MOLECULAR DYNAMICS SIMULATION OF POLISHING PROCESS BASED ON COUPLING VIBRATIONS OF LIQUID

CHINESE JOURNAL OF MECHANICAL ENGINEERING_Vol.19, No.l, 2006●19●HUANG ZhigangMOLECUL AR DYNAMICS SIMULATIONGUO ZhongningOF POLISHING PROCESS BASED ONCHENG XingCOUPLING VIBRATIONS OF LIQUID*Faculty of Electromechanical Engineering.Guangdong University of Technology,Guangzhou 510090, ChinaAbstract: Molecular dynamics method is applied to study the machining mechanisms of polishingYU Damingbased on coupling vibrations of liquid. The physical phenomena of abrasive particles bombarding onsilicon monocrystal surface are simulated using Tersoff potentials. The effects of vibrationparameters, particle size, incident angle and particle material are analyzed and discussed. Materialremoval mechanisms are studied. Deformation and embedment phenomena are found in the simula-DU Xuetions. Bombardment will destroy the crystal structures near the impact point, and adhesion effect isresponsible for final removal of material.LI RongbingKey words: Molecular dynamics simulation Ultra-smooth polishing Ultrasonic vibrationFaculty of EngineenThe Hong Kong Polyechnic UniversityHong Kong, ChinaFor PCVL, the size of abrasive particle is on the level of0 INTRODUCTIONnanometric scale or even atomic scale, thus removal will happenin a very micro area. Under this scale, the polishing mechanismWith the rapid development of optics and microelectronicscan not be explained by conventional continuous bulk theory,and it is hard to be studied by experimental means as well. For-technologies, all kinds of ultra-fine sufaces, such as ultunately, a computational experimental method called moleculartra-smooth laser lens and super-polished silicon slice used fordynamics simulation (MDS) affords a new means to solve thisintegrated circuit, are increasingly demanded. A number of pol-problem. By calculating the molecular/atomic motions, molcu-ishing technologies including mechanical polishing, chemicallar dynamics method can be employed to predict macroscopicpolishing, plasma etching and hybrid polishing methods haveproperties. Because complete atomic trajectories are available inbeen explored. Some of them like chemical mechanical polishingMDS, simulations of dynamic systems, such as machining proc-(CMP) method have already been applied in industry success-ess, are not difficult. Although it is predicted that multi-physicsfully. However, the search for more efficient and cheaper ul-phenomena happen in PCVL, the research of mechanical effectstra-fine polishing method is still going on.Polishing based on coupling vibrations of liquid (PCVL) iswill be a rational start and will surely serve as a base for furtherA novel polishing method, its basic idea is shown in Fig.1.researches. Silicon monocrystals are important materials inNanometric abrasive particles or reactive ions in the polishingmodern industry, and they are the main destination machiningmaterials of PCVL. Thus the simulations of mechanical bom-liquid driven by coupling vibrations, will bombard and brush thebardments on silicon monocrystal are very meaningful.surface of work picce, at the same time, chemical reactions willbe very likely to happen in the process, thus material will be1 THEORY AND SIMULATION METHODremoved by hybrid effects. The most recent experiments haveproved the validity of this method, but the polishing mechanismscalls for further research.1.1 ModelingThe 3D MDS model used to simulate perpendicular bom-bardment is shown in Fig.2.vibrating motionw+一Neytonian altomo Thermostat atom) Fixed atomParticlepolishing motion印pHard wallPolishing liquidSubstrateVibration generatorvibrating motiony |中国煤化工Fig.I Basic idea of PCVLMH.CNMH GFig.2 MDS model of perpendicular bombardment●This project is supported by National Natural Science Foundation of China(No 50375029) and Provincial Natural Science Foundation of Guangdong,Polishing particle driven by ultrasonic vibrations will bom-China(No. 4009486). Received April 12, 2005; received in revised formbard on the silicon monocrystal (100) plane. The system is placedSeptember 12, 2005: