Tribology of amorphous, nanocrystalline, and crystalline slabs of Si, C

PHYSICAL REVIEW B 72, 115202 共2005兲

Tribology of amorphous, nanocrystalline, and crystalline slabs of Si, C, and SiC V. I. Ivashchenko,1 P. E. A. Turchi,2 A. Gonis,2 V. I. Shevchenko,1 and L. A. Ivashchenko1 1Institute

of Problems of Materials Science, NAS of Ukraine, Krzhyzhanovsky Street 3, 03142 Kyiv, Ukraine Livermore National Laboratory (L-353), P. O. Box 808, Livermore, California 94551, USA 共Received 9 March 2005; revised manuscript received 19 April 2005; published 2 September 2005兲

2Lawrence

Atomistic molecular dynamics simulations are applied to the study of sliding friction of a-SiC / a-SiC, a-SiC / c-C, nc-SiC / c-C, and c-Si/ c-C systems. The friction coefficient and the structural evolution of the systems are investigated as functions of sliding velocity, temperature, and normal load. Based on the simulation results, the physics of atomic-scale sliding friction in the semiconductors under investigation is clarified, and the properties are validated with available experimental results. DOI: 10.1103/PhysRevB.72.115202

PACS number共s兲: 61.43.Dq, 71.15.Pd, 71.23.Cq

Recent advances in the deposition of carbon and silicon carbide films hold promise for producing hard protective and wear resistant coatings on a variety of substrates.1–5 It has become important to understand the friction and wear properties of such coatings. Coating surfaces are usually rough, and friction is generated between contacting asperities on the surfaces. The contact area is defined beyond the atomic scale, and various friction models provide insight into the behavior within these contacts.6,7 While a few theoretical investigations of the tribological properties of diamond exist,6,8–11 analogous comprehensive studies on silicon-based materials are yet lacking. In addition, the theoretical science of atomic-scale sliding friction between amorphous and crystalline, amorphous and amorphous, nanocrystalline and crystalline materials is still in its infant stage. At the same time, there is a growing interest in the application of molecular dynamics 共MD兲 simulations to the tribology of metallic systems. Such phenomena as static friction, indentation and cutting, lubrication have been studied. Moreover, MD simulations have been used to investigate microstructural evolution at a sliding metallic interface. 共Reviews on the theoretical investigations of sliding friction in metallic and diamond systems can be found in Refs. 6, 7, and 12.兲 In this paper, we have carried out a series of atomistic MD simulations to gain insight into the physics of sliding friction of silicon-carbon alloys. We have considered the sliding of amorphous, nanostructured, and crystalline heterocouples under different sliding conditions. The pairs of different materials were chosen to simulate the sliding process that most often occurs in tribological experiments, for example, in ball-on-plane and polishing tests.2–5 Sliding friction was investigated as function of sliding velocity 共V兲, temperature 共T兲, and normal load 共FN兲. The sliding systems, analyzed in the present paper, are represented by two sliding blocks 共slabs兲. The lower slab is associated with diamond or a-SiC, while the upper one is made of a-SiC, nc-SiC or c-Si. Experimentally, heat diffuses away from the sliding interface. To simulate this effect, two reservoir regions are located at the outer surface of the upper and lower sliding slabs. During the simulation the reservoirs are thermostated to maintain a constant low temperature. In the reservoirs, external normal 共FN兲 and tangential forces are applied to each atom. The normal force is constant, and the 1098-0121/2005/72共11兲/115202共6兲/$23.00

