Effects of Anisotropy on Single Crystal Silicon in Polishing Non

micromachines

Article Eﬀects of Anisotropy on Single Crystal Silicon in Polishing Non-Continuous Surface

Guilian Wang 1,2, Zhijian Feng 1,2, Yahui Hu 1,2, Jie Liu 1,2 and Qingchun Zheng 1,2,*

1 Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China; [email protected] (G.W.); [email protected] (Z.F.); [email protected] (Y.H.); [email protected] (J.L.) 2 National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China * Correspondence: [email protected]

Received: 19 June 2020; Accepted: 29 July 2020; Published: 30 July 2020

Abstract: A molecular dynamics model of the diamond abrasive polishing the single crystal silicon is established. Crystal surfaces of the single crystal silicon in the Y-direction are (010), (011), and (111) surfaces, respectively. The effects of crystallographic orientations on polishing the non-continuous single crystal silicon surfaces are discussed from the aspects of surface morphology, displacement, polishing force, and phase transformation. The simulation results show that the Si(010) surface accumulates chips more easily than Si(011) and Si(111) surfaces. Si(010) and Si(011) workpieces are deformed in the entire pore walls on the entry areas of pores, while the Si(111) workpiece is a local large deformation on entry areas of the pores. Comparing the recovery value of the displacement in different workpieces, it can be seen that the elastic deformation of the A side in the Si(011) workpiece is larger than that of the A side in other workpieces. Pores cause the tangential force and normal force to fluctuate. The fluctuation range of the tangential force is small, and the fluctuation range of the normal force is large. Crystallographic orientations mainly affect the position where the tangential force reaches the maximum and minimum values and the magnitude of the decrease in the tangential force near the pores. The position of the normal force reaching the maximum and minimum values near the pores is basically the same, and different crystallographic orientations have no obvious effect on the drop of the normal force, except for a slight fluctuation in the value. The high-pressure phase transformation is the main way to change the crystal structure. The Si(111) surface is the cleavage surface of single crystal silicon, and the total number of main phase transformation atoms on the Si(111) surface is the largest among the three types of workpieces. In addition, the phase transformation in Si(010) and Si(011) workpieces extends to the bottom of pores, and the Si(111) workpiece does not extend to the bottom of pores.

Keywords: single crystal silicon; anisotropy; polishing; non-continuous surface

1. Introduction The single crystal silicon has a basically complete lattice structure with different properties in different directions. In order to better understand the mechanical and chemical properties of single crystal silicon, it is necessary to fully understand their properties in each crystallographic orientation. Previous studies have shown that the influence of anisotropy on the processing of materials is mainly reflected in the accumulation of materials, elastoplastic properties, and phase transformation during the processing [1–4], which often play a decisive role in the quality of materials. For porous crystalline materials, the effect of crystallographic orientations on machining is more complicated. Because of

