon Weighted relative contents of sp2 clusters in a-C samples are calculated from their MW Raman data, and are used to locate the samples in the H-free ternary phase diagram shown in Fig. 3(a). The samples are labeled either as a-C (sputtered a-C) or ta-C

(tetragonal a-C) types according to the original reports or the sp3 content of the samples (sp3 P60% for ta-C). We can see that samples with identical labels group naturally together into the same region. Ellipses are drawn to mark the regions corresponding to the types. Following [16], a-C:H samples are further classified into tetragonal a-C:H (ta-C:H), polymeric-like a-C:H (PLCH), diamond-like a-C:H (DLCH), graphite-like a-C:H (GLCH), and graphite-like a-C:H with extra hydrogen (GLCHH) sub-types. These classifications have unique characteristics in growth technique, sp3 and H contents, and properties like optical gap, hardness, and density. The characteristics of these sub-types are summarized from [16] and listed in Table 2 for easy reference. The sp3 content of GLCHH are estimated from dispersion rate of the G peak from the Raman spectra of GLCHH in [16]. MW Raman data of a-C:H samples are analyzed and displayed in the hydrogenated phase diagram shown in Fig. 3(b). The samples are labeled as one of ta-C:H, PLCH, DLCH, GLCH, and GLCHH types whenever possible. The samples without a label due to lack of information are included nonetheless to illustrate the general area that a-C:H samples occupy. It can be seen that samples with identical labels generally group into the same region, and samples without a label generally fall to the area covered by these regions. Ellipses are drawn to mark these regions. It is very interesting to note that ta-C:H overlaps with DLCH/PLCH types in a large region of the diagram. This is in contrary to the traditional sp2–sp3–H ternary phase diagram, which places ta-C:H and DLCH/PLCH types in different regions. This means that the microstructure of the sp3 phase is not unique within this region, and the related properties like H content, hardness, and stress are also non-unique within this region of the diagram [16]. This non-uniqueness issue will be discussed further in later part of the paper. From Fig. 3(a) and (b), we can see that the a-C samples are distributed away from the nr corner, while the a-C:H samples are distributed more evenly with many samples close to it. This means that a-C samples contain little fused aromatic rings while a-C:H samples can have plenty of them. This assertion is supported by the fact that all existing evidences of fused aromatic rings are found in a-C:H samples [10–12]. Robertson and O’Reilly [4] reported evidence of fused aromatic rings in a-C samples. However, the ultraviolet photoemission spectra (UPS) and X-ray absorption near edge structure (XANES) features used to identify the fused aromatic rings can be attributed to nc-graphite instead. The dotted lines in Fig. 3(a) and (b) represent relative contents of the three types of nano-clusters. These lines will be omitted in

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L. Zhang et al. / CARBON 94 (2015) 202–213

Fig. 3. Ternary phase diagrams for a-C samples (a), including sputtered a-C (open symbols) and ta-C (solid symbols) types; and for a-C:H samples (b), including ta-C:H (black), PLCH (magenta), DLCH (red), GLCH (blue), GLCHH (green) types. a-C:H samples without sufficient information for a definite sub-type are draw as open symbols. The Ellipses mark the regions for these types. The arrowed lines represent the as-deposited amorphization paths and the direction of the increasing disorder in the sp2 phase (see Section 4.4). (A color version of this figure can be viewed online.). (See above-mentioned references for further information.)

Table 2 Characteristics of sub-types of a-C:H samples. Growth techniques include electron cyclotron wave resonance (ECWR), plasma beam source (PBS), plasma enhanced chemical vapor deposition (PECVD), electron cyclotron resonance (ECR), dc glow discharge (GD), and magnetron sputtering (MS).

sp3 H Eg Hardness Density Growth technique

ta-C:H

PLCH

DLCH

GLCH

GLCHH

70% 25–30% 2–2.5 eV P20 GPa 2.4 g/cm3 ECWR, PBS

70% 40–60% 2–4 eV Soft 61.2 g/cm3 PECVD

40–60% 20–40% 1–2 eV 620 GPa 2.0 g/cm3 PECVD, ECR

630% 620% 61 eV Soft 1.6 g/cm3 PECVD, GD, MS

30% 30–40% P1 eV Soft 1.3 g/cm3 PECVD

Fig. 4. Pos(G) at 514 nm excitation wavelength for a-C (a) and a-C:H (b). (A color version of this figure can be viewed online.)

the ternary phase diagrams shown in following subsections, so that other properties of amorphous carbon can be displayed in the diagrams. 4.2. The G peak The G peak is the main and universal feature of Raman spectra for all types of amorphous carbon. The position, the width, and the dispersion rate of the G peak have been used to correlate with structures, growth conditions, and properties of amorphous carbon [15,16,20]. However, the effectiveness of such correlations varies with the wavelength of the excitation laser and with the type of the sample. With the linear dispersion model and the sp2 ternary phase diagrams, we can calculate Pos(G) for arbitrary excitation wavelength over whole range of categories of amorphous carbon.

