Diamond and Related Materials 12 (2003) 79–84 0925-9635/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved. PII: S0925-9635Ž03.00006-2 Improving the properties of diamond-like carbon John Robertson* Engineering Department, Cambridge University, Cambridge CB2 1PZ, UK Abstract The electronic properties of diamond-like amorphous carbons have so far been disappointing in terms of their applications. The causes of these limitations are considered and if it is possible to improve them. Defects are not passivated in a-C:H because atomic hydrogen is not stable at the interstitial site in diamond, and this inhibits the migration of H to dangling bonds. The band tails are wide because of the wide range of sp cluster sizes. The cluster size problem could be solved by using precursors2 containing the required sp configuration. The problem of high stress must be solved for the use of diamond-like carbon in micro2 electromechanical systems. � 2003 Elsevier Science B.V. All rights reserved. Keywords: Diamond; Carbon; Amorphous carbon 1. Introduction Diamond-like carbon (DLC) is an amorphous carbon (a-C) or a hydrogenated amorphous carbon (a-C:H) containing a significant fraction of sp bonding w1x.3 Typically, thin films of hydrogen-free DLCs with a very high sp content can be made by filtered cathodic3 vacuum arc, pulsed laser deposition, or mass selected ion beam deposition. On the other hand, hydrogenated amorphous carbon is usually made by plasma enhanced chemical vapour deposition (PECVD) or reactive sput- tering. The sp bonding is generated by ensuring that3 the deposition flux contains a sizeable fraction of medi- um energy ions with an energy approximately 100 eV. DLC has some unique properties such a high elastic modulus, high mechanical hardness, very low surface roughness, and chemical inertness, which make it a valuable material for applications. It is also a semi- conductor with a band gap, which can be varied from approximately 1 to 4 eV. However, its electronic prop- erties are quite restrictive for applications. These prop- erties include a large density of mid-gap states, wide band tails, low carrier mobility and a poor doping response. On the mechanical side, the applications are limited by adhesion to the substrate by the compressive stress created during deposition. *Tel.: q44-1223-33-2689; fax: q44-1223-33-2662. E-mail address:
[email protected] (J. Robertson). The work on DLC was driven by a number of possible electronic applications. It was considered that DLC would be a good electron field emitter, for field emission displays. However, it turned out that the emission was largely extrinsic, and that carbon nanotubes make much better field emitters. Similarly, a-C:H with a wider band gap possesses strong room temperature photolumin- escence, which could be utilized in a display. However, in practice, no viable electroluminescent devices have been produced. Thus, lower disorder is the main need for a dopable semiconductor. This paper considers the fundamental causes of these restrictions and how they can be surmounted. The electronic structure of diamond-like amorphous carbons are controlled by the p states of their sp sites,2 as these states form the band edges w1–3x. The sp sites2 are organized into small clusters, which can consist of chains (olefinic) or rings (aromatic). Although the cluster model has undergone substantial revision w4x, it is still true that the a-C and a-C:H has a range of local band gaps which depend on the size and local configu- ration of these clusters (Fig. 1). Larger clusters have smaller band gaps w3x. The range of cluster sizes is large and is an intrinsic source of disorder. It is the cause of the broad band tails. Tail states trap carriers and so they limit the carrier mobility. The tails in a-C:H are wide enough and they cross in the mid-gap to leave a sizeable density of mid- gap states. Defect states can be defined as those in mid- 80 J. Robertson / Diamond and Related Materials 12 (2003) 79–84 Fig. 1. Schematic band diagram of the variation of local band gap of a-C:H with distance, due to the range of sp cluster sizes.2 Fig. 2. Variation of Urbach energy and Raman G width with optical gap showing the decrease of G width at large gaps. Data from w1,4x, respectively. The Urbach energies are from optical absorption edges of various groups, taken as the slope at an absorption coefficient of 10 cm .3 y1 Fig. 3. Variation of defect density found by ESR in a-C:H and ta-C:H vs. optical gap. gap states which are singly occupied by electrons. Some defects may be dangling bonds, and others are clusters which have a state near mid-gap. This means that the causes of wide tails and large defect densities need to be identified. The width of the band tails is given by the Urbach energy, which is the energy slope of the optical band edge, assuming the absorption coefficient decreases exponentially with photon energy into the gap w1x. Fig. 2 plots the Urbach energy of a-C:H films against their optical gap using data from various groups. The fact that the Urbach energy increases continuously with the band gap means that the mid-gap density of states is always high. Fig. 2 also plots another measure of