- Email: [email protected]
Theoretical simulation of resonance Raman bands of amorphous carbon
thin o ELSEVIER
Thin Solid Fihns 306 (1997) 17-22
Theoretical simulation of resonance Raman bands of amorphous carbon Satoshi Matsunuma Hitachi, Central Research Laboratory, 292 Yoshida-cho, Torsuka-ku, Yokohama 244, Japan
Received 20 November 1996; accepted 23 April 1997
Abstract Simulations of resonance Raman spectra of chromopbore models for amorphous carbon were carried out in consideration of resonance enhancement by using the Albrecht A term. Relative resonance Raman intensity of each vibrational mode was calculated with the electronic transition analysis by a Complete Neglect of Differential Overlaps (CNDO]S~ method including configuration interaction and the vibrational analysis by a Parametric Method 3 (PM3) method. Condensed aromatic cluster containing four to six benzene rings gave similar spectra as reported experimental spectra excited with the incident photon energy of 2.41 or 2.54 eV. A slight high-frequency shift of the main peak of Raman spectrum was simulated on sp 2 clusters of smaller size which have higher resonance energies compared to the above condensed aromatic clusters. These simulated results were cortsistent with reported dependence of incident photon energies for the band shape of Raman spectra and suggested that a complex of many sizes of sp ~ clusters which have six or less benzenes is the origin of resonance Raman spectra of amorphous carbon. Attached sp 3 carbon round sp 2 carbon chromophore showed little effect on the band shape of calculated resonance Raman spectra. It was postulated that information on sp 3 network structure hardly appears in resonance Raman spectra compared to sp 2 cluster when a visible light is used for the excitation. © 1997 Elsevier Science S.A. Ke)words: Raman scattering; Computer simulation; Amorphous materials; Carbon
1. Introduction There is no doubt that amorphous carbon film is a useful material because of its hardness, chemical stability, and electronic properties [1-4]. It allows the application for several electronic devices such as protective layers of magnetic recording disk. Many authors have studied the structure of amorphous carbon layer with spectroscopic analyses and postulated that sp 2 carbon clusters are dispersed in sp 3 carbon network structures. Robertson and O'Reilly studied the valence- and the conduction-band edges of amorphous carbon and concluded that sp: bonded carbon is localized in graphitic clusters which consist of four or more fused six-fold rings [1,2]. These clusters are connected by sp 3 bonded carbon. Tsai and Bogy also suggested that carbon overcoats are comprised of very fine graphite crystallites ( < 2 nm) which are randomly oriented in sp 3 bonding network [3]. Resonance Raman spectra are commonly used for the characterization of amorphous carbon films because the " Fax:
+
81-45460-2323; e-maih [email protected];co.jp.
0040-6090/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0040-6090(97)00255-1
resonance enhancement allows high sensitivity for thin layers. A detection limit for amorphous carbon film was estimated to 1 nm [5]. Broad Raman bands give information on the microscopic structure of amorphous carbon. Empirical band fitting has been applied to analyze Raman spectrum. Especially, two characteristic bands, that is, the G line at 1580 cm - I which is related to a strong Raman active E2g line of large single-crystalline graphite and the D line at 1355 cm -1 which is connected with the A i g disorder mode, are applied to identify amorphous carbon films such as sputtered carbon and diamond-like carbon. An empirical relation between the relative intensity of the D to G lines and the graphitic crystallite size has been obtained [6]. The correlation between mechanical properties such as the wear rate of sputtered carbon overcoats for thin film disk media and the ratio of the area of the D and G bands was also studied. It was reported that Raman spectroscopy revealed no significant differences in the band shapes related to the bonding characteristics of the carbon overlayers formed on the good and poor durability discs [7-13]. Ramsteiner and Wagner have studied resonant Raman
18
S. Matsunuma / Thin Solid Films 306 (1997) 17-22
spectra of amorphous hydrogenated carbon films and observed a well-defined high-frequency shift of the main Raman peak with increasing exciting photon energy [14,15]. This shift has been interpreted in terms of scattering from rr-bonded carbon clusters which is resonantly enhanced for incident photon energies approaching the - 7r * resonance. Many efforts have been made toward theoretical understanding of the structure and physical property of amorphous carbon. Doyle and Dennison [16] have modeled the Raman spectrum of graphitic amorphous carbon with simple classical methods using tings as medium-range structural units without the discussion on the resonant effect. A nearly two-dimensional with a single type of atom and one dominant bond type continuous random network structure has been provided for graphitic amorphous carbon. Wang and He [17] have found that an amorphous carbon network model generated by quenching high-density high-temperature liquid carbon using tight-binding molecular-dynamics simulation contains a large fraction of tetrahedral bonding sites. Marks et al. [18] have also reported simulations of a highly tetrahedral amorphous carbon network using first principles molecular dynamics. The simulated structure consists of 65% four-fold and 35% three-fold coordinated carbon sites. Unexpected small carbon rings containing as few as three atoms have been obtained in the their model. However these models in simulations are somewhat in conflict with experimental suggestions [2,14,15] that graphite-like s p " carbon bonded clusters of four or more fused six-fold rings are interconnected by s p 3 carbon network. Actually there are few theoretical reports on the origin of resonance Raman intensity, especially on the micro structure which contributes to the Raman band by considering the resonance effect. In this study, theoretical simulation of resonance Raman spectra of amorphous carbon is reported by taking account of the resonance effect on scattering intensities through Albrecht A term mechanism with excitation by the visible light.
