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Stress-induced structural phase transition of 3C–SiC with TLK structure in a nano-abrading process
Materials Science in Semiconductor Processing 112 (2020) 104893
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Stress-induced structural phase transition of 3C–SiC with TLK structure in a nano-abrading process Piao Zhou a, Yongwei Zhu a, *, Tao Sun b, c, **, Lin Lin d, Jun Li a, Zikun Wang a, Xue Li a a
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China Zhuhai Qinsun Innovative Materials Co., Limited, Zhuhai, 519000, China c College of Chemistry and Chemical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China d GRINM Semiconductor Materials Co., Ltd, Beijing, 100088, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: SiC Structural transition Nano-abrasion MD simulation Ductile removal
TLK (Terrace-Ledge-Kink) structure such as surface steps is often found on the surface of SiC materials. Removal behavior of SiC substrates with TLK structure has not been studied in a fixed abrasive polishing under nanoabrasion conditions. In this paper, the effect of TLK structure on the abrasion temperature, stress, and struc tural transition of SiC substrates during the nano-abrading process is pursued by molecular dynamics (MD) simulation. The results show that the average stress and temperature decrease with the increase of ledge numbers in the TLK structure. It is found that crystalline-to-amorphous (C–A) phase transition occurs. The high-density amorphorization of SiC is induced by a high shear stress, which transforms to low-density amorphous SiC with the release of shear stress. Furthermore, unlike previous reports, the pressure-induced 6-fold coordinated structure in 3C–SiC in this study, however, does not possess a high-pressured phase transition (HPPT) to rocksalt structure; instead, a disordered structure is found. The ductile domain removal goes through two stages: first through the dislocation nucleation and propagation at the initial abrading stage and is then followed by the plastic flow of the amorphous atoms after sliding over the ledge. The presence of TLK structures benefits the plastic deformation of the SiC substrate.
1. Introduction As a third-generation semiconductor material with high application potentials, silicon carbide is required to have an extremely high surface quality in applications as components in the integrated circuit industry [1]. In addition, it is a prime candidate for Micro-Electro-Mechanical System (MEMS) due to its small bandwidth and high electron mobility [2]. High surface quality is required in the industry application. Fixed abrasive polishing technology is applicable to process the ultra-hard-brittle material by ultra-precision processing to achieve high surface quality [3], and its material removal mechanism at nanoscale is widely studied by molecular dynamics (MD) simulation method. In nano-abrasion, both the high stress and high temperature pro duced by applying diamond abrasives on SiC substrates inevitably cause structural phase transitions, which, in turn, affect the removal mecha nisms of SiC materials. Previous studies have found the zincblende (ZB)to-rocksalt (RS) phase transition [4–8], crystalline-to-amorphous (C–A)
phase transition [9–11], and deformation behaviors [12] of ledge-free SiC substrates in nanoindentation study by using MD simulation. TLK (Terrace-Ledge-Kink) structure such as surface steps on 3C–SiC surface is often observed on crystal substrates derived from either the crystal growth or processing. From Nader’s [13] study, surface steps were found for 3C–SiC grown on Si (111) substrates. Neudeck [14] analyzed the surface morphology of as-grown (111) silicon-face 3C–SiC grown on a 4H–SiC substrate by using atomic force microscope (AFM), and measured the step height on as-grown 3C–SiC surfaces to be 0.25 nm. A clear and regulated step height at 0.25 nm was confirmed by Yan [15] on a SiC surface before and after chemical mechanical polishing. The me chanical consequences of surface steps in nanoindentation have been explored by experiments and MD methods [16–19]. They concluded that surface steps lower the energy threshold required for plastic deforma tion. The previous investigations mainly focus on the influence of sur face steps on the mechanical properties in nano-indentation, while the effect of the surface step structure on the substrate removal in the
* Corresponding author. ** Corresponding author. Zhuhai Qinsun Innovative Materials Co., Limited, Zhuhai, 519000, China. E-mail addresses: [email protected] (Y. Zhu), [email protected] (T. Sun). https://doi.org/10.1016/j.mssp.2019.104893 Received 30 November 2019; Received in revised form 15 December 2019; Accepted 17 December 2019 Available online 17 February 2020 1369-8001/© 2020 Elsevier Ltd. All rights reserved.
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nano-abrasion has not been explored. It is difficult to experimentally analyze the influence of TLK (TerraceLedge-Kink) structure on the structural phase transition of SiC mecha nism during the fixed abrasive polishing process under nano-abrasion conditions. Powerful MD simulation for investigating the transition mechanisms in a fixed abrasive polishing situation is, therefore, applied in our research. In this paper, the structural phase transition, including brittle-ductile (B-D) transition, C-A phase transition and atomic coor dination transition of SiC substrates are analyzed in the presence of surface steps on SiC substrates during the fixed abrasive polishing process.
Table 1 Parameters of molecular dynamics simulation.
2. Simulation method The simulated models are present in Fig. 1a–c. The model consists of a diamond abrasive and a 3C–SiC substrate. The dimension of SiC sub strates is 152.18 � 213.052 � 91.308 Å (X, Y, and Z directions, respectively). The SiC substrate with zincblende structure oriented X ¼ [100], Y ¼ [010], Z ¼ [001]. The radius of diamond abrasives is set at 40 Å. Previous studies have concluded that the cutting velocity has little effect on the surface quality and deformation characteristics of the substrate by MD simulation [20]; the cutting velocity is, therefore, set at 60 m/s for optimizing computational efficiency. Detail parameters of the simulated model are summarized in Table 1. Both the SiC substrate and the diamond abrasive are divided into three layers: a boundary layer, a thermostatic layer, and a Newtonian layer. The boundary layer remains constant to prevent any movement of SiC substrates during the nano-abrading process. The thermostatic layer is next to the boundary layer to equilibrate the temperature of the nano-abrasion system. Newtonian zone is used to analyze the removal mechanism of SiC sub strates. To investigate the effect of TLK structure on the removal
Configuration
Abrading
Substrates Abrasive particle Substrates dimensions Atoms in ledge-free SiC Atoms in SiC with one-layed terrace Atoms in SiC with three-layed terrace Atoms in diamond Abrasive radius abrasion depth Abrading velocity Potential function Timestep
Mono-crystalline Silicon carbide Diamond abrasive 15.218*21.305*9.131 nm 288120 284655 281190 47150 4 nm 2.6 nm 60 m/s ABOP 0.001ps
mechanism of SiC substrates, three different surfaces are built in our simulation: ledge-free surface (Fig. 1a), one-layered ledge in TLK structure (Fig. 1b), and three-layered ledge in TLK structure (Fig. 1c). The schematic diagram of TLK structure is shown in Fig. 1d. The kink structure is ignored in the TLK structure due to little effect on the me chanical removal process. The atomic ledge height corresponds to the thickness of one Si–C bilayer with 0.25 nm. In MD simulation, potential functions play very important roles on the final simulation results. Based on previous research studies on the application of MD simulations to the nano-cutting process of SiC sub strates, the ABOP potential function is adopted for the interaction of Si–Si, C–C, and Si–C atoms [21,22] in our study. The periodic boundary conditions are respectively applied in the x, y, and z three-dimensional directions in our simulations. To better meet the actual working con ditions, the relaxation temperature was set at 298 K. The canonical ensemble (nvt) and micro-canonical ensemble (nve) are applied in the
Fig. 1. The MD simulation model (a) ledge-free SiC (b) one-layered ledge in SiC (c) three-layered ledge in SiC (d) the schematic diagram of TLK structure. 2
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relaxation and cutting process, respectively. The open source software LAMMPS is used as a computing tool for molecular dynamics simulation. The deformation and removal processes in the nano-abrasion are visu alized by OVITO [23].
where N is the number of atoms in the setting area, vi is the velocity of ith atom, Ke is the kinetic energy of atoms, kb is the Boltzmann constant and the value is 1.3806503 � 1023J/K, and T is the temperature of atoms.
