NANOSCALE CUTTING OF MONOCRYSTALLINE SILICON USING MOLECULAR DYNAMICS SIMULATION (2).doc

chinese journal of mechanical engineering vol. 20, no. s, 2007li xiaopingcai minborahman mustafizurdepartment of mechanical engineering,national university of singapore,kent ridge 119260, singaporenanoscale cutting of monocrystalline silicon using molecular dynamics simulation*abstract: it has been found that the brittle material, monocrystalline silicon, can be machined in ductile mode in nanoscale cutting when the tool cutting edge radius is reduced to nanoscale and the undeformed chip thickness is smaller than the tool edge radius. in order to better understand the mechanism of ductile mode cutting of silicon, the molecular dynamics (md) method is employed to simulate the nanoscale cutting of monocrystalline silicon. the simulated variation of the cutting forces with the tool cutting edge radius is compared with the cutting force results from experimental cutting tests and they show a good agreement. the results also indicate that there is silicon phase transformation from monoctystalline to amorphous in the chip formation zone that can be used to explain the cause of ductile mode cutting. moreover, from the simulated stress results, the two necessary conditions of dusiiie mode cutting, the tool cutting edge radius are reduced to nanoscale and the undeformed chip thickness should be smaller than the tool cutting edge radius, have been explained. key words: ductile mode cutting molecular dynamics phase transformation force stress0 introductionmany researchers have reported the results for nanoscale ductile cutting of brittle materials, such as silicon and germanium. liu, et al1), further observed that the ductile cutting mode can be realized when the undeformed chip thickness is smaller than the tool cutting edge radius and the tool cutting edge radius is small enough on a nanoscale. however, the mechanism of nanoscale ductile mode cutting of silicon has not been fully understood and adequately explained.nanoscale cutting involves workpiece deformation in only a few atomic layers near the workpiece surface. at such a small governing length scale, the continuum representation of the problem becomes questionable. to study such a process, the molecular dynamics (md) simulation method seems to be more appropriate.belak, et al21, have studied nanoscale cutting of copper employing the embedded atom method (eam). with the two-dimensional md model, shimada131 investigated the effect of tool edge radius and depth of cut on the chip formation process, subsurface deformation, and specific energy. komanduri, et al4, studied the effect of different tool edge rake angles (from -60 to 60) on nanoscale cutting of monocrystalline silicon with perfectly sharp tool edges.it can be seen that md has been used for simulation of nanoscale cutting and some attempts have been made to simulate such cutting of monocrystalline silicon using md method. however, the mechanism of ductile mode cutting of brittle materials has not been explained clearly using the md method. the two necessary conditions of ductile mode cutting, the undeformed chip thickness is smaller than the tool edge radius and the tool cutting edge radius should be small enough, have not yet been investigated in detail.in this study, the md method is employed to simulate nanoscale cutting of monocrystalline silicon. the simulated variation of the cutting forces with the tool cutting edge radius is compared with the cutting force results from experimental cutting tests. the results also indicated that there is silicon phase transformation from monocrystalline to amorphous in the chip formation zone. moreover, from the simulated stress results, theselected from proceedings of the 7th international conference on frontiers of design and manufacturing (icfdm2006). received october 14, 2006; received in revised form june 5,2007; accepted july 9, 2007two necessary conditions of ductile mode cutting have been explained.1 molecular dynamics method and modelin this study, a three-dimensional molecular dynamics simulation model has been employed. fig. 1 shows a schematic diagram of the md model. in the model, the workpiece is monocrystalline silicon and is divided into three different zones: boundary atom zone, thermostat atom zone and newtonian atom zone. the boundary atoms are fixed in positions to reduce the boundary effects and maintain proper symmetry of the lattice. the motion of the newtonian atoms is determined by the forces produced by the newtons equation of motion. the thermostat atoms, which are used to simulate the heat conduction, are arranged to surround the newtonian atoms to make the boundary temperature close to environment temperature. the diamond cutting tool (0 nominal rake angle and 7 relief angle) is assumed to be finitely rigid. the periodic boundary condition is maintained along the direction perpendicular to the cross section, as shown in fig. 1.j cutting edgecutting directionnewtonian atomsboundary atoms fig. 1 schematic diagram of the md modelfor the cubic diamond lattice of silicon, the tersoff potential151 is found to be able to describe well the energies and geometries, as followsn=/c(r,x/,(r,) + (r,) (1)where , is the site energy, vy is the bond energy about all the atomic bonds, ij label the atoms of the system, r is the length of the ij bond, by is the bond order term, 7i represents a repulsive pair potential, fa represents an attractive pair potential, fc merely represents a smooth 1994-2008chinese journal of mechanical engineering.9.(3)cut-off function to limit the range of the potential.the interactions between silicon atoms and carbon atoms of diamond cutting tool are described by morse potential6*r,) = /?exp-2a(/v - r0) -2exp-a(fi - r) (2)where (r4a, where a is the lattice constant of monocrystalline silicon and is equal to 0.543 2 nm. the working environment temperature was set at 293 k. the integration time step was set at1fs. the cutting speed was set at 20 m/s.2results and discussion2.1 md simulated forces with experimental verificationfig. 