2. Method of calculation Yamaguchi et al. have approximately calculated the resonance Raman intensity of biphenyl negative ions by assuming a scattering tensor of Franck-Condon nature, which originates from the conversion of equilibrium geometry by the transition of visible absorption [19]. According to their treatment on Albrecht A term, theoretical intensity of a resonance Raman band of the mode i is approximately given by the following formula. I i = c o n s t a n t × A'~, --~ c o n s t a n t
3
× o9, (AQ~)
2
(1)
where A,~ is a single tensor component which gives a
Modeling of ohromophore ]
t Calculation on electronic excited state
Normal COordinatecalculation
Oscillator strength Atomic displacement dur ng the electronc trans tion
L matrix V bratlonal frequency
Calculation of relative Raman intensity Fig. 1. Calculation flow of resonance Raman spectra.
significant contribution to the Raman intensity under the present resonance condition, and o9~ is the fundamental frequency of the molecule. AQ i is obtained by projecting the atomic displacements through the electronic transition, which is resonant with the absorption band, into normal coordinate space. Fig. 1 summarizes the calculation flow of resonance Raman spectra. Some models which were candidates for micro structure of amorphous carbon were considered. These models were structurally optimized by Parametric Method 3 (PM3) method of the MOPAC program package [20] in which the convergence criteria of Self-Consistent Field (SCF) calculations were satisfied when the change in total energy on successive iterations was less than 0.000418 kJ/mol. The PM3 method has been demonstrated to have acceptable accuracy for calculation of energy and geometry of organic compounds compared to non-empirical methods such as the ab initio method [21,22]. Oscillator strength for electronic excitation with optimized structure was calculated by Complete Neglect of Differential Overlaps (CNDO/S) method with Configuration Interaction (CI) ]23]. The atomic displacement during the excitation under visible absorption was calculated by semi-empirical C N D O / S method with 25 configurational interactions of one electron excitation. The matrix of the Cartesian normal coordinate vectors (L matrix) were obtained by the PM3 method of MOPAC. The relative Raman intensity was obtained by Eq. (1). Calculated Raman intensity was transferred to the area intensity of the band with the Gaussian band shape. Simulated resonance Raman spectrum was obtained by the summation of those Gaussian bands. It is well known that calculated vibrational frequency and transition energy are a little bit larger than observed values by 10 to 15% because the M e calculation neglects electroncorrelation and anhalanonicity [24]. Therefore calculated values have been commonly scaled by some factors. The author also scaled vibrational frequency by a factor of 0.86 and electronic transition energy by a factor of 0.85. These factors were obtained by the comparison between calculated and observed values on common molecules such as benzene and biphenyl. All calculations were performed on a Silicon Graphics IRIS Indigo workstation.
S. Matsunuma / T h i n Solid Films 306 (1997) J7-22
sp3
3. Results and discussions
bond
]9 H
~
Aromatic sp2 bond
);3 ~ "
3.1. Models for amoq)hous carbon chromophore Many authors have predicted the amorphous carbon model in which clustered benzene rings consisting of sp'carbon are dispersed in sp 3 carbon networks [1-3]. Fig. 2 shows chromophore models of anaorphous carbon in this study for simulation of Raman spectra. These models were considered by referring to previously proposed structures of network models with different sp3/sp ~- ratios [25]. They are called P0, P1, P2, P4 and P6 hereafter, according to their number of benzene rings. All models have around thirty atoms so that every model has ahnost the same number of vibrational modes. Table 1 summarizes their physical characters. P0 is the only model which has one double bond and no benzene ring in a S/")3 carbon framework. These models have more hydrogen atoms compared to experimental data [25] because hydrogen works as a terminator on presented models. It is supposed that rich hydrogen-carbon bonds hardly affect resonance Raman spectra because CH bond has little ~" electron character and has little contribution to resonance effect in the excitation with visible light. In addition, vibrational potentials of CH bond and CC bond are well separated due to the difference in their mass and bond strength. For example, the frequency of CH bond stretching is almost twice that of CC bond stretching. Potential energy distribution on the CC bond stretching modes which appear below 2000 c m - 1 also shows that the CH stretching coordinates have little contribution. Fig. 3 shows simulated resonance Raman spectra of P0, P1, P2, P4 and P6 models. The P6 and P4 model had absorption lines in the visible region and gave Raman spectra with a peak around 1580 cm -1 and a shoulder at 1350 to 1400 cm -t. These characters are similar to measured Raman spectrum of anaorphous carbon excited with a visible laser with photon energy of 2.41 or 2.54 eV [3,7,9-13]. The P1 model also provided a spectrum similar to those of the P4 and P6 models. But P1 has no absorption lines in the visible region and has the least chance of getting the resonance effect with excitation by visible light. Accordingly these results postulated that condensed aromatic models which have four to six benzene
Aliphati6
~_
DO
Pl
P4
C 10H20 C12HI~, CI.,HI6 CIsHI,, C2,Hj,"
30 28 30 32 34
4.0 0.5 0.4 0.1 0
P6
Fig. 2. Chromophore models of amorphous carbon for simulation of resonance Raman spectra.
rings are suitable to represent observed resonance Raman spectra excited in the visible region less than 3 eV. A comparison of these simulated spectra with experimental data which were obtained by varying the incident photon energies would give more interesting remarks. It has been reported that the Raman spectra of hydrogenated amorphous carbon exhibit a pronounced high-frequency shift of the main Raman peak when the incident photon energy increases from 2.2 up to 3.5 eV [14,15]. The relative intensity of the low-frequency shoulder at ~ 1300 cm-1 has been decreased for photon energies up to 3.5 eV. Wagner et al. [15] have assumed the lineshapes for the two individual contributions from phase 1 and phase 2. The scattering efficiency of phase 2 contributing to the high-frequency portion of the total Raman spectrum has been considered to be strongly resonant for photon energies in the range 2.2-3.5 eV. The Raman scattering efficiency of phase 1, in contrast, which contributes to the low-frequency portion has to be assumed to be much less resonant in the above range of photon energies. Simulated cluster models in the present study are supposed to be good examples for the microstructures of phase 1 and phase 2 in their assumption. P6 and P4 have the line shape with a peak around 1580 cm -I and the low-frequency shoulder under the resonance with the photon energy less than 3.1 eV. These features are consistent
Table 1 Formula and the characters of chromophoremodels for simulation of resonance Raman spectra Notation Formula Number sp3/sp 2 Number of of atoms carbon ratio benzene rings P0 PI P2 P4 P6
P2
0 1 2 4 6
Calculated lowest allowed electronic transition (eV) 4.86 4.41 3.77 3.06 2.67
S. Matsunuma / Thin Solid Films 306 (] 997) 17-22
20
25o
rr~llrtliptPi+ir,p
500-
450.