accepted November 2, 2005●20●HUANG Zhigang, et al: Molecular dynamics simulation of polishing process based on coupling vibrations ofliquidin a vacum environment, and is surrounded by hard walls to pre-VYw=F(n)+N,+Ty+P,vent atoms from escaping. Fixed atoms are arranged around New-tonian atoms in the substrate to fix the space. The initial tempera-where Fs is a symmetric two-body term which implies Fs(r) --ture is room temperature (293 K). Thermnostat atoms are employedFs(n), Ny is an asymmetric two-body term, Ty is a three-bodyto simulate heat conduction.term, and Py is the force term related to bond angle.The dimension of the substrate must be large enough tolimit the boundary effects, but on the other hand, the scale of the()=[0()0《2+ 501)2,2]。system should also be controlled to reduce computing time. It is’aOrfound that when the particle size is about 1 nmX1 nmX1 nm,substrates of 9.2 nmX 6.0 nmX 9.2 nm, 10.3 nmX7.1nmX 10.3nm and 11.4 nmX8.1 nmX 11.4 nm almost give out the samearor, ]yresults. Thus a dimension of 9.2 nmX6.0 nmX9.2 nm can bethought of as accuracy enough. Considering the requirement ofJτ=q 2|8(0a)accuracy and eficiency, in most cases, the dimensions employed(4)are 10.3 nmX7.1 nmX10.3 nm (that is 19X13X 19 siliconP,=p, 2 ya(m -r cosOx)e+(ry - rn cosoQw)ez]crystal cell, and containing 37544 atoms).The thermal motions of Newtonian atomsasigned ran-domly according to the initial temperature of system. Meanwhile,中= (c(I)f()自there are additional motions of particles caused by vibratingliquid. Because of the viscosity of polishing liquid, the move-fe(x). 2g(0x)ments of particles fail to keep synchronizing with the ultrasonicVa=rYn a(cosOgx)vibration source. And when there are more than just one vibra-tion sources, coupling efect will be destined to happen. For sim-The objct ey= (1/r) (n;- r1) is the unit vector between atom iplicity, viscosity efet and coupling efect are ignored in simula-and atom j. The symbols in Eq.(4) are defined according toion. Then the additional motions of particle atoms can be esti-Ref:[1].mated according to vibration parametersv= Awcosot a= -Ac2 sinot(1)1.3 Computational detailsMDS does not nced a particular units system, but for con-where v, a is the velocity and acceleration of particle atoms re-venient and computational accuracy, the units system should bespectively, A represents amplitude and 0 is cycle frequency ofmostly chosen basic units in the units system, and all other unidefirappropriately.1 MDS, length, mass, and energy are thevibration. When amplitude is 5 um and vibration frequency is 40can be derived from them. Choosing angstrom (0.1 nm), amukHz (about 250 kHz for cycle frequency), then the maximum(1.6605X10-27 kg) and eV (1.602 2X 10-19 ) as the basic unitsincident velocity is about 1 m/s, and the maximum incident ac-celeration is about 3X 10 m/s?. Because the time scale of MDSis appropriate. Accordingly, the time unit is 10.18 fs, the unit foris very short, generally within peco-seconds (10-12 s), muchvelocity is 9.823 2X10' m/s, and the unit for acceleration isshorter than the vibration period (10-8~10+ s), thus in a single9.649 5x 1017 m/s?.simulation, once additional velocities and aditional accelera-In MDS, time step for integration should be taken into ac-tions are given to particle atoms, no special adjustments arecount carefully. A too short time step would bring unnessaryneeded during the simulation process.computational time, while a rather long time step might affectthe accuracy of the simulation. Generally, the time step should be1.2 Interatomic potentialless than 10 percent of the vibration period of atoms. In simula-The model for atomic interactions in MDS is contained in antion, a time step of 0.1 time unit that is 1.018 fs is chosen (Theinteratomic force law or, equivalently, an interatomic potentialexperimental vibration period of diamond and silicon underenergy function. The precision of the potential function will pri-room temperature is 32.46 fs and 84.03 fs respectively).marily afct the validity of the simulation results. In simulation,In order to save the computational