disorder, the width of the G peak in the Raman spectrum, using data from Tamor and Vassell w5x. The G width is proportional to the bond angle distortions at sp sites. These two2 measures are seen to increase together at smaller band gaps, and they then diverge for wider gaps. The Raman width decreases, but the Urbach energy continues to increase for wider gaps. Thus, the disorder consists of distortions for lower gaps, and of cluster size variations for higher gaps. The sp clusters in wide gap a-C:H are2 mainly sp chains. There is a large range of cluster sizes2 in wide gap a-C:H. This is an unnecessarily wide range. It is a source of disorder not due to stress, and it is the aspect that must be addressed to improve the electronic properties. (Note that ta-C is different to a-C:H. In ta-C the Urbach energy increases continuously with wider gap, see for example w6x, so that its disorder always comes from bond angle distortions.) Fig. 3 plots the defect densities as measured by electron spin resonance (ESR) against the band gap w1x, to emphasize the large defect densities compared to a-Si:H. Defects reduce the diffusion length of carriers. They also inhibit any doping, because dopants must donate enough carriers to sweep the Fermi level through these states. It is clear that the presence of the large hydrogen content of 20–55% in a-C:H does not reduce defect densities by passivating unpaired electrons, in contrast to a-Si:H. To illustrate the problem, Fig. 4 plots the density of states in the gap, assuming exponential tails, for a typical case of a Tauc gap of 2 eV and an Urbach energy of 0.22 eV, equivalent to valence and conduction tail widths of 0.15 eV. This gives a density of ;1019 cm eV at mid-gap, a high value compared to they3 y1 10 cm of a-Si:H. States within an energy band of16 y3 the correlation energy U will be singly occupied. U for this band gap is approximately 0.6 eV w7x, so this gives 6=10 cm states, which is roughly what ESR finds.18 y3 2. Behaviour of hydrogen in a-C:H To understand why hydrogen does not easily passivate defects in a-C:H, consider the relatively behaviour of 81J. Robertson / Diamond and Related Materials 12 (2003) 79–84 Fig. 4. A schematic density of gap states for an a-C:H film, with optical gap of 2 eV and Urbach energy of 0.22 eV. The general layout is the same if the tails have a Gaussian shape instead. Fig. 5. The calculated energies of hydrogen in Si and diamond crystals. hydrogen in Si and diamond w8–13x. Fig. 5 plots the energies of various configurations of a hydrogen atom in a perfect Si crystal w9x or diamond crystal w12,13x, referred to the energy of a free hydrogen atom in the vacuum. A free neutral hydrogen atom, H , can lower0 its energy by entering the Si—it dissolves exothermical- ly in Si. Its most stable site is the bond centre site, BC, which is 1.05 eV more stable than in the vacuum. Thus its energy level is at y1.05 eV in Fig. 5. The Si–Si bond length dilates to allow room for the H atom, and this costs energy, but nevertheless the H has a net gain in energy because it is partly bonded, compared to forming no bonds as a free atom. There are other configurations of H , the tetrahedral interstitial site T0 and hexagonal interstitial site H, which are higher in energy than the BC, but they are still more stable than being in free space. The H can migrate from one BC0 site to the next via the so-called C site, passing over a barrier of approximately 0.3 eV w8x. Molecular H in2 free space is more stable than a hydrogen atom by 2.25 eV per H atom, so this state is placed at y2.25 eV in Fig. 5. H is also stable at a tetrahedral interstitial site2 in Si, lying at approximately y1.9 eV. Another config- uration of two hydrogen atoms in Si is the so-called H * site. This consists of two Si–H bonds with a broken2 Si–Si bond between them. This state lies at y1.65 eV per H atom. (This energy consists roughly of the energy gained by forming one Si–H bond, minus half the energy to break one Si–Si bond.) The energies so far are for H in a defect-free Si lattice. However, if a Si dangling0 bond already exists, the H can bond to it, and this Si–H state lies at y3.3 eV, which is just the energy of the Si–H bond. Fig. 5b shows the equivalent energies for H in a0 diamond lattice, again referred to that of H in free0 space. The H in diamond is still most stable at the0 bond centered interstitial site w9x. However, this state now lies at q2.6 eV, much less stable than in free space. This is partly because the diamond lattice is much smaller than Si, so the strain energy at a BC site is now quite large. The H molecule can be placed at the T2 interstitial site in diamond, but this costs q2.1 eV per H atom, again because of the strain energy. Two hydro- gens can be placed in a H * configuration in diamond,2 this is also unstable at q1.0 eV. It is, however, more stable than the interstitial H . The low stability of these2 interstitial configurations of H is partly due to the lack of space in the diamond lattice but also due to the lack of d orbitals on C, which allow a C atom to overcoor- dinate, which is needed for interstitial sites. In summary, no configuration of H in diamond is stable compared to a free