3. Analysis methods
4. Results and discussion
Structural phase transition is inevitable during the nano-abrasion process. The radial distribution functions (RDFs) before and after pol ishing are analyzed to judge whether the structural phase transition occurs. However, the amorphous transition is difficult to be distin guished by RDF. The coordination number is used to analyze atomic coordination transition. The von Mises stress is a term commonly used to predict the yield behavior of a material [22]. Furthermore, the relationship between shear stress and a perfect dislocation initiation can be expressed as [24].
τpt ¼
2αμbpt d
4.1. Stress and temperature During the nano-abrading process, the strong interaction between abrasives and substrates often leads to increase in structural stress and temperature of the processed substrates, which in turn leads to struc tural phase transitions of materials. Fig. 2 shows the stress and tem perature distribution of processed SiC substrates with a three-layered ledge structure, where the nano-abrading stops after sliding 16.2 nm. The highest hydrostatic stress (Fig. 2a), shear stress (Fig. 2b) and von Mises stress (Fig. 2c) that the processed SiC experienced are all localized in the frontal section of the extrusion zone. Qualitatively speaking, a smaller section of the substrates experiences hydrostatic stress compared to shearing and von Mises stress. It should be noted that there are few hydrostatic and shearing stresses left on the removed chips of SiC substrates where von Mises stress can still be found, indicating that amorphorization does not release von Mises stress as effectively as hy drostatic and shearing stress. The high temperature is highly associated with the removed chips, which means that the heat generated from nano-abrasion is accumulated on the removed chips due to its poor heat conductivity of the disordered structures. The high temperature on the removed chips helps to release stresses, which is consistent with the low hydrostatic and shearing stresses observed in Fig. 2a and b. To quantify the influence of the TLK structure on the stress and temperature, the average stress and temperature of SiC substrates are presented in Fig. 3, which shows that the average hydrostatic stress (Fig. 3a), shear stress (Fig. 3b), von Mises stress (Fig. 3c) and abrasion temperature (Fig. 3d) of SiC substrates in the stable processing stage decrease as the number of ledges in the TLK structure increases. Because the cutting depth is calculated and set based on the highest terrace as the reference point, the more ledges does the substrate possess, the less is the initial cutting depth. The less initial cutting depth means less removed materials and less averaged stress, in turn, a lower averaged temperature on the processed substrates.
(1)
in which bpf represents the Burgers vector of the perfect dislocation, μ is the shear modulus. α is the character of the dislocation. d is the spacing between the dislocation trace line and the sliding surface. The shear stress required to expand a partial dislocation is described as [24].
τpt ¼
2αμbpt γ þ bpt d
(2)
where bpt is the Burgers vector of the partial dislocation, and γ is the stacking fault energy. We can see from the above equation that the dislocation initiation, which indicates the B–D transition, is mainly affected by the shear stress. The Patel-Cohen rationalization is expressed as follows [25]: (3)
W ¼ PεT þ τε
The amorphization normal strain and the hydrostatic component of stress are expressed as εT and P, respectively. τ is the shear stress, and ε represents the amorphization shear strain. From equation (3), amorph ization shear strain induced by C–A transition is related to the shear stress. The interaction of diamond abrasives and SiC substrates inevitably results in the variation of stress and temperature during the nanoabrading process, which in turn affects the structural transition of abrasives and substrates. It is necessary to investigate the cutting stress and abrasion temperature distribution of abrasives and substrates. The von Mises stress can be calculated as follows:
σ vm ðiÞ ¼
� h 1 σxx ðiÞ 2
�2
σyy ðiÞ þ σ yy ðiÞ
�2
σ zz ðiÞ þ ðσzz ðiÞ
4.2. Structural transition Atomic pair distance in a well-defined crystalline material remains constant until external forces, such as nano-abrading in this case, cause structural damages or crystal phase transitions. The RDF intensity of a
�
σxx ðiÞÞ2 þ 6 σ2xy ðiÞ þ σ2zy ðiÞ þ σ2xz ðiÞ
� 1 σxx þ σ yy þ σzz 3
(5)
The equation of abrasion temperature in MD simulation can be expressed as follows: 1X 2 3 mi vi ¼ Nkb T 2 i 2
(6)
Ke ¼ 2mv2
(7)
(4)
fixed set of atomic pair distances in SiC substrates will correspondingly be reduced should the original crystal structure experience changes by nano-abrading. In 3C–SiC crystalline substrates, the inter-atomic dis tances between Si–C, Si–Si/C–C, Si–C and Si–Si were 0.1883, 0.3075, 0.3605, and 0.4348 nm (Fig. 4d), respectively, which is consistent with our calculated distance at 0.1917, 0.3102, 0.3589, and 0.4356 nm in RDF. The small variation (�0.01 nm) of the nearest inter-atomic dis tance in 3C–SiC is caused by energy minimization in the relaxation process. The intensity changes of RDFs of SiC substrates are plotted in Fig. 4 before and after nano-abrading to assist us to access the effect of TLK structure on the structural transition. Intensities of the
The equation of hydrostatic stress is described as follows:
σ hydro ¼
�i�1=2
3
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Fig. 2. Distribution of stress and temperature (a) Hydrostatic stress (b) Shear stress (c) von Mises stress (d) Temperature.
Fig. 3. Averaged stress and temperature of SiC substrates at different TLK structure (a) Hydrostatic stress (b) Shear stress (c) von Mises stress (d) Temperature.
4
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Fig. 4. RDF of SiC substrates before and after nano-abrasion (a) ledge-free SiC (b) one-layered ledge (c) three-layered ledge (d) lattice cell.
during the nano-abrading process. 4.2.1. Amorphization The surface and subsurface morphology of SiC substrates are shown in Fig. 5 when the diamond abrasive is advanced by 18 nm, and show that the machined surface and the ductile chips with strip morphology exhibit a disordered amorphous structure, which is induced by a rapid release of shear stress in the wake of escaping the compression and depression force of the diamond abrasive [26,27]. The amorphous atoms in chips originate from two places: one is from the machined surface, and the other is from the chips itself. Part of amorphous atoms on the machined surface is removed and accumulated at the front end of the diamond abrasive due to the extrusion effect. The other part of high-pressure disorder atoms is removed directly by diamond abrasives and transformed to an amorphous structure under the rapid release of shear stress. In order to analyze the effect of pressure on the amorphous density, amorphous atoms are divided into three regions: region one is the chips region, region two is the high-pressure region, and region three
Fig. 5. The amorphous region of SiC substrates after nano-abrasion.
