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Properties and prospects for non-crystalline carbons
Journal of Non-Crystalline Solids 299–302 (2002) 798–804 www.elsevier.com/locate/jnoncrysol
Section 11. Non-crystalline carbon
Properties and prospects for non-crystalline carbons John Robertson
*
Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK
Abstract The electronic properties of amorphous carbons (a-Cs) are reviewed in terms of their applications. The carrier mobility, doping and disorder have so far proved not good enough for applications. The defects have recently been identified, and this holds out potential to reduce the defect concentration. There are two types of disorder, sp2 cluster size and stress. It is now possible to characterise the bonding and sp2 configurations in detail, particularly by Raman. The disordered sp2 carbons are less studied, now, and hold future promise. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 71.23.)k; 71.23.Cg; 71.55.Jv
1. Introduction The term non-crystalline carbons covers a wide range of materials, from the sp2 bonded amorphous carbons (a-Cs), to the more sp3 bonded diamond-like amorphous carbon (DLC) [1,2], to the nanostructured carbons based on fullerene and nanotube-like configurations [3,4]. We first consider the DLCs, which include both hydrogen-free highly sp3 bonded ‘tetrahedral amorphous carbon’ (ta-C) and the hydrogenated amorphous carbon (a-C:H) which can contain up to 60% hydrogen. The sp3 bonding of diamond gives it the most extreme properties of any solid [5], as summarised in Table 1. Many of the unique properties of diamond also transfer to ta-C, because they arise primarily from the average bond strength. Diamond has the highest atom density of any solid [5]. ta-C also has a very high atomic density. a-C:H does not gen*
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erally attain such high values, but nevertheless the high atomic density of a-C:H films is the basis of their use as diffusion barriers in electronics and food packaging. ta-C also has an extremely high Young’s modulus (760 GPa) [6] and hardness (60– 80 GPa) [7]. a-C:H tends to have lower modulus values than ta-C, mainly because their C–H bonds greatly reduce the mean C–C coordination, but nevertheless its hardness ranges from 15 to 40 GPa and it has a Young’s modulus up to 350 GPa in ta-C:H. The high hardness is the basis of the large range of applications of DLC as wear-resistant coatings, on for example optical components and magnetic hard disk drives. The Young’s modulus or stiffness of ta-C also makes it a potentially important material for micro-electro-mechanical systems (MEMs) [8]. The large elastic modulus of diamond gives it high acoustic phonon velocities. CVD diamond films are being developed for use in surface acoustic wave (SAW) devices. ta-C has similarly large phonon velocities, and would also be valuable in SAWs, with the advantage that of having no grain
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J. Robertson / Journal of Non-Crystalline Solids 299–302 (2002) 798–804
799
Table 1 Properties of diamond and whether these apply (even generally) to ta-C Diamond
Also in tetrahedral amorphous carbon?
Use
Highest Highest Highest Highest Highest Highest Highest
Yes Yes Yes Yes No No No
Diffusion barrier MEMs Protective coating SAWs
atomic density Young’s modulus hardness isotropic phonon velocity electron velocity hole velocity room temperature thermal conductivity
boundaries like polycrystalline CVD diamond and of a low temperature deposition. A further unique property of DLC films is their smoothness. The ability to cover areas without pinholes, nucleation sites or island growth is critical for its use as a protective coating on magnetic disks and heads [9]. Diamond has the largest room temperature thermal conductivity. It is sometimes thought that this property transfers to DLC, but it does not, because the disorder scatters phonons. ta-C has one of the higher thermal conductivities of amorphous solids [10], e.g., compared to silica, but this does not compare with that of crystalline solids.
2. Mobility A key difference between diamond and a-Cs is in their transport properties. Diamond has the highest saturated electron and hole velocities [5]. (These cannot be utilised in devices because the carrier concentrations are so low, due to the large donor and acceptor binding energies.) In a-Cs, there are always some sp2 sites. The sp2 sites possess p states, in addition to the usual r bonds, which form the network. The p states form filled p valence states and empty p conduction states and have a narrower band gap than the r states, so the p states determine the band gap [1]. The presence of p states has a dramatic effect on carrier mobilities. In a-Si:H, disorder creates a narrow range of localised states at the valence and conduction band edges, as Fig 1(a). In contrast, in a-C, the disorder has the effect of localising all p states within the r–r gap [11], as shown in Fig. 1(b). This is due to the additional effect of
Fig. 1. Schematic density of states in (a) a-Si:H and (b) a-C, showing localised states (shaded).
