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Study of the structure of hard graphite-like amorphous carbon films by electron diffraction
Diamond and Related Materials 11 (2002) 1467–1471
Study of the structure of hard graphite-like amorphous carbon films by electron diffraction V. Kulikovskya,*, K. Metlovb, A. Kurdyumova, P. Bohaca, L. Jastrabikb a
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, P.O. Box 61, 18221 Prague 8, Czech Republic b Institute for Problems of Materials Science, Academy of Sciences of Ukraine, 3 Krzhyzhanovsky St., 03142 Kiev, Ukraine Received 21 August 2001; received in revised form 10 October 2001; accepted 29 January 2002
Abstract The structure of thin hard carbon films was investigated by transmission electron diffraction using a filter of inelastically scattered electrons. It was shown for the first time that in the amorphous graphite-like carbon films under considerable compressive stress the interplane distance d002 could be shortened down to approximately 0.300 nm. Also, substantiation was given for a simple procedure for the estimation of the first coordination sphere radius in amorphous carbon films. This radius was determined from the maximum of the corresponding diffraction halo. It was shown that this procedure gave the radius of the first coordination sphere very close to its real value for graphite-like structure but did not work so well for a diamond-like structure. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Graphite-like carbon; Amorphous film; Structure; Electron diffraction
1. Introduction High hardness of hydrogen-free carbon films is usually linked with the presence of sp3-like bonds and these films are called diamond-like. Recently, it was shown that some hard amorphous carbon films contain a high number of sp2 bonds w1–4x. The high hardness (up to 55 GPa) and elasticity (elastic recovery of 85%) of the films obtained by arc evaporation of graphite cathode within a high pressure region created by a nitrogen or helium jet in the vicinity of the arc spot were attributed to the interlinking of sp2-bonded graphene planes with sp3 bonds w1x. The source of the graphene planes was found to be carbon nanoparticles in the form of nanotubes and bucky ‘onions’ present in the plasma. Hard amorphous carbon films were prepared by Ion BeamAssisted deposition (IBAD) w3x. Indirect structural investigation indicated they are composed of a highly compressed and dense sp2 network. Hard conductive films were prepared by magnetron sputtering w2x. *Corresponding author. Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, P.O. Box 61, 18221 Prague 8, Czech Republic. Fax: q420-2-8581448. E-mail address: [email protected] (V. Kulikovsky).
In this work, we first present a direct experimental confirmation of obtaining hard compressed graphite-like films with reduced distance between the (002) graphite planes. We also present substantiation of a simple approach allowing to check whether the structure of the carbon amorphous films is graphite-like. The structure of amorphous carbon a-C and a-C:H films is usually investigated by indirect methods: Raman or infrared spectroscopy, Electron Energy Loss spectroscopy (EELS) and, more rarely, by direct diffraction ones. The use of X-ray or neutron diffraction for the investigation of thin carbon films is problematic because of the low atomic number of carbon andyor small film thickness. In view of very high intrinsic stress, it is also difficult to obtain hard carbon films thicker than 1 mm. For the investigation of thin films, the transmission electron diffraction (TED) method was used in this work. However, it is not simple to obtain the radial distribution function (RDF) directly from electron diffraction measurement and such a procedure relies on many assumptions. The essential difficulties arise from the uncertainty of accounting for the inelastically and multiple elastically scattered electrons. Also, the proper interpretation of RDFs is only possible for isotropic
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bias, (3) by carbon evaporation at floating substrate bias (for comparison). The intensity of the right-hand side of all the plots is increased for convenience. The measurements were carried out for three films for every regime. The intensity curves for films obtained in the same regime were similar each other. The different intensity of the small angle halo for the presented films indicates the existence of texture in the films. The c axis was oriented essentially parallel to the film growth direction for the films deposited at substrate bias voltage y100 V or y150 V and the main interplanar distance
Fig. 1. Schematic representation of electron diffraction from stressed amorphous carbon film.