,
~
Resonance energy= 2.67eV
400.
200 >, 150 I))
loo-
"7. 350 3.06eV = 300.
E t~
n-
250.
50I L I I
3.77eV
200. 150,
4.41eV
100.
501_~ 2000
PO
4,86eV
1600 1200 Ramanshi~ (cm4)
Fig, 3. Simulated resonance Raman spectra of P0, P1, P2, P4, and P6 models.
(c) Mode 73 1387 cm -1
(b) Mode 79 1537 cm -1
(a) Mode 84 1582 cm -1 Fig. 4. Mass-weighted atomic displacements of Raman modes with large intensity around 1580 cm -I and 1350 cm -I of the P6 model. Carbon and hydrogen atoms are indicated by large and small circles, respectively. Mass-weighted atomic displacements are denoted by bold arrows. The amplitude of them is scaled i50 times for clarity.
2000
L I
I ~ I d L + I + I
1600
~ I I
I
1200
Raman shift (crn1) Fig. 5. Simulated resonance Raman spectra of P6 substituted by methyl group. Resonant energies are P6: 2.67, P6ml: 2.67, P6m2: 2.65, and P6m4:2.62 eV, respectively.
with the spectroscopic view of phase 1. On the other hand P0 has the position of the main peak at slightly higher frequency and no shoulder with higher resonant energy comparing to P6 and P4. This outlook agrees with the aspect of phase 2. Fig. 4 illustrates calculated mass-weighted atomic displacements of three Raman modes with large intensity around 1580 cm -1 (G band) and 1350 cm - t (D band) of the P6 model, in this figure the large and small circles indicate carbon and hydrogen atom, respectively. The bold arrows represent atomic displacements. Their lengths are expanded 150 times as large as the actual amplitudes for clarity. It is easily recognized that movement of carbon atoms is large comparing to that of hydrogen. These displacements show that these vibrations are assignable to carbon-carbon bond stretching mode or bending mode of carbon skeleton. The mode 84 (a) in Fig. 4 which had the frequency in the G band region [3] gave similar atomic displacements as the Raman-active E2g m o d e of graphite [1]. The mode 79 (b) with a little bit weaker intensity and lower frequency compared to that of the mode 84 also indicated E2g+like ?tomic displacements. These results suggested that observed G band is originated from many vibrational modes of these condensed aromatic chromophores with induced and deformed symmetry from graphite. The mode 73 (c), which has the frequency in the shoulder region (D bond) [3], has partly similar atomic displacements as the A, g disorder mode of graphite [ 1]. These calculated atomic displacements support the consideration on Raman modes of amorphous carbon by using Raman spectra of micro crystal of Highly Oriented Pyrolytic Graphite (HOPG) [3]. Calculated direction of the electronic transition moment for the first allowed excitation was parallel to the longer axis in the P6 molecule. The reason why the mode 84 of the P6 model gets stronger resonance effect compared to the mode 73 is that the direction of atomic displacement of the mode 84 is coincident with strong electronic transition
S, Matstmuma / Thin Solid Films 3 0 5 (I997) I 7 - 2 2
21
moment in the visible region, so that (AQi)2 in Eq. (1) of mode 84 has a larger value than that of mode 73. 3.2. N e m ' o r k e d sp 3 c a r b o n s t r u c t u r e a r o u n d c h r o m o p h o r e
~' >,
Many authors have suggested that there is a s p 3 carbon network around sp 2 carbon chromophore [3]. The author simulated the effect of substituted sp 3 carbon structure around chromophore on resonance Raman spectrum. Fig. 5 shows calculated resonance Raman spectra of the P6 model, P6 substituted by one methyl group (P6rn 1), substituted by two methyl (P6m2), and substituted by four methyl (P6m4). Calculated line shapes in Fig. 5 are quite similar except for a little difference in the ratio of G and D band intensity. These results suggest that the sp 3 carbon structure which surrounds s p : carbon chromophore hardly affects on the line shapes of resonance Raman spectra. In other words the origin of Raman spectra of amorphous carbon under the condition of strong resonance is mainly attributed to sp ~carbon cluster. Many reports concluded that resonance Raman spectra are not very sensitive with wear character [7-9]. The present results in Fig. 5 on the inertness of sp "~ carbons round sp 2 carbon cluster on resonance Raman spectra and previously reported results [7-9] on the relation between wear character and resonance Raman spectra postulate that delicate differences on the wearing behavior depend on the morphology of a carbon fihn or the structure of sp 3 carbon network rather than the sp 2 cluster structure. 3.3. P o l y e n e s t r u c t u r e
Polyene structure is non-aromatic and one of large 7r electron-conjugated systems, which has been considered to be a candidate for sp 2 carbon chromophore [1,2]. Resonance Raman spectra of polyene structure in Fig. 6, which
PE6 150-
e-
•-
t--
PE5 lOO-
E r'r"
PE4 50-
PE3 0 2000
1600
1200
Raman shift (cm1) Fig. 7. Simulated resonance Raman spectra of polyene structures. Resonant energies are PE6: 3.05, PE5: 3.07, PE4: 3,13, and P E 3 : 4 . 3 5 eV, respectively.