dihedral angle disorder. The strong localisation reduces the electron (field effect) mobility from 0:7 cm2 V1 s1 in a-Si:H down to 105 –106 cm2 V1 s1 in ta-C [12]. The organic conductors also conduct via their p states, and have low carrier mobilities [13]. In this case, the p states form conjugated bonding systems which lead to very strong electron–phonon coupling, so that carriers form polarons. The early organic conductors had similarly low mobilities as ta-C. Recently, much higher mobilities have been achieved, by aligning the p states, either by making crystalline polymers, or by using liquid crystal phases (e.g., [14]). This possibility of alignment uses the greater facility for chemical design in organic materials and also the structural flexibility of their low coordination number. The rigidity of the DLC
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network restricts orbital alignment. Nevertheless, it may be possible to align p states somewhat. DLCs tend to be formed by an ion-dominated deposition process, because this promotes sp3 bonding. The incident ions displace existing atoms. Displacement is anisotropic for sp2 atoms, so that sp2 sites tend to orient with their p orbitals in the film plane. This orientation is confirmed by electron energy loss spectroscopy (EELS) [15]. As-deposited DLCs also has a high compressive stress, due to the iondominated deposition process. This is usually a disadvantage, as it limits the thickness of adherent films. It has been found that thermal annealing of ta-C to 500–600 °C relieves the stress, due to conversion of a few sp2 sites into sp3 sites [7]. In addition, the sp2 sites start to diffuse at this temperature. The stress relief causes the sp2 sites orient with their shorter r bonds in the plane of the film, so their p orbitals align normal to the film [16]. This is a first example of alignment. This may raise the mobility. The drawback at the moment is that the mobile sp2 sites also tend to cluster, which reduces the band gap [17], a considerable disadvantage. The method would be very useful, if this tendency to cluster could be controlled.
(a)
(b)
3. Tail states and defects
Fig. 2. (a) Urbach energy vs. optical gap of a-C:H and ta-C. (b) Comparison of the Urbach energy and Raman G line width, vs. optical gap for a-C:H.
The poor electronic properties of ta-C and a-C:H are also seen in their defects and tail states. Although their optical absorption edge tends to have a gaussian shape, an equivalent Urbach energy can be defined as dE=d logðaÞ at an optical absorption of a ¼ 103 cm1 . The resulting Urbach energies of 0.2–0.5 eV (Fig. 2) are much larger than of good a-Si:H, 0.055 eV. This means that tail states will tail across the mobility gap, and leave a relatively high density of states at mid gap. These mid-gap states are called defects. In a-Si:H, the defect states are under-coordinated sites, or dangling bonds. Half-filled dangling bonds are paramagnetic, seen in electron spin resonance (ESR). The density of defects is very large in a-C:H, ta-C:H and ta-C, compared to in good a-Si:H [2] (Fig. 3). The combination of a large defect density and wide tails inhibits the performance of DLCs as electronic materials.
Fig. 3. Paramagnetic defect density vs. optical gap for a-C:H, ta-C:H and ta-C.
J. Robertson / Journal of Non-Crystalline Solids 299–302 (2002) 798–804
One problem for improving DLC is that the defect has not been properly identified. The similarity of the g-shift of defects in carbons due to the small spin–orbit coupling, the absence of hyperfine signals and the large line width means that the ESR spectra give little structural information. Recently however, von Bardeleben et al. [18] used 90 GHz ESR to reveal the hyperfine lines of a-C:H. They showed that the paramagnetic centres in aC:H were (small) graphitic clusters, rather than isolated sp2 sites. The identification of defects may now allow us to optimise the deposition process, to reduce the defect density. This may not be easy for ta-C itself, which is produced entirely from Cþ ions, but may be possible for plasma deposited a-C:H. The plasma species are radicals such as CH3 , unsaturated species like C2 H2 which can insert directly into bonds, ions like Cn Hmþ and atomic H and Hþ ions [19]. The sticking probability of each species varies widely, so that ions can contribute 10% or less of the total mass growth. In [19], von Keudell and coworkers performed detailed studies on the deposition processes. They note that hydrogen species penetrate much further into the solid than other species, which tend to interact in the surface or the immediate subsurface layer. Atomic H on the other hand can penetrate deeper into the a-C:H, where it can abstract H from existing C-H bonds. This leaves C dangling bonds or other defect configurations. To reduce defect densities, hydrogen should repassivate the defects. Hydrogen generally passivates defects and weak bonds in a-Si:H and other semiconductors. This relies partly on its solubility and mobility at interstitial sites. H is much less soluble in diamond [20], so its behaviour will differ. The nature of the tail states should also be considered. Recall that band edge states in DLCs are formed by p and p states of sp2 clusters. The gap width is determined by the size of the cluster and distortions of the p bonding [1,2]. Thus, each cluster gives rise to a local band gap, depending on its configuration [21]. The optical absorption edge is broad in most DLCs because each film has a range of different sp2 clusters, each with different local band gaps. The Urbach energy therefore represents the range of sp2 cluster configurations in that sample.
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There is another measure of the disorder in DLCs, the width of the Raman graphite (‘G’) peak. Raman spectra are discussed shortly. The G peak is due to stretching vibrations of sp2 –sp2 bonds. The peak width is proportional to distortion and film stress. Fig. 2(b) compares the variation of G width and Urbach energy against the optical gap for a-C:H. For small gap, a-C:H has a small H content and a large sp2 bonding. At intermediate optical gap, 1.5 eV, the C–C sp3 bonding and density are a maximum. At higher optical gap, sp3 content and H content increase further, with larger amounts of polymeric C–H bonding, and the density becomes lower. Fig. 2(b) shows that the G peak width reaches its maximum at a gap of 1.5 eV. The G width then decreases to quite low values in polymeric a-C:H. In contrast, the Urbach energy increases further. This suggests that the G width measures the homogeneous disorder, within a cluster, while the Urbach energy measures the inhomogeneous disorder of the whole sample. The G width is proportional to the compressive stress [22], and it reduces in polymeric a-C:H. This is because the network is quite floppy and exerts little distortion on any clusters. On the other hand, the inhomogeneous disorder and high Urbach energy reflects the range of clusters in polymeric a-C:H. The small homogeneous disorder in polymeric a-C:H is now consistent with Chernyshov and coworkers [23], who proposed a small value of homogeneous disorder from the anti-Stokes luminescence spectrum. Thus, it is necessary to reduce the range of cluster sizes in a-C:H to reduce the large Urbach energy, which is the main origin of low mobility in a-C:H. This requires somehow to produce more mono-dispersed sp2 clusters. Recently, wide band gap ta-C has been made, with a E04 gap of 3.5 eV [24]. It has a very large Urbach energy and wide G peak. This shows that disorder in ta-C is predominantly homogeneous, unlike in a-C:H.