structures. The carbon films can be anisotropic due to their texture, which is often present in the graphite-like structure. In this work, we made an attempt to analyze the TED pattern for the amorphous carbon film avoiding the aforementioned difficulties. 2. Results and discussion The structure of thin hard carbon films was investigated by transmission electron diffraction using a filter of inelastically scattered electrons. The hydrogen-free amorphous carbon films (a-C) were deposited by magnetron sputtering of a carbon target in Ar atmosphere at a pressure of 0.17–0.33 Pa. The power of the discharge was 960 W. The hard (up to 50 GPa) films with thickness of 1.5 mm were obtained on Si substrate at a substrate bias voltage of y100 or y150 V. The films deposited at floating substrate bias had a microhardness of approximately 20 GPa. The films with thickness 30– 60 nm were fabricated under the same conditions on unheated KC1 substrates, for TED experiment the substrate was then dissolved. The detailed information about experimental procedure and some properties of obtained hard carbon films will be reported elsewhere. The electron diffraction pattern of amorphous carbon film usually contains three visible haloes. (Fig. 1). The first, small angle halo appears only if the film contains fragments of graphite-like structure and corresponds to the diffraction from (002) graphite planes. The distance (d002) between these planes can be determined from Bragg’s formula: 2d002sinusnl where 2u is the scattering angle and l is the electron wavelength. Fig. 2 shows the intensity of the electron diffraction patterns I(s) as a function of ss4psinuyl for three films deposited: (1) by sputtering at substrate bias voltage y100 V, (2) by sputtering at floating substrate
Fig. 2. The intensity of the electron diffraction patterns I(s) as a function of ss4psinuyl for three films deposited: (1) by sputtering at substrate bias voltage y100 V; (2) by sputtering at floating substrate bias; (3) by carbon evaporation at floating substrate bias (for comparison). The intensity of the right-hand side of all the plots is increased for convenience.
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for this case was found to be approximately 0.295– 0.305 nm (curve 1). This distance was 0.359–0.375 nm (0.335 nm is the interlayer spacing in graphite) for a-C films obtained without ion bombardment and the intensity of the first halo was considerably lower (curve 2). The very low intensity for the film deposited by carbon evaporation without ion bombardment pointed out that the c axis in the film was oriented perpendicularly to the substrate surface. The corresponding interplanar distance was approximately 0.450–0.460 nm. The observed texture of the films (the same was observed by us and other authors for BN films, e.g. w5,6x) was a consequence of ion or fast atom bombardment where the planes with large interplanar distance were predominantly sputtered if they grow parallel to the substrate. The considerable decrease of d002 for the films obtained at ion bombardment can be explained by the highly stressed sp2 structure of our films. Such a structure was observed for bulk graphite under high pressure (see e.g. R.W. Lynch et al. w7x or a review of F.P. Bundy et al. w8x). The high pressure considerably decreased the distance between the graphite planes but did not appreciably change the in-plane distances. It was reported in w7x that the pressure increase from 0 to 10 GPa led to an inter-plane distance decrease of approximately 11%. Our data show similar dependence. The main source of pressure in our films was the intrinsic stress induced by ion bombardment. Values of intrinsic stress of approximately 8–9 GPa were obtained for a-C film with a thickness of approximately 50 nm, deposited onto Si(111) at a substrate bias of y100 V. This film was deposited simultaneously onto KCl substrate for diffraction measurements, which gave the value of d002f0.300 nm. One may suppose that the values of intrinsic stress for films deposited simultaneously on KCl and Si substrates are of the same order. After the KCl substrate was dissolved, the stress was partially released. However, the intrinsic stress level in the local film regions probably remains very high as a result of the ion bombardment and subimplantation process during film growth. Ions penetrating into the film body can lead to a local increase of film density and compressive stress and, consequently, to the formation of the observed film structure. Thus, we could observe for the first time a very dense and strong compressed structure in the graphite-like film. The possibility of the existence of such a structure for very stressed a-C films was recently discussed by R.G. Lacerda et al. w3x. On the basis of the proposed sp2 carbon structure with shortened interlayer distance, the authors of w3x explained the dependence of the plasmon energy of obtained films as a function of the energy of bombarding ions without reference to sp3 structure. Thus, the presence of the compressed graphite phase in a-C films can explain some contradictory results, whose current explanation is based on the existence of sp3
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bonds. Shortened inter-plane distances in the film were evidenced by TED for (002) planes perpendicular to the film surface, i.e. for the planes which were compressed by the intrinsic stress. Some (002) planes in aC are oriented essentially parallel to the film surface. Such planes do not contribute to the TED pattern, but can be studied with reflection electron diffraction. However, the accuracy of the data, obtained by reflection electron diffraction is very low and the X-ray diffraction is more suitable for this geometry. The existence of the (002) halo implies the existence of graphite-like clusters in the film. The question, whether all the bonds are sp2 or only some of them, remains unanswered. Below we will attempt to answer this question. The intensity distribution and the structure factor F(s) for amorphous solids or nanocrystalline powders with random orientation of nanocrystals can be obtained from the Debye scattering equation by treating each nanocrystal or cluster as a molecule w9x. This approach has a practical importance for the modeling of the structure factor of the assembly of extremely small crystallites with a strong disorder. The structure factor of amorphous solid with one kind of atom, defined as FŽs.s IŽs. yNf2y1, where I(s) is scattered intensity, F(s) is the atomic scattering factor and N is the number of atoms, can be expressed as a sum of the partial structure factors of separate coordination spheres (see, for example, w10x): FŽs.s8knksinŽsrk. ysrk where nk is the number of atoms in the k th coordination sphere, rk is the distance between atoms of k th sphere and some atom, which is chosen as the origin, ss 4psinuyl. The deviation of rk from its equilibrium value increases with the increasing number of coordination spheres, which leads to overlapping of the nearest shells. This fact is expressed by the damping factor chosen as the Gaussian function: FŽs.s8kµnksinŽsrk.expŽyAR2ks2 yr12.