- Email: [email protected]
Atomistic simulation of influence of laser nano-structured diamond abrasive on the polishing behavior of silicon
Materials Science in Semiconductor Processing 105 (2020) 104706
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Atomistic simulation of influence of laser nano-structured diamond abrasive on the polishing behavior of silicon
T
Houfu Daia,b,∗, Yuqi Zhoub, Fa Zhangb a b
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR China College of Mechanical Engineering, Guizhou University, Guiyang, 550025, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Molecular dynamics Subsurface damage Laser nano-structured diamond abrasive Mechanical polishing
Micro/nano-structured surfaces often present many interesting behaviors and lend themselves to advanced functions. To further improve the polishing performance of diamond abrasives, large scale MD (molecular dynamics) simulations are employed to investigate the ultra-precision mechanical polishing of monocrystalline silicon with laser-fabricated nano-structured diamond abrasive. The material removal mechanism during polishing using structured diamond abrasive is studied in detail. The effects of the structured depth, structured width, structured factor, and structured pattern on the material deformation are studied in detail by analyzing the surface morphologies of the polished surface, normal stresses, shear stress, polishing temperature, atomic coordination numbers, von Mises stress, hydrostatic stress, polishing force, and dislocation extraction algorithm (DXA). The simulation results show that a bigger structured width abrasive, smaller structured depth abrasive， higher structured factor abrasive, or rectangle pattern abrasive would cause a larger material removal rate. Moreover, the abrasive with a smaller structured width, smaller structured depth, or higher structured factor tends to polish silicon materials in a more ductile mode. The abrasive with a bigger structured width has a lower hydrostatic stress, better polished surface, and less defect atoms. However, the abrasive with a bigger structured width, smaller structured depth, or higher structured factor results in a larger normal polishing force. Polishing using an abrasive with a higher structured factor leads to more polishing heat. In addition, the abrasive with 33.3% structured factor polishing can reduce the tangential polishing forces.
1. Introduction Improving the surface function of materials by introducing micro/ nano-structured surfaces is of great interest in many fields. In the present industry, compared with simple smooth surfaces, these micro/ nano-structured surfaces can be used to realize many interesting and advanced functions. For instance, surface phenomena play a crucial role in the behavior of engineering parts. Their control and understanding are fundamental to the development of many advanced fields, including electronics, information technology, tribology, energy, optics, biology, and biomimetics [1]. Some micro-textured surfaces can enhance the natural hydrophobicity of surfaces [2]. Textured tool surfaces can reduce the cutting force because of the corresponding decrease in the friction on the rake face [3]. As a result, this paper is devoted to understanding the influence of structured surface on polishing performance during nano-polishing. As well known, monocrystalline silicon is widely applied in computer systems, precision optics, and industrial automation [4].
∗
However, the high stiffness, high hardness, and brittleness of silicon largely limit its practical utility. Therefore, in this study, to reduce the subsurface damage and polishing force, micro/nano-structured surface technology is applied for nanoscale mechanical polishing. Diamond is a prominent material used as polishing abrasive in the semiconductor industry as it is an ideal brittle solid with the largest hardness and resistance to plastic deformation among all materials, in addition to exceptional dimensional homogeneity [5]. However, owing to its extremely high hardness, it is very difficult to structure diamond surfaces using ordinary mechanical tools due to the quick wear of tools. Additionally, when the size of the material is at the micro/nanometer level, such machining becomes very challenging. Many methods have been developed to fabricate the micro/nano structure to overcome these problems. Typical methods are developed, including the elliptical vibration cutting, electrical discharge machining, lithographic machining, laser beam machining, and electron beam machining [6,7]. With the rapid development of femtosecond lasers, micro-nano fabrication can achieve high quality micro/nano-structured surfaces.
Corresponding author. College of Mechanical Engineering, Guizhou University, Guiyang 550025, China. E-mail address: [email protected] (H. Dai).
https://doi.org/10.1016/j.mssp.2019.104706 Received 6 May 2019; Received in revised form 9 August 2019; Accepted 29 August 2019 1369-8001/ © 2019 Elsevier Ltd. All rights reserved.
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 1. MD simulation model of nano-polishing with structured abrasive: (a) 3D MD simulation model; (b) diamond abrasive with square structured pattern; (c) crosssection view of diamond abrasive with square structured pattern. Atoms are colored according to their distance from the center atom of the abrasive.
measure the polishing parameters through experiments at the atomic scale while on the other hand, the discrete nature of materials at the nanoscale makes it inappropriate to analyze nanoscale polishing using the conventional theory based on “continuum mechanics”. Therefore, MD simulation as a theoretical method has become a forceful tool for nanoscale mechanical machining [16–18]. Additionally, according to several researchers [19–22], MD simulations can reveal the mechanism of nano-polishing. So far, little work has been done to examine the effects of structured parameters on the polishing performance. Consequently, the differences between the material removal mechanisms in structured abrasive polishing and conventional polishing are not fully understood. This is the key objective of the current work-to examine the influence of structured parameters including the structured depth, width, factor, and pattern on the polishing performance of hard and brittle materials like silicon. In this study, a nano-polishing model with structured diamond abrasives will be established to first study the effect of the structured depth, width, factor, and pattern on the polishing mechanism. In addition, changes in the atomic structure are investigated by the dislocation extraction algorithm (DXA), coordination number (CN), and stress distribution. Besides, we also analyzed in detail the subsurface of the workpiece by examining the polished surface morphologies, polishing force, and polishing temperature.
Table 1 Simulation parameters. Workpiece Materials Abrasive Materials Dimension of workpiece Numbers of atoms Diamond abrasive radius Abrasive orientation and polishing orientation Initial temperature Polishing distance Time step Polishing velocity Polishing depth Abrasive structured Abrasive structured Abrasive structured Abrasive structured
width depth factor pattern
Silicon diamond 23.3 nm × 9.2 nm × 16.3 nm 179070 4 nm Cubic and [−1 0 0] 300 K 18 nm 1fs Moving velocity = 200 m/s Self-rotation velocity = 100 m/s 2 nm 0.2, 0.4, 0.6 and 0.8 nm 0.2, 0.4 and 0.6 nm 20, 33.3, 50 and 75% Square, rectangle, sphere and cone
Besides, the laser micro-nano machining can be used to manufacture arbitrary surface structures [8]. Hence, laser machining methods are proposed. Micro/nano structured surface technology has been widely applied to the field of ultra-precision machining [9–12]. Therefore, in this study, micro/nano structured surface technology is applied to the ultraprecision polishing of difficult-to-machine materials to improve the polishing performance. Over the past decades, much research has been done on ultraprecision mechanical polishing [13–15]. However, on one hand, it is extremely difficult to observe the polishing process and
2. Simulation method The mechanics model of nano-polishing with structured diamond abrasive is illustrated in Fig. 1. To make the simulation results more accurate and take into account the high thermal conductivity of the 2
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 2. Polishing abrasives with different structured widths: (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm.
Fig. 3. Polished surface morphologies (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm at a polishing distance 18 nm. Atomic coloring is based on their height. (Structured depth, structured factor and structured pattern are 0.6 nm, 33.3%, and rectangle, respectively.)
which is much higher than the actual polishing speed during a real polishing process. Nevertheless, the higher machining speed has only a minor influence on the surface finish quality, machining force, and deformation characteristics [27–30]. The LAMMPS software is employed to perform these MD simulations [31]. OVITO software is utilized to visualize the obtained MD simulations data [32].