4. Doping There have been numerous attempts at substitutional doping of ta-C and a-C:H, particularly
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n-type with nitrogen [25,26]. The largest doping effect is in ta-C, where N has two effects. Up to 0.3%, N addition does not change the sp3 content, and the optical gap remains similar to undoped ta-C. The conductivity increases. From 0.3% to 5– 10% N addition, the sp3 content still remains constant, but the optical gap starts to decrease. The conductivity increases further. Above 5–10% N addition, the sp3 bonding converts to sp2 . The effect of small N additions is a weak doping effect. The effect of 0.3–5% N is actually to convert the existing sp2 sites into larger clusters, and thereby narrow the gap. The direct doping effect of N is small, because it is so difficult to move the Fermi level through the high density of gap states, just like in unhydrogenated a-Si. Secondly, nitrogen can exist at a much larger range of bonding configurations in ta-C or a-C:H, so this lessens the doping efficiency. Similar effects are found in a-C:H but with even weaker doping, even though the defect density can be much less than in ta-C.
5. Field emission Many forms of carbon have been studied for their electron field emission properties [27]. The work on diamond arose from a perception that its negative electron affinity may allow electrons in its conduction band to pass into the vacuum at low applied field. DLC was a related form of carbon with the advantage that it can be formed at room temperature. Some forms of both ta-C and a-C:H showed field emission at low applied fields (3–20 V=lm). Numerous models have been advanced for this process. However, ta-C and particularly a-C:H are electrical insulators. The emission is very localised spatially. It has now become clear that the emission originates from surface damage or soft breakdown, which creates conductive tracks across the film [28]. Often, films that apparently emitting at the lowest applied fields have the highest resistivity and very few emission spots, showing that conduction paths must be involved [29]. Emission always occurs from energies at least 4 eV and usually 5 eV below the vacuum level [30], which requires a large field enhancement. This cannot come from normal sites, as
DLCs are very smooth. Imperfections and/or damage are the likely source of these enhancements. Consequently, no existing carbon system uses a low or negative electron affinity. It is now recognised that carbon nanotubes are the preferable carbon system for field emission, as they give field enhancement naturally and are good electrical conductors. 6. Characterisation There have recently been considerable advances in our ability to measure and understand bonding in DLCs. Diamond is 50% more dense than graphite. It is known that the network of unhydrogenated a-C is a mixture of sp2 and sp3 sites, so that the density should increase linearly with sp3 fraction. This has now been verified, using X-ray reflectivity to directly measure density and EELS to measure sp3 fraction. The low energy EELS spectrum is also used to derive the mass density, via the valence electron density N and the plasmon 1=2 energy, E ¼ hðNe2 =m e0 Þ . This requires knowing the electron effective mass, m m was previously found by fitting the observed plasmon energy of diamond (33.4 eV) to its free electron value. We recently showed [31] that in the Lorentz oscillator model, m is directly related to the refractive index ðnÞ as m ¼ 1 n2 . Thus m is quite constant in a-C, but in a-C:H it falls at high H content (Fig. 4). Raman gives a better understanding of the detailed structure. The Raman spectrum of an
Fig. 4. Sp3 content vs. density for ta-C and a-C:H [31].
J. Robertson / Journal of Non-Crystalline Solids 299–302 (2002) 798–804
amorphous covalent solid is the vibrational density of states (VDOS), weighted by a matrix element [2,32]. The Raman spectra of the various forms of carbon differ; they are usually dominated by the two peaks of disorder graphite, the G peak around 1550 cm1 and the D (disorder) peak around 1350 cm1 even in mainly sp3 bonded a-C. This is only partly explained by the 50–230 times larger scattering intensity of sp2 than sp3 sites, so that the residual sp2 sites control the spectrum even in ta-C. The key point is that in C, the matrix elements enhance certain modes to dominate the spectrum, irrespective of changes in the VDOS. In detail [32], the G mode is the bond-stretching mode of two sp2 sites, whether or not the bonds are in graphitic rings. Perhaps it should not be called G! The D mode is the breathing motion of six-fold sp2 aromatic rings, and requires aromatic bonding. It turns out that the D mode is enhanced by a double resonance effect in graphite [33]. The effect also operates in all sp2 clusters, by confinement [32]. The detailed bonding can be derived from the Raman spectrum from the shift of the G peak and the intensity ratio of the D and G peaks, using the 3-stage model of disorder [32], Fig. 5. In stage 1, the grain size of a perfect plane of graphite is reduced to about 1 nm. In stage 2, the graphite layer is topological disordered, retaining the sp2 bonding. In stage 3, the bonding changes from sp2 to sp3 , and this causes large changes in the sp2 con-
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figuration, from mainly rings to mainly chains and finally to very small chains. In stage 1 the G peak moves up, due to phonon confinement, and the D intensity increases inversely with grain size, to be a maximum at the end of stage 1. In stage 2, the G peak moves down, due to a weakening of sp2 bonding, and the D peak decreases as sp2 ring clusters become disordered. The D peak is zero at the end of stage 2. The G peak has a constant intensity throughout this. In stage 3, the G peak now moves upwards, because the vibrational frequency of C@C chains is higher than sp2 rings, due to their shorter bonds. The G peak also gets wider. The D peak remains zero in stage 3. This assumes that the G peak is represented by a skew Lorentzian line-shape, rather than gaussians which can give spurious D-like peaks. The Raman spectra show us that the sp2 configuration is directly related to the sp3 =sp2 fraction in as-deposited DLC. It is this which allows Raman to indirectly give the sp3 fraction in either a-C:H or ta-C. However, in general the sp2 configuration can be varied independently of the sp3 fraction, by higher temperature deposition, thermal annealing, or adding nitrogen, etc. Thus, the general case requires more care. Sp3 bonds are directly seen only in UV Raman, because the higher energy photons now excite r states [34]. They create a ‘T’ peak at 1040 cm1 . This peak moves down in a-C:H. Multi-wavelength Raman gives the most comprehensive analysis based on the dispersion of each peak with excitation energy [35]. Both the G and D peak can move up in wavenumber as the photon energy increases. Two factors cause G peak dispersion. In purely sp2 bonded a-Cs, the G peak moves closer to 1600 cm1 and saturates, as the photon energy rises. In other forms like ta-C, the G peak can rise above 1600 cm1 for high photon energies. The photons are now selectively exciting the wider band gap sp2 clusters, which tend to be chain-like [35].
