Mechanisms in ion-assisted deposition of superhard coatings: cubic boron nitride–tetrahedral amorphous carbon

Surface and Coatings Technology 97 (1997) 23–32

Mechanisms in ion-assisted deposition of superhard coatings: cubic boron nitride–tetrahedral amorphous carbon S. Reinke *, W. Kulisch Institute of Technical Physics, University of Kassel Heinrich Plett Str. 40, 34109 Kassel, Germany

Abstract Ion-assisted deposition of tetrahedral amorphous carbon (ta-C ) and cubic boron nitride (c-BN ) is compared with existing models (subplantation, stress model, sputter model ). None of the models is found to describe all aspects of a certain deposition process; nevertheless, some general tendencies can be outlined: whereas for ta-C deposition local penetration processes play a role, c-BN grows via attachment of atoms to c-BN crystals. The most important differences exist with respect to relaxation processes: during thermal activation ta-C relaxes towards the sp2 structure, whereas in case of c-BN the crystalline sp3 lattice is even improved. Also, the problems concerning the adhesion of ta-C and c-BN are different: in the case of ta-C the main problem is the high stress which is a consequence of the over-constrained network, whereas the adhesion of c-BN seems to be limited by the mechanical strength of the interface (h-BN nucleation layer). © 1997 Elsevier Science S.A. Keywords: cubic boron nitride; tetrahedral amorphous carbon; ion-assisted deposition; growth models

1. Introduction Nowadays, two principally different approaches concerning the deposition of superhard carbon and BN coatings exist: on the one hand ion-assisted CVD and PVD, and on the other hand CVD methods without significant ion bombardment. The latter are very successful in diamond deposition and lead to pure, wellcrystallized films [1,2]. However, at the present time no chemical way to deposit the other superhard materials cubic boron nitride (c-BN ) and tetrahedral amorphous carbon (ta-C ) has been established. Nevertheless, these materials can be synthesized using ion-assisted deposition techniques which is the subject of this paper.

2. c-BN and ta-C deposition Before going into details of the deposition processes, some basic properties of ta-C and c-BN film have to be addressed. The term ta-C will only be used for films consisting of a mainly sp3-bonded amorphous carbon network with a density around 3 g cm−3. A related hydrogenated modification has been synthesized [3] * Corresponding author. Tel: (+49) 561 4532; Fax: (+49) 561 4136 e-mail: [email protected] 0257-8972/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S 02 5 7 -8 9 7 2 ( 9 7 ) 0 0 39 0 - 3

which was named ta-C:H and will be treated together with ta-C in the following. c-BN films are nanocrystalline with crystal sizes in the range of 5–100 nm. They show the characteristic IR absorption of the c-BN crystal around 1100 cm−1, and their composition (B/N ) is close to stoichiometry. 2.1. Deposition of ta-C and c-BN In the following, we distinguish between methods in which the film forming atoms are either highly energetic (direct energy input) or thermal while energy is supplied by additional ion assistance (indirect energy input). In the case of BN, the energy of the B atoms determines the nature of the process, although nitrogen is almost always supplied with high energy.1 In order to compare different deposition methods, we will use the internal deposition parameters ion energy E , ion to neutral ion ratio W and W*, substrate temperature T and ion angle s of incidence H. In the case of ta-C, W and W* denote the number of ions per incident and incorporated C-atom respectively (W=1 for direct energy input); in 1At high N/B-flux ratios the surface nitrogen concentration equals the bulk concentration [4] and surplus nitrogen diffuses out. Therefore, owing to the stoichiometric environment, a nitrogen ion penetrating in a subsurface position cannot densify the structure in the sense of direct subplantation.

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the case of c-BN W=F/2 and W*=F*/2 with F and F* the number of ions per incident and incorporated boron atom respectively [5]. First, the standard processes (direct ta-C and indirect c-BN deposition) are discussed and afterwards recent results are included.

energy of at least 1 keV [8,19]. A possible reason for the suppression of sp3 formation found with arc and plasma beam deposition at high energies may be a rise of the growth temperature due to the high ion currents used (see Fig. 2a).