Table 2 Calculated amorphous atoms in different regions (as defined in Fig. 5) after nano-abrasion.
abovementioned four pair of atomic distances are reduced after nanoabrading in three different surface structures, including ledge-free structure (Fig. 4a), one-layered ledge in TLK structure (Fig. 4b), and three-layered ledge in TLK structure (Fig. 4c). Based on the discussion above, the reduced intensity of all four sets of atomic pair distances clearly suggests that SiC substrates undergo a structural transition
Ledge-free One-ledged Three-ledged
5
Region 1 (n/nm3)
Region 2 (n/nm3)
Region 3 (n/nm3)
78.7 80.0 76.7
111.0 113.7 110.3
86.3 85.3 85.0
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is the machined region (Fig. 5). The amorphous density is defined as the number of amorphous atoms in unit area (n/nm3) in our simulation. The calculated results are present in Table 2 and show that the amorphous density underneath the front end of diamond abrasives is higher than that of the other amorphous region in all three simulated results. Furthermore, from Fig. 2b, the shear stress on the machined surface and the ductile chips is much lower than the extrusion region. It is proved that high shear stress causes the high-density amorphorization of SiC, which transforms to low-density amorphous SiC with the release of shear stress after abrasive particles move away [28].
are populated in the entire amorphous region. The order and disorder 4-coordinated Si/C atoms are present in the entire undeformed region and partly amorphous region, respectively. The number of 3-coordi nated Si/C atoms is clearly much more than those of 5-and 6-coordi nated Si/C atoms after nano-abrading, and these 3-coordinated Si/C atoms almost exclusively reside in the amorphous region. The large number of 3-coordinated Si/C atoms, combining the low stress results in Fig. 2a–c, suggests that 3-coordinated Si/C atoms are thermodynami cally more stable in amorphous region than 5 and 6-coordinated Si/C atoms. For better illustration of the distributions of different coordinated Si and C atoms during nano-abraded 3C–SiC, Fig. 7 and Fig. 8 only selec tively present a representative number of Si and C with different struc tural configurations. Both 6-coordinated Si and C atoms are found to lie in the frontal section where the highest hydrostatic stress is experienced. On the other hand, different 3-, 4-, 5-, 6-coordinated C and Si with varied number of structural configurations are observed in almost the entire amorphous region. MD simulation had been used to investigate the pressure-induced structural transition of SiC, and found that phase transition from 4-coor dinated ZB structure to a 6-coordinated RS structure occurs in the region with hydrostatic stress higher than 100 GPa[5]. The largest hydrostatic stress in our simulation is larger than 100 GPa; this is also where the 6-fold coordinated structure is observed. However, the HPPT from ZB-RS structural transition is not seen in our simulation. In a perfect 3C–SiC crystal, each Si(C) atom is tetrahedrally bonded to the near C(Si); the generation of 6-coordinated Si is a result of pulling C atoms residing in longer distance closer, leaving the neighboring Si, whose bonding structure becomes unsaturated, scrambling for thermodynamically more stable bonding structures. One 6-coordinated Si(C) will need to bring in two C(Si), leading to one (two-bonds vacant) or two (one-bond) neigh boring Si(C) atoms with bond vacancy compared to its 4-coordination in 3C structure. The most likely scenario for these bond-vacant Si(C) atoms due to generation of 5-, 6-coordinated Si(C) is to remain vacant, but somehow, it is distorted by the imbalanced bonding force to move closer to the bonding C(Si) as observed in Fig. 6. The 4-coordinated C(Si) in amorphous region is not tetrahedrally coordinated and exists in four structural configurations. In 3C–SiC, every Si(C) is bonded by four Cs (Sis) tetrahedrally; thus, every bond breaking equally leads to one
4.2.2. Structural atomic defects Xiao et al. [29] performed MD simulation and reported theoretical results confirming a ZB-RS phase transition. They found the existence of individually 6-coordinated Si/C on the SiC substrates; however, these individually 6-coordinated Si/C are not periodically arranged according to that in RS crystal structure, and are more like the atomic defects than the used term ZB-RS phase transition, which refers to one crystal phase to another. Bonding structure changes of individual atoms in a crystal phase do not qualify as a crystal phase transition because not even one unit of crystal cells for the newly named crystal phase exists. Initiation of such a coordination change for individual atoms may further degrade crystal structures of SiC in the vicinity of other neighboring atoms or might even transform into the author’s proposed RS crystal phase; however, to date, the evidence is not strong enough to be called a phase transition. Therefore, we would prefer to use structural atomic defects to describe the n-coordinated atoms generated from the nano-abrading process. Many types of crystal defects are expected to be generated on SiC substrates when high pressure is applied on SiC substrates by diamond abrasives in the nano-abrading process. Both Si and C are tetrahedrally 4-coordinated in a ledge-free 3C–SiC crystalline substrates. To study the atomic structural transition, the coordination number of Si/C atoms in SiC substrates is calculated in the nano-abrading process. The cut-off bond distance for analyzing the coordination number of Si/C atoms in 3C–SiC is set as 2.4 Å in our simulation [30]. The coordination numbers of all C and Si atoms in SiC after the nano-abrading are presented in Fig. 6. While the 6-coordinated Si/C atoms are only present in the high-pressure region, the 3-coordinated and 5-coordinated Si/C atoms
Fig. 6. Distributions of different coordinated atoms in SiC substrates after nano-abrading (a) 3-coordinated atoms (b) 4-coordinated atoms (c) 5-coordinated atoms (d) 6-coordinated atoms. 6
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Fig. 7. Different coordinated C structures in SiC substrates after nano-abrading (a) Positions of 3-coordinated C atoms (b) Positions of 4-coordinated C atoms (c) Positions of 5-coordinated C atoms (d) Varieties of coordinated C structures.
Fig. 8. Different coordinated Si structures in SiC substrates after nano-abrading (a) Positions of 3-coordinated Si atoms (b) Positions of 4-coordinated Si atoms (c) Positions of 5-coordinated Si atoms (d) Positions of 6-coordinated Si atoms (e) Varieties of coordinated Si structures.
3-coordinated Si and one 3-coordinated C, which is consistent with the appearance of large numbers of 3-coordinated Si/C after nano-abrasion. In summary, our simulation results confirmed that the transition of 4-coordinated to 6-coordinated Si/C atoms on processed SiC substrates occur when hydrostatic stress higher than 100 GPa occurs during nanoabrasion; however, these individual 6-coordinated Si/C atoms are not arranged in a RS structure with regularity but rather in a disorder structure. Many more 3- and 4-coordinated Si/C atoms are generated in the amorphous regions during nano-abrasion, while very limited numbers of 5- and 6-coordinated Si/C atoms are produced.
abrasives not only leads to different atomic coordination transition and C–A transition but also causes B-D transition of SiC substrates. As shown in Fig. 9, the state of dislocation distributions of all three substrates is graphically presented at three different abrading distances with 12.6, 14.4, and 16.2 nm. The diamond abrasive makes the first contact with the ledge at the abrading distance of 12.6 nm (Fig. 9b1-c1); the abrasive tip reaches the ledge at 14.4 nm (Fig. 9b2-c2); and the abrasive abrades through the ledge at 16.2 nm (Fig. 9b3-c3). In ledge-free SiC substrates, only dislocations are found, which propagate along the abrading trail as abrading from 12.6 to 16.2 nm (Fig. 9a) with no new dislocation nucleation. On the other hand, new dislocations are nucleated under neath the frontal section of the diamond abrasive as the diamond abrasive makes contact with the ledge of TLK structure (Figs. 9b&c). The
4.2.3. Brittle-ductile transition The local high stress on SiC substrates generated by diamond 7
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Fig. 9. The dislocation initiation of SiC substrates during abrasion process (a) ledge-free SiC (b) one-layered ledge (c) three-layered ledge.