cost, a method combinedthe subject material is silicon, and the polishing particles arewith cell subdivision and neighbor list approach is used to com-siliconanarbon(diamond). Both silicon and diamond arepute interatomic forces. And Verlet (Leap frog) method-! is usedsemiconductors with covalentbonding and diamond crystalin the integration step to guarantee the numerical accuracy.structure. For these kinds of materials, the traditional pair poten-tials like Lennard-Jones and Morse potentials, etc can not give2 RESULTS AND DISCUSSIONsuficient accuracy. An empirical potential developed by TER-SOFF were proved to be a sccessful function for covalent mate-2.1 Basic phenomenarials. The Tersoff ecnergy can be expressed asl 4The bombardment processes of nanometric diamond parti-cles and silicon particles on silicon monocrystal surface (1 00) areimulated. A typical simulation result? bombardment by dia-(2)mond particle is shown in Fig.3. It is found that although siliconis brittle material at macro scale, however, it shows strong duc-Vv=. f{[fe(n)+b,f(r)]tile characters in nanometric world. These phenomena are foundin numbers of experiments on nanometric cutting. In manywhere the potential energy is decomposed into site energy E; andcases, polishing particle will embed in substrate. Near the em-bonding energy Vy,ry= r:-门is the bond vector fom atomj tobedded region. there will be a deformed region. Crystal struc-atom i, fn and fR are the attractive and repulsive pair potentialtures中国煤化Istable semi-crystal struc-.respectively, and fe is a smooth cutoff function. The detailed: structure formed in theequationsd parameters for Tersoff potential and its refineddeforMHC N M H Gus statels1 by some re-version can be seen in Refs.[1, 2]. The interatomic forces can besearchers.'1 nese phenomena can De explained by viscous flowobtained by calculating the gradient of potential energy Etheory for nanometrie materials. Strong bonds will be built be-tween particle atoms and substrate atoms in contact directly.F=-VE,(n)=-A2v(V+r)(3)These bonds will cause cohesion effects and make polishingparticles stuck on the substrate.CHINESE JOURNAL OF MECHANICAL ENGINEERINGThere will be a significant temperature rise in the deformedBombardment will cause a wave propagating from the im-region once bombardment happens. The peak value of the tem-pact point on the surface of substrate. The waveforms exhibitedperature may reach 1 000 K. Then the temperature rise will slowby the simulations are incomplete. This indicates that the simula-down, because the heat generated in deformed region will betion results about surface wave are seriously affected by theconducted to the surrounding atoms rapidly. High temperatureboundary effect. In order to describe the surface wave accurately,will soften the substrate material, and thus fasten the deformationa much bigger system is needed. Because surface wave is a dy-process. Fig.4 shows the velocity distribution near the impactthat located on a higher level, the time scale ofregion in the bombardment process. According to Dulong -Petit'ssimulation should also be extended significantly. However, thelaw, temperature is proportional to kinetic energy of atoms, sosimulation results by a limited system are still meaningful. Fig 5the thermal effect of bombardment can be expressed by velocityand Fig.6 ilustrate the characters of surface wave. The embed-ditribution.ded/deformed region remains unchanged while the surface 0substrate oscillates. And the amplitude of surface wave is small,& Deformed region24about 10 percents of the height of embedded region. Thus it can速Embedded regionbe thought that surface wave will have lttle effect to the bom-◎Thermostat atombardment process. According to the time step of integration, the。Substrate atomattenuation of surface wave is slow. The amplitude of surface●Particle atomParticlewave only decays 40 percents after 40 000 cycles. The period ofsurface wave is about 3 ps. Considering boundary effect, thisvalue will be higher for real system.Substrate2.7ps3.1ps,,3.Sps4.2psFig3 Bombardment phenomena1 392.7K0.5ps1 253.4KFig.5 Profile of subtate at dferent instant114.1KIn order to express the results clearly, the scalefor axis ) is four times of that for axis耳974.9K835.6K696.3K号0.2-557.1K更口重。