7. Nanotube and nano-crystalline carbon
Fig. 5. Variation of the Raman G mode position and D to G intensity ratio, again sp2 site order, in the 3-stage model.
Carbon nanotubes are a unique, exciting form of carbon consisting of rolled up sheet of graphite. They can be single-walled or multi-walled. High
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quality nanotubes give rise to ballistic electron transport and numerous other effects. The last 20 years has focused on disordered sp3 carbon. It is interesting to consider if disordered sp2 carbon, locally based on nanotubes or other curved carbon, may have some useful effects, which do not require the atomic perfection of ideal nanotubes. Possibilities are in electrochemistry, catalysis, gas absorption and sensors. Raman is again very useful for structural characterisation. There is a radial breathing mode at 150–200 cm1 whose wavenumber varies with nanotube diameter [36]. Its presence shows if there are tubes. The G modes, now called tangential breathing modes, have complex resonant coupling [36]. The D modes again show the amount of atomic disorder in the nanotube, as if in a graphite sheet. Diamond-like carbons have many unique properties, especially mechanical, but their electronic and field emission uses have proved less good. Electronic applications need a way to manipulate their p states to improve performance. Disordered sp2 carbons are less studied at present, and they hold promise if studied with the same effort.
Acknowledgements The author is very grateful to all colleagues at Cambridge and elsewhere whose efforts helped advance our understanding of carbons.
References [1] [2] [3] [4] [5] [6]
J. Robertson, Adv. Phys. 35 (1986) 317. J. Robertson, Prog. Solid State Chem. 21 (1991) 199. G.A.J Amaratunga et al., Nature 383 (1996) 321. P. Milani et al., Diamond Related Mater. 10 (2001) 240. C. Hayman, J.C. Angus, Science 241 (1988) 913. A.C. Ferrari, J. Robertson, M.G. Beghi, C.E. Bottani, R. Ferulano, R. Pastorelli, Appl. Phys. Lett. 75 (1999) 1893. [7] T.A. Friedmann, J.P. Sullivan, J.A. Knapp, D.R. Tallant, D.M. Follstaedt, D.L. Medlin, P.B. Mirkarimi, Appl. Phys. Lett. 71 (1997) 3820.