We will be able to take a global view of these correlations and gain better understanding of them. Pos(G) at 514 nm is calculated for the H-free and the hydrogenated phase diagrams and are shown as isovalue lines in Fig. 4(a) and (b) respectively. The ellipses that mark the regions of the categories are also displayed. We see that Pos(G) of a-C samples is generally valued between 1550 and 1590 cm1, and has little correlation with the distribution of the categories. Similarly, Pos(G) of a-C:H samples has poor correlation with the DLCH, PLCH, and ta-C:H sub-types. It is clear that Pos(G) @514 is not an effective structural marker, even though it has been the most popular wavelength for Raman characterization of amorphous carbon. Pos(G) can be affected significantly by the excitation wavelength. The isovalue lines of Pos(G) at 244 nm for the H-free and the hydrogenated phase diagrams are calculated and shown in

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L. Zhang et al. / CARBON 94 (2015) 202–213

Fig. 5. Pos(G) at 244 nm excitation wavelength for a-C (a) and a-C:H (b). (A color version of this figure can be viewed online.)

Fig. 6. Dispersion rate of a-C (a) and a-C:H (b). (A color version of this figure can be viewed online.)

Fig. 5(a) and (b) respectively. We can see that Pos(G)@244 is quite different from Pos(G)@514 both in range of values and in orientation of the isovalue lines. For a-C samples, we see that Pos(G)@244 can actually differentiate sputtered a-C from ta-C types quite easily. For a-C:H samples, Pos(G)@244 is also a better structural marker. It can differentiate between DLCH and PLCH types and between GLCHH and GLCH types of samples. MW Raman spectroscopy has gained popularity due to advances in instruments and because it can measure the dispersion rate of the G peak, which has strong correlations with the sp3 content, the optical gap, and the Young’s modulus [15,16,20]. In Fig. 6(a) and (b), the isovalue lines of the dispersion rate (Disp) are shown in the H-free and the hydrogenated phase diagrams respectively. We can see that the isovalue lines can be used to characterize a-C samples and differentiate DLCH and PLCH types of samples. Comparing with Pos(G)@514 and Pos(G)@244, Disp can differentiate different common types of amorphous carbon more cleanly, proving that Disp is a better structural marker than Pos(G). Pos(G) at UV excitation is a better structural marker than at visible excitation, but single-wavelength (SW) Pos(G) alone proves to be a poor structural marker; comparatively, Disp is a much better one. However, all these markers represent multiple microstructures along their isovalue lines shown in Figs. 4–6, while the linear dispersion model can pinpoint a sample to a specific microstructure in the ternary phase diagram. Clearly, the combination of the linear dispersion model and the phase diagram provides a much better characterization system. The isovalue lines shown in Figs. 4–6 are calculated using Eqs. (8), (12) and (13). A MATLAB program for calculating and plotting Pos(G) isovalue lines at arbitrary excitation wavelength is provided in online Supplementary data (Appendix A).

4.3. sp3 and H content For most amorphous carbon samples, the microstructure of the sp2 phase is closely connected with that of the sp3 phases, and can be used to characterize both structures. According to [20], the sp3 content of a-C:H samples varies linearly with the dispersion rate of the G peak. The a-C samples are not treated in [20] because the relation becomes nonlinear as the dispersion rate goes past 0.36 cm1/nm. Here, we treat both a-C and a-C:H samples linearly by limiting the maximum dispersion rate. The following approximate linear relation

  sp3 content ¼ min 2:30  DispðGÞ ðcm1 =nmÞ; 0:90 3

ð16Þ

has been used to calculate the sp content for a-C and a-C:H samples. Isovalue lines of sp3 content in the H-free and the hydrogenated phase diagrams are shown in Fig. 7(a) and (b) with the ellipses that mark the categorical regions. We can see that the sp3 contents of the marked regions fall approximately within the ranges expected for these types (see Table 2). For the H-free phase diagram, the isovalue lines of the sp3 content represent diverse sp2 microstructures that correspond to the same sp2/sp3 ratio which all correspond to a single point in the traditional sp2–sp3–H phase diagram. Similar effects exist in the hydrogenated phase diagram (It will be shown that the sp3 isovalue lines have identical H content). This non-uniqueness of the sp2 microstructure in both H-free and hydrogenated amorphous carbon has been noticed before and is usually referred to as the clustering of the sp2 phase [6]. The sp2 phase is assumed to have different degree of clustering while keeping constant sp2–sp3–H composition. Obviously, the sp2 ternary phase diagrams provide

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L. Zhang et al. / CARBON 94 (2015) 202–213

Fig. 7. The sp3 content calculated from the dispersion rate of the G peak for a-C (a) and a-C:H (b). (A color version of this figure can be viewed online.)

a more direct and accurate description of such samples. More on this non-uniqueness issue will be discussed later. We now try to calculate isovalue lines for the H content. According to [6], the optical gap can be related to the sp3 content. The following formula is obtained by fitting the data in Fig. 13 of [6] with a second order polynomial

Eg ¼ 4:59x2  0:561x þ 0:539;

ð17Þ

where Eg is the optical gap, and x is the sp3 content. [16] also provides a relation between Eg and the H content

H ¼ ðEg þ 0:9Þ=9:

ð18Þ

Eq. (18) is only valid for H content P20%. Isovalue lines for the H content are calculated with Eqs. 16–18, and are plotted in Fig. 8. The slope of the H isovalue lines is the same as that of the sp3 ones, confirming that H isovalue lines are also sp3 ones. This is expected since Eqs. 16–18 produce a one-to-one relationship between H and sp3 relative contents. Again, we observe that the H content of the marked regions fall within the expected ranges (see Table 2), except for the ta-C:H type. According to [16], ta-C:H should have 25–30% H content, but Fig. 8 predicts 20–40%. As discussed in Section 4.1, this is the region that has non-unique connections between microstructures of the sp2 phase and the sp3 phase. The H content calculated with Eqs. 16–18 is probably an average of all types of samples. The non-uniqueness of the sp3 phase within this region can lead to non-uniqueness and sudden changes in properties of a-C:H