日。。mo亚417.8K号0.1278.5K139.3 K203040Time tipsFig.6 Attenvation of the amplitude of surface waveIncident velocity: 2 000 m/s; Particle material: diamond;1 026.0 KParticle size: 7x7x5 crystal cell. Ips923.4K820.8 K.2 Effects of vibration parametersThe polishing motion of particle is motivated by ultrasonic718.2 Kvibration. Assuming particle moves in simple harmonic trajec-615.6Ktory synchronizing with the vibration source, the incident veloc-ity and acceleration can be easily defined.513.0KIt's found that acccleration has lttle to do with the polishing410.4 Kprocess, but the effect of incident velocity is great. This resultcan be explained by the kinetic energy accumulation phenome-307.8Knon. Compared with the interatomic potential, the potential en-205.2 K .ergy caused by extemal force can be ignored, thus kinetic energy102.6 Fwill b中国煤化工-ardment process. To thebodiesnjectory, kinetic energy0increath acceleration. And theoooYo°∞°ooxo:o%kineticCINMH Gsue dung imeFig.4 Atomic velocity dstibution in substratetime scale is much shorter then vibration period. According toParticle size: 7X7X5 crystal cell. For convenient,the reasons, the effects of vibration parameters can be studiedthe velocities are expressed in temperature unit.under the condition when vibration velocity reaches the maxi-HUANG Zhigang, et al: Molecular dynamics simulation of polishing procsss based on coupling vibrations of liquidmum value.incident energy. The ratio of volume of embedded/deformedFig.7 shows the relationships between embedded/deformedregion to incident energy is listed in Table.region size and incident velocity. Although the bombardmentproccss will be affected by many other factors, polishing particleTable Relationships between embedded/deformed regionwill not do any damage to substratc when the incident velocity isand incident energy of polishing particlelower than 100 m/s, regardless the effect of other parameters.Volume of embeddedVolume of deformedParticle materialOnce the velocity reaches the minimum-damage threshold, bothregion V(om .eV ) region V/(nm' .eV )_the height and width of embedded/deformed region will almostDiarmond3.8X10 312.2X10 3grow linearly with incident velocity, and the area of embed-Silicon6.0X 10-*4.3>X 10-3ded/deformed region will be proportional to the square of inci-dent velocity.2.4 Effects of incident angleBecause of the collisions among polishing particles and the-0- Hight of embedded regionhecoupling effects between vibration sources, particles will bom-+ Hight of deformed regionhebard the substrate in all directions. When the particles impactWidth of deformed regionbyasubstrate obliquely, they will slide and roll on the sur face of sub-strate as shown in Fig.9. As a result of the rolling movement,some substrate atoms at the back of the sliding direction will beavulsed from the bulk, and make a dent on the substrate. Reflec-tions are not found in the simulations, particles will be eventuallystuck on the substrate. The coefficient listed in Tablc is no longeralid for oblique bombardment, because atom-removal phe-nomenon occurs, and the energy needed for the avulsion of su b-strate atomsnot equal to that needed for embedment and10002000 3 0004000deformation.Velocity v/(m-s-)Fig.7 Effects of incident velocity0psIpsIncident angle: 90*; Paricle material: diamond;Particle size: 7X7X5 crystal cellv=3 000 m/sGenerally, the amplitude of ultrasonic vibration is aboutseveral micrometers. According to the simulation results, in or-der to polish the work piece fficiently, the frequency of vibra-tion source used in PCVL should be higher than 10 MHz. Otherresearchers found that when liquid is vibrated at a frequencys Substratelower than I MHz, cavitation phenomenon would happen. Airbubbles will be generated in the liquid, and the bust of air bub-bles will setoff very high energies. This energy may drive the2ps3psabrasive particles near the bubble to move in a speed