diamond abrasive, the nano-structured diamond abrasive has been modeled as a deformable body although the hardness of diamond abrasive is much higher than that of silicon. In this study, the diamond abrasive particles are simplified and modeled as spherical abrasive particles of radius 4 nm. The motion of the abrasive involves both selfrotation and translation. The self-rotation speed and polishing speed are 100 m/s and 200 m/s, respectively. To eliminate the boundary effect, the dimension of workpiece is taken as 23.3 nm × 9.2 nm × 16.3 nm, which contains 179070 silicon atoms. For eliminating rigid body motion, the boundary atoms of the abrasive and workpiece are fixed in position. The thermostat atoms are used to guarantee a reasonable outward heat conduction, which absorb the heat from the machined zone. Periodic boundary conditions (PBC) are applied in the z direction to save computational time and reduce the size effect. During the nanopolishing process with structured diamond abrasives, the effect of the structured width, depth, factor, and shape cannot be neglected, which significantly influences the subsurface quality and polishing force. As a result, four structured widths (0.2, 0.4, 0.6, and 0.8 n m), three structured depth (0.2, 0.4 and 0.6 nm), four structured factors (20, 33.3, 50, and 75%) and three structured shapes (Square, rectangle, sphere, and cone) are studied. More parameters of the abrasive and polishing used in these simulations are demonstrated in Table 1, where structured factor is the ratio of the nominal surface area of the structured abrasive to nominal surface area of the non-structured abrasive [23]. The interaction potential function is crucial to the accuracy of simulations, which determines the reliability of simulation results. Also, according to the literatures [24,25], a new improved screened cutoff scheme has recently been developed by Pastewka et al. [26], which is very suitable to describe the interaction in covalent systems such as silicon carbide, carbon, and silicon. Hence, in this study, this new potential function is used for describing the interaction inside the workpiece atoms between workpiece atoms and abrasive atoms, and within abrasive atoms. In this study, it must be noted that the polishing speed is 200 m/s,
3. Results and discussion 3.1. Effect of structured width Fig. 2(a)-(d) represent the abrasives with different structured widths. The corresponding MD simulations are presented in Fig. 3(a)(d), which shed light on the analysis of the polishing chips. It is observed that the chipping volume and the volume of material pileups decrease with the increase in structured widths. This information suggests that the abrasive with a bigger structured width shows stronger material removal ability in nano-polishing. Also, it is found that the number of atoms in the groove of abrasive increases as the structured width increases. Since the abrasive with a bigger structured width has larger chip capacity. In Fig. 4(a)-(d), four MD snapshots from the cross-sectional view of the workpiece at different structured widths after the abrasive has advanced by 18 nm are observed. The MD simulation snapshots reveal the differences in the crystal structure of the workpiece during polishing using different structured abrasives. To study this further, Fig. 4(e)–(f) show the evolution of bct5-Si (CN = 5) and Si-II (CN = 6, beta-silicon, metallic and ductile), respectively, during structured abrasive polishing. Clearly, from Fig. 4(a)–(e), the number of bct5-Si decreases with increasing structured width, which implies that the polishing abrasive with a larger structured width produces a better polished surface. Moreover, it is observed from Fig. 4(f) that although the number of Si-II has no obvious change as the structured width increases, the number of Si-II at the structured width d = 0.8 nm is the highest. This indicates 3
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 4. Cross-section views of the polishing process under different structured widths after the abrasive has advanced by 18 nm. (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm. Atoms are colored based on their coordination number (CN). (e) and (f) are the number of Bct5-Si (CN = 5) and Si-II (CN = 6) variation in the workpiece, respectively.
that more ductile and metallic Si-II forms from its original Si–I (CN = 4, alpha-silicon, diamond cubic structure, brittle) when using the abrasive with a structured width of 0.8 nm. Von mises stress is a commonly used yield criterion to assess the yielding of a material [33]. In addition, the von Mises stress and hydrostatic stress have a great influence on the phase transformation, dislocation nucleation, and movement of silicon atoms [31]. Based on available work [18,35,36], the stress tensor of each atom can be evaluated using the following equation: i σαβ =
1 ⎛ 1 mi viα viβ + Ωi ⎜ 2 ⎝
∑ j, j ≠ i
rijβ fijα
⎞ ⎟ ⎠
σhydro =
1 (σxx + σyy + σzz ) 3
(2)
σvon Mises =
2 2 2 (σxx − σyy )2 + (σxx − σzz )2 + (σzz − σyy )2 + 6(σxy + σyz + σxz )
2 (3)
Fig. 5 sheds light on the analysis of the hydrostatic stress and von Mises stress. The difference between the von Mises stresses is immediately evident from this analysis. Fig. 5(a)–(b) illustrate the von Mises and hydrostatic stress distributions for the structured width 0.6 nm abrasive polishing after an abrasive advance to 18 nm, respectively. A nearly identical trend is found for other structured width abrasive polishing processes, and hence, are not repeated. From Fig. 5(a), it can be noted that the highest von Mises stress occurs in the
(1)
The hydrostatic stress σhydro and von Mises stress σvon Mises are evaluated using the following equations: 4
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 5. (a) Von mises stress and (b) hydrostatic stress distribution during nano-polishing after the abrasive advances to 18 nm. (The structured width is 0.6 nm for (a) and (b)). (c) Average subsurface von Mises stress for different structured widths. (d) Variations of subsurface hydrostatic stress. (e) Average subsurface hydrostatic stress at different structured widths.
Fig. 6(a)-(d) shows the cross-sectional views of instantaneous defect structures at different structured widths after an abrasive advance of 18 mm. The crystal defects, dislocation lines, and their Burgers vectors in the workpiece during polishing using structured abrasives are identified by DXA [39,40] In this paper, blue atoms indicate Si–I and gray atoms indicate defect atoms containing Si-II, dislocation atoms, and surface atoms. As shown in Fig. 6 (a)–(d), the structured width greatly influences the quality of the polished surface. For a further comparison, Fig. 6(e) presents the evolution of defect atoms with polishing distance at different structured widths. It is clear from the four simulations that the number of defect atoms increases almost linearly as the increase in the polishing distance. It is evident from Fig. 6(e) that the number of defect atoms decreases with an increase in the structured width. This reconfirms that a diamond abrasive with a larger structured width leads to a better polished surface. To further understand the influence of structured widths on the
groove region of the polishing abrasive. Nonetheless, from Fig. 5(b), it is interesting to see that high hydrostatic stress occurs in the left front of the diamond abrasive. High pressure phase transformation (HPPT) promotes the brittle-ductile transformation in silicon during contact loading [37]. It has been concluded that when the pure hydrostatic stress reaches 11–12 GPa during the machining of silicon, the phase transformation from Si–I to Si-II will take place [37,38]. Fig. 5(c) demonstrates the average subsurface von Mises stress at different structured widths. By comparing abrasives with different structured widths, only a minor difference in the subsurface von Mises stress is observed. This result indicates that the structured width has little effect on the von Mises stress. For a clearer comparison, the average subsurface hydrostatic stress at different structured widths is shown in Fig. 5(e). From Fig. 5(d)–(e), it can be seen that the increase in the structured width causes the decrease in the hydrostatic stress, which leads to the phase transformation of a smaller number of atoms (as shown in Fig. 4) [37]. 5
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 6. Cross-section view of instantaneous defect structures at different structured widths: (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm. (e) Evolution of defect atoms under different structured widths.
in Fig. 7(c). It can be observed that on increasing the structured width d, the value of τxy is nearly the same. Hence, it can be deduced that the structured width d has little influence on the shear stress τxy in polishing. Moreover, it can be noted that the normal stresses σxx and σyy are compressive in nature due to the compression effects from the polishing abrasive. Besides, it is obvious that both σxx and σyy become smaller as the structured width increases. This is because when using a larger structured width polishing abrasive, the silicon workpiece undergoes larger hydrostatic stress. The large hydrostatic stress concentrates the plastic deformation in front of the polishing abrasive, which transforms the silicon workpiece into a more ductile state. Therefore, abrasives with a smaller structured width tend to polish silicon materials in a more ductile mode as compared to other structured abrasives.
polishing temperature, Fig. 7(a) presents a comparison of the subsurface temperature. The friction between the abrasive surface and the workpiece causes the polishing heat. It is observed that as the polishing distance increases, the subsurface temperature rises quickly during the initial polishing stage, and then becomes steady. From Fig. 7(a), it is apparent that with the increase of the structured width, the subsurface temperature varies slightly within a small range. This indicates that the structured width has no evident effect on subsurface temperature. In contrast, the relationship of both the tangential and normal polishing forces with the structured width is demonstrated in Fig. 7(b). The friction between the structured surface of the polishing abrasive and workpiece generates the polishing forces. It is clear that the normal polishing force decreases as the structured width increases. This result indicates that the abrasive with a larger structured width can reduce the normal polishing force. Furthermore, it is obvious that the resultant polishing force is the smallest when the structured width of the abrasive d is 0.6 nm. This suggests that during nano-polishing, the abrasive with the 0.6 nm structured width can result in a smaller resultant polishing force compared with other structured abrasives. The variations of average stresses with structured width are shown
3.2. Effect of structured depth Fig. 8 provides an illustration of the polishing abrasive models with different structured depths. Fig. 8(a)–(c) show the abrasives with structured depths of 0.2 nm, 0.4 nm, and 0.6 nm, respectively. Three corresponding snapshots are shown in Fig. 9(a)-(c), which shows the 6
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 7. Effect of different structured widths. (a) Variation of the average subsurface temperature, (b) variations of polishing forces, and (c) variations of normal stresses σxx , σyy and shear stress τxy .