Fig. 8. The H content calculated from the sp3 content. The gray level of the data points represents the relative stress or hardness of the samples [34,35]. (A color version of this figure can be viewed online.)

samples. Kluba et al. studied the effects of self-bias on the internal stress of a-C:H samples grown with PECVD [34]. They found a sudden increase of the internal stress for bias voltages between 450 V and 550 V. The internal stress returns to normal after further increasing of the bias voltage. The series of samples (squares) grown at various bias voltages are plotted in the phase diagram shown in Fig. 8. The gray-level of the symbol represents the relative internal stress (white means the minimum and black means the maximum stress among the samples). We can see that the three samples which have anomalously hight internal stress coincide with the non-unique region. Dai et al. studied effects of chamber pressure on the hardness of the a-C:H samples grown with magnetron sputtering [35]. They found that the hardness of the sample increases with a lower chamber pressure. The series of samples (circles) grown at various pressures are plotted in Fig. 8 also. The gray-level of the symbols has the similar meaning. Again, we see that the hardness is increased anomalously in the non-unique region. The observed sudden changes in the hardness and the internal stress within the non-unique region could be explained if these samples have ta-C:H instead of DLCH microstructures. With the knowledge of the sp3 and the H content, other properties like the density, the optical gap, and the refractive index can also be calculated quantitatively [16]. Properties like the hardness and the internal stress can be inferred qualitatively from them. 4.4. Amorphization paths According to the three-stage model, amorphous carbon goes from complete order (crystalline graphite) to complete disorder (ta-C), following an amorphization trajectory in the configurational space. In the second and third stages of the trajectory, the sp2 phase goes from nc-graphite to fused aromatic rings and then to olefinic chains. This part of the amorphization trajectory can be mapped directly to a path in the ternary phase diagram (Fig. 3(a)). The path starts from the ng corner, moves along the bottom edge and reaches the nr corner, and then moves toward the nc corner along the left edge. The Pos(G)s at various excitation wavelengths are calculated along this path and are plotted as line segments in Fig. 9. The Raman data points in Fig. 9 are taken from a similar plot in [6,15] which were used to demonstrate the amorphization trajectory. Reasonable agreement is observed indicating that the amorphization trajectory can indeed be mapped to a path in the ternary phase diagram. However, we see from Fig. 3(a) that the actual amorphization path taken by the as-deposited a-C samples (the arrowed line) deviates considerably from the just described path. To distinguish these two types of amorphization paths we shall refer to the path that is mapped directly from the amorphization trajectory in the three-stage model as the ideal

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amorphization path is quite close to the ideal amorphization path. This means that it is much easier to produce fused aromatic rings in a-C:H than in a-C. The Pos(G)s at 514 nm and 244 nm are calculated along the as-deposited amorphization path and are shown in Fig. 10, together with Raman data of a-C:H samples from [16] in a similar plot. Again, reasonable agreement is observed. In addition to the G peak, the D peak in Raman spectra can also be used to characterize the microstructures of amorphous carbon [6,17]. The D peak has its maximum intensity in samples containing pure nc-graphite, and gradually looses its strength along the amorphization path. It looses almost all of its strength at the end of the second stage. Fig. 11 is adapted from Fig. 7 in [6], which shows the evolution of I(D)/I(G) along the ideal amorphization path. The intensity of the D peak I(D) in Fig. 11 is computed by assuming constant I(G) during the evolution. We can see that I(D) goes from 100% to 10% as ng converts nr . This means that only nc-graphite contributes to the D peak, while the fused aromatic ring does not. The D peak comes from the breathing mode (A1g symmetry) in graphene sheets [6]. The lack of D peak contribution from the fused aromatic rings indicates that the fused rings are quite deformed so that the A1g symmetry is totally destroyed. Fig. 9. Pos(G) of a-C samples evolving along the ideal amorphization path. (A color version of this figure can be viewed online.)

amorphization path, and the path followed by the as-deposited samples as the as-deposited amorphization path. The Raman data points shown in Fig. 9 that have nr = 100% are from ion irradiated glassy carbon instead of as-deposited a-C [6,15]. A similar as-deposited amorphization path can be defined for the a-C:H samples (the arrowed line in Fig. 3(b)). The GLCHH type is omitted from this path. Surprisingly, the as-deposited

Fig. 10. Pos(G) as a function of the H content for a-C:H samples evolving along the as-deposited amorphization path shown in Fig. 3(b). (A color version of this figure can be viewed online.)

4.5. Annealing paths It has been observed that the amorphization (disordering) and the annealing (ordering) processes follow different trajectories in the configurational space, and display different Pos(G) values for the same sp3 content [6,15,36]. This effect has been used as experimental evidence for the clustering of the sp2 phase. The sp2 ternary phase diagram can resolve this non-uniqueness and reveal the actual structural changes along the annealing or ordering trajectories. As with the amorphization trajectories, the annealing trajectories can be mapped to paths in the ternary phase diagrams. The relative contents of sp3 clusters of ta-C [36] and ta-C:H [6] samples annealed at various temperatures are calculated and plotted in Fig. 12(a) and (b) respectively. The upper blue arrowed lines are the annealing paths for these samples. The arrows indicate the direction of the increasing temperature and the small points on the lines (A–D) mark the stages of the annealing process. The as-deposited amorphization paths (the lower red arrowed lines) are identical as those in Fig. 3. The isovalue lines of the sp3 content are also plotted. We see that the annealing paths are quite different from the amorphization paths, and the two types of paths form a

Fig. 11. Relative intensity of the D peak I(D) along the ideal amorphization path (adapted from [6]). (A color version of this figure can be viewed online.)