2.1.1. ta-C deposition with direct energy input Usually, ta-C is deposited from energetic carbon ions (direct energy input). The most important deposition methods for ta-C are mass separated ion beam deposition ( IBD) [6–9] and vacuum arc deposition [10–12]. In general, room temperature deposition under normal ion incidence is performed. Similar conditions also occur with plasma beam deposition, the only method leading to ta-C:H up to now [13]. The dependence of the sp3 content on the ion energy is shown schematically in Fig. 1a. With arc and plasma beam deposition, a rise of the sp3 content at several tens of electron-volts is found, followed by a maximum at around 100 eV and a pronounced decrease [10]. IBD shows nearly the same low energy behaviour but high sp3 contents up to an ion

2.1.2. c-BN deposition with indirect energy input c-BN can be deposited with a variety of PVD and CVD deposition methods [5] which supply low energetic boron species (B atoms and various B N H species x y z respectively) and in most cases use a mixture of nitrogen and inert gas (commonly argon) ion bombardment. Fig. 1b shows the boundary between the hexagonal boron nitride (h-BN ) and the c-BN parameter range W* as derived from a detailed data collection [5]. It is h obvious that low ion energies can be compensated by high flux ratios and vice versa. Under suitable deposition conditions, the increase of the sp3 content from pure h-BN to nearly 100% c-BN is extremely steep [20], as indicated schematically in Fig. 1a.

Fig. 1. (a) Schematic dependence of the sp3 content of c-BN and ta-C on the ion energy. In the case of c-BN, F=10 and F=1 were chosen. (b) Energy dependence of the quantities determining the densification according to Eqs. (9) and (10). The bold symbols indicate the experimental parameters for c-BN: the boundary W* for standard c-BN h deposition ( line), and the conditions under which c-BN growth has been shown with reduced ion bombardment (arrows)). The numbers indicate: (1) reduction of the ion bombardment subsequent to c-BN nucleation within the standard parameter range (indirect energy input) [14]; (2) nucleation and growth with the same parameters using IBD (direct energy input) [15]. The broken lines indicate the parameter ranges for direct and indirect [16 ] ta-C deposition. The narrow lines are calculations of 1/f and 1/q [17,18] and refer to the right axis.

2.1.3. Recent results Only a few preliminary experiments concerning the complementary processes of indirect ta-C and direct c-BN deposition exist up to now. Richter et al. [21] showed that with parameters comparable with direct ta-C deposition (W#1 and E =100 eV ) but with indirect energy input by means ion of argon ions no ta-C is obtained. However, Schwan et al. [16 ] deposited ta-C with pure indirect energy input (100 eV argon bombardment and W>5). On the other ¨ hand, Hofsass et al. investigated c-BN deposition purely from B+ and N+ ions with mass-separated ion beam deposition. Previously, only the parameter range of indirect energy input has been investigated [22]; however, recent results show that the ion bombardment can be lowered significantly and c-BN is already obtained at ion energies around 130 eV [15] (arrow 2 in Fig. 1b). In light of these new results, certain parallels concerning the dependence of ta-C and c-BN deposition on the nature of the energy input exist. Another way to reduce the ion bombardment was described very recently: with indirect energy input, after successful nucleation of c-BN at standard parameters the ion energy can be reduced significantly and c-BN growth continues [14,23] (arrow 1 in Fig. 1b). 2.1.4. Parameter dependences The dependences of the sp3 content on the substrate temperature and the ion angle of incidence are shown schematically in Fig. 2. ta-C is usually deposited at room temperature, and a steep decrease of the sp3 content has been found above approximately 150 °C [8,12] and 260 °C for ta-C:H [16 ]. In contrast, increasing the substrate temperature promotes c-BN deposition [24,25] and slightly decreases the required ion bombardment

S. Reinke, W. Kulisch / Surface and Coatings Technology 97 (1997) 23–32

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Fig. 2. Schematic dependence of the sp3 content on substrate temperature and ion angle of incidence when crossing the relevant phase boundaries.