Fig. 8. 3D models of polishing abrasives with different structured depths: (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm.
increase in structured depth, which suggests that a slightly better polished surface can be obtained using the diamond abrasive with a smaller structured depth. After nano-polishing, the von Mises stress distribution at different structured depths is measured, as shown in Fig. 11(a)-(c). It can be seen that the von Mises stress is the highest in the groove of the abrasive. Fig. 11(d) shows the variations of the average von Mises stress at the subsurface region versus the polishing distance under different structured depths. It is apparent that the average subsurface von Mises stress at a structured depth h = 0.2 nm is lower than those at other structured depths, which suggests that the use of a 0.2 nm structured depth reduces the von Mises stress at the subsurface zone. Fig. 12(a) shows the temperature-displacement curves during the
top view of polished surface after 18 nm of abrasive advance under different structured depths. It is evident that the chip volume decreases when the structured depth of abrasive increases, thereby revealing that the diamond abrasive with a smaller structured depth exhibits larger material removal ability in nano-polishing. Additionally, as known, the abrasive with a larger structured depth has a larger chip capacity, which explains the increase in the number of atoms in the abrasive groove with the increase of the structured depth. The cross-sectional views of the workpiece under different structured depths are illustrated in Fig. 10(a–c). Silicon atoms are colored based on the DXA. The number of defect atoms at different structured depths is also evaluated for a better comparison, as seen in Fig. 10(d). It is found that the number of defect atoms decreases slightly with the 7
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 9. Top view of polished surface under different structured depths is (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm. Colors indicate the height of atoms. (The structured width, structured factor, and structured pattern are 0.6 nm, 33.3%, and rectangle, respectively.).
Fig. 10. Structured depths of (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm at the middle of the polishing process. Workpiece atoms are colored by DXA. (Blue: Si–I, gray: defect atoms). (d) Number of defect atoms at different structured depths.
stresses σxx , σyy and shear stress τxy during the polishing process. Obviously, on incrementing the structured depth, τxy is almost unchanged, whereas both σxx and σyy slightly rise. A nearly similar trend is found for different structured depths. These results point out that the abrasive with a smaller structured depth tends to polish silicon materials in a more ductile mode compared with other structured abrasives [27].
structured abrasive polishing process. It is clear that the temperature of the subsurface zone remains unchanged during the steady polishing stage as the structured depth increases. In other words, the structured depth has no significant effect on the subsurface temperature. The average tangential and normal polishing forces under different structured depths are also calculated in Fig. 12(b). It is quite clear that the normal polishing force decreases as the structured depth increases. This implies that the abrasive with a bigger structured depth gives rise to a lower normal polishing force. Additionally, it is found that for polishing with an abrasive of structured depth h = 0.6 nm, the magnitudes of polishing forces are significantly lower than when using other structured abrasives. This implies that the abrasive with a larger structured depth polishing leads to a lower polishing force. In contrast, Fig. 12(c) displays the evolution of stress components including the normal
3.3. Effect of structured factor The 3D models of polishing abrasives with different structured factors and the corresponding polished surface morphologies after 18 nm of polishing are presented in Fig. 13 and Fig. 14(a)-(d), respectively. A noteworthy observation from Fig. 14(a)–(d) is that the chip volume increases with the increasing structured factors, which indicates 8
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 11. After 18 nm of abrasive advance (a) illustration of von Mises stress distribution at different structured depths: (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm. (d) Von mises stress-polishing distance curves under different structured depths.
Fig. 12. (a) Variation of the subsurface temperature, (b) variations of polishing forces, and (c) variations of normal stresses σxx , σyy and shear stress τxy .
fact that the abrasive with a lower structured factor has a stronger chip capacity. A comparison of structured factors 20% and 75% shows that the subsurface temperature decreases slightly with the increase of
that polishing using a bigger structured factor results in a significant increment in the material removal rate. Also, it is apparent that increasing the structured factors decreases the number of atoms in the groove of abrasive during nano-polishing. This can be attributed to the 9
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 13. 3D models of polishing abrasives with different structured factors: (a) 20%, (b) 33.3%, (c) 50%, and (d) 75%.
Fig. 14. Polished surface morphology at different structured factors: (a) 20%, (b) 33.3%, (c) 50%, and (d) 75%. The atoms are colored according to their heights. (The structured width, structured depth and structured pattern are 0.6 nm, 0.6 nm, and rectangle, respectively.)
Fig. 15. Average subsurface temperature vs. polishing distance for four different structured factors (a), average polishing forces, variations of normal stresses (σxx and σyy ) and shear stress τxy with the structured factor (c).
10
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 16. 3D models of polishing abrasives with different structured patterns: (a) square, (b) rectangle, (c) sphere, and (d) cone.
Fig. 17. Variation of polished surface morphology with the change of structured pattern of (a) square, (b) rectangle, (c) sphere, and (d) cone. Atoms are colored by their heights. (The structured width, structured depth and structured factor are 0.6 nm, 0.6 nm and 33.3%, respectively.)
This reveals that the abrasive with a rectangle pattern can enhance the material removal ability in nano-polishing. Furthermore, from Fig. 17(a–d), it is found that for the rectangle-patterned abrasive polishing, the number of atoms in the groove of abrasive is larger than those for other structured abrasives. This means that the abrasive with a rectangle pattern has the largest chip capacity during nano-polishing.
structured factors, which indicates that the abrasive with a lower structured factor polishing generates less polishing heat during nanoscale mechanical polishing. Correspondingly, Fig. 15(b) demonstrates the variation of average polishing forces with the polishing distance. It clearly shows that when the structured factor of the abrasive η is 33.3%, the magnitude of the tangential polishing force is the lowest, which implies that the abrasive with 33.3% structured factor polishing can reduce the tangential polishing forces during nano-polishing. In addition to this, it must be noted that the value of the normal polishing force at structured factors η = 20% or 33.3% is lower than that at structured factors η = 50% or 75%. This indicates that the abrasive with a lower structured factor polishing results in a smaller normal polishing force. The normal stresses σxx , σyy and shear stress τxy at the subsurface zone change with structured factors is carefully checked, as presented in Fig. 15(c). It is evident that the shear stress τxy was roughly of the same order under different structured factors. It means that τxy is basically dependent on the structured factor. Furthermore, from Fig. 15(c), the increase in structured factors causes slight increase of the compressive normal stresses σxx and σyy . This result indicates that the abrasive with a higher structured factor tends to polish silicon materials in a more ductile mode.
4. Conclusions In this paper, MD simulations of nano-polishing for monocrystalline silicon are applied to examine the effects of structured depth, structured width, structured factor and structured pattern. The main conclusions that can be drawn are: The abrasive with a bigger structured width has a stronger material removal ability, lower hydrostatic stress, better polished surface, and less defect atoms, but it causes a higher normal polishing force. The diamond abrasive with a smaller structured depth provides larger material removal ability, a slightly better polished surface, and tends to polish silicon materials in a more ductile mode, whereas it results in a higher polishing force. Although a higher structured factor polishing leads to a more ductile polishing mode and a larger material remove rate, it results in a larger normal polishing force, more polishing heat, and smaller chip capacity.
3.4. Effect of structured pattern Fig. 16(a–d) shows the 3D models of polishing abrasives with different structured patterns. Fig. 16(a)–(d) visualize the abrasives with structured patterns of square, rectangle, sphere, and cone, respectively. The four corresponding MD simulations are demonstrated in Fig. 17(a–d). Fig. 17(a–d) display the variation of polished surface morphology with the structured patterns of abrasives. Clearly, it is seen that when the surface of the structured abrasive has a rectangle pattern, the material removal rate is the biggest; but if the surface of the structured abrasives is conical, the material removal rate is the smallest.