H, whereas all configurations of H in Si were. In a mixed network of C–C and C_C bonds, there are bound states for H. A C_C bond can convert into a C–C–H group with an unpaired electron on the first C. This state lies at y1.56 eV using simple bond energies. The network of a-C:H is more open than that of diamond, so the destabilization of interstitial H sites due to strain could be reduced. Nevertheless, the lack of C d orbitals still destabilizes interstitial sites. The relevance of this discussion is as follows. Hydro- gen is essential to making a-Si:H a viable electronic material, because it passivates its dangling bonds and so it greatly reduces its density of mid-gap states to ;10 cm . Hydrogen also reduces the number of16 y3 weak bonds, which form the tail states w14x, and so this makes the band tail distribution much sharper. These processes occur during growth. The growing surface of a-Si:H is much more hydrogen-rich than the bulk. As this surface layer is buried by subsequent overgrowth, it greatly rearrange its bonding, loosing H to become bulk a-Si:H. This process ultimately creates 82 J. Robertson / Diamond and Related Materials 12 (2003) 79–84 Fig. 6. Atomic and ionic processes during the deposition of a-C:H, showing those which occur on the surface, those which can occur deeper, due to hydrogen. a material with few dangling bonds w15x. This can happen because H atoms can enter the metastable interstitial sites while the rearrangement occurs, without being expelled out of the solid, because the interstitial H sites are more stable than the vacuum. This keeps a supply of excess, weakly bonded, mobile H atoms available, if needed, to passivate any unpaired dangling bonds that may be created by the rearrangement. The Hs can hop between BC sites via other configurations over a barrier of approximately 0.3 eV, so they can find any required dangling bond site. Note that the dangling bond density of a-Si:H is determined by the processes which occur as the H-rich surface layer becomes buried and the bonds rearrange to form bulk a-Si:H. The surface layer contains a certain DB density due to a balance between H abstraction and addition, but whatever this density is, it is modified by bond rearrangements as the surface layer is buried. This is discussed in detail elsewhere w15x. 3. Dangling bond reduction Now consider the growth of a-C:H. Dangling bonds (DBs) will be created on its surface from surface C–H groups by a H abstraction reaction, and they will be saturated by the addition of atomic H, 0 0'C–HqH™'C qH (1)2 0 0'C qH™'C–H (2) The density of dangling bonds is then the ratio of rates of these two reactions, u sk yk (3)DB 1 2 These cross-sections of these reactions have been measured by Kuppers w16x as 0.05 and 1.3 A , so the2˚ ratio is 0.04. Thus, a 4% concentration of dangling bonds is expected on the a-C:H surface in the presence of a plasma with atomic H. This surface layer becomes buried by deposition of subsequent layers, and this DB concentration will be quenched in unless a passivation process occurs. A dangling bond or other unpaired electron can also be created inside the solid. Being small and light, atomic H and hydrogen ions H have sufficient range that0 q they can create DBs well into the solid by abstracting H from a C–H bond w17x. Alternatively, DBs could be formed just by atomic displacement by carbon ions, within a smaller range of the surface. How could these DBs become passivated? Hydrogen species are not soluble in the sp network according to3 Fig. 5. H molecules formed by reaction (Eq. (1)) are2 expelled from the a-C:H solid to the surface or an internal void, as they are insoluble in a-C:H. Because of the lack of stability of interstitial H or H in sp0 32 networks, there is no reservoir of hydrogen in the solid a-C:H available to passivate the DBs. The only source of unpaired H in the solid a-C:H is that trapped at C_C bonds. However, as sp C sites do not percolate across2 the sample, it is unclear that this H can diffuse to its needed sites. This different behaviour of H in C from Si is the significant problem in the reduction of the dangling bond density in a-C:H. Thus, the presence of atomic H or H ions in the plasma should be minimisedq for a-C:H deposition, the opposite of the situation for a- Si:H. 4. Sharpening the band tails Alternatively, can the band tails in wider-gap a-C:H be made sharper? This requires the growth of a-C:H with more mono-dispersed sp cluster sizes. Generally,2 deposition of a-C:H or tetrahedral amorphous carbon (ta-C) is carried out under strongly ion bombardment conditions Fig. 6. Wider gap ‘polymeric’ a-C:H is formed in less aggressive conditions. Nevertheless, the random bond-breaking events during ion bombardment create a range of sp cluster sizes. There is no control2 of cluster size. This contrasts with the control of config- urations in organic conductors allowed by choice of synthetic pathways. A way to achieve some control would be to use a precursor already containing the desired sp configuration, and to assemble this by2 plasma-assisted polymerization. It is known that benzene rings are not easily broken down at lower self-bias voltages, as found by Tamor et al. w18x. Another