[26 ]. Therefore, as indicated in Fig. 2a, conditions exist where an increase of the temperature leads from h-BN into the c-BN parameter range. Furthermore, the existence of a principal minimum temperature of about 150 °C for c-BN deposition has been shown [27]. In principle, c-BN can be deposited at least up to 900 °C with CVD [28,29] and 1300 °C with PVD [30]. Fig. 2b schematically shows the sp3 content of ta-C films to decrease with increasing angle of incidence [31,32]. On the other hand, c-BN deposition is possible with ion angles between 0° [33] and 80° [27]. Increasing the angle leads to a slight reduction the ion bombardment required for c-BN growth [34]. Therefore, starting from conditions slightly below the c-BN parameter range at normal incidence the behaviour illustrated schematically in Fig. 2b is obtained. 2.1.5. Nucleation So far, only the growth processes of ta-C and c-BN have been discussed. However, the nucleation process also has to be considered. ta-C shows no phase evolution during its growth; only a mixing layer with a thickness comparable with the ion range, where substrate–film intermixing occurs, has been reported [35]. On the other hand, c-BN shows a well-defined nucleation sequence which has been found with indirect [36 ] as well as direct PVD [37] and also with CVD [38]. First, a few nanometres thick amorphous layer is obtained which has not been characterized sufficiently up to now; however, the existence of a mixing layer is most likely. In the following, an h-BN layer occurs which is textured with its c-axis parallel to the substrate surface. The thickness of this layer varies between 5 and 30 nm for PVD and 50–100 nm for CVD. On top of this layer, textured c-BN is obtained with one [111] direction parallel to the substrate surface. Under these conditions, strong geometrical similarities between [0002]-textured h-BN and c-BN exist [39–42] which are believed to play a significant role in the nucleation process [18].

2.1.6. Properties of ta-C and c-BN films The maximum sp3-content of ta-C films is about 80%, whereas nearly pure c-BN films (except for the nucleation sequence) can be achieved with PVD methods. CVD of c-BN leads to less pure films with maximum c-BN contents of about 80%; the reason for this is related to the presence of hydrogen in CVD processes [43,44]. Both, ta-C and c-BN exhibit large compressive stresses in the gigapascal range. In the case of c-BN, annealing at temperatures above 800 °C reduces the stress [45,46 ] and improves the crystallinity of the films; this is reflected by a narrowing of the c-BN X-ray diffraction peaks [47]. In contrast, annealing of ta-C films results in a phase transformation to sp2-bonded material for which different transition temperatures between 400 °C [48] and 750 °C [49,50] have been reported.

3. Ion-assisted deposition In general, the process of ion-assisted deposition can be divided into three phases on different time scales: the collision cascade (10−14 s), subsequent energy dissipation via phonons (thermal spike, 10−11 s) and thermal processes on a macroscopic time scale. These processes form the basis of several models of ta-C and c-BN growth. In general, the processes of sp3 phase formation and relaxation can be distinguished, and this is taken into account in the overview in Table 1. In the following, the models will only be sketched briefly; for a detailed review we refer to Ref. [18]. 3.1. Modelling of ta-C deposition Two classes of models which differ by the role of the thermal spike have been proposed for ta-C deposition. In the quenching model, the thermal spike is assumed to cause the formation of sp3 bonds directly. By calculat-

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Table 1 Summary of the relevant processes included in the various models for c-BN and ta-C deposition. T denotes the substrate temperature; TS s and CC are abbreviations for thermal spike and collision cascade respectively Model

Phase formation

c-BN Quenching [51] TS: quenching Indirect subplantation [52] CC: knock-on implantation Dynamic stress [53] CC: interstitial formation Sputtering [18] attachment

ta-C Quenching [54] Direct subplantation [55] Static stress [56 ]

TS: quenching CC: penetration CC: interstitial formation

Relaxation

TS:sp2 T sp2 s TS:cryst. c-BN

TS:sp2 TS:sp2

f

with E 5/3 ion 1/W*f+0.016p E 0 E −E 1 f=1−exp − ion (2) E 2 n i s3e (3) E 5/3 ion 1/W*+0.016p E 0 Here, f(E ) denotes the penetration probability of an ion ion. E and E are parameters which can be determined, 1 2 e.g. by TRIM simulations [18,17]. Furthermore, n is i the number of interstitials produced per ion [42] and e is the Young’s modulus of the film. In order to relate the density and the stress to sp3 phase formation, basic assumptions have to be made: according to the subplantation model, the hybridization is determined by the local density, whereas the stress model assumes an HP–HT-like phase transition. r=r