Perfect dislocations and other dislocations (Fig. 10) are found in all three studied SiC substrates, while the nano-abrading distance reaches 18 nm. The dislocations in our simulations reside, on the other hand, in the lower region behind the diamond abrasive particle as abrasives slide over the ledge. One may speculate that no new dislocation is nucleated after the abrasives pass through the ledge; furthermore, the velocity of dislocation propagation is slower than that of the sliding abrasive. The dislocations generated at the front end of diamond abrasives lead to the ductile removal of brittle materials in the initial sliding stage. However, the mechanism for ductile domain removal is changed when abrasives slide over the ledge where the dislocations stay behind the diamond abrasive particle. In Fig. 10a1-a3, we can see that there are a large number of amorphous atoms underneath and in front of the diamond abrasive; this is due to plastic flow of amorphous atoms caused by structural stress and local high temperature generated by the frictional heat between SiC substrates and diamond abrasives. The plastic flow of the amorphous atoms on the substrate surface becomes the driving force for ductile domain removal in the ledge-free region of the SiC substrates. 5. Summary The influence of TLK structures on the deformation and removal mechanism of SiC substrates during the nano-abrading process was studied in a fixed abrasive polishing by using MD simulation method. The obtained results are summarized as follows: The average hydrostatic stress, shear stress, von Mises stress, and temperature of SiC substrates decrease with the increase of ledges in TLK structure. Because of the extrusion effect between abrasives and sub strates, SiC substrates undergo C–A transition and B-D transition. The amorphous density in the high-pressure region is higher than that in the chips region and machined region where the shear stress is released. Tetrahedrally coordinated crystalline Si and C atoms in the SiC substrate are partially transformed to amorphous 3-, 4-, 5- and 6-coordinated Si and C atoms under the pressure applied by abrasive particles on SiC substrates. Furthermore, 3- and 4-coordinated Si and C atoms are the most populated ones in the amorphous region. The 6-coordinated structure is only found in region where hydrostatic stress is higher
Fig. 10. The dislocation distribution of SiC substrates after abrasion (a) ledgefree SiC (b) one-layered ledge (c) three-layered ledge.
nucleated dislocations increase until the abrasive tip passes the ledge. Dislocation propagation is seen alone, and no new dislocation is found at the abrading distance of 16.2 nm, shown in Fig. 9b3 and Fig. 9c3. This MD simulation clearly indicates that the existence of TLK on SiC sub strates lead to new dislocation nucleation, which cannot be found on substrates with no TLK structures. 8
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than 100 GPa. Unlike the report from Ref. [29], the 6-coordinated Si and C atoms in our simulation are not arranged according to the RS structure with regularity but rather in a disorder state. During the nano-abrading process, perfect dislocations and other dislocations are generated in SiC substrates. The step structure is found to assist the dislocation nucleation of the SiC substrate. The MD results suggest that during nano-abrasion, SiC is removed in ductile domain through the dislocation nucleation and propagation at the initial stage and then followed by the plastic flow of the amorphous atoms after sliding over the ledge.
[8] H.Y. Xiao, F. Gao, X.T. Zu, W.J. Weber, Ab initio molecular dynamics simulation of a pressure induced zinc blende to rocksalt phase transition in SiC, J. Phys. Condens. Matter 21 (2009) 245801. [9] H.P. Chen, R.K. Kalia, A. Nakano, P. Vashishta, I. Szlufarska, Multimillion-atom nanoindentation simulation of crystalline silicon carbide: orientation dependence and anisotropic pileup, J. Appl. Phys. 102 (2007) 1409–1452. [10] A. Noreyan, J.G. Amar, Molecular dynamics simulations of nanoscratching of 3C SiC, Wear 265 (2008) 956–962. [11] I. Szlufarska, R.K. Kalia, A. Nakano, P. Vashishta, Atomistic mechanisms of amorphization during nanoindentation of SiC: a molecular dynamics study, Phys. Rev. B 71 (2005) 174111–174113. [12] B. Zhu, D. Zhao, Y. Tian, S. Wang, H. Zhao, J. Zhang, Study on the deformation mechanism of spherical diamond indenter and its influence on 3C-SiC sample during nanoindentation process via molecular dynamics simulation, Mater. Sci. Semicond. Process. 90 (2019) 143–150. [13] R. Nader, M. Kazan, E. Moussaed, T. Stauden, M. Niebelschütz, P. Masri, J. Pezoldt, Surface morphology of Ge-modified 3C-SiC/Si films, Surf. Interface Anal. 40 (2010) 1310–1317. [14] P.G. Neudeck, A.J. Trunek, J.A. Powell, Atomic force microscope observation of growth and defects on as-grown (111) 3C-SiC mesa surfaces, Mrs Proceedings 815 (2004) J5–J32. [15] Z. Yan, G. Pan, X. Shi, S. Zhang, G. Hua, G. Luo, Effects of ultra-smooth surface atomic step morphology on chemical mechanical polishing (CMP) performances of sapphire and SiC wafers, Tribol. Int. 87 (2015) 145–150. [16] M.R. Shankar, Surface steps lead to heterogeneous contact mechanics and facilitate dislocation nucleation in nanoindentation, Appl. Phys. Lett. 90 (2007) 12588. [17] D. Shan, L. Yuan, B. Guo, Multiscale simulation of surface step effects on nanoindentation, Mater. Sci. Eng., A 412 (2005) 264–270. [18] J.A. Zimmerman, C.L. Kelchner, P.A. Klein, J.C. Hamilton, S.M. Foiles, Surface step effects on nanoindentation, Phys. Rev. Lett. 87 (2001) 165507. [19] J.D. Kiely, J.E. Houston, R.Q. Hwang, Effect of surface steps on the plastic threshold in nanoindentation, Phys. Rev. Lett. 81 (1998) 4424–4427. [20] 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. [21] S. Goel, W. Bin Rashid, X. Luo, A. Agrawal, V.K. Jain, A theoretical assessment of surface defect machining and hot machining of nanocrystalline silicon carbide, J. Manuf. Sci. Eng. 136 (2014). [22] S.Z. Chavoshi, X. Luo, Molecular dynamics simulation study of deformation mechanisms in 3C–SiC during nanometric cutting at elevated temperatures Materials, Science and Engineering: A 654 (2016) 400–417. [23] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool, Model Simul Mater Sc 18 (2009) 15012. [24] X. Chen, R. Schneider, P. Gumbsch, C. Greiner, Microstructure evolution and deformation mechanisms during high rate and cryogenic sliding of copper, Acta Mater. 161 (2018) 138–149. [25] S. Zhao, R. Flanagan, E.N. Hahn, B. Kad, B.A. Remington, C.E. Wehrenberg, R. Cauble, K. More, M.A. Meyers, Shock-induced amorphization in silicon carbide, Acta Mater. 158 (2018) 206–213. [26] J. Patten, W. Gao, K. Yasuto, Ductile regime nanomachining of single-crystal silicon carbide, J. Manuf. Sci. Eng. 127 (2005) 522–532. [27] J. Patten, R. Fesperman, S. Kumar, S. Mcspadden, J. Qu, M. Lance, R. Nemanich, J. Huening, High-pressure phase transformation of silicon nitride, Appl. Phys. Lett. 83 (2003) 4740. [28] S.K. Deb, M. Wilding, M. Somayazulu, P.F. Mcmillan, Pressure-induced amorphization and an amorphous-amorphous transition in densified porous silicon, Nature 414 (2001) 528. [29] G. Xiao, S. To, G. Zhang, The mechanism of ductile deformation in ductile regime machining of 6H SiC, Comput. Mater. Sci. 98 (2015) 178–188. [30] J.P. Rino, I. Ebbsj€ o, P.S. Branicio, R.K. Kalia, A. Nakano, F. Shimojo, P. Vashishta, Short- and intermediate-range structural correlations in amorphous silicon carbide: A molecular dynamics study, Phys. Rev. B 70 (2004) 2199–2208.