Acknowledgements The authors would like to appreciate the fund project for the introduction of talents in Guizhou University (No. [2017]24), Guizhou Province Education Department Youth Science and technology talent growth project (No. [2018]110), and National Natural Science Foundation cultivation project for young teachers of Guizhou University (No. [2017]5788). 11
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
References
[21] L. Zhang, H. Zhao, Z. Ma, H. Huang, C. Shi, W. Zhang, A study on phase transformation of monocrystalline silicon due to ultra-precision polishing by molecular dynamics simulation, AIP Adv. 2 (2012) 899. [22] Y. Yang, H. Zhao, L. Zhang, M. Shao, H. Liu, H. Huang, Molecular dynamics simulation of self-rotation effects on ultra-precision polishing of single-crystal copper, AIP Adv. 3 (2013) 899. [23] C. Walter, T. Komischke, E. Weingärtner, K. Wegener, Structuring of CBN grinding tools by ultrashort pulse laser ablation, Procedia CIRP 14 (2014) 31–36. [24] S. Goel, A. Kovalchenko, A. Stukowski, G. Cross, Influence of microstructure on the cutting behaviour of silicon, Acta Mater. 105 (2016) 464–478. [25] Y. Wang, J. Xu, J. Zhang, Q. Chen, Y. Ootani, Y. Higuchi, N. Ozawa, J.M. Martin, K. Adachi, M. Kubo, Tribochemical reactions and graphitization of diamond-like carbon against alumina give volcano-type temperature dependence of friction coefficients: a tight-binding quantum chemical molecular dynamics simulation, Carbon 133 (2018) 350–357. [26] L. Pastewka, A. Klemenz, P. Gumbsch, M. Moseler, Screened empirical bond-order potentials for Si-C, Phys. Rev. B 87 (2013) 205410. [27] Y. Wang, J. Shi, C. Ji, A numerical study of residual stress induced in machined silicon surfaces by molecular dynamics simulation, Appl. Phys. A Mater. 115 (2014) 1263–1279. [28] Z.C. Lin, J.C. Huang, The influence of different cutting speeds on the cutting force and strain–stress behaviors of single crystal copper during nano-scale orthogonal cutting, J. Mater. Process. Technol. 201 (2008) 477–482. [29] J.J. Zhang, T. Sun, Y.D. Yan, Y.C. Liang, S. Dong, Molecular dynamics simulation of subsurface deformed layers in AFM-based nanometric cutting process, Appl. Surf. Sci. 254 (2008) 4774–4779. [30] P. Zhu, Y. Hu, T. Ma, H. Wang, Molecular dynamics study on friction due to ploughing and adhesion in nanometric scratching process, Tribol. Lett. 41 (2011) 41–46. [31] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1–19. [32] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Model. Simul. Mater. Sci. Eng. 18 (2009) 015012. [33] S.Z. Chavoshi, X. Luo, Molecular dynamics simulation study of deformation mechanisms in 3C–SiC during nanometric cutting at elevated temperatures, Mat. Sci. Eng. A-Struct. 654 (2016) 400–417. [35] H. Dai, G. Chen, Q. Fang, J. Yin, The effect of tool geometry on subsurface damage and material removal in nanometric cutting single-crystal silicon by a molecular dynamics simulation, Appl. Phys. A Mater. 122 (2016) 804. [36] S. Goel, X. Luo, R.L. Reuben, Wear mechanism of diamond tools against single crystal silicon in single point diamond turning process, Tribol. Int. 57 (2013) 272–281. [37] D.E. Kim, S.I. Oh, Atomistic simulation of structural phase transformations in monocrystalline silicon induced by nanoindentation, Nanotechnology 17 (2006) 2259. [38] Y.H. Lin, T.C. Chen, A molecular dynamics study of phase transformations in monocrystalline Si under nanoindentation, Appl. Phys. A Mater. 92 (2008) 571. [39] A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Model. Simul. Mater. Sci. Eng. 18 (2010) 085001. [40] A. Sedlmayr, E. Bitzek, D.S. Gianola, R. Gunther, R. Mönig, O. Kraft, Existence of two twinning-mediated plastic deformation modes in Au nanowhiskers, Acta Mater. 60 (2012) 3985–3993.
[1] A.A.G. Bruzzone, H.L. Costa, P.M. Lonardo, D.A. Lucca, Advances in engineered surfaces for functional performance, CIRP Ann. - Manuf. Technol. 57 (2008) 750–769. [2] M. Callies, Y. Chen, F. Marty, A. Pépin, D. Quéré, Microfabricated textured surfaces for super-hydrophobicity investigations, Microelectron. Eng. 78 (2005) 100–105. [3] N. Kawasegi, H. Sugimori, H. Morimoto, N. Morita, I. Hori, Development of cutting tools with microscale and nanoscale textures to improve frictional behavior, Precis. Eng. 33 (2009) 248–254. [4] Z. Liang, Y. Wu, X. Wang, W. Zhao, A new two-dimensional ultrasonic assisted grinding (2D-UAG) method and its fundamental performance in monocrystal silicon machining, Int. J. Mach. Tool Manuf. 50 (2010) 728–736. [5] Z.J. Yuan, Y.X. Yao, M. Zhou, Q.S. Bal, Lapping of single crystal diamond tools, CIRP Ann. - Manuf. Technol. 52 (2003) 285–288. [6] J. Zhang, T. Cui, C. Ge, Y. Sui, H. Yang, Review of micro/nano machining by utilizing elliptical vibration cutting, Int. J. Mach. Tool Manuf. 106 (2016) 109–126. [7] B. Guo, Q. Zhao, On-machine dry electric discharge truing of diamond wheels for micro-structured surfaces grinding, Int. J. Mach. Tool Manuf. 88 (2015) 62–70. [8] P.W. Butler-Smith, D.A. Axinte, M. Daines, Preferentially oriented diamond microarrays: a laser patterning technique and preliminary evaluation of their cutting forces and wear characteristics, Int. J. Mach. Tool Manuf. 49 (2009) 1175–1184. [9] S. Okuyama, Y. Nakamura, S. Kawamura, Cooling action of grinding fluid in shallow grinding, Int. J. Mach. Tool Manuf. 33 (1993) 13–23. [10] H.W. Zheng, H. Gao, A general thermal model for grinding with slotted or segmented wheel, CIRP Ann. - Manuf. Technol. 43 (1994) 287–290. [11] B. Guo, Q. Zhao, X. Fang, Precision grinding of optical glass with laser microstructured coarse-grained diamond wheels, J. Mater. Process. Technol. 214 (2014) 1045–1051. [12] T. Sugihara, T. Enomoto, Development of a cutting tool with a nano/micro-textured surface—improvement of anti-adhesive effect by considering the texture patterns, Precis. Eng. 33 (2009) 425–429. [13] C.F. Cheung, L.T. Ho, P. Charlton, L.B. Kong, W.B. Lee, Analysis of surface generation in the ultraprecision polishing of freeform surfaces, P. I. Mech. Eng. B-J. Eng. 224 (2010) 59–73. [14] J. Guo, H. Suzuki, S. Morita, Y. Yamagata, T. Higuchi, A real-time polishing force control system for ultraprecision finishing of micro-optics, Precis. Eng. 37 (2013) 787–792. [15] H. Suzuki, S. Hamada, T. Okino, M. Kondo, Y. Yamagata, T. Higuchi, Ultraprecision finishing of micro-aspheric surface by ultrasonic two-axis vibration assisted polishing, CIRP Ann. - Manuf. Technol. 59 (2010) 347–350. [16] H. Dai, G. Chen, C. Zhou, Q. Fang, X. Fei, A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation, Appl. Surf. Sci. 393 (2017) 405–416. [17] H. Dai, G. Chen, S. Li, Q. Fang, B. Hu, Influence of laser nano-structured diamond tools on the cutting behaviour of silicon by molecular dynamics simulation, RSC Adv. 7 (2017) 15596–15612. [18] S. Goel, X. Luo, A. Agrawal, R.L. Reuben, Diamond machining of silicon: a review of advances in molecular dynamics simulation, Int. J. Mach. Tool Manuf. 88 (2015) 131–164. [19] L. Zhang, H. Tanaka, Atomic scale deformation in silicon monocrystals induced by two-body and three-body contact sliding, Tribol. Int. 31 (1998) 425–433. [20] I. Zarudi, W.C.D. Cheong, J. Zou, L.C. Zhang, Atomistic structure of monocrystalline silicon in surface nano-modification, Nanotechnology 15 (2003) 104.