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Fig. 12. The annealing paths and the hysteresis loops of ta-C (a) and ta-C:H (b). (A color version of this figure can be viewed online.)

Fig. 13. a-C samples doped with B, N, Ag, Ni, Ti, and Zn elements (a), and irradiated with Au+, Bi+, Ga+, Ge+, Si+, and Xe+ ions (b). The arrowed lines represent the migration paths and the directions of increasing strength of doping or irradiation. The stars represent common destinations of the migration paths. (A color version of this figure can be viewed online.)

loop, crossing only at the beginning and the end, similar to the order–disorder hysteresis loops discussed in [6]. Furthermore, the annealing paths can be used to infer changes in the microstructure of the sp2 phase during the annealing process. We start from the annealing path for the ta-C samples shown in Fig. 12(a). First of all, we notice that during the initial segment of the path between point A and B (annealing temperature is less than 800° [36]), the aromatic ring cluster is reduced (Dnr = 0.14), while both the nc-graphite and the olefinic chain clusters are slightly increased (Dng = 0.07, Dnc = 0.07). This means that approximately half of the depleted aromatic rings are converted either directly or indirectly to the olefinic chains instead of all to the nc-graphite. This is very surprising since annealing has been assumed to be a pure graphitization process and both the fused aromatic ring and the olefinic chain clusters are expected to convert to nc-graphite during this process. Comparing with the isovalue lines of the sp3 content, one can see that the sp3 content remain constant during this segment of the annealing path while the microstructure of the sp2 phase changes considerably. Other types of measurements in [36] confirm the structural changes indicated by the AB segment in the phase diagram. EELS measurement and I(T)/I(G) ratio in UV (224 nm) Rama spectra proves constant sp3 content as suggested by the AB segment; while the measured resistivity decreases continuously during this segment, corroborating with the increase of nc-graphite clusters between point A and B. Only when the fused aromatic rings are almost all depleted near the turning point C (nr = 0.06), do the olefinic chains start to deplete. At point D, the ta-C sample is annealed at 1000°, the fused aromatic rings are completely gone, while the weighted relative content nc = 0.52 is still much higher than its initial value of 0.43.

The increase of the olefinic chain clusters at the initial stage of the annealing is clearly observed. After point D, the system simply converts its olefinic chains to nc-graphite directly until the whole system becomes graphitic. The annealing path shown in Fig. 12(b) reveals less dramatic structural changes in the annealed ta-C:H samples. From point A to B, the olefinic chain clusters stay almost constant while the aromatic rings convert directly to nc-graphite. From point B to C, the olefinic clusters start to convert to nc-graphite with increasing speed while the conversion speed of the aromatic rings start to decrease. Finally at point C, the aromatic ring cluster is completely depleted while the olefinic chain starts to convert to nc-graphite quickly until the whole system becomes graphitic. From the isovalue lines, we can see that the sp3 content of the system decreases continuously without the initial invariant stage displayed in the ta-C samples. From the annealing paths of the ta-C and the ta-C:H samples, we see that the aromatic rings are always depleted earlier and faster than the olefinic chains during the annealing process. Combining this with the observation of the scarcity of fused aromatic rings in a-C (Section 4.1), one can see that H-free or dehydrogenated amorphous carbon is not a suitable environment for fused aromatic rings. 4.6. Modification processes Even though there are many deposition methods for amorphous carbon, most of them require carbon ions or hydrocarbon radicals of certain energy and density to produce films with adequate mechanical and adhesion strength. This requirement constrains

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the as-deposited samples to the region spanned by the as-deposited amorphization paths shown in Fig. 3(a) and (b). It is possible to create amorphous carbon systems in other regions of the phase diagram through modifications like doping and irradiation. Distinct patterns can be observed from the migration paths taken by these modified samples. 4.6.1. Modification of a-C samples The migration paths of a-C samples doped with B, N, Ag, Ni, Ti, and Zn elements [30,37–40] are shown in Fig. 13(a), and that of a-C samples irradiated with Au+, Bi+, Ga+, Ge+, Si+, and Xe+ ions [41,6] are plotted in Fig. 13(b). The lines are guide for the eyes, and the arrows indicate the direction of increasing modification strengths, such as doping concentration or irradiation dose. Most of the data points are calculated by combining SW Pos(G) and sp3 content data because MW Pos(G) data are not available. Before discussing the migration paths of these modified samples, we notice that the hardness and the internal stress are correlated strongly with the sp3 content of a-C samples [1,7]. According to Fig. 7(a), we expect the nc corner to have the highest hardness and internal stress and the ng corner to have the lowest ones. It has been observed that doped amorphous carbon tends to have reduced internal stress [2,37,38]. On the other hand, ion irradiation on highly stressed amorphous carbon (ta-C) tends to reduce its internal stress [42,43], while that on fully relaxed amorphous carbon (sputtered a-C or glassy carbon) tends to increase it [44,45]. Therefore, we expect the modified a-C samples to move toward either the ng or the nc corner. It is very surprising to observe in Fig. 13(a) that some of the doped a-C samples (B, Ag, Ni, and Ti) move toward and reaching the nr corner instead of the ng corner, while other doped a-C samples (N, Zn) moves toward the bottom edge. Only one of the doped a-C samples (Ni) moves directly toward the ng corner. However, all ion irradiated a-C samples (Si+, Ge+, Ga+, Bi+, Au+, and Xe+) in Fig. 13(b) move toward the nr corner. From these migration paths, we can see that the nr corner attracts both the doped and the irradiated a-C samples, even though it has neither the lowest nor the highest internal stress within the phase diagram. This pattern indicates that foreign atoms are good nucleation sites for the fused aromatic rings during doping or irradiation process, and that low energy configurations can be formed between foreign atoms and fused aromatic rings. 4.6.2. Modification of a-C:H samples Migration paths of a-C:H samples doped with B, N, I, Si, Ag, and Ti elements [21,30,46–51] are shown in Fig. 14(a), and that of