∂ ysrk where A is a phenomenological damping parameter. The value of As0 corresponds to ideal nanocrystals without disorder. The more disorder is present, the higher is the value of A. Increasing A leads to a rapid decrease of contributions from distant shells. This is why it is sufficient to consider the contributions of only a finite number of shells in amorphous solid. The partial structure factor for first coordination sphere is given by: FŽs.sn1sinŽsr1. ysr1 The first strong maximum (we did not consider other ones) of this function is at sr1s7.725, which corresponds to the radius of the first coordination sphere r1s
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Table 1 Calculated values of the first coordination sphere radius (r1 ) for (a) graphite and (b) diamond as a function of the number of considered coordination spheres (a) Graphite K nk rk, nm r1(As0), nm r1(As0.005) r1(As0.02) (b) Diamond K nk rk, nm r1(As0), nm r1(As0.005) r1(As0.02)
1 3 0.142 0.142 0.143 0.145
2 6 0.246 0.137 0.138 0.141
3 3 0.284 0.141 0.141 0.143
4 6 0.376 0.142 0.142 0.143
5 6 0.426 0.145 0.143 0.143
6 6 0.492 0.143 0.143 0.143
7 6 0.512 0.145 0.144 0.143
1 4 0.154 0.154 0.155 0.157
2 12 0.252 0.141 0.142 0.147
3 12 0.296 0.151 0.151 0.151
4 6 0.357 0.146 0.147 0.150
5 12 0.389 0.147 0.148 0.150
6 24 0.437 0.137 0.154 0.150
7 16 0.463 0.147 0.158 0.150
7.725ys. This value can also be obtained from the Ehrenfest equation w11x: 2rsinus1.23l Such an approach, based on the Ehrenfest equation, was recently proposed by Yu. I. Sozin w12x for the express estimation of short-range order in amorphous solids. However, the Ehrenfest equation is exactly applicable only for gas molecules with one interatomic distance. In a general case, the consideration of the contribution of other coordination spheres for amorphous solid may lead to a strong shift of this maximum and, as a consequence, to uncertainty in the determination of r1. Furthermore, we will attempt to verify how much the contribution of other coordination spheres influences the position of the maximum corresponding to r1 for graphite and diamond structures. We have calculated the values of r1 based on the coordination number (nk) and interatomic distances (rk) for the nearest coordination spheres of graphite and diamond (Table 1). We took into account that there is disorder between layers in graphite structure and used only intralayer values of rk for the calculations. The values of r1 were calculated by the formula 7.725ys, where s corresponds to the position of the maximum from the first coordination sphere (third halo in Figs. 1 and 2). This position shifted consistently when contributions from two, three, etc. coordination spheres were taken into account. The calculation was performed for ˚ 2. Only 7 first spheres three values of A: 0, 0.005, 0.02 A were taken into account. This corresponds to a cluster size of approximately 1.0 nm. This size corresponds to the short-order range that is usually inferred from the RDF data w13,14x. One could see that r1 for graphite structure was close to the real value and at increasing disorder (increase of A) the difference between the real r1s0.142 nm and the calculated value becomes smaller. This tendency is also present for the diamond structure.
However, the scatter of the calculated values of r1 around the real one (0.154 nm) is significantly larger. These estimates are valid only for small clusters. However, taking additional coordination spheres into account influences the calculated position of the peak only negligibly. This is due to structural disorder as facilitated by the damping factor. Thus, if the first diffraction halo corresponds to reflection from (002) graphitic planes, one may conclude that such film contains graphite-like clusters. This does not mean, however, that the film does not contain diamond-like bonds. If the measured radius of the first coordination sphere is equal to 0.141–0.143 nm, one may conclude that the graphite-like structure is dominant in such a film. If this value is larger than 0.143 nm, it means that this structure may contain diamond-like bonds. All our films deposited onto KCl substrates, both with and without ion bombardment, had values of r1s 0.140–0.142 nm, but the d002 distance varied significantly. The different intensity of the third halo for considered films (Fig. 2) correlates with that for the first halo and is a manifestation of the film texture. The higher intensity of the first halo, the lower that for the third one. Thus, the films obtained were graphite-like, which was also indicated by their relatively high electrical conductivity (these data will be published elsewhere). It should be noted that the values of r1 for amorphous carbon films inferred from the RDF data and reported in literature differ from one another w13–17x. This may be due to the different structure andyor (for films obtained by the same method w15–17x) because of the aforementioned difficulties in RDF calculation. For example, for the a-C films deposited by arc evaporation, the r1 was reported to be 0.151 w15x, 0.143 w16x and 0.148 nm w17x. Let us estimate the sensitivity of the proposed method if the graphite-like film contains only small amount of atoms with sp3 bonds. We determined r1 of such a
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case one can consider that sp3 bonds are present in the film. 3. Conclusions
Fig. 3. Dependence of the first coordination sphere radius r1 on the fraction (x) of sp3 atoms in the mixture of graphite and diamond for two variants of F(s) calculation (see text): 1) F(s)s(1yx) F(graphite, 7 spheres)qxF(diamond, 1 sphere), 2) F(s)s (1yx) F(graphite, 7 spheres)qxF(diamond, 7 spheres).