2 forces acting on the cutting tool and stressed zones in the chip formation zoneas shown in fig. 2, the forces acting on the cutting tool include cutting force fc, which is in the cutting direction, and thrust force ft, which is perpendicular to the cutting direction. r is the cutting tool edge radius and ac represents the undeformed chip thickness. in this set of md simulations, the undeformed chip thickness was fixed at ac = 2 nm, and the cutting tool edge radii were set as 2.5, 3.0, 4.0 and 5.0 nm, respectively. therefore, the undeformed chip thickness was always less than cutting tool edge radii to ensure ductile mode cutting conditions.the md simulated forces acting on the cutting tool are shown in fig. 3, from which, three obvious features can be observed. first, the thrust force is much larger than the cutting force during cutting, which is different from that in conventional cutting, where the cutting force is generally greater than the thrust force and the tool cutting edge radius is far smaller compared to the undeformed chip thickness. second, the cutting force has no significant changes as the tool edge radius increases with the undeformed chip thickness fixed. third, unlike the cutting force, the thrust force obviously increases as the cutting tool edge radius is increased.2803.5 4.0 radius r/ran fig. 3 md simulated cutting forcesfor verification of the md simulated cutting force results in this study, nanoscale ductile mode cutting of monocrystalline silicon wafer with single crystal diamond tools were conducted and the cutting forces were measured. in the experiment, four diamond tools of different cutting edge radii were applied and facing cuts in ductile mode was conducted. the cutting edge radii were 52.70, 71.10, 97.00 and 110.10 nm, respectively. the undeformed chip thickness was fixed at 9.587 nm.the three cutting force features observed from the md simulated results can also be seen from experimental tests of nanoscale ductile mode cutting of monocrystalline silicon wafer, as shown in fig. 4.100 no506070 80 90 radius r/ran fig. 4 forces by the experimentthe good agreement between the md simulated results and the experimental cutting results for the trends of cutting forces in variation with tool edge radius indicates that the present md model and simulation system can be used for simulation of the nanoscale ductile mode cutting of silicon.2.2 the phase transformation in the chip formation zonefig. 5 shows the output result of the md simulation. in the simulation, the undeformed chip thickness was set at 2.0 nm and the value of radius of cutting tool edge was 2.5 nm. the silicon workpiece could be divided into chip formation zone and non-chip formation zone. in the non-chip formation zone, the silicon atoms were regularly arranged. in the chip formation zone, the arrangement of the atoms was amorphous. fig. 6 shows the distribution frequency of interatomic bond length. in the non-chip formation zone, the distribution of interatomic bond length concentrated near the value of bond length l =0.235 nm. this denotes that the atoms were vibrating at the equilibrium positions1994-2008 hin acade ic rnal 1 crone 1 g o e. air t e rv/ 10li xiaoping, et al: nanoscale cutting of monocrystalline silicon using molecular dynamics simulation(a) chip formation zoneand the bond length was 0.235 nm. however, in the chip formation zone, the interatomic bond length varied in a wide range. this further indicates the existence of the amorphous phase in the chip formation zone.(b) non-chip formation zonefig. 5 output result of md simulationfig. 8 illustrates how a crack can be screened by compressive stresses. it can be seen that when o is a compressive stress, the crack is prevented from propagating, without which it is easy to propagate. since it is possible that rw changes from compressive to tensile in zone a when the undeformed chip thickness is near or larger than tool cutting edge radius, crack propagation in zone a is easy to take place, leading to the transition from ductile mode to brittle mode in the chip formation zone. this could explain the first necessary condition of ductile mode cutting, the undeformed chip thickness is smaller than the tool edge radius.tig. 8 schematic illr/jovion of a cil sciecncc by compressive rtre*se:chip forma.:ot zcve non-chip formation zone0.8v0.6s i04.c 0.20.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 interatomic bond length i/nm fig. 6 distribution frequency of interatomic bond length of the silicon workpiece materialfrom fig. 6, it can be known mat most of the interatomic bond lengths became longer than before. the recent research indicates that for pure silicon71, the hardness is inverse proportional to d*s, where d represents the interatomic bond length. therefore, longer bond lengths mean that silicon becomes softer than before. this is a basic precondition for ductile mode cutting of silicon.13 stresses2.53.03.54.0undeformed chip thickness s/nmstresses in the chip formation zone a in cutting at different undeformed chip thicknessesin fig. 2, zone a is near to workpiece surface and is in a critical stress condition in relation to the mode of chip formation. in this set of simulations, the tool cutting edge radius was fixed at 4.0 nm with a range of undeformed chip thickness, 2.0, 3.2 and 4.0 nm. fig. 7 shows the normal stresses a, i physics in thenano-indentation of silicon monocrystaiaj jsmf. international journala, 1999,42:546-550. 7 gao f, he jv vu e, el al. i!a,-d;s of covaieut cr;stalsj. physicalreview letters, 200, si. 015502.biographical notesli xiaoping received his phd degree from university of new south wales, australia in 1991, and joined national university of singapore, singapore, in 1992, where he is currently a professor in department of mechanical engineering. his current research interests include neurosensors