12
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Atomistic simulation of influence of laser nano-structured diamond abrasive on the polishing behavior of silicon
T
Houfu Daia,b,∗, Yuqi Zhoub, Fa Zhangb a b
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR China College of Mechanical Engineering, Guizhou University, Guiyang, 550025, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Molecular dynamics Subsurface damage Laser nano-structured diamond abrasive Mechanical polishing
Micro/nano-structured surfaces often present many interesting behaviors and lend themselves to advanced functions. To further improve the polishing performance of diamond abrasives, large scale MD (molecular dynamics) simulations are employed to investigate the ultra-precision mechanical polishing of monocrystalline silicon with laser-fabricated nano-structured diamond abrasive. The material removal mechanism during polishing using structured diamond abrasive is studied in detail. The effects of the structured depth, structured width, structured factor, and structured pattern on the material deformation are studied in detail by analyzing the surface morphologies of the polished surface, normal stresses, shear stress, polishing temperature, atomic coordination numbers, von Mises stress, hydrostatic stress, polishing force, and dislocation extraction algorithm (DXA). The simulation results show that a bigger structured width abrasive, smaller structured depth abrasive， higher structured factor abrasive, or rectangle pattern abrasive would cause a larger material removal rate. Moreover, the abrasive with a smaller structured width, smaller structured depth, or higher structured factor tends to polish silicon materials in a more ductile mode. The abrasive with a bigger structured width has a lower hydrostatic stress, better polished surface, and less defect atoms. However, the abrasive with a bigger structured width, smaller structured depth, or higher structured factor results in a larger normal polishing force. Polishing using an abrasive with a higher structured factor leads to more polishing heat. In addition, the abrasive with 33.3% structured factor polishing can reduce the tangential polishing forces.
1. Introduction Improving the surface function of materials by introducing micro/ nano-structured surfaces is of great interest in many fields. In the present industry, compared with simple smooth surfaces, these micro/ nano-structured surfaces can be used to realize many interesting and advanced functions. For instance, surface phenomena play a crucial role in the behavior of engineering parts. Their control and understanding are fundamental to the development of many advanced fields, including electronics, information technology, tribology, energy, optics, biology, and biomimetics [1]. Some micro-textured surfaces can enhance the natural hydrophobicity of surfaces [2]. Textured tool surfaces can reduce the cutting force because of the corresponding decrease in the friction on the rake face [3]. As a result, this paper is devoted to understanding the influence of structured surface on polishing performance during nano-polishing. As well known, monocrystalline silicon is widely applied in computer systems, precision optics, and industrial automation [4].
∗
However, the high stiffness, high hardness, and brittleness of silicon largely limit its practical utility. Therefore, in this study, to reduce the subsurface damage and polishing force, micro/nano-structured surface technology is applied for nanoscale mechanical polishing. Diamond is a prominent material used as polishing abrasive in the semiconductor industry as it is an ideal brittle solid with the largest hardness and resistance to plastic deformation among all materials, in addition to exceptional dimensional homogeneity [5]. However, owing to its extremely high hardness, it is very difficult to structure diamond surfaces using ordinary mechanical tools due to the quick wear of tools. Additionally, when the size of the material is at the micro/nanometer level, such machining becomes very challenging. Many methods have been developed to fabricate the micro/nano structure to overcome these problems. Typical methods are developed, including the elliptical vibration cutting, electrical discharge machining, lithographic machining, laser beam machining, and electron beam machining [6,7]. With the rapid development of femtosecond lasers, micro-nano fabrication can achieve high quality micro/nano-structured surfaces.
Corresponding author. College of Mechanical Engineering, Guizhou University, Guiyang 550025, China. E-mail address: [email protected] (H. Dai).
https://doi.org/10.1016/j.mssp.2019.104706 Received 6 May 2019; Received in revised form 9 August 2019; Accepted 29 August 2019 1369-8001/ © 2019 Elsevier Ltd. All rights reserved.
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 1. MD simulation model of nano-polishing with structured abrasive: (a) 3D MD simulation model; (b) diamond abrasive with square structured pattern; (c) crosssection view of diamond abrasive with square structured pattern. Atoms are colored according to their distance from the center atom of the abrasive.
measure the polishing parameters through experiments at the atomic scale while on the other hand, the discrete nature of materials at the nanoscale makes it inappropriate to analyze nanoscale polishing using the conventional theory based on “continuum mechanics”. Therefore, MD simulation as a theoretical method has become a forceful tool for nanoscale mechanical machining [16–18]. Additionally, according to several researchers [19–22], MD simulations can reveal the mechanism of nano-polishing. So far, little work has been done to examine the effects of structured parameters on the polishing performance. Consequently, the differences between the material removal mechanisms in structured abrasive polishing and conventional polishing are not fully understood. This is the key objective of the current work-to examine the influence of structured parameters including the structured depth, width, factor, and pattern on the polishing performance of hard and brittle materials like silicon. In this study, a nano-polishing model with structured diamond abrasives will be established to first study the effect of the structured depth, width, factor, and pattern on the polishing mechanism. In addition, changes in the atomic structure are investigated by the dislocation extraction algorithm (DXA), coordination number (CN), and stress distribution. Besides, we also analyzed in detail the subsurface of the workpiece by examining the polished surface morphologies, polishing force, and polishing temperature.
Table 1 Simulation parameters. Workpiece Materials Abrasive Materials Dimension of workpiece Numbers of atoms Diamond abrasive radius Abrasive orientation and polishing orientation Initial temperature Polishing distance Time step Polishing velocity Polishing depth Abrasive structured Abrasive structured Abrasive structured Abrasive structured
width depth factor pattern
Silicon diamond 23.3 nm × 9.2 nm × 16.3 nm 179070 4 nm Cubic and [−1 0 0] 300 K 18 nm 1fs Moving velocity = 200 m/s Self-rotation velocity = 100 m/s 2 nm 0.2, 0.4, 0.6 and 0.8 nm 0.2, 0.4 and 0.6 nm 20, 33.3, 50 and 75% Square, rectangle, sphere and cone
Besides, the laser micro-nano machining can be used to manufacture arbitrary surface structures [8]. Hence, laser machining methods are proposed. Micro/nano structured surface technology has been widely applied to the field of ultra-precision machining [9–12]. Therefore, in this study, micro/nano structured surface technology is applied to the ultraprecision polishing of difficult-to-machine materials to improve the polishing performance. Over the past decades, much research has been done on ultraprecision mechanical polishing [13–15]. However, on one hand, it is extremely difficult to observe the polishing process and
2. Simulation method The mechanics model of nano-polishing with structured diamond abrasive is illustrated in Fig. 1. To make the simulation results more accurate and take into account the high thermal conductivity of the 2
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 2. Polishing abrasives with different structured widths: (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm.
Fig. 3. Polished surface morphologies (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm at a polishing distance 18 nm. Atomic coloring is based on their height. (Structured depth, structured factor and structured pattern are 0.6 nm, 33.3%, and rectangle, respectively.)
which is much higher than the actual polishing speed during a real polishing process. Nevertheless, the higher machining speed has only a minor influence on the surface finish quality, machining force, and deformation characteristics [27–30]. The LAMMPS software is employed to perform these MD simulations [31]. OVITO software is utilized to visualize the obtained MD simulations data [32].