mixture as a function of the fraction (x) of sp3 atoms. ˚ 2 and for This calculation was performed for As0.01A two variants of the structure, with structure factors represented as: 1) F(s)s(1yx)F(graphite, 7 spheres) qxF(diamond, 1 sphere) 2) F(s)s(1yx)F(graphite, 7 spheres) qxF(diamond, 7 spheres) where F(graphite, 7 spheres), for example, denotes the structure factor for graphite with 7 coordination spheres taken into account. These two variants of the structure factor correspond to the cases: (1) if the graphite-like clusters connect each other by a few isolated sp3 bonds; and (2) if there are diamond clusters in the graphite matrix. Fig. 3 shows the dependence of r1 on the fraction x of sp3 atoms in the mixture. One can see that the value of r1 depends on the calculation procedure (1) or (2). When seven diamond spheres are taken into account, the value of r1 depends linearly on x. Generally speaking, this method cannot provide high accuracy and sensitivity to the small addition of diamond bonds up to 10%, as well as a method based on RDF calculation (9% sp3 gives r1s0.142 nm w18x, which is the value for the pure graphite). However, when xG10%, the value of r1 is higher than 0.143 nm. Such sensitivity and accuracy can be reached in the experiment. In this
It was shown for the first time that in the amorphous graphite-like carbon films under considerable compressive stress caused by subimplantation process during film growth, the lattice constant d002 could be shortened down to 0.300 nm. We have developed and substantiated a simple procedure using the transmission electron diffraction data to determine whether the carbon film is graphite- or diamond-like. It was also shown that for the graphite-like structure, the radius of the first coordination sphere, determined by this procedure, is very close to the real one; which is not the case for the diamond-like structure. For our films, which were graphite-like, this procedure gave the same first coordination sphere radius independently of whether the film is under stress or not. Acknowledgments This work has been supported by the Grant NATO SFP 972523. References w1x G.A.J. Amaratunga, M. Chhowalla, C.J. Kiely, I. Alexandrou, R Aharonov, RM. Devenish, Nature 383 (1996) 321. w2x D. Camino, A.H.S. Jones, D. Mercs, D.G. Teer, Vacuum 52 (1999) 125. w3x R.G. Lacerda, P. Hammer, F. Alvarez, F.C. Marques, F.L. Freire, Diamond Relat. Mater. 9 (2000) 796. w4x R.G. Lacerda, F.C. Marques, Appl. Phys. Lett. 73 (1998) 617. w5x V.Yu. Kulikovsky, L.R. Shaginyan, V.M. Vereschaka, N.G. Hatynenko, Diamond Relat. Mater. 4 (1995) 113. w6x D.J. Kester, K.S. Ailey, R.F. Davis, Diamond Relat. Mater. 3 (1994) 332. w7x R.W. Lynch, H.G. Drickamer, J. Chem. Phys. 44 (1966) 181. w8x F.R. Bundy, W.A. Bassett, M.S. Weathers, R.J. Hemley, H.K. Mao, A.F. Goncharov, Carbon 34 (1996) 141. w9x B.E. Warren, X-Ray Diffraction, Massachusetts Institute of Technology, 1969. w10x A.F. Skrishevsky, The structure analysis of liquids, Moskou, 1971 (in Russian). w11x P. Ehrenfest, Prog. Amst. Acad. 17 (1915) 1132. w12x Y.I. Sozin, Kristallographiya 39 (1994) 10, In Russian. w13x D.G. Green, D.R. McKenzie, P.B. Lukins, Mater. Sci. Forum 52&53 (1989) 103. w14x F. Li, J. Lannin, Phys. Rev. Lett. 65 (1990) 1905. w15x J. Kakinoki, K. Katada, T. Hanava, T. Ino, Acta Crystallogr. 13 (1960) 171. w16x B.T. Boiko, L.S. Palatnik, A.S. Derevyanchenko, Dokl. Akad. Nauk SSSR 179 (1968) 316, In Russian. w17x L.E. Hall, D.R. McKenzie, Philosoph. Mag. 80 (2000) 525. w18x D. Beeman, J. Silverman, R. Lynds, M.R. Anderson, Phys. Rev. B 30 (1984) 870.