have strong resonance effects with the excitation in the visible region, were also simulated. Obtained spectra in Fig. 7 show that polyene moiety gave an only resonant line of CC bond streiching mode which appeared at 1590 to 1640 cm -1 . These calculated line shapes completely differ from observed spectra of amorphous carbon in the excitation with the incident photon energy of 2.41 or 2.54 eV [3,7,9-13]. But recently reported photon-energy-dependent effects in Raman spectra of amorphous carbon show a high-frequency shift from 1500 cm -1 to 1600 cm -1 of the main Raman peak and a decrease of the intensity of the low-frequency shoulder at ~ 1300 cm -1 relative to the main peak for photon energies increasing up to 3.5 eV [15]. As shown in Fig. 7, a slight high-frequency shift of the Raman peak of polyenes with increasing photon energy is consistent with the above reported observation. Although lower melting points of polyene molecules than of condensed aromatics [26], the possibility that polyene structure is one of sp ~- chromophores in amorphous carbon can not be eliminated in consideration of these spectral features.
4. Conclusion
sp3
PE3
PE4
bond
s
2"
PE5 PE6 Fig. 6. Calculatedpolyene structures.
Simulations of resonance Raman spectra of chromophore models for amorphous carbon were carried out in consideration of resonant mechanism through Albrecht A term. Condensed aromatic clusters which contained four to six benzene rings gave similar band shape with resonant energies less than 3.1 eV as previously reported spectra which were observed by the excitation with a visible (2.41 or 2.54 eV) laser and were considered to be a portion of the origin of resonance Raman spectra of amorphous carbon. The other portion of the origin was postulated to be ~mall sp 2 cluster which was simulated to show a slight high-frequency shift of the main Raman peak with higher incident energy compared to the above fused aromatics.
22
S. Matsunuma / Thin Solid Fihns 306 (1997) 17-22
The relationship between the excitation energies and the band shape of calculated resonance Raman spectra fairly reproduced the reported dependence of the incident photon energy for the spectral feature of the observed Raman spectra. Attached sp 3 carbon round s p 2 carbon chromophore little affected on calculated resonance Raman spectra. These results suggest that it is difficult to detect sp 3 carbon network round sp 2 cluster with resonance Raman spectroscopy excited with a visible laser.
Acknowledgements The author is grateful to Dr. Yuzuru Hosoe, Dr. Yoshihiro Shiroishi, and Dr. Heigo Ishihara for their helpful discussion and encouragement.
References [I] [2] [3] [4]
J. Robertson, Adv. Phys. 35 (1986) 3t7. J. Robertson, E.P. O'Reilly, Phys. Rev. B 35 (1987) 2946. H. Tsai, D.B. Bogy, J. Vac. Sci. Technol. A A5 (1987) 3287. B. Bhushan, Tribology and Mechanics of Magnetic Storage Devices, Springer-Verlag, New York, 1990, p. 634. [5] J.W. Ager UI, IEEE Trans. Mag. 29 (1993) 259. [6] F. Tuinstra, J.L. Koenig, J. Chem. Phys. 53 (1970) 1126. [7] S. Smith, P. Mee, M. Smalten, K. Merchant, Tribology and Mechanics of Magnetic Storage Systems, rot. 4, SP-26, Soc. Tribol. Lubr. Eng., Park Ridge, 1989, p. 93.
[8] E.H. Lee, D.M. ttembree Jr., G.R. Ran, L.K. Mansur, Phys. Rev. B 48 (1993) 15540. ~9] C.-J. Lu. D.B. Bogy, S.S. Rosenbtum, G.J. Tessmer, Thin Solid Films 268 (1995) 83. [10] B. Marchon, N. Heiman, M.R. Khan, A. Lautie, J.W. Ager III, D.K. Veirs, J. Appl. Phys. 69 (199t) 5748. [11] T.J. Dines, D. Tither, A. Dehbi, A. Matthews, Carbon 29 (1991) 225. [12] M. Yoshikawa, N. Nagai, M. Matsuki, H. Fukuda, G. Katagiri, H. lshida, A. Ishitani, I. Nagai, Phys. Rev. B 46 (1992) 7169. [t3] J.E. gaunt, L. DuPlessis, Tribol. Trans. 36 (t993) 19. [14] M. Ramsteiner, J. Wagner, Appl, Phys. Lett. 51 (I987) 1355. [15] J. Wagner, M. Ramsteiner, Ch. Wild, P. Koidl, Phys. Rev. B40 (1989) 1817. [16] T.E. Doyle, J.R. Dennison, Phys. Rev. B51 (1995) 196. [17] C.Z. Wang, K.M. Ho, Phys. Rev. Lett. 71 (1993) 1184. [18] N.A. Marks, D.R. McKenzie, B.A. Paitthorpe, M. Bernasconi, M. Parrinelto, Phys. Rev. Lett. 76 (1996) 768. [19] S. yamaguchi, N. Yoshimizu, S. Maeda, J. Phys. Chem. 82 (1978) t078. [20] MOPAC Ver. 6 by Jd. Stewart, Quantum Chemistry Program Exchange (QCPE) #455; Ver. 6.01 by T. Hirano, JCPE Newsletter, 2 (1991) 26. [21] J.J.P. Stewart, J. Comp. Chem. i0 (t989) 209. [22] J.J.P, Stewart, J. Comp. Chem. 10 (1989) 221. [23] R. Pariser~ J. Chem. Phys. 24 (1956) 250. [24] J. Pacansky, W. Koch, M.D. Miller, J. Am. Chem. Soc. 113 (1991) 317. [25] J.C. Angus, Y. Wang, R.W. Hoffman, New Diamond Science and Technology, Material Research Soc., Pittsburg, 1991, p. 1i. [26] Z. Rappopnrt, Compiled, CRC Handbook of Tables for Organic Compound Identification, The Chemical Rubber, Cleveland, 1967, p. 12.