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Piao Zhou: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization. Yongwei Zhu: Conceptualization, Methodol ogy, Resources, Writing - review & editing, Supervision, Funding acquisition. Tao Sun: Conceptualization, Methodology, Writing - review & editing, Supervision. Lin Lin: Writing - review & editing. Jun Li: Writing - review & editing. Zikun Wang: Software. Xue Li: Software. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51675276) and Jiangsu Province Key Laboratory of Precision and Micro-manufacturing Technology. References [1] S. Goel, The current understanding on the diamond machining of silicon carbide, J. Phys. Appl. Phys. 47 (2014) 243001. [2] D. Lim, H. Jee, J.W. Kim, J. Moon, S. Lee, S.S. Choi, J. Boo, Deposition of epitaxial silicon carbide films using high vacuum MOCVD method for MEMS applications, Thin Solid Films 459 (2004) 7–12. [3] Q.F. Luo, J. Lu, X.P. Xu, A comparative study on the material removal mechanisms of 6H-SiC polished by semi-fixed and fixed diamond abrasive tools, Wear 350–351 (2016) 99–106. [4] M. Mishra, I. Szlufarska, Possibility of high-pressure transformation during nanoindentation of SiC, Acta Mater. 57 (2009) 6156–6165. [5] F. Shimojo, I.I. Ebbsjo, R.K. Kalia, A. Nakano, J.P. Rino, P. Vashishta, Molecular dynamics simulation of structural transformation in silicon carbide under pressure, Phys. Rev. Lett. 84 (2000) 3338. [6] A. Noreyan, J.G. Amar, I. Marinescu, Molecular dynamics simulations of nanoindentation of β-SiC with diamond indenter, Mater. Sci. Eng., B 117 (2005) 235–240. [7] M.S. Miao, M. Prikhodko, W.R. Lambrecht, Comment on “orthorhombic intermediate state in the zinc blende to rocksalt transformation path of SiC at high pressure”, Phys. Rev. Lett. 88 (2002) 189601.
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Stress-induced structural phase transition of 3C–SiC with TLK structure in a nano-abrading process Piao Zhou a, Yongwei Zhu a, *, Tao Sun b, c, **, Lin Lin d, Jun Li a, Zikun Wang a, Xue Li a a
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China Zhuhai Qinsun Innovative Materials Co., Limited, Zhuhai, 519000, China c College of Chemistry and Chemical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China d GRINM Semiconductor Materials Co., Ltd, Beijing, 100088, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: SiC Structural transition Nano-abrasion MD simulation Ductile removal
TLK (Terrace-Ledge-Kink) structure such as surface steps is often found on the surface of SiC materials. Removal behavior of SiC substrates with TLK structure has not been studied in a fixed abrasive polishing under nanoabrasion conditions. In this paper, the effect of TLK structure on the abrasion temperature, stress, and struc tural transition of SiC substrates during the nano-abrading process is pursued by molecular dynamics (MD) simulation. The results show that the average stress and temperature decrease with the increase of ledge numbers in the TLK structure. It is found that crystalline-to-amorphous (C–A) phase transition occurs. The high-density amorphorization of SiC is induced by a high shear stress, which transforms to low-density amorphous SiC with the release of shear stress. Furthermore, unlike previous reports, the pressure-induced 6-fold coordinated structure in 3C–SiC in this study, however, does not possess a high-pressured phase transition (HPPT) to rocksalt structure; instead, a disordered structure is found. The ductile domain removal goes through two stages: first through the dislocation nucleation and propagation at the initial abrading stage and is then followed by the plastic flow of the amorphous atoms after sliding over the ledge. The presence of TLK structures benefits the plastic deformation of the SiC substrate.
1. Introduction As a third-generation semiconductor material with high application potentials, silicon carbide is required to have an extremely high surface quality in applications as components in the integrated circuit industry [1]. In addition, it is a prime candidate for Micro-Electro-Mechanical System (MEMS) due to its small bandwidth and high electron mobility [2]. High surface quality is required in the industry application. Fixed abrasive polishing technology is applicable to process the ultra-hard-brittle material by ultra-precision processing to achieve high surface quality [3], and its material removal mechanism at nanoscale is widely studied by molecular dynamics (MD) simulation method. In nano-abrasion, both the high stress and high temperature pro duced by applying diamond abrasives on SiC substrates inevitably cause structural phase transitions, which, in turn, affect the removal mecha nisms of SiC materials. Previous studies have found the zincblende (ZB)to-rocksalt (RS) phase transition [4–8], crystalline-to-amorphous (C–A)
phase transition [9–11], and deformation behaviors [12] of ledge-free SiC substrates in nanoindentation study by using MD simulation. TLK (Terrace-Ledge-Kink) structure such as surface steps on 3C–SiC surface is often observed on crystal substrates derived from either the crystal growth or processing. From Nader’s [13] study, surface steps were found for 3C–SiC grown on Si (111) substrates. Neudeck [14] analyzed the surface morphology of as-grown (111) silicon-face 3C–SiC grown on a 4H–SiC substrate by using atomic force microscope (AFM), and measured the step height on as-grown 3C–SiC surfaces to be 0.25 nm. A clear and regulated step height at 0.25 nm was confirmed by Yan [15] on a SiC surface before and after chemical mechanical polishing. The me chanical consequences of surface steps in nanoindentation have been explored by experiments and MD methods [16–19]. They concluded that surface steps lower the energy threshold required for plastic deforma tion. The previous investigations mainly focus on the influence of sur face steps on the mechanical properties in nano-indentation, while the effect of the surface step structure on the substrate removal in the
* Corresponding author. ** Corresponding author. Zhuhai Qinsun Innovative Materials Co., Limited, Zhuhai, 519000, China. E-mail addresses: [email protected] (Y. Zhu), [email protected] (T. Sun). https://doi.org/10.1016/j.mssp.2019.104893 Received 30 November 2019; Received in revised form 15 December 2019; Accepted 17 December 2019 Available online 17 February 2020 1369-8001/© 2020 Elsevier Ltd. All rights reserved.
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nano-abrasion has not been explored. It is difficult to experimentally analyze the influence of TLK (TerraceLedge-Kink) structure on the structural phase transition of SiC mecha nism during the fixed abrasive polishing process under nano-abrasion conditions. Powerful MD simulation for investigating the transition mechanisms in a fixed abrasive polishing situation is, therefore, applied in our research. In this paper, the structural phase transition, including brittle-ductile (B-D) transition, C-A phase transition and atomic coor dination transition of SiC substrates are analyzed in the presence of surface steps on SiC substrates during the fixed abrasive polishing process.
Table 1 Parameters of molecular dynamics simulation.