Study of the structure of hard graphite-like amorphous carbon films by electron diffraction V. Kulikovskya,*, K. Metlovb, A. Kurdyumova, P. Bohaca, L. Jastrabikb a
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, P.O. Box 61, 18221 Prague 8, Czech Republic b Institute for Problems of Materials Science, Academy of Sciences of Ukraine, 3 Krzhyzhanovsky St., 03142 Kiev, Ukraine Received 21 August 2001; received in revised form 10 October 2001; accepted 29 January 2002
Abstract The structure of thin hard carbon films was investigated by transmission electron diffraction using a filter of inelastically scattered electrons. It was shown for the first time that in the amorphous graphite-like carbon films under considerable compressive stress the interplane distance d002 could be shortened down to approximately 0.300 nm. Also, substantiation was given for a simple procedure for the estimation of the first coordination sphere radius in amorphous carbon films. This radius was determined from the maximum of the corresponding diffraction halo. It was shown that this procedure gave the radius of the first coordination sphere very close to its real value for graphite-like structure but did not work so well for a diamond-like structure. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Graphite-like carbon; Amorphous film; Structure; Electron diffraction
1. Introduction High hardness of hydrogen-free carbon films is usually linked with the presence of sp3-like bonds and these films are called diamond-like. Recently, it was shown that some hard amorphous carbon films contain a high number of sp2 bonds w1–4x. The high hardness (up to 55 GPa) and elasticity (elastic recovery of 85%) of the films obtained by arc evaporation of graphite cathode within a high pressure region created by a nitrogen or helium jet in the vicinity of the arc spot were attributed to the interlinking of sp2-bonded graphene planes with sp3 bonds w1x. The source of the graphene planes was found to be carbon nanoparticles in the form of nanotubes and bucky ‘onions’ present in the plasma. Hard amorphous carbon films were prepared by Ion BeamAssisted deposition (IBAD) w3x. Indirect structural investigation indicated they are composed of a highly compressed and dense sp2 network. Hard conductive films were prepared by magnetron sputtering w2x. *Corresponding author. Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, P.O. Box 61, 18221 Prague 8, Czech Republic. Fax: q420-2-8581448. E-mail address: [email protected] (V. Kulikovsky).
In this work, we first present a direct experimental confirmation of obtaining hard compressed graphite-like films with reduced distance between the (002) graphite planes. We also present substantiation of a simple approach allowing to check whether the structure of the carbon amorphous films is graphite-like. The structure of amorphous carbon a-C and a-C:H films is usually investigated by indirect methods: Raman or infrared spectroscopy, Electron Energy Loss spectroscopy (EELS) and, more rarely, by direct diffraction ones. The use of X-ray or neutron diffraction for the investigation of thin carbon films is problematic because of the low atomic number of carbon andyor small film thickness. In view of very high intrinsic stress, it is also difficult to obtain hard carbon films thicker than 1 mm. For the investigation of thin films, the transmission electron diffraction (TED) method was used in this work. However, it is not simple to obtain the radial distribution function (RDF) directly from electron diffraction measurement and such a procedure relies on many assumptions. The essential difficulties arise from the uncertainty of accounting for the inelastically and multiple elastically scattered electrons. Also, the proper interpretation of RDFs is only possible for isotropic
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bias, (3) by carbon evaporation at floating substrate bias (for comparison). The intensity of the right-hand side of all the plots is increased for convenience. The measurements were carried out for three films for every regime. The intensity curves for films obtained in the same regime were similar each other. The different intensity of the small angle halo for the presented films indicates the existence of texture in the films. The c axis was oriented essentially parallel to the film growth direction for the films deposited at substrate bias voltage y100 V or y150 V and the main interplanar distance
Fig. 1. Schematic representation of electron diffraction from stressed amorphous carbon film.
structures. The carbon films can be anisotropic due to their texture, which is often present in the graphite-like structure. In this work, we made an attempt to analyze the TED pattern for the amorphous carbon film avoiding the aforementioned difficulties. 2. Results and discussion The structure of thin hard carbon films was investigated by transmission electron diffraction using a filter of inelastically scattered electrons. The hydrogen-free amorphous carbon films (a-C) were deposited by magnetron sputtering of a carbon target in Ar atmosphere at a pressure of 0.17–0.33 Pa. The power of the discharge was 960 W. The hard (up to 50 GPa) films with thickness of 1.5 mm were obtained on Si substrate at a substrate bias voltage of y100 or y150 V. The films deposited at floating substrate bias had a microhardness of approximately 20 GPa. The films with thickness 30– 60 nm were fabricated under the same conditions on unheated KC1 substrates, for TED experiment the substrate was then dissolved. The detailed information about experimental procedure and some properties of obtained hard carbon films will be reported elsewhere. The electron diffraction pattern of amorphous carbon film usually contains three visible haloes. (Fig. 1). The first, small angle halo appears only if the film contains fragments of graphite-like structure and corresponds to the diffraction from (002) graphite planes. The distance (d002) between these planes can be determined from Bragg’s formula: 2d002sinusnl where 2u is the scattering angle and l is the electron wavelength. Fig. 2 shows the intensity of the electron diffraction patterns I(s) as a function of ss4psinuyl for three films deposited: (1) by sputtering at substrate bias voltage y100 V, (2) by sputtering at floating substrate
Fig. 2. The intensity of the electron diffraction patterns I(s) as a function of ss4psinuyl for three films deposited: (1) by sputtering at substrate bias voltage y100 V; (2) by sputtering at floating substrate bias; (3) by carbon evaporation at floating substrate bias (for comparison). The intensity of the right-hand side of all the plots is increased for convenience.
