Analysis the complex interaction among flexible nanoparticles and materials surface in the mechanical polishing process

Applied Surface Science 257 (2011) 3363–3373

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Analysis the complex interaction among flexible nanoparticles and materials surface in the mechanical polishing process Xuesong Han a,∗ , Yong X. Gan b a b

School of Mechanical Engineering, Tianjin University, 300072, PR China Department of Mechanical, Industrial and Manufacturing Engineering, University of Toledo, OH 43606, USA

a r t i c l e

i n f o

Article history: Received 9 August 2010 Received in revised form 3 November 2010 Accepted 3 November 2010 Available online 16 November 2010 Keywords: Nanoparticle Mechanical polishing Molecular dynamics Multibody Complex

a b s t r a c t Mechanical polishing (MP), being the important technique of realizing the surface planarization, has already been widely applied in the area of microelectronic manufacturing and computer manufacturing technology. The surface planarization in the MP is mainly realized by mechanical process which depended on the microdynamic behavior of nanoparticle. The complex multibody interaction among nanoparticles and materials surface is different from interaction in the macroscopic multibody system which makes the traditional classical materials machining theory cannot accurately uncover the mystery of the surface generation in the MP. Large-scale classical molecular dynamic (MD) simulation of interaction among nanoparticles and solid surface has been carried out to investigate the physical essence of surface planarization. The particles with small impact angle can generate more uniform global planarization surface but the materials removal rate is lower. The shear interaction between particle and substrate may induce large friction torque and lead to the rotation of particle. The translation plus rotation makes the nanoparticle behaved like micro-milling tool. The results show that the nanoparticles may aggregrate together and form larger cluster thus deteriorate surface the quality. This MD simulation results illuminate that the final planarized surface can only be acquired by synergic behavior of all particles using various means such as cutting, impacting, scratching, indentation and so on. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Recently, with increasing demands for functional enhancement, ultra-lapping or polishing has been recognized as a critical technology for the functional materials of the precision machinery components, optical components, and electronic components. For instance, in line with the rapid progress in miniaturization and high integration in electronic components, the dimensional accuracy of the components is shifting from on the order of micrometers (10−6 m) to nanometers (10−9 m). The manufacturing precision has already been improved from micrometer level to nanometer level (nanofabrication technology). It has already become the goals of all high technologies to acquire super-smooth and defect-free surface. Such requirement has approached the limit of manufacturing technology. Under this circumstance, any change of the flow field or conflict in physical-chemical factors could deteriorate the surface quality, any tiny hard particle may generate large pits or mark in the surface. Further study on physical aspects of nanometer manufacturing technology is crucial for obtaining planarization surface with

∗ Corresponding author. Tel.: +86 13342083836. E-mail addresses: [email protected], [email protected] (X. Han). 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.11.026

nanometer level roughness. Today, mechanical polishing technology has already become attractive research item. Despite intense theoretical and experimental research on MP [1–9], there is still serious lack of fundamental understanding of this process. Although MP technology has already been widely accepted in industry, its application still rests on the semi-empirical stage. Presently, the researchers cannot give convinced illumination about the mechanism of MP. The reason for this is that the MP process is a complex system characterized by multiphase, multiscale and multilevel, at the same time being a micro/nano-tribology behavior related to complex chemical-physical process. It is not the geometrical downsizing but should exist some new discipline dominates the material remove and surface generation process in the MP technique. Ultraprecision polishing is a technology that accurately produces geometrically dimensional shapes in the nanometer order. These functional materials or components should be produced to a completely smooth mirror surface to work as functional materials. Polishing is carried out without letting fine abrasive particles generate brittle fractures on the work surfaces, while removing these materials little by little only by means of plastic deformation, to finally produce a smooth mirror surface. For such polishing, fine abrasives of below 1 mm and pads of pitch, wax, synthetic resin, or artificial leather are used to realize smooth mirror finishing. Fine