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a-C:H samples irradiated with He+, N+, and Ag+ ions [52–54] in Fig. 14(b). The symbols, the lines, and the arrows all have similar meanings as those in Fig. 13. The hardness and internal stress of a-C:H do not have a direct correlation with the sp3 content as those of a-C. Instead, they depend on both the sp3 and the H content. In general, we expect high hardness and internal stress in a-C:H samples with the combination of high sp3 and low H content, of which ta-C:H is a good example. Therefore, we expect the doped or irradiated samples to move toward the ng corner which has the lowest hardness and internal stress. Again, we are surprised to see in Fig. 14(a) that many modified a-C:H samples move toward locations other than the ng corner. The Si and one of the N doped a-C:H samples move toward the nr corner, the Ag, I, and Ti doped ones move toward the right edge, and the B doped sample toward the bottom edge. Only the Ag and one of the N doped a-C:H samples move toward the ng corner directly. On the other hand, all ion irradiated a-C:H samples (N+, Ag+, and He+) in Fig. 14(b) move toward the nr corner, similar to the irradiated a-C samples. As with the modified a-C samples, we interpret the concentration of migration destinations at the nr corner and the right and bottom edges as an indication that foreign atoms can serve as nucleation sites for microstructures in these regions.

5. Discussions The linear dispersion model and the ternary phase diagram built upon it have successfully reproduced the linear dispersion effect in Raman spectra (Fig. 2), classification of a-C and a-C:H sub-types (Fig. 3), and properties like Pos(G), Disp, sp3 content, and H content of these sub-types (Figs. 4–8). The linear dispersion model also reproduced structural changes during the amorphization trajectories (Figs. 9 and 10) and the annealing processes (Fig. 12). These agreements validate the methodology used in this research and confirm indirectly assertion (2) for the linear dispersion model (see Section 2). Weighted relative contents of the sp2 clusters give a direct representation of microstructure of the sp2 phase, which corresponds uniquely to that of the sp3 phase in most samples. Structural characteristics and structural changes of amorphous carbon manifest themselves as distributions and as migration paths in the ternary phase diagrams, which can be studied with MW Raman spectra from at least two excitation wavelengths. Such a representation is very important in finding deeper connections buried in the Raman data, or in communicating investigative results among different research groups.

Fig. 14. a-C:H samples doped with B, N, I, Si, Ag, and Ti elements (a), and irradiated with He+, N+, and Ag+ ions (b). The arrowed lines represent the migration paths and the directions of increasing strength of doping or irradiation. The stars represent common destinations of the migration paths. (A color version of this figure can be viewed online.)

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It has been realized that the sp2 phase can have different microstructure or degree of clustering under the same value of sp2 and sp3 contents. This non-uniqueness is absent in the sp2 phase diagrams as the microstructure of the sp2 phase is represented directly by the relative contents of the clusters. On the other hand, certain region of the hydrogenated phase diagram has non-unique sp3 microstructure which can be completely resolved by the sp2–sp3–H phase diagram. It seems that the sp2 phase diagram and the traditional sp2–sp3–H phase diagram complement each other in describing the relation between the microstructures of the sp2 and the sp3 phases. The calculation of the relative contents depends sensitively on the parameters in the phenomenological model. Errors in these parameters can affect the calculations quite significantly. However, it is observed that variations in these parameters tend to shift all calculation results uniformly, leaving patterns in the migration paths unchanged. Therefore, the reading and analysis carried out in this work is to some extent immune to such errors. Errors can also come from the measurement or the analysis of MW Raman spectra. Using three types of fitting functions (Lorentzian, Breit–Wigner–Fano, and Gaussian), [20] was able to obtain the upper bound of the errors in Disp as 0.03 cm1/nm. Using this upper bound of errors and Eqs. (14), we can get the upper bounds of the errors in the relative contents as Dng = 0.16, Dnr and Dnc = 0.12 for a-C samples and Dnr and Dnc = 0.21 for a-C:H samples. We can see that errors introduced by using Pos(G) data from different fitting methods can be significant, however discussions of general locations and general trends should be still possible and the obtained conclusions still valid. When data are analyzed with identical method and discussions only concern relative position in the phase diagram, these type of errors does not affect the analysis. Most of the data points in Figs. 13 and 14 are obtained from SW Pos(G) data and estimated sp3 content. From Eq. (16), one can calculate the Disp from the sp3 content. With Disp, Pos(G), and excitation wavelength k, one can calculate intercept b. Since the sp3 content of many of the data points are estimated from the I(D)/I(G) ratio or the G peak FWHM, significant errors can be introduced. MW Raman studies of modified amorphous carbons are desired and will provide more conclusive results. A heterogeneous two-phase model similar in spirit to our linear dispersion model was proposed by Ramsteiner and Wagner [55] to explain the shifting of the G peak in different a-C:H samples. The Raman spectra were assumed to come from the superposition of scattering intensities from two phases in the system. The changes in the relative contents of the two phases would produce an apparent shift in the G peak. However, the two phases were incorrectly identified as the sp3 and the sp2 carbons in the system.