uniform tangential force applied to each reservoir atom is a time-dependent quantity chosen such that the average tangential velocity in the reservoir is constant ±V / 2 equal and opposite in sign in the upper and lower reservoirs. Hence, the forces are applied only to the atoms in the reservoirs. Except for the temperature control and force application, the atoms in the reservoirs are treated the same way as those in the rest of the system, and the atoms are free to enter or leave the reservoir regions. A number of the reservoir atoms is maintained constant during MD simulations. In the corresponding experiments, the initial ball/plane contact is made when the ball is rotating, i.e., there is a relative speed between the ball and the plane. The simulation is initiated in a similar fashion. At t = 0, all the atoms in the upper slab are given a velocity in the positive x direction with a magnitude equal to V / 2, while all the atoms belonging to the lower slab are given a velocity in the negative x direction with exactly the same magnitude V / 2. Therefore, at t = 0 the relative sliding velocity of the system is V. Atoms interact with each other through the same interparticle potentials whether they are in the reservoir or not. Since we consider sliding system based on Si and C atoms, the Tersoff pair potential is appropriate for MD simulations.13 It was shown that this potential provides correct results in many applications.13–16 The selection of a proper classical potential is crucial to reproduce the real physical behavior of a system under sliding conditions. Prior to carrying out the simulations on sliding, we have generated the sliding slabs by equilibrating bulk samples under twodimensional periodic boundary conditions for 20 ps. The a -SiC sample was generated by slow cooling the melt from 8000 K down to 300 K.16 The nc-SiC bulk sample represents the amorphous structure of a-SiC with one 3C u SiC cubic cluster with a side of 8.9 Å positioned on the lower 共001兲 plane of the basic simulation cell. The nanocrystallite was fixed during cooling, and a cooling rate of about 1013 K / s was considered. All the sliding couples were fitted to provide the same box sizes in the x and y directions 共ax , ay兲. The 506-atom upper slabs of a-SiC and nc-SiC were fitted to the 550-atom lower diamond block with a bulk modulus 共B兲 of 2.2 Mbar for the upper blocks.13 The simulation box is ax = ay = 17.8 Å. In the case of the c-Si/ c-C sliding system, we have chosen a 576atom diamond cluster, i.e., 6 ⫻ 6 ⫻ 2共a0兲 with a0 = 3.56 Å,

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FIG. 1. Friction coefficient of a-SiC / a-SiC, a-SiC / c-C, nc-SiC / c-C, and c-Si/ c-C sliding systems under the following sliding conditions: V = 100 m / s, T = 300 K, and FN = 1 nN as a function of sliding time. The solid lines correspond to the friction coefficients averaged over 25 points.

which gives ax = ay = 21.36 Å. To fit the upper silicon slab to this size, we have chosen a 4 ⫻ 4 ⫻ 4共a0兲 cluster with a0 = 5.34 Å. Thus, our lattice parameter for silicon is smaller by 1.7% compared with the experimental value of 5.43 Å. Prior to sliding, both contact slabs were equilibrated during 20 ps. All the sliding processes occurred during 50 ps under NVT conditions 共constant number of particles, volume, and temperature兲. The ratio between the friction force and the normal force gives the friction coefficient ␮. The average value of ␮共t兲 was calculated after 15 ps sliding. This time is sufficient for reaching the steady-state friction. The friction coefficient of the sliding systems was calculated for V, T, and FN in the range of 5 – 800 m / s, 300– 3000 K, and 0.5– 5 nN, respectively. Figure 1 displays typical plots of the time evolution of the friction-coefficient for each system under consideration as observed during MD simulations. The friction coefficient clearly exhibits a transient overshoot before it settles down to an average steady-state value. During the transient stage, the friction coefficient reaches a maximum value 共␮max兲 of about 0.5 for almost all tests. The steady state is reached after about a 10 Å sliding. The jump of the friction coefficient during the transient stage 共⌬␮兲 decreases in the sequence 共c-Si兲-共nc-SiC兲-共a-SiC兲 sliding on a diamond slab. Naturally, the oscillation of the friction coefficient decreases when sliding occurs on crystalline slabs. Transient behavior