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abrasive particles are retained on the pad surface resiliently and plastically, and the work surfaces are scratched microscopically. Polishing actions are by far smaller if compared with lapping, contributing to the successful applications to the brittle materials such as single crystal silicon. The final surface integrity acquired using MP technique is mainly depended on the microdynamic behavior of nanoparticles. The complex multibody interaction among nanoparticles and materials surface is different from interaction in the macroscopic scale which makes the traditional classical materials machining theory cannot accurately uncover the mystery of the surface generation in the MP. Interaction between nanoparticle and solid surface are of fundamental importance to science and technology. The appearance of macroscopic particle-surface interactions is well known from experiences in daily life. As the size of the particles decreases and approaches molecular dimensions, their atomic nature becomes increasingly important. Interactions on the molecular level may be studied experimentally using molecular beam techniques, and theoretically by molecular dynamics simulations. In the current paper MD simulations are employed to study the interactions between silicon nanoparticle and silicon substrate. Nanoparticles are relatively large and may be expected to behave as “macroscopic” particles in some respects. At the same time they are small enough to permit the long-time simulations necessary for investigation of self structural organization processes. Interactions between nanoparticles and surfaces have now received considerable attention for more than a decade due to their relevance for both fundamental and applied research. A variety of processes may occur depending

Fig. 1. MD computation model.

on the properties of the nanoparticle, the available energy and the energy transfer rates involved. A straightforward interpretation of experimental results is often not possible due to the complexity of the dynamics. The use of MD simulation techniques has therefore become a very important tool in this field. Molecular dynamics simulation [10], by virtue of its high temporal and spatial resolution, can offer an ideal approach to gain insights into atomic scale process and understand their mechanisms [11–16]. A remarkable enhancement in computational capability (computer hardware) and high performance computation techniques (parallel computation) has enabled us employing large scale classical MD method to investigate the nanometric tribology process and gain insights into this atomistic behavior. 2. Molecular-dynamics simulation methodology The atomic configuration of the system studied is illustrated in Fig. 1. Silicon atoms of particle and substrate are initially arranged

Fig. 2. MD simulation of complex interaction among nanoparticles and substrate purple: particle1, cyan: particle2, green: particle3 (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article).

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in diamond cubic structure with a constant lattice parameter of ˚ The dimension of silicon workpiece is 180 × 55 × 50 A˚ 3 along 5.43 A. x, y and z directions. The moving speed is 100 m/s, the environment ˚ the particle diameter temperature is 293 K, the depth of cut is 8 A, ˚ the timestep is 2.5 × 10−15 s. is 16 A, Presently, there exists some simplifying of the computation model and the theoretical study of the polishing technology is not reaching the real solution. The influence of heat transfer (induced by atmosphere and slurry) can be minimized as this computation model falls into atomic length scale. The mechanical effect exerted by the slurry is assumed as inertia boundary conditions and set as the initial velocity of the nanoparticle. For covalent systems, the Tersoff potential [17] is used to depict the interaction between the silicon atoms and atoms of the abrasive particle as follows:

ij = fc (rij )[fR (rij ) + bij fA (rij )]

(1)

With Eq. (1), the interaction force between silicon atoms can be obtained by calculating the negative gradient of . The computation of atom trajectory requires numerical integration of the differential equations from initial state which the abrasive particle is approaching the wafer but has not touched yet to the final state which a layer of material has been removed from the wafer. There variety of methods available for performing this numerical integration such as fourth-order Runge–Kutta method, Leap-Frog method, Verlet method, VelocityVerlet method and so on. The Velocity-Verlet method is a symplectic algorithm which can prevent the energy dissipation and have high computation efficiency, this paper adopted this method

as follows: rin+1 = rin + hvn +

vn+1 = i

h2 n F 2m i

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here rin+1 , vn+1 and Fin+1 are position, velocity and force at n + 1 i step of the ith atom while rin , vni and Fin are position, velocity and force at n step of the ith atom, h is timestep, m is mass of atom. 3. Results and discussion 3.1. Microdynamic behavior of particles with zero impact angle Fig. 2 gives the MD simulation of complex interaction among nanoparticles and single crystal silicon substrate. First, these particles move parallel to the x direction but the rotational movement gradually been induced as the planarization process goes on. The translation plus rotation makes the nanoparticle behaved like micro-milling tool. But this tool is flexible fixed and without definite shape. The tool should keep its dynamic behavior (micro and nanoscale inertia) between two discrete planarizing events if there is not external load exerted on it. As there is no rigid constraint which makes the tools gradually deviating from their original track, namely, the tool and substrate keep away from each other little by little. The particles were lifted after impacting the substrate materials. The animation movie also shows that only weak adhesion effect exists between substrate materials and particle 2 (particle 3). This dynamic trajectory leads to the first peak adjacent to the particles being planarized sufficiently while the last peak remains almost unplanarized. The interaction force between par-