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for this case was found to be approximately 0.295– 0.305 nm (curve 1). This distance was 0.359–0.375 nm (0.335 nm is the interlayer spacing in graphite) for a-C films obtained without ion bombardment and the intensity of the first halo was considerably lower (curve 2). The very low intensity for the film deposited by carbon evaporation without ion bombardment pointed out that the c axis in the film was oriented perpendicularly to the substrate surface. The corresponding interplanar distance was approximately 0.450–0.460 nm. The observed texture of the films (the same was observed by us and other authors for BN films, e.g. w5,6x) was a consequence of ion or fast atom bombardment where the planes with large interplanar distance were predominantly sputtered if they grow parallel to the substrate. The considerable decrease of d002 for the films obtained at ion bombardment can be explained by the highly stressed sp2 structure of our films. Such a structure was observed for bulk graphite under high pressure (see e.g. R.W. Lynch et al. w7x or a review of F.P. Bundy et al. w8x). The high pressure considerably decreased the distance between the graphite planes but did not appreciably change the in-plane distances. It was reported in w7x that the pressure increase from 0 to 10 GPa led to an inter-plane distance decrease of approximately 11%. Our data show similar dependence. The main source of pressure in our films was the intrinsic stress induced by ion bombardment. Values of intrinsic stress of approximately 8–9 GPa were obtained for a-C film with a thickness of approximately 50 nm, deposited onto Si(111) at a substrate bias of y100 V. This film was deposited simultaneously onto KCl substrate for diffraction measurements, which gave the value of d002f0.300 nm. One may suppose that the values of intrinsic stress for films deposited simultaneously on KCl and Si substrates are of the same order. After the KCl substrate was dissolved, the stress was partially released. However, the intrinsic stress level in the local film regions probably remains very high as a result of the ion bombardment and subimplantation process during film growth. Ions penetrating into the film body can lead to a local increase of film density and compressive stress and, consequently, to the formation of the observed film structure. Thus, we could observe for the first time a very dense and strong compressed structure in the graphite-like film. The possibility of the existence of such a structure for very stressed a-C films was recently discussed by R.G. Lacerda et al. w3x. On the basis of the proposed sp2 carbon structure with shortened interlayer distance, the authors of w3x explained the dependence of the plasmon energy of obtained films as a function of the energy of bombarding ions without reference to sp3 structure. Thus, the presence of the compressed graphite phase in a-C films can explain some contradictory results, whose current explanation is based on the existence of sp3
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bonds. Shortened inter-plane distances in the film were evidenced by TED for (002) planes perpendicular to the film surface, i.e. for the planes which were compressed by the intrinsic stress. Some (002) planes in aC are oriented essentially parallel to the film surface. Such planes do not contribute to the TED pattern, but can be studied with reflection electron diffraction. However, the accuracy of the data, obtained by reflection electron diffraction is very low and the X-ray diffraction is more suitable for this geometry. The existence of the (002) halo implies the existence of graphite-like clusters in the film. The question, whether all the bonds are sp2 or only some of them, remains unanswered. Below we will attempt to answer this question. The intensity distribution and the structure factor F(s) for amorphous solids or nanocrystalline powders with random orientation of nanocrystals can be obtained from the Debye scattering equation by treating each nanocrystal or cluster as a molecule w9x. This approach has a practical importance for the modeling of the structure factor of the assembly of extremely small crystallites with a strong disorder. The structure factor of amorphous solid with one kind of atom, defined as FŽs.s IŽs. yNf2y1, where I(s) is scattered intensity, F(s) is the atomic scattering factor and N is the number of atoms, can be expressed as a sum of the partial structure factors of separate coordination spheres (see, for example, w10x): FŽs.s8knksinŽsrk. ysrk where nk is the number of atoms in the k th coordination sphere, rk is the distance between atoms of k th sphere and some atom, which is chosen as the origin, ss 4psinuyl. The deviation of rk from its equilibrium value increases with the increasing number of coordination spheres, which leads to overlapping of the nearest shells. This fact is expressed by the damping factor chosen as the Gaussian function: FŽs.s8kµnksinŽsrk.expŽyAR2ks2 yr12.∂ ysrk where A is a phenomenological damping parameter. The value of As0 corresponds to ideal nanocrystals without disorder. The more disorder is present, the higher is the value of A. Increasing A leads to a rapid decrease of contributions from distant shells. This is why it is sufficient to consider the contributions of only a finite number of shells in amorphous solid. The partial structure factor for first coordination sphere is given by: FŽs.sn1sinŽsr1. ysr1 The first strong maximum (we did not consider other ones) of this function is at sr1s7.725, which corresponds to the radius of the first coordination sphere r1s