Thin Solid Fihns 306 (1997) 17-22
Theoretical simulation of resonance Raman bands of amorphous carbon Satoshi Matsunuma Hitachi, Central Research Laboratory, 292 Yoshida-cho, Torsuka-ku, Yokohama 244, Japan
Received 20 November 1996; accepted 23 April 1997
Abstract Simulations of resonance Raman spectra of chromopbore models for amorphous carbon were carried out in consideration of resonance enhancement by using the Albrecht A term. Relative resonance Raman intensity of each vibrational mode was calculated with the electronic transition analysis by a Complete Neglect of Differential Overlaps (CNDO]S~ method including configuration interaction and the vibrational analysis by a Parametric Method 3 (PM3) method. Condensed aromatic cluster containing four to six benzene rings gave similar spectra as reported experimental spectra excited with the incident photon energy of 2.41 or 2.54 eV. A slight high-frequency shift of the main peak of Raman spectrum was simulated on sp 2 clusters of smaller size which have higher resonance energies compared to the above condensed aromatic clusters. These simulated results were cortsistent with reported dependence of incident photon energies for the band shape of Raman spectra and suggested that a complex of many sizes of sp ~ clusters which have six or less benzenes is the origin of resonance Raman spectra of amorphous carbon. Attached sp 3 carbon round sp 2 carbon chromophore showed little effect on the band shape of calculated resonance Raman spectra. It was postulated that information on sp 3 network structure hardly appears in resonance Raman spectra compared to sp 2 cluster when a visible light is used for the excitation. © 1997 Elsevier Science S.A. Ke)words: Raman scattering; Computer simulation; Amorphous materials; Carbon
1. Introduction There is no doubt that amorphous carbon film is a useful material because of its hardness, chemical stability, and electronic properties [1-4]. It allows the application for several electronic devices such as protective layers of magnetic recording disk. Many authors have studied the structure of amorphous carbon layer with spectroscopic analyses and postulated that sp 2 carbon clusters are dispersed in sp 3 carbon network structures. Robertson and O'Reilly studied the valence- and the conduction-band edges of amorphous carbon and concluded that sp: bonded carbon is localized in graphitic clusters which consist of four or more fused six-fold rings [1,2]. These clusters are connected by sp 3 bonded carbon. Tsai and Bogy also suggested that carbon overcoats are comprised of very fine graphite crystallites ( < 2 nm) which are randomly oriented in sp 3 bonding network [3]. Resonance Raman spectra are commonly used for the characterization of amorphous carbon films because the " Fax:
+
81-45460-2323; e-maih [email protected];co.jp.
0040-6090/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0040-6090(97)00255-1
resonance enhancement allows high sensitivity for thin layers. A detection limit for amorphous carbon film was estimated to 1 nm [5]. Broad Raman bands give information on the microscopic structure of amorphous carbon. Empirical band fitting has been applied to analyze Raman spectrum. Especially, two characteristic bands, that is, the G line at 1580 cm - I which is related to a strong Raman active E2g line of large single-crystalline graphite and the D line at 1355 cm -1 which is connected with the A i g disorder mode, are applied to identify amorphous carbon films such as sputtered carbon and diamond-like carbon. An empirical relation between the relative intensity of the D to G lines and the graphitic crystallite size has been obtained [6]. The correlation between mechanical properties such as the wear rate of sputtered carbon overcoats for thin film disk media and the ratio of the area of the D and G bands was also studied. It was reported that Raman spectroscopy revealed no significant differences in the band shapes related to the bonding characteristics of the carbon overlayers formed on the good and poor durability discs [7-13]. Ramsteiner and Wagner have studied resonant Raman
18
S. Matsunuma / Thin Solid Films 306 (1997) 17-22
spectra of amorphous hydrogenated carbon films and observed a well-defined high-frequency shift of the main Raman peak with increasing exciting photon energy [14,15]. This shift has been interpreted in terms of scattering from rr-bonded carbon clusters which is resonantly enhanced for incident photon energies approaching the - 7r * resonance. Many efforts have been made toward theoretical understanding of the structure and physical property of amorphous carbon. Doyle and Dennison [16] have modeled the Raman spectrum of graphitic amorphous carbon with simple classical methods using tings as medium-range structural units without the discussion on the resonant effect. A nearly two-dimensional with a single type of atom and one dominant bond type continuous random network structure has been provided for graphitic amorphous carbon. Wang and He [17] have found that an amorphous carbon network model generated by quenching high-density high-temperature liquid carbon using tight-binding molecular-dynamics simulation contains a large fraction of tetrahedral bonding sites. Marks et al. [18] have also reported simulations of a highly tetrahedral amorphous carbon network using first principles molecular dynamics. The simulated structure consists of 65% four-fold and 35% three-fold coordinated carbon sites. Unexpected small carbon rings containing as few as three atoms have been obtained in the their model. However these models in simulations are somewhat in conflict with experimental suggestions [2,14,15] that graphite-like s p " carbon bonded clusters of four or more fused six-fold rings are interconnected by s p 3 carbon network. Actually there are few theoretical reports on the origin of resonance Raman intensity, especially on the micro structure which contributes to the Raman band by considering the resonance effect. In this study, theoretical simulation of resonance Raman spectra of amorphous carbon is reported by taking account of the resonance effect on scattering intensities through Albrecht A term mechanism with excitation by the visible light.