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The polishing process can be considered as a process with energy release. A rough surface has high energy and a smooth surface has low energy. Fig. 6 shows the variation of particle energy in the planarization process. The potential energy of particle1 gradually increased as it began to impact the substrate. The reason for this phenomenon is that the particle surface became rough and chemical active after the planarization. The kinetic energy of the particle1 is decreased because it doing work in the impacting process. Both

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ticle 1 and particle2 increases after the two particles approach each other from 500 timestep (Fig. 3). Initially, the dynamic behavior of the two particles is influenced by the interaction between particle and the substrate which affect the surface planarization. This kind of substrate-particle interaction act as integrate motion constraint because the substrate is fixed. It is just this particle relative kinematic motion realizing the surface planarization. The particle-particle interaction belongs to non-integrate motion constraint because the two particles also move independently. The interaction force between the two particles becomes stronger as they come closer and become a flexible constraint being exerted on the particles which makes the two particles moving like a unity. The same condition is also induced between particle2 and particle3 (Fig. 3). But the interaction force between this two particles increases after 1000 timestep which is different from the conditions between particle1 and particle2. The reason for this may be that after 500 timestep the particle1 begins to impact the substrate surface thus hindering it from moving ahead but the similar process takes 1000 timestep for particle2. Furthermore, the interaction force between particle1 and particle2 is much stronger than that of the force between particle2 and particle3 which means stronger force field generated between particle1 and prticle2. Finally, a new kind of flexible-many-body-tool (FMBT) is generated after 1000 timestep. The linkage between these particles belongs to internal flexible force field which is different from the macroscopic tools such as grinding wheel. The evolvement model of this process is described in Fig. 4. This FMBT is not the same as the large atomic cluster because each body has its own geometry and physical feature. Fig. 5 also shows the center track of these particles after 1500 timestep which illuminates that they do not form larger cluster.

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the potential energy and the kinetic energy of the particles gradually come into a steady status at the end of impacting process. The graph of tangential interaction force (Fig. 7) illuminates the complex interaction between particle and substrate materials. Different from the beginning of impacting, there still interaction after the particle1 leaves the substrate. This phenomenon justifies that there are part of substrate materials adhere to the particle. This adsorptive materials may gradually evolves as outer surface layer of particle and act as the cutting tool to keep on planarized the substrate. The tangential interaction force gradually decreases and finally reaches a stable status which means there is little interaction between particle and substrate materials. Fig. 8 gives the energy of substrate in the MP process. The potential function gradually increased as the MP process going on which means the deteriorating of surface roughness and the improving of surface planarization.

This also means that the MP is a multiscale ultraprecision surface machining technology. The final planarized materials surface can only be achieved by synergic behavior of all particles using various means such as cutting, impacting, scratching, indentation and so on. The nanometer level global surface planarization cannot be realized by single or small part of particles. The kinetic energy of substrate materials gradually increased as the MP goes along as the external particles doing work to it. 3.2. Microdynamic behavior of particles with different impact angle The MD simulation results about the effects of different impact angle on nanoparticle dynamic behavior are shown in Figs. 9 and 10. The particles begin to approach each other as the impact angle

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increasing form 5◦ to 15◦ . The larger atom cluster gradually comes into being while the impact angle in the range of 10–15◦ . The particle center track shows that there exists inflection point where particle2 and particle3 experiences from gradually approaching to gradually separating. These particles ought to maintain their state of uniform motion unless being acted by external force. The substrate materials may act as activate external load which change the status of particle dynamic behavior and the relationship among different particles. The particles with different impact angle generate different planarization surface. The particles with 5◦ impact angle induced the best planarization surface. Fig. 10 shows that only the center track of the particle1 changed with different impact angle. That is to say, particle1 is the only effective tool of accomplishing

the surface planarization process under different impact angles. The center track of all particles has inflection point in the MP process showed in the MD simulation. The particles ought to maintain their state of uniform motion unless external force acted upon it. The first inflection point should be the place where the planarization initialization. The surface force and other microscopic force may have a great influence upon the dynamic behavior of particles because this process happened in the microscopic scale. Complex tribology interaction (cutting, scratching, indentation, plough etc.) between particle and substrate as well as interaction among particle themselves is continually induced. The particles have to adjust its dynamic track accordingly. The center track of particle2 and particle3 gradually turned from irregular curve into straight line

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Fig. 9. MD simulation of complex interaction among nanoparticles and substrate with different impact angle.