ing the ‘‘temperature’’ evolution on the basis of the macroscopic equation of heat transport, for an initial energy in the 100 eV range, typical spike diameters of a few nanometres have been found [57] where the temperature exceeds 1000 K. During a spike, atoms can diffuse; the number of jumps during a spike which require a thermal activation energy E has been calculated to be 0 E 5/3 ion (1) n #0.016p r E 0 where E is the primary ion energy and p a dimensionion less parameter of the order of unity. Weissemantel et al. pointed out the generation of high temperature–high pressure (HP–HT )-like conditions within a thermal spike [54]. By comparison with the equilibrium phase diagram of carbon, the formation of sp3 bonds is discussed. However, it is not diamond, which is the stable modification under the assumed conditions, that occurs but the metastable ta-C that is formed; this is attributed to the high quenching rates of 1014–1015 K s−1. Quenching processes can be simulated by molecular dynamics (MD) calculations. Indeed in the case of carbon, amorphous structures comparable with those observed experimentally have been calculated [58,59]. Recently, the role of the substrate temperature on quenching processes has been pointed out [51]; at least with crystalline materials, high temperatures lower the thermal conductivity. This results in a decrease of the quenching rate, which is believed to be the reason for the formation of crystalline materials. In the second class of models (direct subplantation model [55], static stress model [56,60]), the processes relevant for the phase formation are related to the collision cascade. Its main role is the formation of interstitials which leads to a local densification, and hence to the formation of compressive stress. The thermal spike is regarded to be detrimental to sp3 formation

A B

in these models since it induces relaxation processes according to Eq. (1). Taking into account a balance between interstitial formation and relaxation processes, simple analytic equations for the density r [61] and the stress s [56 ] have been derived: 0

A B B

A

A B

3.2. Modelling of c-BN deposition The basic ideas of the models outlined above have also been proposed for c-BN deposition. The static stress model was adopted from ta-C nearly without any change [62]. The existence of crystalline phases is explained by the higher substrate temperatures compared with ta-C. A thermodynamic analysis of the Gibbs free energy shows that the [0002] texture of the h-BN nucleation layer and the [111] texture of the subsequent c-BN found experimentally during the nucleation process are the most stable configurations under the influence of a biaxial stress field [63]. A model focusing on the dynamic stress present during c-BN growth has been developed by Mirkarimi et al. [53]. Again, the role of the collision cascade for the generation of defects is pointed out, but now a thermal defect recombination with a rate constant

A

B

E a3n exp − 0 (4) 0 kT s is assumed. The maximum interstitial concentration Nmax (and subsequently the maximum stress) has been i found to scale as Nmax 3 i

S

WEmE ion a

(5)

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Fig. 3. The densification dependence on E according to the model of Robertson (Eqs. (2) and (6)). The parameters were chosen according to i Robertson’s work [52,61]. For direct subplantation: p=0.3, E =25 eV, E =65 eV (from TRIM calculations in Ref. [61]). For indirect subplantap q tion: E =72 eV, E =100 eV (from TRIM calculations in Ref. [17]) and W*=1 and 10 respectively. Also, following Robertson [52] E =6 eV was p∞ q∞ 0 taken for c-BN which is twice the value used for ta-C [61]). a=0 was assumed leading to maximum densification. The inset shows the penetration probability f(E ) and the number of interstitials created in the first monolayer q(E ). The bold horizontal line indicates the density of diamond i i and c-BN.

where m is the ion mass and a the rate constant according to Eq. (4). Also, the subplantation model has been modified in the case of c-BN deposition. In order to describe the formation of crystalline material, interstitial condensation and attachment to c-BN crystals is assumed. Furthermore, indirect energy input is taken into account due to recoil implantation processes of surface atoms (the formation of a Frenkel pair inside the bulk does not densify the structure). This approach leads to the expression for the densification [52]

C

r=r 1+ 0

qb/(a+b)

D

(6) E 5/3 ion 1/W*−qb/(a+b)+0.016p E 0 which is quite similar to Eq. (2). Here a and b are rate constants for interstitial vacancy recombination and interstitial condensation respectively. q denotes the probability of an incident ion generating an indirect subplantation process2 [17,18] instead of the penetration probability f which was erroneously used by Robertson [52]. The energy dependence of q was determined by TRIM calculations [17]; the inset of Fig. 3 shows a higher threshold energy for q and only approximately half the saturation value of f. This indicates that the process of indirect subplantation is less effective than direct subplantation. A different approach is regarded with the sputter

A B

2Knocking a surface atom below the first monolayer.

model [18,64], which describes an evolutional growth process: the phase with the higher growth velocity dominates and finally overgrows the competing one. The model further assumes attachment processes (preferential bonding [5]) instead of a phase conversion. The main role of the ion bombardment is selective sputtering of h-BN with respect to c-BN which influences the growth velocities: without ion bombardment, h-BN always occurs because of its lower density (u >u ). h c However, in a certain range close to the re-sputter boundary u >u can be achieved and c-BN deposition c h occurs. The sputter model can be quantified, leading to the following conditions for the boundary W between h h-BN and c-BN, and the re-sputter boundary W [64,17]: c s (7) W= B c Y c s 1 W = B (8) h Y g c with Y /[Y (r −r )] h g= h c c r −r c h Here s (T ) denotes the sticking probability of boron B s and Y (E ,m,H) the sputter yields of h-BN and c-BN. h,c ion In contrast to the above models, no relaxation of the bond structure towards the sp2-bonded h-BN is assumed: once c-BN is formed, relaxation is always directed towards the crystalline c-BN.