2. Method of calculation Yamaguchi et al. have approximately calculated the resonance Raman intensity of biphenyl negative ions by assuming a scattering tensor of Franck-Condon nature, which originates from the conversion of equilibrium geometry by the transition of visible absorption [19]. According to their treatment on Albrecht A term, theoretical intensity of a resonance Raman band of the mode i is approximately given by the following formula. I i = c o n s t a n t × A'~, --~ c o n s t a n t
3
× o9, (AQ~)
2
(1)
where A,~ is a single tensor component which gives a
Modeling of ohromophore ]
t Calculation on electronic excited state
Normal COordinatecalculation
Oscillator strength Atomic displacement dur ng the electronc trans tion
L matrix V bratlonal frequency
Calculation of relative Raman intensity Fig. 1. Calculation flow of resonance Raman spectra.
significant contribution to the Raman intensity under the present resonance condition, and o9~ is the fundamental frequency of the molecule. AQ i is obtained by projecting the atomic displacements through the electronic transition, which is resonant with the absorption band, into normal coordinate space. Fig. 1 summarizes the calculation flow of resonance Raman spectra. Some models which were candidates for micro structure of amorphous carbon were considered. These models were structurally optimized by Parametric Method 3 (PM3) method of the MOPAC program package [20] in which the convergence criteria of Self-Consistent Field (SCF) calculations were satisfied when the change in total energy on successive iterations was less than 0.000418 kJ/mol. The PM3 method has been demonstrated to have acceptable accuracy for calculation of energy and geometry of organic compounds compared to non-empirical methods such as the ab initio method [21,22]. Oscillator strength for electronic excitation with optimized structure was calculated by Complete Neglect of Differential Overlaps (CNDO/S) method with Configuration Interaction (CI) ]23]. The atomic displacement during the excitation under visible absorption was calculated by semi-empirical C N D O / S method with 25 configurational interactions of one electron excitation. The matrix of the Cartesian normal coordinate vectors (L matrix) were obtained by the PM3 method of MOPAC. The relative Raman intensity was obtained by Eq. (1). Calculated Raman intensity was transferred to the area intensity of the band with the Gaussian band shape. Simulated resonance Raman spectrum was obtained by the summation of those Gaussian bands. It is well known that calculated vibrational frequency and transition energy are a little bit larger than observed values by 10 to 15% because the M e calculation neglects electroncorrelation and anhalanonicity [24]. Therefore calculated values have been commonly scaled by some factors. The author also scaled vibrational frequency by a factor of 0.86 and electronic transition energy by a factor of 0.85. These factors were obtained by the comparison between calculated and observed values on common molecules such as benzene and biphenyl. All calculations were performed on a Silicon Graphics IRIS Indigo workstation.
S. Matsunuma / T h i n Solid Films 306 (1997) J7-22
sp3
3. Results and discussions
bond
]9 H
~
Aromatic sp2 bond
);3 ~ "
3.1. Models for amoq)hous carbon chromophore Many authors have predicted the amorphous carbon model in which clustered benzene rings consisting of sp'carbon are dispersed in sp 3 carbon networks [1-3]. Fig. 2 shows chromophore models of anaorphous carbon in this study for simulation of Raman spectra. These models were considered by referring to previously proposed structures of network models with different sp3/sp ~- ratios [25]. They are called P0, P1, P2, P4 and P6 hereafter, according to their number of benzene rings. All models have around thirty atoms so that every model has ahnost the same number of vibrational modes. Table 1 summarizes their physical characters. P0 is the only model which has one double bond and no benzene ring in a S/")3 carbon framework. These models have more hydrogen atoms compared to experimental data [25] because hydrogen works as a terminator on presented models. It is supposed that rich hydrogen-carbon bonds hardly affect resonance Raman spectra because CH bond has little ~" electron character and has little contribution to resonance effect in the excitation with visible light. In addition, vibrational potentials of CH bond and CC bond are well separated due to the difference in their mass and bond strength. For example, the frequency of CH bond stretching is almost twice that of CC bond stretching. Potential energy distribution on the CC bond stretching modes which appear below 2000 c m - 1 also shows that the CH stretching coordinates have little contribution. Fig. 3 shows simulated resonance Raman spectra of P0, P1, P2, P4 and P6 models. The P6 and P4 model had absorption lines in the visible region and gave Raman spectra with a peak around 1580 cm -1 and a shoulder at 1350 to 1400 cm -t. These characters are similar to measured Raman spectrum of anaorphous carbon excited with a visible laser with photon energy of 2.41 or 2.54 eV [3,7,9-13]. The P1 model also provided a spectrum similar to those of the P4 and P6 models. But P1 has no absorption lines in the visible region and has the least chance of getting the resonance effect with excitation by visible light. Accordingly these results postulated that condensed aromatic models which have four to six benzene
Aliphati6
~_
DO
Pl
P4
C 10H20 C12HI~, CI.,HI6 CIsHI,, C2,Hj,"
30 28 30 32 34
4.0 0.5 0.4 0.1 0
P6
Fig. 2. Chromophore models of amorphous carbon for simulation of resonance Raman spectra.
rings are suitable to represent observed resonance Raman spectra excited in the visible region less than 3 eV. A comparison of these simulated spectra with experimental data which were obtained by varying the incident photon energies would give more interesting remarks. It has been reported that the Raman spectra of hydrogenated amorphous carbon exhibit a pronounced high-frequency shift of the main Raman peak when the incident photon energy increases from 2.2 up to 3.5 eV [14,15]. The relative intensity of the low-frequency shoulder at ~ 1300 cm-1 has been decreased for photon energies up to 3.5 eV. Wagner et al. [15] have assumed the lineshapes for the two individual contributions from phase 1 and phase 2. The scattering efficiency of phase 2 contributing to the high-frequency portion of the total Raman spectrum has been considered to be strongly resonant for photon energies in the range 2.2-3.5 eV. The Raman scattering efficiency of phase 1, in contrast, which contributes to the low-frequency portion has to be assumed to be much less resonant in the above range of photon energies. Simulated cluster models in the present study are supposed to be good examples for the microstructures of phase 1 and phase 2 in their assumption. P6 and P4 have the line shape with a peak around 1580 cm -I and the low-frequency shoulder under the resonance with the photon energy less than 3.1 eV. These features are consistent
Table 1 Formula and the characters of chromophoremodels for simulation of resonance Raman spectra Notation Formula Number sp3/sp 2 Number of of atoms carbon ratio benzene rings P0 PI P2 P4 P6
P2
0 1 2 4 6
Calculated lowest allowed electronic transition (eV) 4.86 4.41 3.77 3.06 2.67
S. Matsunuma / Thin Solid Films 306 (] 997) 17-22
20
25o
rr~llrtliptPi+ir,p
500-
450.