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Fig. 10. Interaction nanoparticles and their center track with different impact angle.

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which illuminates the decreasing of their planarization behavior. The MD simulation in Fig. 9 also provides intuitionistic description of this evolvement process. There are little wear or deformation of particle3 after the impact angle increased to 15◦ . This not means that no other external force acted on particle3 because its center track is not a straight line and there are still complex force field between particle2 and particle3 as shown in Fig. 10. The dynamic trajectory of particle3 gradually turned into straight line after the disappearing of external potential field, namely, after the impacted angle increased to 25◦ . The evolvement of center track of particle2 is similar with that of particle3. The center track of particle1 is different because it planarized the substrate materials under different impact angles. There are stronger similarity about the dynamic trajectory of particle1 and particle2 with the 5◦ impact angle because stronger interaction potential field is buildup between them. There are com-

plex synergetic motion tendency between them. This tendency is gradually enhanced with the increasing of impact angles. These three particles are built into larger atomic cluster while the impact angle falls in the range of 10–20◦ . Their dynamic trajectory exhibit amazing coherence. The cohesion strength among particles reaches the maximum value while the impact angle is 15◦ . After that the two body atomic cluster (particle1 and particle2) continually generated while the impact angle falls in the range of 25–35◦ . There exists large similarity between their dynamic trajectories because of internal flexible constraint between them, namely, the effect of empirical force field. This flexible constraint gradually diminished after the impact angle increased to 40◦ . There are not any interaction exists among these particles after the impact angle increased to 45◦ and they finally interact with the substrate separately. Too large atomic clusters will induce surface damage and thus degrade the surface quality. The generation of larger atomic

Fig. 11. Illustration of effective planarization area.

Fig. 12. Microscopic dynamic behavior evolvement model.

X. Han, Y.X. Gan / Applied Surface Science 257 (2011) 3363–3373

cluster may not entirely depend on chemical environment but have a tight relationship with the surrounding physical boundary conditions. This MD simulation results illuminate that the chemical additives itself cannot eliminate the atomic cluster phenomenon entirely. 4. Conclusion It is assumed in the past that the influences of the mechanical actions of the abrasives (ultra-microcutting actions) that correspond to the cutting blade, and of the frictional actions of the pads can be considered as the factors that produce affected layers during polishing. The generation of fine plastic-cutting chips by the scratching behaviors of abrasives can be the influencing mechanism, which, however, given that the mechanical actions are extremely small, seems irrational unless other actions are taken into account. The polishing is a many body nanometer machining technology, and there exists complex interaction among particles as well as the interaction among particles and substrate materials. As this interaction falls into the nanometer regime, it is not downsizing but some new discipline and mechanism dominate the MP technology. Traditional continuum mechanics or experimental method cannot give reasonable explanation about this microscopic dynamic process. It seems that only combining all kinds of particle actions and various characteristic polishing conditions can the physical essence of MP be discovered. The authors investigate MP process of single crystal silicon using MD simulation method, after that drew some conclusions: (1) The particles with 0◦ impact angle can generate uniform global planarization surface but the materials removal rate is lower. The non integration motion constraint gradually induced among particles which makes their dynamic behavior more synergetic to some extent. The rotational motion is induced as there are mainly shear interaction between particle and substrate which induce large friction torque and exerted upon particle. The translation plus rotation makes the nanoparticle behaved like micro-milling tool. The tribology behavior is more prone to rolling friction rather than sliding friction. (2) The flexible-many-body-tool (FMBT) is generated after 1000 timestep. The linkage between these particles is internal flexible force field which is different from the macroscopic tools such as grinding tool wheel. This FMBT is not the same as the large atomic cluster because each body has its own geometry and physical feature. (3) The substrate surface roughness may deteriorate while the surface planarization was improved if only a few particles play an important role. This also means that the final planarized surface can only be achieved by synergic behavior of all particles using various means such as cutting, impacting, scratching, indentation and so on. (4) The particles with different impact angle generate different planarization surface because of their different effective planarization area as shown in Fig. 11. The particles with larger impacting angle may induce larger impact effect along y direc-