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3.3. Discussion The energy dependence of vacuum arc deposition of ta-C and plasma beam deposition of ta-C:H, as shown schematically in Fig. 1a, can be fitted to Eq. (2) (direct subplantation) and Eq. (3) (static stress model ) by a suitable choice of the relevant parameters [13,55,61]. However, the more general IBD data of Fig. 1a cannot be fitted with Eqs. (2) and (3), indicating that at least the quantitative description of the thermal spike relaxation process is not correct. Fig. 3 shows that the subplantation model, in contrast to the stress concept, takes the differences between direct and indirect ta-C deposition into account. The quenching model, which points out collective processes instead of local densification, is in agreement with MD simulations. However, it should also be noted that in this case a stepwise densification is required because a phase transition (sp2sp3) is accompanied by strong volume changes. Therefore, densification can be regarded as the most general process of all bulk growth models. The densifying flux of material below the surface has to be sustained by direct penetration or knock-on collisions. Effective densification can only occur if the flux of atoms reaching subsurface positions at least equals the flux of incorporated atoms. If this is not the case, part of the material would be incorporated at the surface and no complete densification could be achieved. The condition for densification can be expressed as q≥1/W*

(9)

f≥1/W*

(10)

for indirect and direct energy input respectively. In Fig. 1b, the quantities 1/q and 1/f are compared with experimental data concerning W*. It can be seen that during direct as well as indirect ta-C deposition the respective equations (Eqs. (9) and (10)) are fulfilled. Densified structures like ta-C are over-constrained in view of the constraint model [65] and, therefore, tend to relax towards the sp2 structure via plastic flow. This process is supported by high temperatures, which may account for the temperature dependence of ta-C deposition. During the growth process, relaxation occurs near the surface, whereas with post-depositional annealing a rearrangement of the bulk is required. This may be the reason for the different critical temperatures of 150 °C and at least 400 °C for both processes. Phase formation of c-BN is discussed in different ways. However, since c-BN crystals are about an order of magnitude larger than typical spike dimensions, the film must grow via attachment of material to existing c-BN crystals. The bonding structure of material added to the film is determined by the state of its surrounding, which is confirmed by the recent experiments were

nucleation and growth have been separated (see above). In principle, either the attachment of single atoms, as assumed in the sputter and indirect subplantation models, or the attachment of ensembles of atoms (thermal spike) are possible. In the case of the latter, it has to be taken into account that a thermal spike cools down from its outer part so that the spike region can adapt to the crystal structure of the surrounding [57]. As discussed above for ta-C, the quenching process requires a stepwise densification of h-BN. However, amorphous modifications with densities between h-BN and c-BN (which in analogy to ta-C should be named ta-BN ) have not been found so far. In agreement, MD calculations simulating the quenching process show a segregation of boron and nitrogen atoms at high densities but no formation of c-BN [66 ]. On the other hand, densities up to 2.7 g cm−3 have been found for amorphous boron-rich BN films obtained with ion-beamassisted deposition [67]. In this case the stoichiometry constraint does not hold, and nitrogen ions can densify boron-rich regions even with indirect energy input. It should be noted that, according to Fig. 1b, the nucleation process of c-BN always takes place under conditions where densification can occur in principle. On the other hand, the recent experiments (separation of nucleation and growth; arrow 1 in Fig. 1b) show that the c-BN growth process is possible under conditions where Eq. (9) is not fulfilled. However, the role of the required residual ion bombardment is not clear in this concept. In view of the stress model, it may be necessary to generate a certain stress required for c-BN growth. In Fig. 4, the predictions of the different models are compared with the experimental results of the standard c-BN deposition process. The observed energy dependence is well described by the sputter model, whereas indirect subplantation (and also the direct stress model not shown in Fig. 4) cannot account for the compensational behaviour of ion energy and W*. However, the

Fig. 4. Comparison of the predictions of the sputter model, the subplantation model (onset of densification with Dr/r=0.1), and the dynamic stress model with experimental data of c-BN deposition. For details of the data collection, we refer to Ref. [5].