[8] J.P. Sullivan, T.A. Friedmann, K. Hjort, MRS Bull. (2001) 309. [9] J. Robertson, Thin Solid Films 383 (2001) 81. [10] C.J. Morath, H.J. Maris, J.J. Cuomo, D.L. Pappas, A. Grill, V.V. Patel, J.P. Doyle, K.L. Saenger, J. Appl. Phys. 76 (1994) 2636. [11] C.W. Chen, J. Robertson, J. Non-Cryst. Solids 227 (1998) 602. [12] F.J. Clough, W.I. Milne, B.Y. Kleinsorge, J. Robertson, G. Amaratunga, B.N. Roy, Electron. Lett. 32 (1996) 498. [13] C.P. Jarrett, R.H. Friend, A.R. Brown, D.M. deLeeuw, J. Appl. Phys. 77 (1995) 6289. [14] M. Redecker, D.D.C. Bradley, M. Inbasekaran, E.P. Woo, Appl. Phys. Lett. 74 (1999) 1400. [15] J. Kulik, G. Lempert, E. Grossman, Y. Lifshitz, Mater. Res. Soc. Symp. Proc. 593 (2000) 305. [16] A. Ilie, Diamond Related Mater. 10 (2001) 207. [17] A.C. Ferrari, B. Kleinsorge, N.A. Morrison, A. Hart, V. Stolojan, J. Robertson, J. Appl. Phys. 85 (1999) 7191. [18] H.J. von Bardeleben, J.L. Cantin, A. Zeinert, B. Racine, K. Zellama, P.N. Lai, Appl. Phys. Lett. 78 (2001) 2843. [19] C. Hopf, T. Schwarz-Selinger, W. Jacob, A. von Keudell, J. Appl. Phys. 87 (2000) 2719; A. von Keudell, T. Schwarz-Selonger, W. Jacob, J. Appl. Phys. 89 (2001) 2979. [20] J.P. Goss, R. Jones, M.I. Heggie, C.P. Ewels, P.R. Briddon, S. Oberg, Phys. Rev. B (2002), to be published. [21] J. Robertson, Philos. Mag. B 66 (1992) 199. [22] M.A. Tamor, W.C. Vassel, J. Appl. Phys. 76 (1994) 3823. [23] S.V. Chernsychov, E.I. Terukov, V.A. Vassilyev, A.S. Volkov, J. Non-Cryst. Solids 134 (1991) 218. [24] K. Teo, A.C. Ferrari, et al., Diamond Related Mater. (2001), to be published. [25] C.A. Davis, D.R. McKenzie, Y. Yin, E. Kravtchinskaia, G.A.J. Amaratunga, V.S. Veerasamy, Philos. Mag. B 69 (1994) 1133. [26] B. Kleinsorge, A.C. Ferrari, J. Robertson, W.I. Milne, J. Appl. Phys. 88 (2000) 1149. [27] J. Robertson, J. Vac. Sci. Technol. B 17 (1999) 659. [28] O.M. Kuttel, O. Gr€ oning, C. Emmenberger, L. Schlapbach, Carbon 37 (1999) 745. [29] O. Gr€ oning, O.M. K€ uttel, P. Gr€ oning, L. Schlapbach, J. Vac. Sci. Technol. B 17 (1999) 1064. [30] K.B.T. Teo et al., New Diamond Frontier Carbon 11 (2001) 235. [31] A.C. Ferrari, A. LiBassi, B.K. Tanner, V. Stolojan, J. Yuan, L.M. Brown, S.E. Rodil, B. Kleinsorge, J. Robertson, Phys. Rev. B 62 (2000) 11089. [32] A.C. Ferrari, J. Robertson, Phys. Rev. B 61 (2000) 14095. [33] C. Thomsen, S. Reich, Phys. Rev. Lett. 85 (2000) 5214. [34] K.W.R. Gilkes, H.S. Sands, D.N. Batchelder, J. Robertson, W.I. Milne, Appl. Phys. Lett. 70 (1997) 1980. [35] A.C. Ferrari, J. Robertson, Phys. Rev. B 64 (2001) 75414. [36] M.S. Dresselhaus, P.C. Eklund, Adv. Phys. 49 (2000) 705.
Section 11. Non-crystalline carbon
Properties and prospects for non-crystalline carbons John Robertson
*
Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK
Abstract The electronic properties of amorphous carbons (a-Cs) are reviewed in terms of their applications. The carrier mobility, doping and disorder have so far proved not good enough for applications. The defects have recently been identified, and this holds out potential to reduce the defect concentration. There are two types of disorder, sp2 cluster size and stress. It is now possible to characterise the bonding and sp2 configurations in detail, particularly by Raman. The disordered sp2 carbons are less studied, now, and hold future promise. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 71.23.)k; 71.23.Cg; 71.55.Jv
1. Introduction The term non-crystalline carbons covers a wide range of materials, from the sp2 bonded amorphous carbons (a-Cs), to the more sp3 bonded diamond-like amorphous carbon (DLC) [1,2], to the nanostructured carbons based on fullerene and nanotube-like configurations [3,4]. We first consider the DLCs, which include both hydrogen-free highly sp3 bonded ‘tetrahedral amorphous carbon’ (ta-C) and the hydrogenated amorphous carbon (a-C:H) which can contain up to 60% hydrogen. The sp3 bonding of diamond gives it the most extreme properties of any solid [5], as summarised in Table 1. Many of the unique properties of diamond also transfer to ta-C, because they arise primarily from the average bond strength. Diamond has the highest atom density of any solid [5]. ta-C also has a very high atomic density. a-C:H does not gen*
Tel.: +44-1223 332 689; fax: +44-1223 332 662. E-mail address: [email protected] (J. Robertson).
erally attain such high values, but nevertheless the high atomic density of a-C:H films is the basis of their use as diffusion barriers in electronics and food packaging. ta-C also has an extremely high Young’s modulus (760 GPa) [6] and hardness (60– 80 GPa) [7]. a-C:H tends to have lower modulus values than ta-C, mainly because their C–H bonds greatly reduce the mean C–C coordination, but nevertheless its hardness ranges from 15 to 40 GPa and it has a Young’s modulus up to 350 GPa in ta-C:H. The high hardness is the basis of the large range of applications of DLC as wear-resistant coatings, on for example optical components and magnetic hard disk drives. The Young’s modulus or stiffness of ta-C also makes it a potentially important material for micro-electro-mechanical systems (MEMs) [8]. The large elastic modulus of diamond gives it high acoustic phonon velocities. CVD diamond films are being developed for use in surface acoustic wave (SAW) devices. ta-C has similarly large phonon velocities, and would also be valuable in SAWs, with the advantage that of having no grain
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 9 8 5 - 1
J. Robertson / Journal of Non-Crystalline Solids 299–302 (2002) 798–804
799
Table 1 Properties of diamond and whether these apply (even generally) to ta-C Diamond
Also in tetrahedral amorphous carbon?