6. Conclusions The microstructure of the sp2 phase is modeled as coexisting nc-graphite, fused aromatic ring, and olefinic chain clusters. Their relative contents characterize the microstructure of the sp2 phase and in turn characterize that of the sp3 phase for most amorphous carbon types. A phenomenological linear dispersion model is derived to calculate the G peak position from weighted relative contents and vice versa. The weighted relative contents are then used to construct ternary phase diagrams for the sp2 phase in H-free and hydrogenated amorphous carbon. The ternary phase diagrams provide quantitative predictions for the G peak position and the dispersion rate, which in turn provide quantitative estimation of properties like sp3 content, H content, optical gap, density, and refractive index. Other properties like the hardness and the internal stress can be inferred qualitatively. It is assumed and

indirectly verified that meaningful physical discussions can be carried out by regarding these weighted relative contents as the true relative contents of the sp2 clusters. MW Raman spectra data from this and other studies are used to locate a-C and a-C:H samples in the ternary phase diagrams. Patterns in the distribution or the migration paths of these samples lead to the following conclusions and observations on amorphous carbon: (1) The sp2 ternary phase diagram can be used to classify a-C and a-C:H samples into well known types. Identical type of a-C or a-C:H samples groups naturally into the same region, which predicts the same range of G peak position, dispersion rate, sp3 content, H content, optical gap, density, refractive index, hardness, and internal stress as known for that type. (2) ta-C:H is found to have similar sp2 microstructures with the overlapping DLCH/PLCH, but different sp3 microstructures. (3) The non-uniqueness of the sp2 microstructure in the traditional sp2–sp3–H phase diagram is absent in the sp2 ternary phase diagrams, while the non-uniqueness of the sp3 microstructure in the hydrogenated ternary phase diagram does not exist in the sp2–sp3–H phase diagram. The two types of phase diagrams complement each other while describing the relation between the microstructures of the sp2 and the sp3 phases. (4) The second and third stages of the amorphization trajectory described by the three-stage model can be mapped into paths in the ternary phase diagrams. The as-deposited amorphization path in the H-free phase diagram deviates considerably from the ideal amorphization path described by the three-stage model, while that in the hydrogenated phase diagram deviates only slightly. (5) As-deposited a-C samples contain little fused aromatic rings, while the sp2 phase of a-C:H samples can be dominated by fused aromatic ring clusters. (6) Fused aromatic ring clusters do not contribute to the D peak in Raman spectra because they are deformed and have lost the A1g symmetry. The fused aromatic rings are different from the nc-graphite not only in size but also in symmetry. (7) The annealed ta-C and ta-C:H samples follow paths different from the their amorphization paths and form close loops with them, similar to the hysteresis loops described by the three-stage model. (8) During the annealing process, the aromatic ring clusters are always depleted earlier and faster than the olefinic chain clusters. Under relatively low annealing temperature, the olefinic chain clusters in ta-C samples increase rather than decrease with the annealing temperature. (9) Base on observation (5) and (8), one can conclude that H-free or dehydrogenated amorphous carbon is not a suitable environment for fused aromatic rings. (10) Doping and irradiation create amorphous carbon samples with more aromatic ring clusters. It means that foreign atoms can serve as nucleation sites for fused aromatic ring clusters, and in some cases for olefinic chain clusters as well. With these conclusions and observations, we have demonstrated the usefulness of the linear dispersion model and the sp2 ternary phase diagram based upon it. Acknowledgments The Authors acknowledges support by the National Basic Research Program of China under grant No. 2012CB933502 and No. 2012CB933503, and would like to thank Professor Jincheng Zheng for many insightful discussions.