example may be used xylene. Amorphous silicon carbide (a- SiC:H) alloys from xylene were previously found to 83J. Robertson / Diamond and Related Materials 12 (2003) 79–84 Fig. 7. Schematic of orientation of sp sites and p states (a) as-2 deposited and (b) after thermal annealing. have a strong UV luminescence which was attributed to transitions within retained aromatic units w19,20x. This suggests that configuration control might be possible. A narrowing of the band tails would increase carrier mobilities. However, it is unlikely that the mobility of carriers can be increased above 1 cm (V s) because2 y1 of the unusual nature of disorder in p bonded systems. The disorder has the effect of localizing all p states within the s–s* gap w21x. The organic conductors also conduct via their p states, and they have low carrier mobilities w22x. In this case, the p states form conjugated bonding systems. The conductivity can be limited by hopping between molecules. 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 w23x. 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 network restricts orbital align- ment. Nevertheless, it may be possible to align p states somewhat. DLCs tend to be formed by an ion-dominated deposition process, because this promotes sp bonding.3 The incident ions displace existing atoms. Displacement is anisotropic for sp atoms, so that sp sites tend to be2 2 oriented with their bonds perpendicular to the plane of the film and their p orbitals in the film plane, as shown schematically in Fig. 7. This orientation is confirmed by electron energy loss spectroscopy w24x. As-deposited DLCs also have a high compressive stress, due to the ion-dominated deposition process. It has been found that thermal annealing of ta-C to 500– 600 8C relieves the stress, due to conversion of a few sp sites into sp sites w25,26x. In addition, the sp sites2 3 2 start to diffuse at this temperature. The stress relief causes the sp sites to orient with their shorter s bonds2 in the plane of the film, so their p orbitals align normal to the film w27x. This is a first example of alignment. This may be possible to use this to raise the mobility. The drawback at the moment is that the mobile sp sites2 also tend cluster, which reduces the band gap w26x, is a considerable disadvantage. The method would be very useful, if this tendency to cluster could be controlled. 5. Improving mechanical properties Given that it will require considerable effort to improve electronic properties, it is useful to consider the mechanical properties. DLC has remarkable mechanical properties, such as a high hardness and high elastic modulus. Ta-C is preferred in this sense, as it retains its properties to high temperatures without degradation due to loss of hydrogen. A recent interest for ta-C is in microelectro-mechanical systems (MEMS). The advan- tage of ta-C here is not only just its higher modulus but also that it can be hydrophobic, and so it would be less prone to stiction, which is a major problem on the micro-scale. However, the intrinsic stress of DLCs and ta-C is a significant restriction in the application of these materials in MEMS and as protective coatings. In coatings, the stress restricts the maximum thickness of an adherent film. In MEMS, a zero stress film is required, as the device must be free-standing. The intrinsic stress in DLC is compressive and arises from the growth mechanism of subplantation. It can be relieved by thermal annealing to approximately 600 8C w25,26x, without loss of the sp bonding or elastic3 modulus. Sullivan et al. w28x have used ta-C to fabricate some MEMS devices. This area has much potential. The stress in ta-C restricts the thickness of adherent films on Si to approximately 100–200 nm. Much thicker ta-C films can be grown on compliant substrates w29– 31x. The substrate should be a carbide former like Ti or Cr and also plastic, unlike Si. The stress can be reduced by using multilayers of alternatively hard and softer a-C. The softer a-C can be made by operating the cathodic arc with a pulsed negative substrate bias, so that it is also a plasma ion immersion implantation (PIII) system. The pulsing allows large voltages to be applied without breaking down the plasma. Alternatively, the pulsed deposition can be used throughout the deposition phase. These methods are covered by McKenzie w32x and Tay w33x. Note that in general, pulsed cathodic arcs seem able to give thicker ta-C films w29x, even if not operated in PIII mode, whereas DC arcs have more difficulty. 6. Conclusions The paper points out the relatively inferior electronic properties of amorphous carbon such as its wide band tails and a high defect density, which make doping difficult. It is shown that the wide band tails in wider 84 J. Robertson / Diamond and Related Materials 12 (2003) 79–84 gap a-C:H could be reduced by using growth precursors which contain defined sp groups to control the sp2 2 cluster size. It was shown that the properties of atomic H in the a-Si and a-C networks differ fundamentally, in that atomic H is not soluble in a-C. This makes H unable to passivate dangling bonds during deposition. 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