,
~
Resonance energy= 2.67eV
400.
200 >, 150 I))
loo-
"7. 350 3.06eV = 300.
E t~
n-
250.
50I L I I
3.77eV
200. 150,
4.41eV
100.
501_~ 2000
PO
4,86eV
1600 1200 Ramanshi~ (cm4)
Fig, 3. Simulated resonance Raman spectra of P0, P1, P2, P4, and P6 models.
(c) Mode 73 1387 cm -1
(b) Mode 79 1537 cm -1
(a) Mode 84 1582 cm -1 Fig. 4. Mass-weighted atomic displacements of Raman modes with large intensity around 1580 cm -I and 1350 cm -I of the P6 model. Carbon and hydrogen atoms are indicated by large and small circles, respectively. Mass-weighted atomic displacements are denoted by bold arrows. The amplitude of them is scaled i50 times for clarity.
2000
L I
I ~ I d L + I + I
1600
~ I I
I
1200
Raman shift (crn1) Fig. 5. Simulated resonance Raman spectra of P6 substituted by methyl group. Resonant energies are P6: 2.67, P6ml: 2.67, P6m2: 2.65, and P6m4:2.62 eV, respectively.
with the spectroscopic view of phase 1. On the other hand P0 has the position of the main peak at slightly higher frequency and no shoulder with higher resonant energy comparing to P6 and P4. This outlook agrees with the aspect of phase 2. Fig. 4 illustrates calculated mass-weighted atomic displacements of three Raman modes with large intensity around 1580 cm -1 (G band) and 1350 cm - t (D band) of the P6 model, in this figure the large and small circles indicate carbon and hydrogen atom, respectively. The bold arrows represent atomic displacements. Their lengths are expanded 150 times as large as the actual amplitudes for clarity. It is easily recognized that movement of carbon atoms is large comparing to that of hydrogen. These displacements show that these vibrations are assignable to carbon-carbon bond stretching mode or bending mode of carbon skeleton. The mode 84 (a) in Fig. 4 which had the frequency in the G band region [3] gave similar atomic displacements as the Raman-active E2g m o d e of graphite [1]. The mode 79 (b) with a little bit weaker intensity and lower frequency compared to that of the mode 84 also indicated E2g+like ?tomic displacements. These results suggested that observed G band is originated from many vibrational modes of these condensed aromatic chromophores with induced and deformed symmetry from graphite. The mode 73 (c), which has the frequency in the shoulder region (D bond) [3], has partly similar atomic displacements as the A, g disorder mode of graphite [ 1]. These calculated atomic displacements support the consideration on Raman modes of amorphous carbon by using Raman spectra of micro crystal of Highly Oriented Pyrolytic Graphite (HOPG) [3]. Calculated direction of the electronic transition moment for the first allowed excitation was parallel to the longer axis in the P6 molecule. The reason why the mode 84 of the P6 model gets stronger resonance effect compared to the mode 73 is that the direction of atomic displacement of the mode 84 is coincident with strong electronic transition
S, Matstmuma / Thin Solid Films 3 0 5 (I997) I 7 - 2 2
21
moment in the visible region, so that (AQi)2 in Eq. (1) of mode 84 has a larger value than that of mode 73. 3.2. N e m ' o r k e d sp 3 c a r b o n s t r u c t u r e a r o u n d c h r o m o p h o r e
~' >,
Many authors have suggested that there is a s p 3 carbon network around sp 2 carbon chromophore [3]. The author simulated the effect of substituted sp 3 carbon structure around chromophore on resonance Raman spectrum. Fig. 5 shows calculated resonance Raman spectra of the P6 model, P6 substituted by one methyl group (P6rn 1), substituted by two methyl (P6m2), and substituted by four methyl (P6m4). Calculated line shapes in Fig. 5 are quite similar except for a little difference in the ratio of G and D band intensity. These results suggest that the sp 3 carbon structure which surrounds s p : carbon chromophore hardly affects on the line shapes of resonance Raman spectra. In other words the origin of Raman spectra of amorphous carbon under the condition of strong resonance is mainly attributed to sp ~carbon cluster. Many reports concluded that resonance Raman spectra are not very sensitive with wear character [7-9]. The present results in Fig. 5 on the inertness of sp "~ carbons round sp 2 carbon cluster on resonance Raman spectra and previously reported results [7-9] on the relation between wear character and resonance Raman spectra postulate that delicate differences on the wearing behavior depend on the morphology of a carbon fihn or the structure of sp 3 carbon network rather than the sp 2 cluster structure. 3.3. P o l y e n e s t r u c t u r e
Polyene structure is non-aromatic and one of large 7r electron-conjugated systems, which has been considered to be a candidate for sp 2 carbon chromophore [1,2]. Resonance Raman spectra of polyene structure in Fig. 6, which
PE6 150-
e-
•-
t--
PE5 lOO-
E r'r"
PE4 50-
PE3 0 2000
1600
1200
Raman shift (cm1) Fig. 7. Simulated resonance Raman spectra of polyene structures. Resonant energies are PE6: 3.05, PE5: 3.07, PE4: 3,13, and P E 3 : 4 . 3 5 eV, respectively.