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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbon.2015.06. 055. References [1] J. Robertson, Diamond-like amorphous carbon, Mat Sci Eng R 37 (2002) 129– 281. [2] J. Vetter, 60 years of DLC coatings: historical highlights and technical review of cathodic arc processes to synthesize various DLC types, and their evolution for industrial applications, Surf Coat Tech 257 (2014) 213–240. [3] K. Bewilogua, D. Hofmann, History of diamond-like carbon films—From first experiments to worldwide applications, Surf Coat Tech 242 (2014) 214–225. [4] J. Robertson, E.P. O’Reilly, Electronic and atomic structure of amorphous carbon, Phys Rev B 35 (1987) 2946–2957. [5] J. Robertson, Electronic and atomic structure of diamond-like carbon, Semicond Sci Technol 18 (2003) S12–S19. [6] A.C. Ferrari, J. Robertson, Interpretation of Raman spectra of disordered and amorphous carbon, Phys Rev B 61 (2000) 14095–14107. [7] A.C. Ferrari, J. Robertson, Raman spectroscopy of amorphous, nanostructured, diamond-like carbon, and nanodiamond, Philos Trans R Soc Lond A 362 (2004) 2477–2512. [8] S. Miyagawa, S. Nakao, J. Choi, M. Ikeyama, Y. Miyagawa, Effects of target bias voltage on the electrical conductivity of DLC films deposited by PBII/D with a bipolar pulse, Nucl Instrum Meth B 242 (2006) 346–348. [9] A.Y. Kolpakov, A.I. Poplavsky, M.E. Galkina, S.S. Manokhin, J.V. Gerus, The local crystallization in nanoscale diamond-like carbon films during annealing, Appl Phys Lett 105 (2014) 233110. [10] J.L. Bredas, G.B. Street, Electronic properties of amorphous carbon films, J Phys C: Solid State Phys 18 (1985). L651-5. [11] S. Matsunuma, Theoretical simulation of resonance Raman bands of amorphous carbon, Thin Solid Films 306 (1997) 17–22. [12] R. Arenall, A.C.Y. Liu, Clustering of aromatic rings in near-frictionless hydrogenated amorphous carbon films probed using multiwavelength Raman spectroscopy, Appl Phys Lett 91 (2007) 211903. [13] F. Piazza, A. Golanski, S. Schulze, G. Relihan, Transpolyacetylene chains in hydrogenated amorphous carbon films free of nanocrystalline diamond, Appl Phys Lett 82 (2003) 358–360. [14] M. Rybachuk, A. Hu, J.M. Bell, Resonant Raman scattering from polyacetylene and poly(p-phenylene vinylene) chains included into hydrogenated amorphous carbon, Appl Phys Lett 93 (2008) 051904. [15] A.C. Ferrari, J. Robertson, Resonant Raman spectroscopy of disordered, amorphous, and diamondlike carbon, Phys Rev B 64 (2001) 075414. [16] C. Casiraghi, A.C. Ferrari, J. Robertson, Raman spectroscopy of hydrogenated amorphous carbons, Phys Rev B 72 (2005) 085401. [17] C. Thomsen, S. Reich, Double resonant Raman scattering in graphite, Phys Rev Lett 85 (2000) 5214–5217. [18] P. Mallet-Ladeira, P. Puech, C. Toulouse, M. Cazayous, N. Ratel-Ramond, P. Weisbecker, et al., A Raman study to obtain crystallite size of carbon materials: a better alternative to the Tuinstra–Koenig law, Carbon 80 (2014) 629–639. [19] S. Piscanec, F. Mauri, A.C. Ferrari, M. Lazzeri, J. Robertson, Ab initio resonant Raman spectra of diamond-like carbons, Diam Relat Mater 14 (2005) 1078– 1083. [20] W.G. Cui, Q.B. Lai, L. Zhang, F.M. Wang, Quantitative measurements of sp3 content in DLC films with Raman spectroscopy, Surf Coat Tech 205 (2010) 1995–1999. [21] F.M. Wang, M.W. Chen, Q.B. Lai, Metallic contacts to nitrogen and boron doped diamond-like carbon films, Thin Solid Films 518 (2010) 3332–3336. [22] Q.Y. Li, F.M. Wang, L. Zhang, Study of colors of diamond-like carbon films, Sci China Phys Mech 3 (2013) 545–550. [23] J. Wasyluk, T.S. Perova, D.W.M. Lau, M.B. Taylor, D.G. McCulloch, J. Stopford, et al., Ultraviolet and visible Raman analysis of thin a-C films grown by filtered cathodic arc deposition, Diam Relat Mater 19 (2010) 514–517. [24] A. Sikora, F. Garrelie, C. Donnet, A.S. Loir, J. Fontaine, J.C. Sanchez-Lopez, et al., Structure of diamondlike carbon films deposited by femtosecond and nanosecond pulsed laser ablation, J Appl Phys 108 (2010) 113516. [25] F.X. Liu, K.L. Yao, Z.L. Liu, Different substrate materials effect on structure of taC films by Raman spectroscopy for magnetic recording sliders, J Non-Cryst Solids 353 (2007) 2545–2549. [26] F.X. Liu, K.L. Yao, Z.L. Liu, Substrate bias effect on structure of tetrahedral amorphous carbon films by Raman spectroscopy, Diam Relat Mater 16 (2007) 1746–1751. [27] G. Adamopoulos, K.W.R. Gilkes, J. Robertson, N.M.J. Conway, B.Y. Kleinsorge, A. Buckley, et al., Ultraviolet Raman characterisation of diamond-like carbon films, Diam Relat Mater 8 (1999) 541–544.