Use
Highest Highest Highest Highest Highest Highest Highest
Yes Yes Yes Yes No No No
Diffusion barrier MEMs Protective coating SAWs
atomic density Young’s modulus hardness isotropic phonon velocity electron velocity hole velocity room temperature thermal conductivity
boundaries like polycrystalline CVD diamond and of a low temperature deposition. A further unique property of DLC films is their smoothness. The ability to cover areas without pinholes, nucleation sites or island growth is critical for its use as a protective coating on magnetic disks and heads [9]. Diamond has the largest room temperature thermal conductivity. It is sometimes thought that this property transfers to DLC, but it does not, because the disorder scatters phonons. ta-C has one of the higher thermal conductivities of amorphous solids [10], e.g., compared to silica, but this does not compare with that of crystalline solids.
2. Mobility A key difference between diamond and a-Cs is in their transport properties. Diamond has the highest saturated electron and hole velocities [5]. (These cannot be utilised in devices because the carrier concentrations are so low, due to the large donor and acceptor binding energies.) In a-Cs, there are always some sp2 sites. The sp2 sites possess p states, in addition to the usual r bonds, which form the network. The p states form filled p valence states and empty p conduction states and have a narrower band gap than the r states, so the p states determine the band gap [1]. The presence of p states has a dramatic effect on carrier mobilities. In a-Si:H, disorder creates a narrow range of localised states at the valence and conduction band edges, as Fig 1(a). In contrast, in a-C, the disorder has the effect of localising all p states within the r–r gap [11], as shown in Fig. 1(b). This is due to the additional effect of
Fig. 1. Schematic density of states in (a) a-Si:H and (b) a-C, showing localised states (shaded).
dihedral angle disorder. The strong localisation reduces the electron (field effect) mobility from 0:7 cm2 V1 s1 in a-Si:H down to 105 –106 cm2 V1 s1 in ta-C [12]. The organic conductors also conduct via their p states, and have low carrier mobilities [13]. In this case, the p states form conjugated bonding systems which lead to very strong electron–phonon coupling, so that carriers form polarons. The early organic conductors had similarly low mobilities as ta-C. Recently, much higher mobilities have been achieved, by aligning the p states, either by making crystalline polymers, or by using liquid crystal phases (e.g., [14]). This possibility of alignment uses the greater facility for chemical design in organic materials and also the structural flexibility of their low coordination number. The rigidity of the DLC
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network restricts orbital alignment. Nevertheless, it may be possible to align p states somewhat. DLCs tend to be formed by an ion-dominated deposition process, because this promotes sp3 bonding. The incident ions displace existing atoms. Displacement is anisotropic for sp2 atoms, so that sp2 sites tend to orient with their p orbitals in the film plane. This orientation is confirmed by electron energy loss spectroscopy (EELS) [15]. As-deposited DLCs also has a high compressive stress, due to the iondominated deposition process. This is usually a disadvantage, as it limits the thickness of adherent films. It has been found that thermal annealing of ta-C to 500–600 °C relieves the stress, due to conversion of a few sp2 sites into sp3 sites [7]. In addition, the sp2 sites start to diffuse at this temperature. The stress relief causes the sp2 sites orient with their shorter r bonds in the plane of the film, so their p orbitals align normal to the film [16]. This is a first example of alignment. This may raise the mobility. The drawback at the moment is that the mobile sp2 sites also tend to cluster, which reduces the band gap [17], a considerable disadvantage. The method would be very useful, if this tendency to cluster could be controlled.
(a)
(b)
3. Tail states and defects
Fig. 2. (a) Urbach energy vs. optical gap of a-C:H and ta-C. (b) Comparison of the Urbach energy and Raman G line width, vs. optical gap for a-C:H.
The poor electronic properties of ta-C and a-C:H are also seen in their defects and tail states. Although their optical absorption edge tends to have a gaussian shape, an equivalent Urbach energy can be defined as dE=d logðaÞ at an optical absorption of a ¼ 103 cm1 . The resulting Urbach energies of 0.2–0.5 eV (Fig. 2) are much larger than of good a-Si:H, 0.055 eV. This means that tail states will tail across the mobility gap, and leave a relatively high density of states at mid gap. These mid-gap states are called defects. In a-Si:H, the defect states are under-coordinated sites, or dangling bonds. Half-filled dangling bonds are paramagnetic, seen in electron spin resonance (ESR). The density of defects is very large in a-C:H, ta-C:H and ta-C, compared to in good a-Si:H [2] (Fig. 3). The combination of a large defect density and wide tails inhibits the performance of DLCs as electronic materials.
Fig. 3. Paramagnetic defect density vs. optical gap for a-C:H, ta-C:H and ta-C.