2. Simulation method The simulated models are present in Fig. 1a–c. The model consists of a diamond abrasive and a 3C–SiC substrate. The dimension of SiC sub strates is 152.18 � 213.052 � 91.308 Å (X, Y, and Z directions, respectively). The SiC substrate with zincblende structure oriented X ¼ [100], Y ¼ [010], Z ¼ [001]. The radius of diamond abrasives is set at 40 Å. Previous studies have concluded that the cutting velocity has little effect on the surface quality and deformation characteristics of the substrate by MD simulation [20]; the cutting velocity is, therefore, set at 60 m/s for optimizing computational efficiency. Detail parameters of the simulated model are summarized in Table 1. Both the SiC substrate and the diamond abrasive are divided into three layers: a boundary layer, a thermostatic layer, and a Newtonian layer. The boundary layer remains constant to prevent any movement of SiC substrates during the nano-abrading process. The thermostatic layer is next to the boundary layer to equilibrate the temperature of the nano-abrasion system. Newtonian zone is used to analyze the removal mechanism of SiC sub strates. To investigate the effect of TLK structure on the removal
Configuration
Abrading
Substrates Abrasive particle Substrates dimensions Atoms in ledge-free SiC Atoms in SiC with one-layed terrace Atoms in SiC with three-layed terrace Atoms in diamond Abrasive radius abrasion depth Abrading velocity Potential function Timestep
Mono-crystalline Silicon carbide Diamond abrasive 15.218*21.305*9.131 nm 288120 284655 281190 47150 4 nm 2.6 nm 60 m/s ABOP 0.001ps
mechanism of SiC substrates, three different surfaces are built in our simulation: ledge-free surface (Fig. 1a), one-layered ledge in TLK structure (Fig. 1b), and three-layered ledge in TLK structure (Fig. 1c). The schematic diagram of TLK structure is shown in Fig. 1d. The kink structure is ignored in the TLK structure due to little effect on the me chanical removal process. The atomic ledge height corresponds to the thickness of one Si–C bilayer with 0.25 nm. In MD simulation, potential functions play very important roles on the final simulation results. Based on previous research studies on the application of MD simulations to the nano-cutting process of SiC sub strates, the ABOP potential function is adopted for the interaction of Si–Si, C–C, and Si–C atoms [21,22] in our study. The periodic boundary conditions are respectively applied in the x, y, and z three-dimensional directions in our simulations. To better meet the actual working con ditions, the relaxation temperature was set at 298 K. The canonical ensemble (nvt) and micro-canonical ensemble (nve) are applied in the
Fig. 1. The MD simulation model (a) ledge-free SiC (b) one-layered ledge in SiC (c) three-layered ledge in SiC (d) the schematic diagram of TLK structure. 2
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relaxation and cutting process, respectively. The open source software LAMMPS is used as a computing tool for molecular dynamics simulation. The deformation and removal processes in the nano-abrasion are visu alized by OVITO [23].
where N is the number of atoms in the setting area, vi is the velocity of ith atom, Ke is the kinetic energy of atoms, kb is the Boltzmann constant and the value is 1.3806503 � 1023J/K, and T is the temperature of atoms.
3. Analysis methods
4. Results and discussion
Structural phase transition is inevitable during the nano-abrasion process. The radial distribution functions (RDFs) before and after pol ishing are analyzed to judge whether the structural phase transition occurs. However, the amorphous transition is difficult to be distin guished by RDF. The coordination number is used to analyze atomic coordination transition. The von Mises stress is a term commonly used to predict the yield behavior of a material [22]. Furthermore, the relationship between shear stress and a perfect dislocation initiation can be expressed as [24].
τpt ¼
2αμbpt d
4.1. Stress and temperature During the nano-abrading process, the strong interaction between abrasives and substrates often leads to increase in structural stress and temperature of the processed substrates, which in turn leads to struc tural phase transitions of materials. Fig. 2 shows the stress and tem perature distribution of processed SiC substrates with a three-layered ledge structure, where the nano-abrading stops after sliding 16.2 nm. The highest hydrostatic stress (Fig. 2a), shear stress (Fig. 2b) and von Mises stress (Fig. 2c) that the processed SiC experienced are all localized in the frontal section of the extrusion zone. Qualitatively speaking, a smaller section of the substrates experiences hydrostatic stress compared to shearing and von Mises stress. It should be noted that there are few hydrostatic and shearing stresses left on the removed chips of SiC substrates where von Mises stress can still be found, indicating that amorphorization does not release von Mises stress as effectively as hy drostatic and shearing stress. The high temperature is highly associated with the removed chips, which means that the heat generated from nano-abrasion is accumulated on the removed chips due to its poor heat conductivity of the disordered structures. The high temperature on the removed chips helps to release stresses, which is consistent with the low hydrostatic and shearing stresses observed in Fig. 2a and b. To quantify the influence of the TLK structure on the stress and temperature, the average stress and temperature of SiC substrates are presented in Fig. 3, which shows that the average hydrostatic stress (Fig. 3a), shear stress (Fig. 3b), von Mises stress (Fig. 3c) and abrasion temperature (Fig. 3d) of SiC substrates in the stable processing stage decrease as the number of ledges in the TLK structure increases. Because the cutting depth is calculated and set based on the highest terrace as the reference point, the more ledges does the substrate possess, the less is the initial cutting depth. The less initial cutting depth means less removed materials and less averaged stress, in turn, a lower averaged temperature on the processed substrates.
(1)
in which bpf represents the Burgers vector of the perfect dislocation, μ is the shear modulus. α is the character of the dislocation. d is the spacing between the dislocation trace line and the sliding surface. The shear stress required to expand a partial dislocation is described as [24].
τpt ¼
2αμbpt γ þ bpt d
(2)
where bpt is the Burgers vector of the partial dislocation, and γ is the stacking fault energy. We can see from the above equation that the dislocation initiation, which indicates the B–D transition, is mainly affected by the shear stress. The Patel-Cohen rationalization is expressed as follows [25]: (3)
W ¼ PεT þ τε
The amorphization normal strain and the hydrostatic component of stress are expressed as εT and P, respectively. τ is the shear stress, and ε represents the amorphization shear strain. From equation (3), amorph ization shear strain induced by C–A transition is related to the shear stress. The interaction of diamond abrasives and SiC substrates inevitably results in the variation of stress and temperature during the nanoabrading process, which in turn affects the structural transition of abrasives and substrates. It is necessary to investigate the cutting stress and abrasion temperature distribution of abrasives and substrates. The von Mises stress can be calculated as follows:
σ vm ðiÞ ¼
� h 1 σxx ðiÞ 2
�2
σyy ðiÞ þ σ yy ðiÞ
�2
σ zz ðiÞ þ ðσzz ðiÞ
4.2. Structural transition Atomic pair distance in a well-defined crystalline material remains constant until external forces, such as nano-abrading in this case, cause structural damages or crystal phase transitions. The RDF intensity of a
�
σxx ðiÞÞ2 þ 6 σ2xy ðiÞ þ σ2zy ðiÞ þ σ2xz ðiÞ
� 1 σxx þ σ yy þ σzz 3
(5)
The equation of abrasion temperature in MD simulation can be expressed as follows: 1X 2 3 mi vi ¼ Nkb T 2 i 2
(6)
Ke ¼ 2mv2
(7)
(4)
fixed set of atomic pair distances in SiC substrates will correspondingly be reduced should the original crystal structure experience changes by nano-abrading. In 3C–SiC crystalline substrates, the inter-atomic dis tances between Si–C, Si–Si/C–C, Si–C and Si–Si were 0.1883, 0.3075, 0.3605, and 0.4348 nm (Fig. 4d), respectively, which is consistent with our calculated distance at 0.1917, 0.3102, 0.3589, and 0.4356 nm in RDF. The small variation (�0.01 nm) of the nearest inter-atomic dis tance in 3C–SiC is caused by energy minimization in the relaxation process. The intensity changes of RDFs of SiC substrates are plotted in Fig. 4 before and after nano-abrading to assist us to access the effect of TLK structure on the structural transition. Intensities of the
The equation of hydrostatic stress is described as follows:
σ hydro ¼
�i�1=2
3
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Fig. 2. Distribution of stress and temperature (a) Hydrostatic stress (b) Shear stress (c) von Mises stress (d) Temperature.