S. Reinke, W. Kulisch / Surface and Coatings Technology 97 (1997) 23–32

recent results outlined above show that c-BN can also be deposited without significant sputtering, i.e. under conditions where nearly all of the material is incorporated within the film. Thus, at the present time, it must be concluded that none of the present quantitative models can describe all aspects of c-BN formation. The most important difference from ta-C deposition, however, concerns the relaxation process. Whereas thermal activation in the case of ta-C leads towards the sp2 phase, c-BN remains sp3-bonded and only the stress is reduced. This fact must be taken into account in future models concerning c-BN deposition.

4. Stress Both ta-C and c-BN films show high compressive stress in the gigapascal range. Stress in thin films leads to shear forces at the interface between the film and the substrate, as illustrated schematically in Fig. 5. The shear stress t is proportional to the film thickness [68], so that at a certain thickness it reaches the critical shear stress t . Here, locally a dislocation is generated which c moves along the film plane leading to crack formation. In general, two measures for solving the adhesion problem exist. The first is to reduce the stress during the growth process. The second, which is referred to in Section 5, is the modification of the interface which is related to the nucleation process. The stresses in ta-C films have been found to be roughly proportional to their sp3 content [13]. Therefore, it can be concluded that stress is closely related to the over-constrained structure of ta-C and a significant stress reduction process cannot be found. In contrast, the stress of the crystalline c-BN films can be reduced in principle. As in view of certain applications

Fig. 5. Schematic representation of the forces generated by stress in thin films. Left: ta-C; right: c-BN with h-BN nucleation layer.

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annealing is not acceptable, measures to reduce the stress during the growth process must be found. To meet this end, the stress model of Davis ( Eq. (3)) has to be considered again. The term 1/W* in the denominator can be neglected in the case of the standard c-BN growth process [69]. For n the dependence i n 3E , as derived from TRIM, is used [42] instead of i ion n 3EE as proposed by Davis [56 ]. This finally leads i ion to s3eE−2/3 ion

(11)

which has been compared to experimental data [42]. The steep increase of s at the boundary between h-BN and c-BN observed experimentally is, according to Eq. (11), determined by a change in the Young’s modulus. Therefore, the high stress values of c-BN films can also be regarded as a consequence of the presence of c-BN rather than the reason for it as assumed by the stress model [62]. With increasing ion energy, the stress is reduced due to thermal-spike-induced relaxation processes; however, the agreement between experiment and theory is only qualitative [42], indicating again the uncertainties in the description of thermal spike relaxation processes. Fig. 6 shows stress values of c-BN films deposited with different techniques. Although a comparison of different stress data is rather difficult, in agreement with the above discussion the stress is tendentially highest at low ion energies. This holds for CVD as well as PVD deposition. Up to now, the influence of deposition parameters like substrate temperature and W on the stress has not been investigated systematically. Therefore, it is likely that, in the future, stress may be further reduced and values of 1–3 GPa which are acceptable for tribological applications can be reached reproducibly.

Fig. 6. Compilation of literature data on compressive stress in c-BN films. Only films with q ≥0.7 have been taken into account. Data stem c from Refs. [20,45,70–74].

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5. Adhesion Adhesion is determined by the properties of the interface between a thin film and substrate and is, therefore, closely related to the nucleation process. In the case of c-BN, mainly deposition on silicon has been investigated. Without special measures to improve adhesion, the critical thickness d of c-BN films lies in the c range between 100 and 300 nm [26,75], whereas with ta-C:H values up to 800 nm have been reported [13]. In the case of c-BN, modification of the interface due to interlayers has been shown to enhance the adhesion successfully [45,47,76,75]. The adhesion of thin films is normally investigated by scratch tests. The shear stress induced by a tip with radius r and force W is given by the relation [77] rH c (12) Er2−r2 c where r =(W/pH )0.5 denotes the contact radius and H c the Vickers hardness of the substrate. In Table 2, the results of scratch tests on c-BN films reported in the literature are summarized. It can be seen that with quite elaborate measures the critical shear stress can be increased to values of 2–3 GPa. In particular, gradient layers and substrate film intermixing due to high energy ion bombardment have been found useful. In these cases, the interface is broadened, which leads to a reduction of the local shear forces. In general, the adhesion strength is determined by a large variety of parameters (e.g. purity, grain size, intermixing between film and substrate) and cannot be simply calculated. However, the mechanical properties of the materials involved can be considered. In Table 3 the shear modulus G and the tensile strength s of t different carbon and BN modifications are summarized. As expected, h-BN (c), which corresponds to an orientation with the c-axis perpendicular to the substrate surface, shows the lowest mechanical stability. However, even the mechanical properties of h-BN as found within the nucleation sequence are about an order of magnitude t=