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One problem for improving DLC is that the defect has not been properly identified. The similarity of the g-shift of defects in carbons due to the small spin–orbit coupling, the absence of hyperfine signals and the large line width means that the ESR spectra give little structural information. Recently however, von Bardeleben et al. [18] used 90 GHz ESR to reveal the hyperfine lines of a-C:H. They showed that the paramagnetic centres in aC:H were (small) graphitic clusters, rather than isolated sp2 sites. The identification of defects may now allow us to optimise the deposition process, to reduce the defect density. This may not be easy for ta-C itself, which is produced entirely from Cþ ions, but may be possible for plasma deposited a-C:H. The plasma species are radicals such as CH3 , unsaturated species like C2 H2 which can insert directly into bonds, ions like Cn Hmþ and atomic H and Hþ ions [19]. The sticking probability of each species varies widely, so that ions can contribute 10% or less of the total mass growth. In [19], von Keudell and coworkers performed detailed studies on the deposition processes. They note that hydrogen species penetrate much further into the solid than other species, which tend to interact in the surface or the immediate subsurface layer. Atomic H on the other hand can penetrate deeper into the a-C:H, where it can abstract H from existing C-H bonds. This leaves C dangling bonds or other defect configurations. To reduce defect densities, hydrogen should repassivate the defects. Hydrogen generally passivates defects and weak bonds in a-Si:H and other semiconductors. This relies partly on its solubility and mobility at interstitial sites. H is much less soluble in diamond [20], so its behaviour will differ. The nature of the tail states should also be considered. Recall that band edge states in DLCs are formed by p and p states of sp2 clusters. The gap width is determined by the size of the cluster and distortions of the p bonding [1,2]. Thus, each cluster gives rise to a local band gap, depending on its configuration [21]. The optical absorption edge is broad in most DLCs because each film has a range of different sp2 clusters, each with different local band gaps. The Urbach energy therefore represents the range of sp2 cluster configurations in that sample.
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There is another measure of the disorder in DLCs, the width of the Raman graphite (‘G’) peak. Raman spectra are discussed shortly. The G peak is due to stretching vibrations of sp2 –sp2 bonds. The peak width is proportional to distortion and film stress. Fig. 2(b) compares the variation of G width and Urbach energy against the optical gap for a-C:H. For small gap, a-C:H has a small H content and a large sp2 bonding. At intermediate optical gap, 1.5 eV, the C–C sp3 bonding and density are a maximum. At higher optical gap, sp3 content and H content increase further, with larger amounts of polymeric C–H bonding, and the density becomes lower. Fig. 2(b) shows that the G peak width reaches its maximum at a gap of 1.5 eV. The G width then decreases to quite low values in polymeric a-C:H. In contrast, the Urbach energy increases further. This suggests that the G width measures the homogeneous disorder, within a cluster, while the Urbach energy measures the inhomogeneous disorder of the whole sample. The G width is proportional to the compressive stress [22], and it reduces in polymeric a-C:H. This is because the network is quite floppy and exerts little distortion on any clusters. On the other hand, the inhomogeneous disorder and high Urbach energy reflects the range of clusters in polymeric a-C:H. The small homogeneous disorder in polymeric a-C:H is now consistent with Chernyshov and coworkers [23], who proposed a small value of homogeneous disorder from the anti-Stokes luminescence spectrum. Thus, it is necessary to reduce the range of cluster sizes in a-C:H to reduce the large Urbach energy, which is the main origin of low mobility in a-C:H. This requires somehow to produce more mono-dispersed sp2 clusters. Recently, wide band gap ta-C has been made, with a E04 gap of 3.5 eV [24]. It has a very large Urbach energy and wide G peak. This shows that disorder in ta-C is predominantly homogeneous, unlike in a-C:H.
4. Doping There have been numerous attempts at substitutional doping of ta-C and a-C:H, particularly
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n-type with nitrogen [25,26]. The largest doping effect is in ta-C, where N has two effects. Up to 0.3%, N addition does not change the sp3 content, and the optical gap remains similar to undoped ta-C. The conductivity increases. From 0.3% to 5– 10% N addition, the sp3 content still remains constant, but the optical gap starts to decrease. The conductivity increases further. Above 5–10% N addition, the sp3 bonding converts to sp2 . The effect of small N additions is a weak doping effect. The effect of 0.3–5% N is actually to convert the existing sp2 sites into larger clusters, and thereby narrow the gap. The direct doping effect of N is small, because it is so difficult to move the Fermi level through the high density of gap states, just like in unhydrogenated a-Si. Secondly, nitrogen can exist at a much larger range of bonding configurations in ta-C or a-C:H, so this lessens the doping efficiency. Similar effects are found in a-C:H but with even weaker doping, even though the defect density can be much less than in ta-C.
5. Field emission Many forms of carbon have been studied for their electron field emission properties [27]. The work on diamond arose from a perception that its negative electron affinity may allow electrons in its conduction band to pass into the vacuum at low applied field. DLC was a related form of carbon with the advantage that it can be formed at room temperature. Some forms of both ta-C and a-C:H showed field emission at low applied fields (3–20 V=lm). Numerous models have been advanced for this process. However, ta-C and particularly a-C:H are electrical insulators. The emission is very localised spatially. It has now become clear that the emission originates from surface damage or soft breakdown, which creates conductive tracks across the film [28]. Often, films that apparently emitting at the lowest applied fields have the highest resistivity and very few emission spots, showing that conduction paths must be involved [29]. Emission always occurs from energies at least 4 eV and usually 5 eV below the vacuum level [30], which requires a large field enhancement. This cannot come from normal sites, as
DLCs are very smooth. Imperfections and/or damage are the likely source of these enhancements. Consequently, no existing carbon system uses a low or negative electron affinity. It is now recognised that carbon nanotubes are the preferable carbon system for field emission, as they give field enhancement naturally and are good electrical conductors. 6. Characterisation There have recently been considerable advances in our ability to measure and understand bonding in DLCs. Diamond is 50% more dense than graphite. It is known that the network of unhydrogenated a-C is a mixture of sp2 and sp3 sites, so that the density should increase linearly with sp3 fraction. This has now been verified, using X-ray reflectivity to directly measure density and EELS to measure sp3 fraction. The low energy EELS spectrum is also used to derive the mass density, via the valence electron density N and the plasmon 1=2 energy, E ¼ hðNe2 =m e0 Þ . This requires knowing the electron effective mass, m m was previously found by fitting the observed plasmon energy of diamond (33.4 eV) to its free electron value. We recently showed [31] that in the Lorentz oscillator model, m is directly related to the refractive index ðnÞ as m ¼ 1 n2 . Thus m is quite constant in a-C, but in a-C:H it falls at high H content (Fig. 4). Raman gives a better understanding of the detailed structure. The Raman spectrum of an
Fig. 4. Sp3 content vs. density for ta-C and a-C:H [31].