Fig. 3. Averaged stress and temperature of SiC substrates at different TLK structure (a) Hydrostatic stress (b) Shear stress (c) von Mises stress (d) Temperature.
4
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Fig. 4. RDF of SiC substrates before and after nano-abrasion (a) ledge-free SiC (b) one-layered ledge (c) three-layered ledge (d) lattice cell.
during the nano-abrading process. 4.2.1. Amorphization The surface and subsurface morphology of SiC substrates are shown in Fig. 5 when the diamond abrasive is advanced by 18 nm, and show that the machined surface and the ductile chips with strip morphology exhibit a disordered amorphous structure, which is induced by a rapid release of shear stress in the wake of escaping the compression and depression force of the diamond abrasive [26,27]. The amorphous atoms in chips originate from two places: one is from the machined surface, and the other is from the chips itself. Part of amorphous atoms on the machined surface is removed and accumulated at the front end of the diamond abrasive due to the extrusion effect. The other part of high-pressure disorder atoms is removed directly by diamond abrasives and transformed to an amorphous structure under the rapid release of shear stress. In order to analyze the effect of pressure on the amorphous density, amorphous atoms are divided into three regions: region one is the chips region, region two is the high-pressure region, and region three
Fig. 5. The amorphous region of SiC substrates after nano-abrasion.
Table 2 Calculated amorphous atoms in different regions (as defined in Fig. 5) after nano-abrasion.
abovementioned four pair of atomic distances are reduced after nanoabrading in three different surface structures, including ledge-free structure (Fig. 4a), one-layered ledge in TLK structure (Fig. 4b), and three-layered ledge in TLK structure (Fig. 4c). Based on the discussion above, the reduced intensity of all four sets of atomic pair distances clearly suggests that SiC substrates undergo a structural transition
Ledge-free One-ledged Three-ledged
5
Region 1 (n/nm3)
Region 2 (n/nm3)
Region 3 (n/nm3)
78.7 80.0 76.7
111.0 113.7 110.3
86.3 85.3 85.0
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is the machined region (Fig. 5). The amorphous density is defined as the number of amorphous atoms in unit area (n/nm3) in our simulation. The calculated results are present in Table 2 and show that the amorphous density underneath the front end of diamond abrasives is higher than that of the other amorphous region in all three simulated results. Furthermore, from Fig. 2b, the shear stress on the machined surface and the ductile chips is much lower than the extrusion region. It is proved that high shear stress causes the high-density amorphorization of SiC, which transforms to low-density amorphous SiC with the release of shear stress after abrasive particles move away [28].
are populated in the entire amorphous region. The order and disorder 4-coordinated Si/C atoms are present in the entire undeformed region and partly amorphous region, respectively. The number of 3-coordi nated Si/C atoms is clearly much more than those of 5-and 6-coordi nated Si/C atoms after nano-abrading, and these 3-coordinated Si/C atoms almost exclusively reside in the amorphous region. The large number of 3-coordinated Si/C atoms, combining the low stress results in Fig. 2a–c, suggests that 3-coordinated Si/C atoms are thermodynami cally more stable in amorphous region than 5 and 6-coordinated Si/C atoms. For better illustration of the distributions of different coordinated Si and C atoms during nano-abraded 3C–SiC, Fig. 7 and Fig. 8 only selec tively present a representative number of Si and C with different struc tural configurations. Both 6-coordinated Si and C atoms are found to lie in the frontal section where the highest hydrostatic stress is experienced. On the other hand, different 3-, 4-, 5-, 6-coordinated C and Si with varied number of structural configurations are observed in almost the entire amorphous region. MD simulation had been used to investigate the pressure-induced structural transition of SiC, and found that phase transition from 4-coor dinated ZB structure to a 6-coordinated RS structure occurs in the region with hydrostatic stress higher than 100 GPa[5]. The largest hydrostatic stress in our simulation is larger than 100 GPa; this is also where the 6-fold coordinated structure is observed. However, the HPPT from ZB-RS structural transition is not seen in our simulation. In a perfect 3C–SiC crystal, each Si(C) atom is tetrahedrally bonded to the near C(Si); the generation of 6-coordinated Si is a result of pulling C atoms residing in longer distance closer, leaving the neighboring Si, whose bonding structure becomes unsaturated, scrambling for thermodynamically more stable bonding structures. One 6-coordinated Si(C) will need to bring in two C(Si), leading to one (two-bonds vacant) or two (one-bond) neigh boring Si(C) atoms with bond vacancy compared to its 4-coordination in 3C structure. The most likely scenario for these bond-vacant Si(C) atoms due to generation of 5-, 6-coordinated Si(C) is to remain vacant, but somehow, it is distorted by the imbalanced bonding force to move closer to the bonding C(Si) as observed in Fig. 6. The 4-coordinated C(Si) in amorphous region is not tetrahedrally coordinated and exists in four structural configurations. In 3C–SiC, every Si(C) is bonded by four Cs (Sis) tetrahedrally; thus, every bond breaking equally leads to one
4.2.2. Structural atomic defects Xiao et al. [29] performed MD simulation and reported theoretical results confirming a ZB-RS phase transition. They found the existence of individually 6-coordinated Si/C on the SiC substrates; however, these individually 6-coordinated Si/C are not periodically arranged according to that in RS crystal structure, and are more like the atomic defects than the used term ZB-RS phase transition, which refers to one crystal phase to another. Bonding structure changes of individual atoms in a crystal phase do not qualify as a crystal phase transition because not even one unit of crystal cells for the newly named crystal phase exists. Initiation of such a coordination change for individual atoms may further degrade crystal structures of SiC in the vicinity of other neighboring atoms or might even transform into the author’s proposed RS crystal phase; however, to date, the evidence is not strong enough to be called a phase transition. Therefore, we would prefer to use structural atomic defects to describe the n-coordinated atoms generated from the nano-abrading process. Many types of crystal defects are expected to be generated on SiC substrates when high pressure is applied on SiC substrates by diamond abrasives in the nano-abrading process. Both Si and C are tetrahedrally 4-coordinated in a ledge-free 3C–SiC crystalline substrates. To study the atomic structural transition, the coordination number of Si/C atoms in SiC substrates is calculated in the nano-abrading process. The cut-off bond distance for analyzing the coordination number of Si/C atoms in 3C–SiC is set as 2.4 Å in our simulation [30]. The coordination numbers of all C and Si atoms in SiC after the nano-abrading are presented in Fig. 6. While the 6-coordinated Si/C atoms are only present in the high-pressure region, the 3-coordinated and 5-coordinated Si/C atoms
Fig. 6. Distributions of different coordinated atoms in SiC substrates after nano-abrading (a) 3-coordinated atoms (b) 4-coordinated atoms (c) 5-coordinated atoms (d) 6-coordinated atoms. 6
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Fig. 7. Different coordinated C structures in SiC substrates after nano-abrading (a) Positions of 3-coordinated C atoms (b) Positions of 4-coordinated C atoms (c) Positions of 5-coordinated C atoms (d) Varieties of coordinated C structures.