213

[28] F.X. Liu, K.L. Yao, Z.L. Liu, Substrate tilting effect on structure of tetrahedral amorphous carbon films by Raman spectroscopy, Surf Coat Tech 201 (2007) 7235–7240. [29] J.R. Shi, X. Shi, Z. Sun, S.P. Lau, B.K. Tay, H.S. Tan, Resonant Raman studies of tetrahedral amorphous carbon films, Diam Relat Mater 10 (2001) 76–81. [30] A.C. Ferrari, S.E. Rodil, J. Robertson, Interpretation of infrared and Raman spectra of amorphous carbon nitrides, Phys Rev B 67 (2003) 155306. [31] C. Casiraghi, F. Piazza, A.C. Ferrari, D. Grambole, J. Robertson, Bonding in hydrogenated diamond-like carbon by Raman spectroscopy, Diam Relat Mater 14 (2005) 1098–1102. [32] F. Piazza, Hard-hydrogenated tetrahedral amorphous carbon films by distributed electron cyclotron resonance plasma, Int J Refract Met H 24 (2006) 39–48. [33] M.A. Tamor, J.A. Haire, C.H. Wu, K.C. Hass, Correlation of the optical gaps and Raman spectra of hydrogenated amorphous carbon films, Appl Phys Lett 54 (1989) 123–125. [34] A. Kluba, D. Bociaga, M. Dudek, Hydrogenated amorphous carbon films deposited on 316L stainless steel, Diam Relat Mater 19 (2010) 533–536. [35] H.Y. Dai, J. Chen, R.Z. Xue, T. Li, Z.P. Chen, Analysis of hydrogenated amorphous carbon films deposited by middle frequency pulsed unbalanced magnetron sputtering, J Non-Cryst Solids 363 (2013) 77–83. [36] A.C. Ferrari, B. Kleinsorge, N.A. Morrison, A. Hart, V. Stolojan, J. Robertson, Stress reduction and bond stability during thermal annealing of tetrahedral amorphous carbon, J Appl Phys 85 (1999) 7191–7197. [37] M.L. Tan, J.Q. Zhu, J.C. Han, W. Gao, A.P. Liu, X. Han, et al., Raman characterization of boron doped tetrahedral amorphous carbon films, Mater Res Bull 43 (2008) 453–462. [38] S. Gayathri, N. Kumar, R. Krishnan, T.R. Ravindran, S. Amirthapandian, S. Dash, et al., Influence of transition metal doping on the tribological properties of pulsed laser deposited DLC films, Ceram Int 41 (2015) 1797–1805. [39] N.W. Khun, E. Liu, G.C. Yang, Structure, scratch resistance and corrosion performance of nickel doped diamond-like carbon thin films, Surf Coat Tech 204 (2010) 3125–3130. [40] H. Wong, Y.M. Foong, D.H.C. Chua, Improving the conductivity of diamond-like carbon films with zinc doping and its material properties, Appl Surf Sci 257 (2011) 9616–9620. [41] P. Philipp, L. Bischoff, U. Treske, B. Schmidt, J. Fiedler, R. Hubner, et al., The origin of conductivity in ion-irradiated diamond-like carbon – Phase transformation and atomic ordering, Carbon 80 (2014) 677–690. [42] D.G. McCulloch, E.G. Gerstner, D.R. McKenzie, S. Prawer, R. Kalish, Ion implantation in tetrahedral amorphous carbon, Phys Rev B 52 (1995) 850–857. [43] D.H. Lee, S. Fayeulle, K.C. Walter, M. Nastasi, Internal stress reduction in diamond like carbon thin films by ion irradiation, Nucl Instrum Meth B 148 (1999) 216–220. [44] J.A. Hinks, S.J. Haigh, G. Greaves, F. Sweeney, C.T. Pan, R.J. Young, et al., Dynamic microstructural evolution of graphite under displacing irradiation, Carbon 68 (2014) 273–284. [45] D.G. McCulloch, S. Prawer, A. Hoffman, Structural investigation of xenon-ionbeam-irradiated glassy carbon, Phys Rev B 50 (1994) 5905–5917. [46] A.M.M. Omera, S. Adhikaria, S. Adhikary, M. Rusop, H. Uchida, M. Umeno, et al., Iodine doping in amorphous carbon thin-films for optoelectronic devices, Phys B 376–7 (2006) 316–319. [47] H. Nakazawa, R. Kamata, S. Okuno, Deposition of silicon-doped diamond-like carbon films by plasma-enhanced chemical vapor deposition using an intermittent supply of organosilane, Diam Relat Mater 51 (2015) 7–13. [48] B. Racine, A.C. Ferrari, N.A. Morrison, I. Hutchings, W.I. Milne, J. Robertson, Properties of amorphous carbon–silicon alloys deposited by a high plasma density source, J Appl Phys 90 (2001) 5002–5012. [49] Š. Meškinis, A. Vasiliauskas, K. Šlapikas, G. Niaura, R. Juške˙nas, M. Andrulevicˇius, et al., Structure of the silver containing diamond like carbon films: study by multiwavelength Raman spectroscopy and XRD, Diam Relat Mater 40 (2013) 32–37. [50] H.W. Choi, R.H. Dauskardt, S.C. Lee, K.R. Lee, K.H. Oh, Characteristic of silver doped DLC films on surface properties and protein adsorption, Diam Relat Mater 17 (2008) 252–257. [51] L. Qiang, B. Zhang, Y. Zhou, J.Y. Zhang, Improving the internal stress and wear resistance of DLC film by low content Ti doping, Solid State Sci 20 (2013) 17– 22. [52] G.A. Baratta, M.M. Arena, G. Strazzulla, L. Colangeli, V. Mennella, E. Bussoletti, Raman spectroscopy of ion irradiated amorphous carbons, Nucl Instrum Meth B 116 (1996) 195–199. [53] S. Nakao, A. Kinomura, T. Sonoda, Nitrogen implantation into diamond-like carbon films prepared by bipolar-type plasma based ion implantation, Nucl Instrum Meth B 307 (2013) 333–339. [54] D. Batory, J. Gorzedowski, B. Rajchel, W. Szymanski, L. Kolodziejczyk, Silver implanted diamond-like carbon coatings, Vacuum 110 (2014) 78–86. [55] M. Ramsteiner, J. Wagner, Resonant Raman scattering of hydrogenated amorphous carbon: evidence for p bonded carbon clusters, Appl Phys Lett 51 (1987) 1355–1357.