in friction is commonly observed in experiments and simulations on sliding of diamond such as 共DLC兲 films,5 metallic glasses,12 and crystalline materials.5,17 It is believed that subsurface microstructures are developed during the transient period. We have thoroughly investigated the microstructure of the contact zone before and after sliding. In Fig. 2 we show the atomic configurations of the a-SiC / a-SiC, a-SiC / c-C, and c-Si/ c-C sliding couples at the beginning and at the end of sliding under different sliding conditions. In addition, in Fig. 3 the microstructure evolution of the c-Si/ c-C and a-SiC / c-C systems after sliding at various velocities is presented. Based on these results and taking into account the findings on other sliding systems, we come to the following concepts of sliding behavior of the systems under investigation. In the case of the c-Si/ c-C sliding couple, the lattice disordering of the lower layers of the upper block occurs during sliding. So, the friction of c-Si/ c-C is analogous to the one occurring between two amorphous slabs. The lattice disordering occurs mostly during the transient period, although the dynamic formation of microstructure takes place during the entire sliding time. The disordered region increases with sliding distance. The silicon slab becomes denser during sliding mainly due to a densification of the disordered region. We suppose that the densification of the disordered samples when sliding along hard surfaces 共for example, the diamondlike surface兲 is the general feature of the sliding behavior of disordered materials. The sliding plane shifts inside the silicon slab, because of the high adhesion of the silicon layers to the diamond surface. These layers move together with the diamond block. No material mixing is observed at the silicon-diamond interface. The observed microstructure changes can be explained by the difference in bond strength that increases in the sequence Si- Si, Si- C, and C - C. Such a situation is likely to be general and can be observed for other sliding heteroslabs with different bond strengths. The sliding of the a-SiC slab on the diamond block leads to the densification of the amorphous slab. Since in a-SiC the disordered region is larger than that in c-Si, the extent of densification of the amorphous slab is higher than that of the silicon slab. The sharp interface is preserved during sliding. Appreciable material mixing in the vicinity of the sliding interface is not observed, and the same is true for the adhesion of the amorphous material to the diamond surface. Therefore one can expect that the abrasive wear of a-SiC films will be lower than that of silicon wafers, as was experimentally found in ball-on-plane tests.3,4 The adhesion wear is expected to be predominant in the c-Si/ c-C sliding, despite the low friction coefficient caused by the creation of the amorphous sliding interface within the silicon block. For the a-SiC / a-SiC sliding couples, the upper and lower slabs are chemically identical. Therefore, in the simulations, mixing is observed and the mixed layer grows as sliding proceeds further in time. The mixing of the atoms of the upper and lower blocks is mostly caused by the motion of the contacting blocks. Self-diffusion could also give rise to mixing. However, to achieve the observed amount of mixing, a much longer time or a much higher temperature would be required. We note that material interfacial mixing was revealed also in sliding of metallic glasses.12 In addition to

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FIG. 2. 共010兲 Cross sections of atomic configurations of a-SiC / a -SiC 共upper sequence兲, a-SiC / c-C 共middle sequence兲, and c-Si/ c-C 共lower sequence兲 sliding systems after 50 ps simulation. Si: large open circles, C: small full circles. Only part of the carbon atoms belonging to the lower diamond slab is shown. Sample notation: 共V关m / s兴 − T关K兴 − FN关nN兴兲.

FIG. 3. 共010兲 Cross sections of atomic configurations of c-Si/ c-C 共upper sequence兲 and a-SiC / c-C 共lower sequence兲 sliding systems after 50 ps simulation at V = 0, 100, and 500 m / s, T = 300 K, and FN = 1 nN.