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tion thus counteract part of the lifting effect induced by planarization and then improving the efficiency of MP. The particles with larger impacting angle can only cover small effective planarization area and deteriorate the effect of global planarization. (5) The particles ought to maintain their state of uniform motion unless acted upon by an external force. Four different microscopic behavior models may be induced in the MP process as shown in Fig. 12. There are may be one or several kinds of them together interact with substrate materials at one time. This result also illuminates that the chemical additives itself cannot eliminate the atomic cluster phenomenon entirely. Acknowledgement This research was supported by Specialised Research Fund for the Doctoral Program of Higher Education of the Ministry of Education of China (no. 200800561097) and The Visiting Faculty Research Program of The University of Toledo. References [1] F.W. Preston, The theory and design of plate glass polishing machine, J. Soc. Glass. Tech. 11 (44) (1927) 214–256. [2] V.H. Nguyen, F.G. Shi, Modeling of the removal rate in chemical mechanical polishing, Proc. SPIE Int. Soc. Opt. Eng. 4181 (2000) 161–167. [3] G. Fu, A. Chandra, S. Guha, et al., A plasticity-based model of material removal in chemical-mechanical polishing (CMP), IEEE Trans. Semicond. Manuf. 14 (4) (2001) 406–417. [4] J.F. Luo, D.A. Dornfeld, Effects of abrasive size distribution in chemical mechanical planarization: modeling and verification, IEEE Trans. Semicond. Manuf. 16 (3) (2003) 469–476. [5] S.R. Runnels, I. Kim, J. Schleuter, et al., Modeling tool for chemical-mechanical polishing design and evaluation, IEEE Trans. Semicond. Manuf. 11 (3) (1998) 501–510. [6] D.A. Litton, S.H. Garofalini, Modeling of hydrophilic wafer bonding by molecular dynamics simulations, J. Appl. Phys. 89 (11) (2001) 6013–6023. [7] Y.-J. Kang, Y.N. Prasad, I.-K. Kim, S.-J. Jung, J.-G. Park, Synthesis of Fe metal precipitated colloidal silica and its application to W chemical mechanical polishing (CMP) slurry, J. Colloid Interface Sci. 349 (1) (2010) 402–407. [8] X.S. Han, Y.Z. Hu, S.Y. Yu, Investigation of material removal mechanism of silicon wafer in the chemical mechanical polishing process using molecular dynamics simulation method, Appl. Phys. A-Mater. Sci. Process. 95 (3) (2009) 899– 905. [9] X.S. Han, Study micromechanism of surface planarization in the polishing technology using numerical simulation method, Appl. Surf. Sci. 253 (14) (2007) 6211–6216. [10] J.M. Haile, Molecular Dynamics Simulation-Element Method, WileyInterscience, New York, 1997, pp. 332–339. [11] K. Ueda, H.N. Fu, K. Manabe, Atomic scale level chip formation of amorphous metal investigated by using AFM and MD-RPFEM simulation, Machining Sci. Technol. 3 (1) (1999) 61–75. [12] R. Komanduri, N. Chandrasekaran, L.M. Raff, MD simulation of exit failure in nanometric cutting, Mater. Sci. Eng. 311 (1–2) (2001) 1–12. [13] X.S. Han, S.Y. Yu, Molecular dynamics simulation of nanometric cutting process based on symplectic algorithm, Trans. CSME 41 (4) (2005) 17–21. [14] X.S. Han, S.Y. Yu, Investigation of tool geometry in nanometric cutting by molecular dynamics simulation, J. Mater. Process. Technol. 129 (1–3) (2002) 105–108. [15] X.S. Han, S.Y. Yu, Molecular dynamics simulation of nanometric grinding-the effect of crystal anisotropy on the quality of machined surface, Key Eng. Mater. 258–259 (2004) 361–365. [16] L.C. Zhang, H. Tanaka, Atomic scale deformation in silicon monocrystals induced by two-body and three-body contact sliding, Tribol. Int. 31 (8) (1998) 425–433. [17] J. Tersoff, Modeling solid state chemistry: interatomic potential for multicomponent systems, Phys. Rev. B 39 (1989) 5566–5570.