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Table 1 Calculated values of the first coordination sphere radius (r1 ) for (a) graphite and (b) diamond as a function of the number of considered coordination spheres (a) Graphite K nk rk, nm r1(As0), nm r1(As0.005) r1(As0.02) (b) Diamond K nk rk, nm r1(As0), nm r1(As0.005) r1(As0.02)
1 3 0.142 0.142 0.143 0.145
2 6 0.246 0.137 0.138 0.141
3 3 0.284 0.141 0.141 0.143
4 6 0.376 0.142 0.142 0.143
5 6 0.426 0.145 0.143 0.143
6 6 0.492 0.143 0.143 0.143
7 6 0.512 0.145 0.144 0.143
1 4 0.154 0.154 0.155 0.157
2 12 0.252 0.141 0.142 0.147
3 12 0.296 0.151 0.151 0.151
4 6 0.357 0.146 0.147 0.150
5 12 0.389 0.147 0.148 0.150
6 24 0.437 0.137 0.154 0.150
7 16 0.463 0.147 0.158 0.150
7.725ys. This value can also be obtained from the Ehrenfest equation w11x: 2rsinus1.23l Such an approach, based on the Ehrenfest equation, was recently proposed by Yu. I. Sozin w12x for the express estimation of short-range order in amorphous solids. However, the Ehrenfest equation is exactly applicable only for gas molecules with one interatomic distance. In a general case, the consideration of the contribution of other coordination spheres for amorphous solid may lead to a strong shift of this maximum and, as a consequence, to uncertainty in the determination of r1. Furthermore, we will attempt to verify how much the contribution of other coordination spheres influences the position of the maximum corresponding to r1 for graphite and diamond structures. We have calculated the values of r1 based on the coordination number (nk) and interatomic distances (rk) for the nearest coordination spheres of graphite and diamond (Table 1). We took into account that there is disorder between layers in graphite structure and used only intralayer values of rk for the calculations. The values of r1 were calculated by the formula 7.725ys, where s corresponds to the position of the maximum from the first coordination sphere (third halo in Figs. 1 and 2). This position shifted consistently when contributions from two, three, etc. coordination spheres were taken into account. The calculation was performed for ˚ 2. Only 7 first spheres three values of A: 0, 0.005, 0.02 A were taken into account. This corresponds to a cluster size of approximately 1.0 nm. This size corresponds to the short-order range that is usually inferred from the RDF data w13,14x. One could see that r1 for graphite structure was close to the real value and at increasing disorder (increase of A) the difference between the real r1s0.142 nm and the calculated value becomes smaller. This tendency is also present for the diamond structure.
However, the scatter of the calculated values of r1 around the real one (0.154 nm) is significantly larger. These estimates are valid only for small clusters. However, taking additional coordination spheres into account influences the calculated position of the peak only negligibly. This is due to structural disorder as facilitated by the damping factor. Thus, if the first diffraction halo corresponds to reflection from (002) graphitic planes, one may conclude that such film contains graphite-like clusters. This does not mean, however, that the film does not contain diamond-like bonds. If the measured radius of the first coordination sphere is equal to 0.141–0.143 nm, one may conclude that the graphite-like structure is dominant in such a film. If this value is larger than 0.143 nm, it means that this structure may contain diamond-like bonds. All our films deposited onto KCl substrates, both with and without ion bombardment, had values of r1s 0.140–0.142 nm, but the d002 distance varied significantly. The different intensity of the third halo for considered films (Fig. 2) correlates with that for the first halo and is a manifestation of the film texture. The higher intensity of the first halo, the lower that for the third one. Thus, the films obtained were graphite-like, which was also indicated by their relatively high electrical conductivity (these data will be published elsewhere). It should be noted that the values of r1 for amorphous carbon films inferred from the RDF data and reported in literature differ from one another w13–17x. This may be due to the different structure andyor (for films obtained by the same method w15–17x) because of the aforementioned difficulties in RDF calculation. For example, for the a-C films deposited by arc evaporation, the r1 was reported to be 0.151 w15x, 0.143 w16x and 0.148 nm w17x. Let us estimate the sensitivity of the proposed method if the graphite-like film contains only small amount of atoms with sp3 bonds. We determined r1 of such a
V. Kulikovsky et al. / Diamond and Related Materials 11 (2002) 1467–1471
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case one can consider that sp3 bonds are present in the film. 3. Conclusions
Fig. 3. Dependence of the first coordination sphere radius r1 on the fraction (x) of sp3 atoms in the mixture of graphite and diamond for two variants of F(s) calculation (see text): 1) F(s)s(1yx) F(graphite, 7 spheres)qxF(diamond, 1 sphere), 2) F(s)s (1yx) F(graphite, 7 spheres)qxF(diamond, 7 spheres).