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FIG. 4. Density N共z兲 of the a-SiC / a-SiC sliding system after 50 ps simulation as a function of distance along the z direction. The vertical arrow indicates the interface region with the low density. The sliding conditions V = 800 m / s, T = 300 K, FN = 0.5 nN.

these peculiarities, the a-SiC / a-SiC sliding is accompanied by the formation of a low-density region near the sliding interface at V 艌 100 m / s. In Fig. 4 we show the density of the a-SiC / a-SiC pair in the z direction after 50 ps sliding. The reduction of the density is seen around the sliding plane. The notion of excess free volume in metallic glasses has been discussed by Spaepan and Turnbull18 and Argon.19 It follows from these findings that the reduction of the density near the sliding interface at high speed sliding is a general feature of the sliding of two noncrystalline systems. The character of the sliding of the nc-SiC slab on a diamond block is similar to that of the amorphous slab. However, the presence of the 3C u SiC islet slightly modifies the sliding phenomenon. In particular, the crystallite atoms mix with other atoms of the amorphous slab, and consequently the crystallite disappears mostly during the transient period. As in the case of the a-SiC / c-C sliding pairs, for the nc-SiC / c-C sliding systems, the weak carbon diffusion to-

FIG. 5. Friction coefficients averaged over 25 points of c-Si/ c-C, a-SiC / c-C 共the sliding conditions are the same as for the c-Si/ c-C pair兲, and a-SiC / a-SiC sliding systems as a function of sliding time.

FIG. 6. Steady-state friction coefficient of a-SiC / a-SiC 共open circles兲, nc-SiC / c-C 共full squares兲, a-SiC / c-C 共open squares兲, and c-Si/ c-C 共full triangles兲 sliding systems after 50 ps sliding as a function of sliding velocity 共V兲, temperature 共T兲, and normally applied force 共FN兲.

wards the upper slab is observed at the highest T, FN, and, to a lesser extent, V. Figure 5 shows the influence of temperature and normal load on the character of the friction of a-SiC / a-SiC, a-SiC / c-C, and c-Si/ c-C sliding couples. Temperature and normal load have a similar effect on the friction coefficient for all the systems. An increase in both factors lowers the value of ␮m. At high temperature, during the transient period, the friction coefficient reaches a maximum value faster than at low temperature. The oscillations are smeared out with an increase in normal load and are insensitive to varying temperature. The results of the investigations of the friction coefficient under various sliding conditions are summarized in Fig. 6. The steady-state friction coefficient of all the sliding couples decreases with an increase in sliding velocity, temperature, and normal load. Most likely, the reduction of ␮ with increasing sliding velocity occurs owing to strengthening the systematic atomic motion related to the excited phonons and because the average shear stress at the sliding interface decreases as V rises. The reduction in shear stress results from decreasing the atomic-scale roughness of the sliding surfaces caused by the densification of the disordered upper layers during high-speed sliding. On the other hand, the noted densification can be considered as a hardening of the interface region, in which case an increase in V will promote a reduction of the friction coefficient. It should be noted that at low-speed sliding, there is enough time for the sliding layers to relax and disordering does not arise. In this case, the motion often becomes intermittent, with the system alternately sticking and slipping forward.7 The intensity of the phonons excited at previous slips can be not enough to promote subsequent slip events. Under such conditions, friction is relatively insensitive to sliding speed,20 or increases with V.21,22 To establish the role of the temperature control on sliding,