Fig. 8. Different coordinated Si structures in SiC substrates after nano-abrading (a) Positions of 3-coordinated Si atoms (b) Positions of 4-coordinated Si atoms (c) Positions of 5-coordinated Si atoms (d) Positions of 6-coordinated Si atoms (e) Varieties of coordinated Si structures.
3-coordinated Si and one 3-coordinated C, which is consistent with the appearance of large numbers of 3-coordinated Si/C after nano-abrasion. In summary, our simulation results confirmed that the transition of 4-coordinated to 6-coordinated Si/C atoms on processed SiC substrates occur when hydrostatic stress higher than 100 GPa occurs during nanoabrasion; however, these individual 6-coordinated Si/C atoms are not arranged in a RS structure with regularity but rather in a disorder structure. Many more 3- and 4-coordinated Si/C atoms are generated in the amorphous regions during nano-abrasion, while very limited numbers of 5- and 6-coordinated Si/C atoms are produced.
abrasives not only leads to different atomic coordination transition and C–A transition but also causes B-D transition of SiC substrates. As shown in Fig. 9, the state of dislocation distributions of all three substrates is graphically presented at three different abrading distances with 12.6, 14.4, and 16.2 nm. The diamond abrasive makes the first contact with the ledge at the abrading distance of 12.6 nm (Fig. 9b1-c1); the abrasive tip reaches the ledge at 14.4 nm (Fig. 9b2-c2); and the abrasive abrades through the ledge at 16.2 nm (Fig. 9b3-c3). In ledge-free SiC substrates, only dislocations are found, which propagate along the abrading trail as abrading from 12.6 to 16.2 nm (Fig. 9a) with no new dislocation nucleation. On the other hand, new dislocations are nucleated under neath the frontal section of the diamond abrasive as the diamond abrasive makes contact with the ledge of TLK structure (Figs. 9b&c). The
4.2.3. Brittle-ductile transition The local high stress on SiC substrates generated by diamond 7
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Fig. 9. The dislocation initiation of SiC substrates during abrasion process (a) ledge-free SiC (b) one-layered ledge (c) three-layered ledge.
Perfect dislocations and other dislocations (Fig. 10) are found in all three studied SiC substrates, while the nano-abrading distance reaches 18 nm. The dislocations in our simulations reside, on the other hand, in the lower region behind the diamond abrasive particle as abrasives slide over the ledge. One may speculate that no new dislocation is nucleated after the abrasives pass through the ledge; furthermore, the velocity of dislocation propagation is slower than that of the sliding abrasive. The dislocations generated at the front end of diamond abrasives lead to the ductile removal of brittle materials in the initial sliding stage. However, the mechanism for ductile domain removal is changed when abrasives slide over the ledge where the dislocations stay behind the diamond abrasive particle. In Fig. 10a1-a3, we can see that there are a large number of amorphous atoms underneath and in front of the diamond abrasive; this is due to plastic flow of amorphous atoms caused by structural stress and local high temperature generated by the frictional heat between SiC substrates and diamond abrasives. The plastic flow of the amorphous atoms on the substrate surface becomes the driving force for ductile domain removal in the ledge-free region of the SiC substrates. 5. Summary The influence of TLK structures on the deformation and removal mechanism of SiC substrates during the nano-abrading process was studied in a fixed abrasive polishing by using MD simulation method. The obtained results are summarized as follows: The average hydrostatic stress, shear stress, von Mises stress, and temperature of SiC substrates decrease with the increase of ledges in TLK structure. Because of the extrusion effect between abrasives and sub strates, SiC substrates undergo C–A transition and B-D transition. The amorphous density in the high-pressure region is higher than that in the chips region and machined region where the shear stress is released. Tetrahedrally coordinated crystalline Si and C atoms in the SiC substrate are partially transformed to amorphous 3-, 4-, 5- and 6-coordinated Si and C atoms under the pressure applied by abrasive particles on SiC substrates. Furthermore, 3- and 4-coordinated Si and C atoms are the most populated ones in the amorphous region. The 6-coordinated structure is only found in region where hydrostatic stress is higher
Fig. 10. The dislocation distribution of SiC substrates after abrasion (a) ledgefree SiC (b) one-layered ledge (c) three-layered ledge.
nucleated dislocations increase until the abrasive tip passes the ledge. Dislocation propagation is seen alone, and no new dislocation is found at the abrading distance of 16.2 nm, shown in Fig. 9b3 and Fig. 9c3. This MD simulation clearly indicates that the existence of TLK on SiC sub strates lead to new dislocation nucleation, which cannot be found on substrates with no TLK structures. 8
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than 100 GPa. Unlike the report from Ref. [29], the 6-coordinated Si and C atoms in our simulation are not arranged according to the RS structure with regularity but rather in a disorder state. During the nano-abrading process, perfect dislocations and other dislocations are generated in SiC substrates. The step structure is found to assist the dislocation nucleation of the SiC substrate. The MD results suggest that during nano-abrasion, SiC is removed in ductile domain through the dislocation nucleation and propagation at the initial stage and then followed by the plastic flow of the amorphous atoms after sliding over the ledge.
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Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Piao Zhou: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization. Yongwei Zhu: Conceptualization, Methodol ogy, Resources, Writing - review & editing, Supervision, Funding acquisition. Tao Sun: Conceptualization, Methodology, Writing - review & editing, Supervision. Lin Lin: Writing - review & editing. Jun Li: Writing - review & editing. Zikun Wang: Software. Xue Li: Software. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51675276) and Jiangsu Province Key Laboratory of Precision and Micro-manufacturing Technology. References [1] S. Goel, The current understanding on the diamond machining of silicon carbide, J. Phys. Appl. Phys. 47 (2014) 243001. [2] D. Lim, H. Jee, J.W. Kim, J. Moon, S. Lee, S.S. Choi, J. Boo, Deposition of epitaxial silicon carbide films using high vacuum MOCVD method for MEMS applications, Thin Solid Films 459 (2004) 7–12. [3] Q.F. Luo, J. Lu, X.P. Xu, A comparative study on the material removal mechanisms of 6H-SiC polished by semi-fixed and fixed diamond abrasive tools, Wear 350–351 (2016) 99–106. [4] M. Mishra, I. Szlufarska, Possibility of high-pressure transformation during nanoindentation of SiC, Acta Mater. 57 (2009) 6156–6165. [5] F. Shimojo, I.I. Ebbsjo, R.K. Kalia, A. Nakano, J.P. Rino, P. Vashishta, Molecular dynamics simulation of structural transformation in silicon carbide under pressure, Phys. Rev. Lett. 84 (2000) 3338. [6] A. Noreyan, J.G. Amar, I. Marinescu, Molecular dynamics simulations of nanoindentation of β-SiC with diamond indenter, Mater. Sci. Eng., B 117 (2005) 235–240. [7] M.S. Miao, M. Prikhodko, W.R. Lambrecht, Comment on “orthorhombic intermediate state in the zinc blende to rocksalt transformation path of SiC at high pressure”, Phys. Rev. Lett. 88 (2002) 189601.
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