mixture as a function of the fraction (x) of sp3 atoms. ˚ 2 and for This calculation was performed for As0.01A two variants of the structure, with structure factors represented as: 1) F(s)s(1yx)F(graphite, 7 spheres) qxF(diamond, 1 sphere) 2) F(s)s(1yx)F(graphite, 7 spheres) qxF(diamond, 7 spheres) where F(graphite, 7 spheres), for example, denotes the structure factor for graphite with 7 coordination spheres taken into account. These two variants of the structure factor correspond to the cases: (1) if the graphite-like clusters connect each other by a few isolated sp3 bonds; and (2) if there are diamond clusters in the graphite matrix. Fig. 3 shows the dependence of r1 on the fraction x of sp3 atoms in the mixture. One can see that the value of r1 depends on the calculation procedure (1) or (2). When seven diamond spheres are taken into account, the value of r1 depends linearly on x. Generally speaking, this method cannot provide high accuracy and sensitivity to the small addition of diamond bonds up to 10%, as well as a method based on RDF calculation (9% sp3 gives r1s0.142 nm w18x, which is the value for the pure graphite). However, when xG10%, the value of r1 is higher than 0.143 nm. Such sensitivity and accuracy can be reached in the experiment. In this
It was shown for the first time that in the amorphous graphite-like carbon films under considerable compressive stress caused by subimplantation process during film growth, the lattice constant d002 could be shortened down to 0.300 nm. We have developed and substantiated a simple procedure using the transmission electron diffraction data to determine whether the carbon film is graphite- or diamond-like. It was also shown that for the graphite-like structure, the radius of the first coordination sphere, determined by this procedure, is very close to the real one; which is not the case for the diamond-like structure. For our films, which were graphite-like, this procedure gave the same first coordination sphere radius independently of whether the film is under stress or not. Acknowledgments This work has been supported by the Grant NATO SFP 972523. References w1x G.A.J. Amaratunga, M. Chhowalla, C.J. Kiely, I. Alexandrou, R Aharonov, RM. Devenish, Nature 383 (1996) 321. w2x D. Camino, A.H.S. Jones, D. Mercs, D.G. Teer, Vacuum 52 (1999) 125. w3x R.G. Lacerda, P. Hammer, F. Alvarez, F.C. Marques, F.L. Freire, Diamond Relat. Mater. 9 (2000) 796. w4x R.G. Lacerda, F.C. Marques, Appl. Phys. Lett. 73 (1998) 617. w5x V.Yu. Kulikovsky, L.R. Shaginyan, V.M. Vereschaka, N.G. Hatynenko, Diamond Relat. Mater. 4 (1995) 113. w6x D.J. Kester, K.S. Ailey, R.F. Davis, Diamond Relat. Mater. 3 (1994) 332. w7x R.W. Lynch, H.G. Drickamer, J. Chem. Phys. 44 (1966) 181. w8x F.R. Bundy, W.A. Bassett, M.S. Weathers, R.J. Hemley, H.K. Mao, A.F. Goncharov, Carbon 34 (1996) 141. w9x B.E. Warren, X-Ray Diffraction, Massachusetts Institute of Technology, 1969. w10x A.F. Skrishevsky, The structure analysis of liquids, Moskou, 1971 (in Russian). w11x P. Ehrenfest, Prog. Amst. Acad. 17 (1915) 1132. w12x Y.I. Sozin, Kristallographiya 39 (1994) 10, In Russian. w13x D.G. Green, D.R. McKenzie, P.B. Lukins, Mater. Sci. Forum 52&53 (1989) 103. w14x F. Li, J. Lannin, Phys. Rev. Lett. 65 (1990) 1905. w15x J. Kakinoki, K. Katada, T. Hanava, T. Ino, Acta Crystallogr. 13 (1960) 171. w16x B.T. Boiko, L.S. Palatnik, A.S. Derevyanchenko, Dokl. Akad. Nauk SSSR 179 (1968) 316, In Russian. w17x L.E. Hall, D.R. McKenzie, Philosoph. Mag. 80 (2000) 525. w18x D. Beeman, J. Silverman, R. Lynds, M.R. Anderson, Phys. Rev. B 30 (1984) 870.