diamond abrasive, the nano-structured diamond abrasive has been modeled as a deformable body although the hardness of diamond abrasive is much higher than that of silicon. In this study, the diamond abrasive particles are simplified and modeled as spherical abrasive particles of radius 4 nm. The motion of the abrasive involves both selfrotation and translation. The self-rotation speed and polishing speed are 100 m/s and 200 m/s, respectively. To eliminate the boundary effect, the dimension of workpiece is taken as 23.3 nm × 9.2 nm × 16.3 nm, which contains 179070 silicon atoms. For eliminating rigid body motion, the boundary atoms of the abrasive and workpiece are fixed in position. The thermostat atoms are used to guarantee a reasonable outward heat conduction, which absorb the heat from the machined zone. Periodic boundary conditions (PBC) are applied in the z direction to save computational time and reduce the size effect. During the nanopolishing process with structured diamond abrasives, the effect of the structured width, depth, factor, and shape cannot be neglected, which significantly influences the subsurface quality and polishing force. As a result, four structured widths (0.2, 0.4, 0.6, and 0.8 n m), three structured depth (0.2, 0.4 and 0.6 nm), four structured factors (20, 33.3, 50, and 75%) and three structured shapes (Square, rectangle, sphere, and cone) are studied. More parameters of the abrasive and polishing used in these simulations are demonstrated in Table 1, where structured factor is the ratio of the nominal surface area of the structured abrasive to nominal surface area of the non-structured abrasive [23]. The interaction potential function is crucial to the accuracy of simulations, which determines the reliability of simulation results. Also, according to the literatures [24,25], a new improved screened cutoff scheme has recently been developed by Pastewka et al. [26], which is very suitable to describe the interaction in covalent systems such as silicon carbide, carbon, and silicon. Hence, in this study, this new potential function is used for describing the interaction inside the workpiece atoms between workpiece atoms and abrasive atoms, and within abrasive atoms. In this study, it must be noted that the polishing speed is 200 m/s,
3. Results and discussion 3.1. Effect of structured width Fig. 2(a)-(d) represent the abrasives with different structured widths. The corresponding MD simulations are presented in Fig. 3(a)(d), which shed light on the analysis of the polishing chips. It is observed that the chipping volume and the volume of material pileups decrease with the increase in structured widths. This information suggests that the abrasive with a bigger structured width shows stronger material removal ability in nano-polishing. Also, it is found that the number of atoms in the groove of abrasive increases as the structured width increases. Since the abrasive with a bigger structured width has larger chip capacity. In Fig. 4(a)-(d), four MD snapshots from the cross-sectional view of the workpiece at different structured widths after the abrasive has advanced by 18 nm are observed. The MD simulation snapshots reveal the differences in the crystal structure of the workpiece during polishing using different structured abrasives. To study this further, Fig. 4(e)–(f) show the evolution of bct5-Si (CN = 5) and Si-II (CN = 6, beta-silicon, metallic and ductile), respectively, during structured abrasive polishing. Clearly, from Fig. 4(a)–(e), the number of bct5-Si decreases with increasing structured width, which implies that the polishing abrasive with a larger structured width produces a better polished surface. Moreover, it is observed from Fig. 4(f) that although the number of Si-II has no obvious change as the structured width increases, the number of Si-II at the structured width d = 0.8 nm is the highest. This indicates 3
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 4. Cross-section views of the polishing process under different structured widths after the abrasive has advanced by 18 nm. (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm. Atoms are colored based on their coordination number (CN). (e) and (f) are the number of Bct5-Si (CN = 5) and Si-II (CN = 6) variation in the workpiece, respectively.
that more ductile and metallic Si-II forms from its original Si–I (CN = 4, alpha-silicon, diamond cubic structure, brittle) when using the abrasive with a structured width of 0.8 nm. Von mises stress is a commonly used yield criterion to assess the yielding of a material [33]. In addition, the von Mises stress and hydrostatic stress have a great influence on the phase transformation, dislocation nucleation, and movement of silicon atoms [31]. Based on available work [18,35,36], the stress tensor of each atom can be evaluated using the following equation: i σαβ =
1 ⎛ 1 mi viα viβ + Ωi ⎜ 2 ⎝
∑ j, j ≠ i
rijβ fijα
⎞ ⎟ ⎠
σhydro =
1 (σxx + σyy + σzz ) 3
(2)
σvon Mises =
2 2 2 (σxx − σyy )2 + (σxx − σzz )2 + (σzz − σyy )2 + 6(σxy + σyz + σxz )
2 (3)
Fig. 5 sheds light on the analysis of the hydrostatic stress and von Mises stress. The difference between the von Mises stresses is immediately evident from this analysis. Fig. 5(a)–(b) illustrate the von Mises and hydrostatic stress distributions for the structured width 0.6 nm abrasive polishing after an abrasive advance to 18 nm, respectively. A nearly identical trend is found for other structured width abrasive polishing processes, and hence, are not repeated. From Fig. 5(a), it can be noted that the highest von Mises stress occurs in the
(1)
The hydrostatic stress σhydro and von Mises stress σvon Mises are evaluated using the following equations: 4
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 5. (a) Von mises stress and (b) hydrostatic stress distribution during nano-polishing after the abrasive advances to 18 nm. (The structured width is 0.6 nm for (a) and (b)). (c) Average subsurface von Mises stress for different structured widths. (d) Variations of subsurface hydrostatic stress. (e) Average subsurface hydrostatic stress at different structured widths.
Fig. 6(a)-(d) shows the cross-sectional views of instantaneous defect structures at different structured widths after an abrasive advance of 18 mm. The crystal defects, dislocation lines, and their Burgers vectors in the workpiece during polishing using structured abrasives are identified by DXA [39,40] In this paper, blue atoms indicate Si–I and gray atoms indicate defect atoms containing Si-II, dislocation atoms, and surface atoms. As shown in Fig. 6 (a)–(d), the structured width greatly influences the quality of the polished surface. For a further comparison, Fig. 6(e) presents the evolution of defect atoms with polishing distance at different structured widths. It is clear from the four simulations that the number of defect atoms increases almost linearly as the increase in the polishing distance. It is evident from Fig. 6(e) that the number of defect atoms decreases with an increase in the structured width. This reconfirms that a diamond abrasive with a larger structured width leads to a better polished surface. To further understand the influence of structured widths on the
groove region of the polishing abrasive. Nonetheless, from Fig. 5(b), it is interesting to see that high hydrostatic stress occurs in the left front of the diamond abrasive. High pressure phase transformation (HPPT) promotes the brittle-ductile transformation in silicon during contact loading [37]. It has been concluded that when the pure hydrostatic stress reaches 11–12 GPa during the machining of silicon, the phase transformation from Si–I to Si-II will take place [37,38]. Fig. 5(c) demonstrates the average subsurface von Mises stress at different structured widths. By comparing abrasives with different structured widths, only a minor difference in the subsurface von Mises stress is observed. This result indicates that the structured width has little effect on the von Mises stress. For a clearer comparison, the average subsurface hydrostatic stress at different structured widths is shown in Fig. 5(e). From Fig. 5(d)–(e), it can be seen that the increase in the structured width causes the decrease in the hydrostatic stress, which leads to the phase transformation of a smaller number of atoms (as shown in Fig. 4) [37]. 5
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 6. Cross-section view of instantaneous defect structures at different structured widths: (a) 0.2 nm, (b) 0.4 nm, (c) 0.6 nm, and (d) 0.8 nm. (e) Evolution of defect atoms under different structured widths.
in Fig. 7(c). It can be observed that on increasing the structured width d, the value of τxy is nearly the same. Hence, it can be deduced that the structured width d has little influence on the shear stress τxy in polishing. Moreover, it can be noted that the normal stresses σxx and σyy are compressive in nature due to the compression effects from the polishing abrasive. Besides, it is obvious that both σxx and σyy become smaller as the structured width increases. This is because when using a larger structured width polishing abrasive, the silicon workpiece undergoes larger hydrostatic stress. The large hydrostatic stress concentrates the plastic deformation in front of the polishing abrasive, which transforms the silicon workpiece into a more ductile state. Therefore, abrasives with a smaller structured width tend to polish silicon materials in a more ductile mode as compared to other structured abrasives.
polishing temperature, Fig. 7(a) presents a comparison of the subsurface temperature. The friction between the abrasive surface and the workpiece causes the polishing heat. It is observed that as the polishing distance increases, the subsurface temperature rises quickly during the initial polishing stage, and then becomes steady. From Fig. 7(a), it is apparent that with the increase of the structured width, the subsurface temperature varies slightly within a small range. This indicates that the structured width has no evident effect on subsurface temperature. In contrast, the relationship of both the tangential and normal polishing forces with the structured width is demonstrated in Fig. 7(b). The friction between the structured surface of the polishing abrasive and workpiece generates the polishing forces. It is clear that the normal polishing force decreases as the structured width increases. This result indicates that the abrasive with a larger structured width can reduce the normal polishing force. Furthermore, it is obvious that the resultant polishing force is the smallest when the structured width of the abrasive d is 0.6 nm. This suggests that during nano-polishing, the abrasive with the 0.6 nm structured width can result in a smaller resultant polishing force compared with other structured abrasives. The variations of average stresses with structured width are shown
3.2. Effect of structured depth Fig. 8 provides an illustration of the polishing abrasive models with different structured depths. Fig. 8(a)–(c) show the abrasives with structured depths of 0.2 nm, 0.4 nm, and 0.6 nm, respectively. Three corresponding snapshots are shown in Fig. 9(a)-(c), which shows the 6
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 7. Effect of different structured widths. (a) Variation of the average subsurface temperature, (b) variations of polishing forces, and (c) variations of normal stresses σxx , σyy and shear stress τxy .