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amorphous covalent solid is the vibrational density of states (VDOS), weighted by a matrix element [2,32]. The Raman spectra of the various forms of carbon differ; they are usually dominated by the two peaks of disorder graphite, the G peak around 1550 cm1 and the D (disorder) peak around 1350 cm1 even in mainly sp3 bonded a-C. This is only partly explained by the 50–230 times larger scattering intensity of sp2 than sp3 sites, so that the residual sp2 sites control the spectrum even in ta-C. The key point is that in C, the matrix elements enhance certain modes to dominate the spectrum, irrespective of changes in the VDOS. In detail [32], the G mode is the bond-stretching mode of two sp2 sites, whether or not the bonds are in graphitic rings. Perhaps it should not be called G! The D mode is the breathing motion of six-fold sp2 aromatic rings, and requires aromatic bonding. It turns out that the D mode is enhanced by a double resonance effect in graphite [33]. The effect also operates in all sp2 clusters, by confinement [32]. The detailed bonding can be derived from the Raman spectrum from the shift of the G peak and the intensity ratio of the D and G peaks, using the 3-stage model of disorder [32], Fig. 5. In stage 1, the grain size of a perfect plane of graphite is reduced to about 1 nm. In stage 2, the graphite layer is topological disordered, retaining the sp2 bonding. In stage 3, the bonding changes from sp2 to sp3 , and this causes large changes in the sp2 con-
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figuration, from mainly rings to mainly chains and finally to very small chains. In stage 1 the G peak moves up, due to phonon confinement, and the D intensity increases inversely with grain size, to be a maximum at the end of stage 1. In stage 2, the G peak moves down, due to a weakening of sp2 bonding, and the D peak decreases as sp2 ring clusters become disordered. The D peak is zero at the end of stage 2. The G peak has a constant intensity throughout this. In stage 3, the G peak now moves upwards, because the vibrational frequency of C@C chains is higher than sp2 rings, due to their shorter bonds. The G peak also gets wider. The D peak remains zero in stage 3. This assumes that the G peak is represented by a skew Lorentzian line-shape, rather than gaussians which can give spurious D-like peaks. The Raman spectra show us that the sp2 configuration is directly related to the sp3 =sp2 fraction in as-deposited DLC. It is this which allows Raman to indirectly give the sp3 fraction in either a-C:H or ta-C. However, in general the sp2 configuration can be varied independently of the sp3 fraction, by higher temperature deposition, thermal annealing, or adding nitrogen, etc. Thus, the general case requires more care. Sp3 bonds are directly seen only in UV Raman, because the higher energy photons now excite r states [34]. They create a ‘T’ peak at 1040 cm1 . This peak moves down in a-C:H. Multi-wavelength Raman gives the most comprehensive analysis based on the dispersion of each peak with excitation energy [35]. Both the G and D peak can move up in wavenumber as the photon energy increases. Two factors cause G peak dispersion. In purely sp2 bonded a-Cs, the G peak moves closer to 1600 cm1 and saturates, as the photon energy rises. In other forms like ta-C, the G peak can rise above 1600 cm1 for high photon energies. The photons are now selectively exciting the wider band gap sp2 clusters, which tend to be chain-like [35].
7. Nanotube and nano-crystalline carbon
Fig. 5. Variation of the Raman G mode position and D to G intensity ratio, again sp2 site order, in the 3-stage model.
Carbon nanotubes are a unique, exciting form of carbon consisting of rolled up sheet of graphite. They can be single-walled or multi-walled. High
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quality nanotubes give rise to ballistic electron transport and numerous other effects. The last 20 years has focused on disordered sp3 carbon. It is interesting to consider if disordered sp2 carbon, locally based on nanotubes or other curved carbon, may have some useful effects, which do not require the atomic perfection of ideal nanotubes. Possibilities are in electrochemistry, catalysis, gas absorption and sensors. Raman is again very useful for structural characterisation. There is a radial breathing mode at 150–200 cm1 whose wavenumber varies with nanotube diameter [36]. Its presence shows if there are tubes. The G modes, now called tangential breathing modes, have complex resonant coupling [36]. The D modes again show the amount of atomic disorder in the nanotube, as if in a graphite sheet. Diamond-like carbons have many unique properties, especially mechanical, but their electronic and field emission uses have proved less good. Electronic applications need a way to manipulate their p states to improve performance. Disordered sp2 carbons are less studied at present, and they hold promise if studied with the same effort.
Acknowledgements The author is very grateful to all colleagues at Cambridge and elsewhere whose efforts helped advance our understanding of carbons.
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