muchhigher than the minimum-damage velocity threshold. But theeffect of cavitation should be avoided in PCVL, because it isuncontrollable.2.3 Effects of particle sizeThe effect of particle size is studied by analyzing the em-bedded/deformed region. It is found that when the incident ve-locity is the same, the. depth of embedded/deformedregionchanges slowly, but the width and area of embedded/deformedregion almost grows linearly with the particle size (see Fig.8).Fig.9 Phenomena of oblique bombardment0- Hight of embedded region heExcept for incident angle, initial atude is another factor一△Width of embedded region bethat will afct the bombardment process, but it seems that ef-十Hight of deforned regionhdfects of these two factors will mutually influenced. When the+ r Width of deformed regionbsmagnitude of incident velocity is defined, the impact effect atnormal direction depends mainly on incident angle, but the tan-gential sliding'movement and the rolling movement are complexresults of attitude and incident angle. Fig. 10 ilustrates the size ofdeformed region caused by particles with different incident angleand initial atude. It is clearly shown that the height of the egion, which measures the normal impact mainly, is mostly de-cided by the incident angle. However, width of the deformed200---- Aregion is a combined function of atitude and incident angle.Sectionalarea of particle A/mm2Fig.8 Eiects of paricle size2.5中国煤化工Incident angle: 90; Incident velocity: 1 000 m/s;trates bombarded withParticle material: diamondsiliconHCNMHGred.Fig.11showsthebombarument pnenomenon oI s1con particle. Compared withSynthesizing these results and the effects of vibration pa-the results shown in Figl, the deformation of silicon particle isrameters, it is deduced that, when the incident velocity is highermore evident. This can be easily explained by the difference ofthan the minimum-damage threshold, the volume of embed-bond strength, or the diference of microhardness, of these twoded/deformed region is approximately in direct proportion tokinds of materials (the microhardness of silicon and diamond isCHINESE JOURNAL OF MECHANICAL ENGINEERING●23●12.5 GPa and 98.7 GPa respectively). The deformation of parti-Some of them will break off duc to the continuously actions, andcle will enlarge the nose radius, and thus increase the resistancecarrying substrate atoms with them. Material then is removed byof moving deeper into substrate. The height of embedded/de-adhesion effect eventually. As we know, generally the micro-formed then will be lowered. It is known that in the single ma-profile of workpiece is not an ideal plane, but a shape with cha-chining dent has a bigger width-to-height ratio, the polishingotic peak. The atoms on the tip of the peak may be cut off byquality will be better. Thus, if taking polishing quality into ac-polishing particle, but the cutting effect will not be discussedcount solely, silicon particle will be more preferable. On thehere.other hand, according to Table, the polishing efficiency of dia-In order to throw a light on the material-removal mecha-mond particle will be higher.nism by adhesion effect, Molecular Dynamics simulations areapplied. The simultions start from the equilibrium state of pre-vious bombardment process. Continuously impacts on polishingRectangle serial Triangle serialparticles are simulated by assigning a constant outward velocityIncidenton the particle atoms. Simulation results are shown in Fig.12.angleParticle0ps6-Substrate ?43重2-Substrate16ps60Incident angle a/(°)Fig.10 Eftects of atude and incident angle00 Hight of deformed region hd▲■Width of deformed region buMagnitude of incident velocity: 3 000 m/s;Particle material: diarmond;Particle size: 7X7X S crystal cellSilicon particleNoseFig.11 Bombardment of silicon particle.6 Discussion of material removal mechanismBombardment will destroy the crystal structures near theimpact point, but no atoms will be removed by spattering. Whenparticles impact the workpiece obliquely, some atoms will betore out of the material. However, once contacts, strong bondsFig.12 Material