Fig. 8. 3D models of polishing abrasives with different structured depths: (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm.
increase in structured depth, which suggests that a slightly better polished surface can be obtained using the diamond abrasive with a smaller structured depth. After nano-polishing, the von Mises stress distribution at different structured depths is measured, as shown in Fig. 11(a)-(c). It can be seen that the von Mises stress is the highest in the groove of the abrasive. Fig. 11(d) shows the variations of the average von Mises stress at the subsurface region versus the polishing distance under different structured depths. It is apparent that the average subsurface von Mises stress at a structured depth h = 0.2 nm is lower than those at other structured depths, which suggests that the use of a 0.2 nm structured depth reduces the von Mises stress at the subsurface zone. Fig. 12(a) shows the temperature-displacement curves during the
top view of polished surface after 18 nm of abrasive advance under different structured depths. It is evident that the chip volume decreases when the structured depth of abrasive increases, thereby revealing that the diamond abrasive with a smaller structured depth exhibits larger material removal ability in nano-polishing. Additionally, as known, the abrasive with a larger structured depth has a larger chip capacity, which explains the increase in the number of atoms in the abrasive groove with the increase of the structured depth. The cross-sectional views of the workpiece under different structured depths are illustrated in Fig. 10(a–c). Silicon atoms are colored based on the DXA. The number of defect atoms at different structured depths is also evaluated for a better comparison, as seen in Fig. 10(d). It is found that the number of defect atoms decreases slightly with the 7
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 9. Top view of polished surface under different structured depths is (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm. Colors indicate the height of atoms. (The structured width, structured factor, and structured pattern are 0.6 nm, 33.3%, and rectangle, respectively.).
Fig. 10. Structured depths of (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm at the middle of the polishing process. Workpiece atoms are colored by DXA. (Blue: Si–I, gray: defect atoms). (d) Number of defect atoms at different structured depths.
stresses σxx , σyy and shear stress τxy during the polishing process. Obviously, on incrementing the structured depth, τxy is almost unchanged, whereas both σxx and σyy slightly rise. A nearly similar trend is found for different structured depths. These results point out that the abrasive with a smaller structured depth tends to polish silicon materials in a more ductile mode compared with other structured abrasives [27].
structured abrasive polishing process. It is clear that the temperature of the subsurface zone remains unchanged during the steady polishing stage as the structured depth increases. In other words, the structured depth has no significant effect on the subsurface temperature. The average tangential and normal polishing forces under different structured depths are also calculated in Fig. 12(b). It is quite clear that the normal polishing force decreases as the structured depth increases. This implies that the abrasive with a bigger structured depth gives rise to a lower normal polishing force. Additionally, it is found that for polishing with an abrasive of structured depth h = 0.6 nm, the magnitudes of polishing forces are significantly lower than when using other structured abrasives. This implies that the abrasive with a larger structured depth polishing leads to a lower polishing force. In contrast, Fig. 12(c) displays the evolution of stress components including the normal
3.3. Effect of structured factor The 3D models of polishing abrasives with different structured factors and the corresponding polished surface morphologies after 18 nm of polishing are presented in Fig. 13 and Fig. 14(a)-(d), respectively. A noteworthy observation from Fig. 14(a)–(d) is that the chip volume increases with the increasing structured factors, which indicates 8
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 11. After 18 nm of abrasive advance (a) illustration of von Mises stress distribution at different structured depths: (a) 0.2 nm, (b) 0.4 nm, and (c) 0.6 nm. (d) Von mises stress-polishing distance curves under different structured depths.
Fig. 12. (a) Variation of the subsurface temperature, (b) variations of polishing forces, and (c) variations of normal stresses σxx , σyy and shear stress τxy .
fact that the abrasive with a lower structured factor has a stronger chip capacity. A comparison of structured factors 20% and 75% shows that the subsurface temperature decreases slightly with the increase of
that polishing using a bigger structured factor results in a significant increment in the material removal rate. Also, it is apparent that increasing the structured factors decreases the number of atoms in the groove of abrasive during nano-polishing. This can be attributed to the 9
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 13. 3D models of polishing abrasives with different structured factors: (a) 20%, (b) 33.3%, (c) 50%, and (d) 75%.
Fig. 14. Polished surface morphology at different structured factors: (a) 20%, (b) 33.3%, (c) 50%, and (d) 75%. The atoms are colored according to their heights. (The structured width, structured depth and structured pattern are 0.6 nm, 0.6 nm, and rectangle, respectively.)
Fig. 15. Average subsurface temperature vs. polishing distance for four different structured factors (a), average polishing forces, variations of normal stresses (σxx and σyy ) and shear stress τxy with the structured factor (c).
10
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
Fig. 16. 3D models of polishing abrasives with different structured patterns: (a) square, (b) rectangle, (c) sphere, and (d) cone.
Fig. 17. Variation of polished surface morphology with the change of structured pattern of (a) square, (b) rectangle, (c) sphere, and (d) cone. Atoms are colored by their heights. (The structured width, structured depth and structured factor are 0.6 nm, 0.6 nm and 33.3%, respectively.)
This reveals that the abrasive with a rectangle pattern can enhance the material removal ability in nano-polishing. Furthermore, from Fig. 17(a–d), it is found that for the rectangle-patterned abrasive polishing, the number of atoms in the groove of abrasive is larger than those for other structured abrasives. This means that the abrasive with a rectangle pattern has the largest chip capacity during nano-polishing.
structured factors, which indicates that the abrasive with a lower structured factor polishing generates less polishing heat during nanoscale mechanical polishing. Correspondingly, Fig. 15(b) demonstrates the variation of average polishing forces with the polishing distance. It clearly shows that when the structured factor of the abrasive η is 33.3%, the magnitude of the tangential polishing force is the lowest, which implies that the abrasive with 33.3% structured factor polishing can reduce the tangential polishing forces during nano-polishing. In addition to this, it must be noted that the value of the normal polishing force at structured factors η = 20% or 33.3% is lower than that at structured factors η = 50% or 75%. This indicates that the abrasive with a lower structured factor polishing results in a smaller normal polishing force. The normal stresses σxx , σyy and shear stress τxy at the subsurface zone change with structured factors is carefully checked, as presented in Fig. 15(c). It is evident that the shear stress τxy was roughly of the same order under different structured factors. It means that τxy is basically dependent on the structured factor. Furthermore, from Fig. 15(c), the increase in structured factors causes slight increase of the compressive normal stresses σxx and σyy . This result indicates that the abrasive with a higher structured factor tends to polish silicon materials in a more ductile mode.
4. Conclusions In this paper, MD simulations of nano-polishing for monocrystalline silicon are applied to examine the effects of structured depth, structured width, structured factor and structured pattern. The main conclusions that can be drawn are: The abrasive with a bigger structured width has a stronger material removal ability, lower hydrostatic stress, better polished surface, and less defect atoms, but it causes a higher normal polishing force. The diamond abrasive with a smaller structured depth provides larger material removal ability, a slightly better polished surface, and tends to polish silicon materials in a more ductile mode, whereas it results in a higher polishing force. Although a higher structured factor polishing leads to a more ductile polishing mode and a larger material remove rate, it results in a larger normal polishing force, more polishing heat, and smaller chip capacity.
3.4. Effect of structured pattern Fig. 16(a–d) shows the 3D models of polishing abrasives with different structured patterns. Fig. 16(a)–(d) visualize the abrasives with structured patterns of square, rectangle, sphere, and cone, respectively. The four corresponding MD simulations are demonstrated in Fig. 17(a–d). Fig. 17(a–d) display the variation of polished surface morphology with the structured patterns of abrasives. Clearly, it is seen that when the surface of the structured abrasive has a rectangle pattern, the material removal rate is the biggest; but if the surface of the structured abrasives is conical, the material removal rate is the smallest.