Table 3 Tensile strength s and shear modulus G of carbon and BN t modifications. As shear modulus, the relevant values of c are taken; 44 G of h-BN (a) was estimated from the Vickers hardness according to G#HV/8 which holds for c-BN and several other ceramics [81] Material

s (GPa) t

G (GPa)

Diamond c-BN

3

[82]

h-BN (a) h-BN (c)

0.04 0.0028

[84] [83]

578 300 550 70 2–3

[82] [83] [81] [83]

smaller than those of c-BN. If we take as a rough estimation for the critical shear stress t #G/30 [85], we c get values of t of approximately 2–3 GPa for h-BN (a) c which correspond to the best experimental values of Table 2. Therefore, at least for thin films under sliding applications, the adhesion is limited by the h-BN nucleation layer which is confirmed by recent TEM investigations [86 ]. In the future, ways to avoid the nucleation layer have to be investigated systematically. In the case of ta-C deposition no nucleation sequence occurs, and the mechanical properties of ta-C are comparable with those of diamond. If a suitable mixing and chemical reaction (carbide formation) with the substrate can be achieved, the interface of ta-C films should be very stable, because carbides also show good mechanical properties. Therefore, the main problem limiting adhesion of ta-C films is the high stress which, however, cannot be reduced because it is a consequence of the over-constraint structure of ta-C.

6. Summary The processes of ion-assisted ta-C and c-BN deposition have been discussed in light of experimental data. Significant differences concerning the substrate temperature and the ion angle of incidence have been found. Whereas ta-C requires low temperatures and normal ion

Table 2 Scratch test experiments with c-BN films on silicon substrates using different measures of adhesion improvement. W denotes the critical load, r c the tip radius and v the scratch speed; d is the critical film thickness above which peeling occures; the critical shear stress was calculated according c to Eq. (12) Reference

Deposition

d (nm) c

Scratch test

[78] [79] [47]

direct on Si BN ion mixing boron gradient layer Ti film+annealing direct on Si Si gradient layer on WC, 330 °C Si gradient layer on WC, 600 °C boron gradient layer

<150 >600

r=0.2 mm v=100 m min−1 r=0.05 mm v=0.1 m min−1 r=0.2 mm v=0.01 m min−1

[75]

[80]

<300 1500

r=0.2 mm

W (N ) c 30 0.75 1.6 <70 #80 12

t (GPa) c 1.88 1.2 1.74 <2.87 #3 1.0

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incidence, c-BN deposition is supported by high temperatures and oblique ion incidence. Several models have been proposed in order to explain the experimental data. In general, the deposition process can be divided into phase formation and relaxation processes. None of the simple models is able to describe all aspects of ta-C or c-BN deposition; however, some basic statements can be made. Whereas phase formation in the case of ta-C can be achieved by local densification due to penetration (direct energy input) or recoil implantation (indirect energy input), c-BN grows via attachment of material to c-BN crystals. ta-C deposition and the c-BN nucleation process always take place under conditions where bulk densification is possible. In contrast, recent results, in our view, show that the c-BN growth process proceeds without bulk densification. The most striking differences between ta-C and c-BN concern the relaxation process. Whereas thermal activation transforms ta-C into the sp2 state, annealing of c-BN stabilizes the sp3 structure and reduces the stress. For both cases, a thermal-spike-induced relaxation process has been proposed; however, discrepancies with experimental data indicate that the simple description of thermal spikes which is generally used is not correct. The main problem concerning industrial application of ta-C and c-BN is their poor adhesion. This is related to the stress and the mechanical strength of the interface. Here, the situation is somewhat complementary. Whereas in the case of ta-C the stress is the consequence of the structure, reduction of the stress of c-BN films is in principle possible. On the other hand, the interface of ta-C films does not seem to be critical, whereas in the case of c-BN the textured h-BN of the nucleation sequence is the weakest link limiting adhesion.

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