removal mechanism by adhesion efetwill be formed between particle atoms and substrate atoms.Whatever the incident direction is, the reflctivity is not strongIn Fig.12, material removal phenomena are found clearly.enough to overcome these bond forces. Consequently, the parti-Several layers of substrate atoms, which contact with the particlecle can not flee from the surface, and no material is actually re-atoms中国煤化工r subtrate and adhere onmoved. Thus impact to substratc is only the first stcp of machin-the sur; of crystal reconstruc-ing, other actions will be responsible for the final removal oftion, n|YHembedded region. Thematerial.deformObviously, impact phenomenon will not only happen be-sion ffct, and only the ator; in the deformed region will havetween particle and substrate, but will also happen among parti-the possibility to be removed. This indicates that although bom-cles. Polishing particles stuck on the substrate will be subject tobardment effect will not remove material actually, it decides thethe impacts of other particles and molecules of polishing liquid.machining capacity of PCVL.●24●HUANG Zhigang, et al: Mlecular dynamics simulation of polishing process based on coupling vibrations of liquid1999, 42(4): 546-559.3 CONCLUSIONS2] TERSOFF J. New empirical approach for the structure and energy ofcovalent systems(J]. Physical Review B (Condensed Matter, 1988,37(12):6 991-7 00.The machining mechanism of PCVL is investigated by the3} RAPAPORT D C. The at of molecular dynamics simulation[M]. 2nduse of Molecular Dynamics approaches. Bombardment of nano-metric paticles on silicon monocrystal surface (100) and the4] BIFANO T G, DoW T G, SCATTERGOOD R 0. Ductile regime grind-material removal mechanism is simulated using Tersoff potential.ing: a new tchnology for machining brite materials[J]. ASME Interma-Effects of vibration parameters, particle size, incident angle andtional Joumals for Industy.1991,113:184-189.. .. .particle materials are discussed. The conclusions can be drawn asZARUDI I, ZHANG L C. Subsurface damage in sigle-crystal silicon duefollows.to grinding and polishing[J]. Joumals of Material Science, 1996, 15:(1) When polishing particle with certain incident velocityimpacts the substrate, crystal structures near the impact pointBiographical noteswill collapse and be replaced by semi -crystal structures. At thesame time, bombardment will cause thermo effect and surfaceHUANG Zhigang, bom in 1975, is curently a doctoral candidate in Guang-wave on the substrate.dong University of Technology, China. His research interests include compu-tational experiment and simulation, and non- traditional machining.(2) If incident velocity is up to the minimum-damageTel: +86-20-37627775; E-mail: huangzg@gdut.edu.cnthreshold, efect of perpendicular impact is mainly decided byincident energy.GUO Zhongning, dean in School of Electromechanical Engineeing, Guang-(3) Oblique bombardment with certain angle will avulsedong University of Technology, China. His research interests include specialsubstrate atoms from the bulk. But no matter what incident angle,machining and ultra-fine machining.particle will be trapped on substrate.CHEN Xin, leader of CIMS Lab, Guangdong University of Technology,(4) The machining efficiency of diamond particle will beChina. His research interests include CIMS and advanced machining tech-higher, but the polishing quality will be worse than that of siliconparticle.(5) Bombardment will destroy the crystal structures near theYU Daming, professor in the Hong Kong Polytechnic University, Hong Kong,China. His research areas include advanced manufacturing technology, manu-impact point, but adhesion effect is responsible for final removalfacturing strategy and knowledge management.of material.DU Xue, PhD candidate in the Hong Kong Polytechnie University,ity, HongReferencesKong, China.1] ZHANG Liangchi, TANAKA H. On the mechanics and physics in theLI Rongbing, Cheng Yick chi chair professor in the Hong Kong Polytechnicnanoindentation of silicon monocrystals([J]. JSME Intemnational Joumals,University, Hong Kong. China.中国煤化工MYHCNMHG