Acknowledgements The authors would like to appreciate the fund project for the introduction of talents in Guizhou University (No. [2017]24), Guizhou Province Education Department Youth Science and technology talent growth project (No. [2018]110), and National Natural Science Foundation cultivation project for young teachers of Guizhou University (No. [2017]5788). 11
Materials Science in Semiconductor Processing 105 (2020) 104706
H. Dai, et al.
References
[21] L. Zhang, H. Zhao, Z. Ma, H. Huang, C. Shi, W. Zhang, A study on phase transformation of monocrystalline silicon due to ultra-precision polishing by molecular dynamics simulation, AIP Adv. 2 (2012) 899. [22] Y. Yang, H. Zhao, L. Zhang, M. Shao, H. Liu, H. Huang, Molecular dynamics simulation of self-rotation effects on ultra-precision polishing of single-crystal copper, AIP Adv. 3 (2013) 899. [23] C. Walter, T. Komischke, E. Weingärtner, K. Wegener, Structuring of CBN grinding tools by ultrashort pulse laser ablation, Procedia CIRP 14 (2014) 31–36. [24] S. Goel, A. Kovalchenko, A. Stukowski, G. Cross, Influence of microstructure on the cutting behaviour of silicon, Acta Mater. 105 (2016) 464–478. [25] Y. Wang, J. Xu, J. Zhang, Q. Chen, Y. Ootani, Y. Higuchi, N. Ozawa, J.M. Martin, K. Adachi, M. Kubo, Tribochemical reactions and graphitization of diamond-like carbon against alumina give volcano-type temperature dependence of friction coefficients: a tight-binding quantum chemical molecular dynamics simulation, Carbon 133 (2018) 350–357. [26] L. Pastewka, A. Klemenz, P. Gumbsch, M. Moseler, Screened empirical bond-order potentials for Si-C, Phys. Rev. B 87 (2013) 205410. [27] Y. Wang, J. Shi, C. Ji, A numerical study of residual stress induced in machined silicon surfaces by molecular dynamics simulation, Appl. Phys. A Mater. 115 (2014) 1263–1279. [28] Z.C. Lin, J.C. Huang, The influence of different cutting speeds on the cutting force and strain–stress behaviors of single crystal copper during nano-scale orthogonal cutting, J. Mater. Process. Technol. 201 (2008) 477–482. [29] J.J. Zhang, T. Sun, Y.D. Yan, Y.C. Liang, S. Dong, Molecular dynamics simulation of subsurface deformed layers in AFM-based nanometric cutting process, Appl. Surf. Sci. 254 (2008) 4774–4779. [30] P. Zhu, Y. Hu, T. Ma, H. Wang, Molecular dynamics study on friction due to ploughing and adhesion in nanometric scratching process, Tribol. Lett. 41 (2011) 41–46. [31] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1–19. [32] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Model. Simul. Mater. Sci. Eng. 18 (2009) 015012. [33] S.Z. Chavoshi, X. Luo, Molecular dynamics simulation study of deformation mechanisms in 3C–SiC during nanometric cutting at elevated temperatures, Mat. Sci. Eng. A-Struct. 654 (2016) 400–417. [35] H. Dai, G. Chen, Q. Fang, J. Yin, The effect of tool geometry on subsurface damage and material removal in nanometric cutting single-crystal silicon by a molecular dynamics simulation, Appl. Phys. A Mater. 122 (2016) 804. [36] S. Goel, X. Luo, R.L. Reuben, Wear mechanism of diamond tools against single crystal silicon in single point diamond turning process, Tribol. Int. 57 (2013) 272–281. [37] D.E. Kim, S.I. Oh, Atomistic simulation of structural phase transformations in monocrystalline silicon induced by nanoindentation, Nanotechnology 17 (2006) 2259. [38] Y.H. Lin, T.C. Chen, A molecular dynamics study of phase transformations in monocrystalline Si under nanoindentation, Appl. Phys. A Mater. 92 (2008) 571. [39] A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Model. Simul. Mater. Sci. Eng. 18 (2010) 085001. [40] A. Sedlmayr, E. Bitzek, D.S. Gianola, R. Gunther, R. Mönig, O. Kraft, Existence of two twinning-mediated plastic deformation modes in Au nanowhiskers, Acta Mater. 60 (2012) 3985–3993.
[1] A.A.G. Bruzzone, H.L. Costa, P.M. Lonardo, D.A. Lucca, Advances in engineered surfaces for functional performance, CIRP Ann. - Manuf. Technol. 57 (2008) 750–769. [2] M. Callies, Y. Chen, F. Marty, A. Pépin, D. Quéré, Microfabricated textured surfaces for super-hydrophobicity investigations, Microelectron. Eng. 78 (2005) 100–105. [3] N. Kawasegi, H. Sugimori, H. Morimoto, N. Morita, I. Hori, Development of cutting tools with microscale and nanoscale textures to improve frictional behavior, Precis. Eng. 33 (2009) 248–254. [4] Z. Liang, Y. Wu, X. Wang, W. Zhao, A new two-dimensional ultrasonic assisted grinding (2D-UAG) method and its fundamental performance in monocrystal silicon machining, Int. J. Mach. Tool Manuf. 50 (2010) 728–736. [5] Z.J. Yuan, Y.X. Yao, M. Zhou, Q.S. Bal, Lapping of single crystal diamond tools, CIRP Ann. - Manuf. Technol. 52 (2003) 285–288. [6] J. Zhang, T. Cui, C. Ge, Y. Sui, H. Yang, Review of micro/nano machining by utilizing elliptical vibration cutting, Int. J. Mach. Tool Manuf. 106 (2016) 109–126. [7] B. Guo, Q. Zhao, On-machine dry electric discharge truing of diamond wheels for micro-structured surfaces grinding, Int. J. Mach. Tool Manuf. 88 (2015) 62–70. [8] P.W. Butler-Smith, D.A. Axinte, M. Daines, Preferentially oriented diamond microarrays: a laser patterning technique and preliminary evaluation of their cutting forces and wear characteristics, Int. J. Mach. Tool Manuf. 49 (2009) 1175–1184. [9] S. Okuyama, Y. Nakamura, S. Kawamura, Cooling action of grinding fluid in shallow grinding, Int. J. Mach. Tool Manuf. 33 (1993) 13–23. [10] H.W. Zheng, H. Gao, A general thermal model for grinding with slotted or segmented wheel, CIRP Ann. - Manuf. Technol. 43 (1994) 287–290. [11] B. Guo, Q. Zhao, X. Fang, Precision grinding of optical glass with laser microstructured coarse-grained diamond wheels, J. Mater. Process. Technol. 214 (2014) 1045–1051. [12] T. Sugihara, T. Enomoto, Development of a cutting tool with a nano/micro-textured surface—improvement of anti-adhesive effect by considering the texture patterns, Precis. Eng. 33 (2009) 425–429. [13] C.F. Cheung, L.T. Ho, P. Charlton, L.B. Kong, W.B. Lee, Analysis of surface generation in the ultraprecision polishing of freeform surfaces, P. I. Mech. Eng. B-J. Eng. 224 (2010) 59–73. [14] J. Guo, H. Suzuki, S. Morita, Y. Yamagata, T. Higuchi, A real-time polishing force control system for ultraprecision finishing of micro-optics, Precis. Eng. 37 (2013) 787–792. [15] H. Suzuki, S. Hamada, T. Okino, M. Kondo, Y. Yamagata, T. Higuchi, Ultraprecision finishing of micro-aspheric surface by ultrasonic two-axis vibration assisted polishing, CIRP Ann. - Manuf. Technol. 59 (2010) 347–350. [16] H. Dai, G. Chen, C. Zhou, Q. Fang, X. Fei, A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation, Appl. Surf. Sci. 393 (2017) 405–416. [17] H. Dai, G. Chen, S. Li, Q. Fang, B. Hu, Influence of laser nano-structured diamond tools on the cutting behaviour of silicon by molecular dynamics simulation, RSC Adv. 7 (2017) 15596–15612. [18] S. Goel, X. Luo, A. Agrawal, R.L. Reuben, Diamond machining of silicon: a review of advances in molecular dynamics simulation, Int. J. Mach. Tool Manuf. 88 (2015) 131–164. [19] L. Zhang, H. Tanaka, Atomic scale deformation in silicon monocrystals induced by two-body and three-body contact sliding, Tribol. Int. 31 (1998) 425–433. [20] I. Zarudi, W.C.D. Cheong, J. Zou, L.C. Zhang, Atomistic structure of monocrystalline silicon in surface nano-modification, Nanotechnology 15 (2003) 104.
12