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we performed simulations in the case where the temperature was controlled both in the reservoirs and over all the volume of the sliding slabs. The average temperature of the upper block in the a-SiC / c-C sliding with V = 100, 500, and 800 m / s at constant temperature of 300 K of the reservoirs was found to increase up to 600, 1200, and 1400 K, respectively, after a 10 Å slide. The reduction of the temperature in the interface region to 300 K 共by corresponding rescaling the velocities perpendicular the sliding direction兲 leads to an increase of ␮ by a factor two. We deduce from this finding that the thermal activated motion is responsible for the decrease in ␮ with an increase in the sliding velocity and the temperature of the sliding slabs. From our atomistic simulations the behavior of ␮ that depends on sliding velocity and temperature is consistent with the ␮共V兲 and ␮共T兲 dependences established in experiments on c-Si and DLC film sliding.2,5 As for the ␮共P兲 dependence, the behavior of ␮ under normal load requires some explanation. In most cases of macroscopic friction, the friction force increases proportionally to the load, a relation known as the Amontons law. According to the model that describes the experimental situation,20 the contact area increases proportionally to the load to keep a constant normal pressure. By assuming a fixed constant shear stress in the contact region, Amontons’ law follows. In atomic-scale MD simulations, the contact area is a constant, and because of adhesion, the contact is established even at negative loads. Thus, the results displayed in Fig. 6 can be interpreted as follows: at the constant contact area, the friction force, and hence the average shear stress, are nearly independent of the normal load. We have established that the temperature of the sliding interface weakly changes during sliding under various loads. This indicates that the friction coefficient has to behave as a decreasing function of the normal pressure. Our sliding model for the c-Si/ c-C couple predicts a reduction of ␮ with an increase in the normal load, in agreement with the ␮共FN兲 dependence determined from the measurements performed on Si 共001兲 and DLC surfaces with a Si 共001兲 ball.2 In addition, there have been several studies on the effect of load on ␮ for diamond sliding on diamond. It has been reported that various dependences on load are obtained for different crystal and polished orientations.8 It is difficult to compare these traditional friction measurements to results of atomistic modeling over large heterogeneous samples. The friction coefficient obtained from the nc-SiC / c-C sliding system at low sliding velocities is slightly lower than that of the a-SiC / c-C system. However the ␮ converge toward a similar value for both systems with increasing veloc-

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S. Yang, D. Camino, A. H. S. Jones, and D. G. Teer, Surf. Coat. Technol. 124, 110 共2000兲. 2 H. Liu and B. Bhushman, J. Vac. Sci. Technol. A 21, 1528 共2003兲. 3 J. Esteve, A. Lousa, E. Martinez, H. Huck, E. B. Halac, and M. Reinoso, Diamond Relat. Mater. 10, 1053 共2001兲.

ity. At high speed sliding, the disappearance of the nanocrystallite is faster than at low speed sliding, and the higher the velocity is, the closer nc-SiC behaves as a-SiC. In conclusion, our atomistic MD simulations have revealed important tribological properties of sliding friction between amorphous, nanostructured, and crystalline slabs of Si, C, and SiC. The main of results are as follows. The friction coefficient has an initial transient before reaching an apparent steady state value. The jump of the friction coefficient during the transient stage decreases in the sequence 共c-Si兲-共nc-SiC兲-共a-SiC兲 sliding on a diamond slab. The sliding of the silicon slab on the diamond surface is accompanied by appearing a disordered region that increases with sliding velocity. The disordered layers of c-Si, a-SiC, and nc-SiC samples become denser during sliding on the diamond surface, for which reason the friction coefficient is a decreasing function of sliding velocity. For the a-SiC / a-SiC sliding pairs, the mixing of the atoms of both the slabs is observed and the mixed layer grows as sliding proceeds further in time. At high-speed friction, the low density region near the sliding plane arises. This region increases with V. We suppose that the latter circumstance can lead to reducing ␮ with rising sliding velocity. Another factor leading to reducing the friction coefficient in all the sliding systems under investigation is the strengthening of thermally activation motion, caused by either an outer heating of sliding samples, or raising sliding velocity. In atomistic MD simulations, at the constant contact area, the friction force and hence the average shear stress are obtained to be independent of the normal load. As a consequence, the friction coefficient of all the sliding systems reduces with increasing the normal pressure. For the nc-SiC / c-C high-speed sliding system, the crystallite atoms mix with other atoms of the amorphous slab, and consequently the crystallite disappears mostly during the transient period. Our friction model predicts that abrasive wear of the c-Si slab should be higher than that of the a-SiC sample in agreement with the results of ball-on-plane tests. Finally, the proposed procedure that is based on atomistic MD simulations is general enough to be applicable to other systems of practical interest. This work has been supported in part under the contracts CRDF No. UK-E2-2589-KV-04 and STCU No. 1590-C. The work of P.T. and A.G. was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48.

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