have strong resonance effects with the excitation in the visible region, were also simulated. Obtained spectra in Fig. 7 show that polyene moiety gave an only resonant line of CC bond streiching mode which appeared at 1590 to 1640 cm -1 . These calculated line shapes completely differ from observed spectra of amorphous carbon in the excitation with the incident photon energy of 2.41 or 2.54 eV [3,7,9-13]. But recently reported photon-energy-dependent effects in Raman spectra of amorphous carbon show a high-frequency shift from 1500 cm -1 to 1600 cm -1 of the main Raman peak and a decrease of the intensity of the low-frequency shoulder at ~ 1300 cm -1 relative to the main peak for photon energies increasing up to 3.5 eV [15]. As shown in Fig. 7, a slight high-frequency shift of the Raman peak of polyenes with increasing photon energy is consistent with the above reported observation. Although lower melting points of polyene molecules than of condensed aromatics [26], the possibility that polyene structure is one of sp ~- chromophores in amorphous carbon can not be eliminated in consideration of these spectral features.
4. Conclusion
sp3
PE3
PE4
bond
s
2"
PE5 PE6 Fig. 6. Calculatedpolyene structures.
Simulations of resonance Raman spectra of chromophore models for amorphous carbon were carried out in consideration of resonant mechanism through Albrecht A term. Condensed aromatic clusters which contained four to six benzene rings gave similar band shape with resonant energies less than 3.1 eV as previously reported spectra which were observed by the excitation with a visible (2.41 or 2.54 eV) laser and were considered to be a portion of the origin of resonance Raman spectra of amorphous carbon. The other portion of the origin was postulated to be ~mall sp 2 cluster which was simulated to show a slight high-frequency shift of the main Raman peak with higher incident energy compared to the above fused aromatics.
22
S. Matsunuma / Thin Solid Fihns 306 (1997) 17-22
The relationship between the excitation energies and the band shape of calculated resonance Raman spectra fairly reproduced the reported dependence of the incident photon energy for the spectral feature of the observed Raman spectra. Attached sp 3 carbon round s p 2 carbon chromophore little affected on calculated resonance Raman spectra. These results suggest that it is difficult to detect sp 3 carbon network round sp 2 cluster with resonance Raman spectroscopy excited with a visible laser.
Acknowledgements The author is grateful to Dr. Yuzuru Hosoe, Dr. Yoshihiro Shiroishi, and Dr. Heigo Ishihara for their helpful discussion and encouragement.
References [I] [2] [3] [4]
J. Robertson, Adv. Phys. 35 (1986) 3t7. J. Robertson, E.P. O'Reilly, Phys. Rev. B 35 (1987) 2946. H. Tsai, D.B. Bogy, J. Vac. Sci. Technol. A A5 (1987) 3287. B. Bhushan, Tribology and Mechanics of Magnetic Storage Devices, Springer-Verlag, New York, 1990, p. 634. [5] J.W. Ager UI, IEEE Trans. Mag. 29 (1993) 259. [6] F. Tuinstra, J.L. Koenig, J. Chem. Phys. 53 (1970) 1126. [7] S. Smith, P. Mee, M. Smalten, K. Merchant, Tribology and Mechanics of Magnetic Storage Systems, rot. 4, SP-26, Soc. Tribol. Lubr. Eng., Park Ridge, 1989, p. 93.
[8] E.H. Lee, D.M. ttembree Jr., G.R. Ran, L.K. Mansur, Phys. Rev. B 48 (1993) 15540. ~9] C.-J. Lu. D.B. Bogy, S.S. Rosenbtum, G.J. Tessmer, Thin Solid Films 268 (1995) 83. [10] B. Marchon, N. Heiman, M.R. Khan, A. Lautie, J.W. Ager III, D.K. Veirs, J. Appl. Phys. 69 (199t) 5748. [11] T.J. Dines, D. Tither, A. Dehbi, A. Matthews, Carbon 29 (1991) 225. [12] M. Yoshikawa, N. Nagai, M. Matsuki, H. Fukuda, G. Katagiri, H. lshida, A. Ishitani, I. Nagai, Phys. Rev. B 46 (1992) 7169. [t3] J.E. gaunt, L. DuPlessis, Tribol. Trans. 36 (t993) 19. [14] M. Ramsteiner, J. Wagner, Appl, Phys. Lett. 51 (I987) 1355. [15] J. Wagner, M. Ramsteiner, Ch. Wild, P. Koidl, Phys. Rev. B40 (1989) 1817. [16] T.E. Doyle, J.R. Dennison, Phys. Rev. B51 (1995) 196. [17] C.Z. Wang, K.M. Ho, Phys. Rev. Lett. 71 (1993) 1184. [18] N.A. Marks, D.R. McKenzie, B.A. Paitthorpe, M. Bernasconi, M. Parrinelto, Phys. Rev. Lett. 76 (1996) 768. [19] S. yamaguchi, N. Yoshimizu, S. Maeda, J. Phys. Chem. 82 (1978) t078. [20] MOPAC Ver. 6 by Jd. Stewart, Quantum Chemistry Program Exchange (QCPE) #455; Ver. 6.01 by T. Hirano, JCPE Newsletter, 2 (1991) 26. [21] J.J.P. Stewart, J. Comp. Chem. i0 (t989) 209. [22] J.J.P, Stewart, J. Comp. Chem. 10 (1989) 221. [23] R. Pariser~ J. Chem. Phys. 24 (1956) 250. [24] J. Pacansky, W. Koch, M.D. Miller, J. Am. Chem. Soc. 113 (1991) 317. [25] J.C. Angus, Y. Wang, R.W. Hoffman, New Diamond Science and Technology, Material Research Soc., Pittsburg, 1991, p. 1i. [26] Z. Rappopnrt, Compiled, CRC Handbook of Tables for Organic Compound Identification, The Chemical Rubber, Cleveland, 1967, p. 12.