Micromachines 2020, 11, 742; doi:10.3390/mi11080742 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 742 2 of 16 the special geometric structure, the bearing capacity of porous materials will be reduced, and it is difficult to obtain an ideal surface using traditional processing methods [5–9]. Therefore, grasping the structural and property differences caused by the anisotropy of the porous crystalline material during the processing is crucial for selecting the process parameters to obtain an ideal processing surface. Different crystallographic orientations bring various structures and peculiar mechanical properties, which widen the application of crystal materials. However, it also causes many problems in processing and manufacturing. In order to obtain crystals with higher precision and better mechanical properties, many scholars have done extensive research on the anisotropy of crystals. Filippov et al. [10] studied the influence of crystallographic orientations and azimuth indenter orientations on indentation hardness and modulus by Vickers indentation on (100), (110), and (111) surfaces of single crystal aluminum. Tang et al. [11] compared the anisotropic behavior of crystals with experimental results and found that the extended anisotropic Drucker yield criterion can accurately simulate the anisotropy of FCC (face-centered cubic), BCC (body-centered cubic), and HCP (hexagonal close-packed) metals. Armstrong et al. [12] conducted stress calculations on the (111) and (100) surfaces of α-iron, and discovered the dislocation reaction mechanism of enhanced strain hardening during the process of the nano-indentation. Kitsuya et al. [13] studied crystallographic orientations on some metals, and the crystal plasticity analysis based on the information obtained from experiments showed that the anisotropy of mechanical properties is greatly affected by the crystallographic orientations. Bürger et al. [14] tested the shear creep behavior of nickel-based single crystal superalloys and found that the shear deformation in the [112] loading direction is much faster than that in the [011] loading direction on the (110) surface. Zhan et al. [15] reported the mechanical deformation of the single crystal Ti2AlC MAX phase using microcolumn compression tests with a series of crystallographic orientations, and found that non-classical crystallographic slip is caused by the strong dependence of crystallographic slip on both the analytical shear stress and the stress perpendicular to the slip plane. Frydrych et al. [16] studied the yield stress, hardened texture, and twin anisotropy of AZ31B extruded bars, and concluded that the twinning activity mainly affects the mechanical response through texture changes. Xie et al. [17] studied the removal mechanism of single crystal copper in the close-to-atomic scale by molecular dynamics, and simulated the influence of anisotropy on cutting force and material distribution of the surface. It was found that the minimum chip thickness can be reduced to a single atomic layer in an atomic scale using rounding tools for mechanical cutting. Frodal et al. [18] studied three aluminum alloys with different grain structures and crystal textures, and found that effects of yield strength and work hardening depend on plastic anisotropy. Pogrebnjak et al. [19,20] studied two kinds of nano-multilayer films CrN/MoN and TiN/SiC through experiments, and found that the preferred crystallographic orientation will change under different voltages. Meanwhile, the effect of temperature on the physicochemical and functional properties of the TiN/SiC multilayer film was explored. The research results are consistent with the first principle MD (molecular dynamics) calculation of the TiN/SiC heterostructure. The above studies on metals and alloys show that the anisotropy of crystals will have a significant impact on the yield strength, work hardening, and shear slip dislocation of metals and alloys. Reasonable selection of crystallographic orientations can effectively optimize the processing of metals and alloys, and improve the processing quality. Unlike metals and alloys, some studies have found that hard and brittle crystal materials are prone to cracks and chipping during the processing, and the crystallographic orientation is closely related to the generation of cracks during the processing of brittle materials. In order to overcome the influences of the anisotropy on the processing of hard and brittle materials, it is imperative to study the anisotropy of hard and brittle materials. Meng et al. [21] focused on the influences of crystallographic anisotropy on 6H-SiC slip deformation and nanomachining performance, and made important contributions to understand the microdeformation and nanomachining processes of 6H-SiC. Cang et al. [22] observed obvious elastic anisotropy in glass and found that the elastic anisotropy shows a strong correlation with molecular orientations. Chen et al. [23] did some research on cutting SiO2 and found that (100) [00-1] crystallographic orientation has a large range of damage extension, Micromachines 2020,, 11,, 742x 33 of of 16 new phase is generated in the (111) [-101] crystallographic orientation. Nagai et al. [24] discussed the (110)formation [1–10] mechanism crystallographic of U-shaped orientation diamond has the smallest grooves damage based range,on the and experimental a new phase results, is generated and insuccessfully the (111) [-101] obtained crystallographic a U-shaped orientation.diamond trench Nagai wi etth al. vertical [24] discussed {111} sidewalls the formation for power mechanism devices. of U-shapedLiu et al. diamond[25] analyzed grooves the based internal on thereasons experimental for the results,anisotropy and successfullyof the frictional obtained force a when U-shaped the diamond slided trench on with the vertical diamond, {111} which sidewalls was mainly for power caused devices. by amorphous Liu et al. [25defects,] analyzed dislocations, the internal and reasonsvon Mises for shear the anisotropy strain. Zhao of theet al. frictional [26] simulated force when the thecrack diamond fracture slided modes on of the the diamond, glass layer which and wassilicon mainly layer caused with (100), by amorphous (110), and defects, (111) surfaces. dislocations, The andchanges von Misesof crack shear edge strain. quality Zhao in etdifferent al. [26] simulatedcutting directions the crack and fracture different modes layers of thewere glass obtained. layer andIt was silicon found layer that with anisotropy (100), (110), of the and silicon (111) surfaces.layer has Thean important changes of influence crack edge on quality the fracture in diff erentmodecutting and crack directions edge quality and di ffoferent the layerstwo layers. were obtained.Rickhey et It al. was [27] found analyzed that anisotropy changes of of the the crack silicon size layer in hasSi(001), an important Si(110), and influence Si(111) on orientations, the fracture modewhich andwere crack in good edge qualityagreement of the with two experiment layers. Rickheys and et proved al. [27] analyzedthe rationality changes of of the the simplified crack size innumerical Si(001), Si(110),model. andThese Si(111) studies orientations, about the whichanisotro werepy inof goodhard agreementand brittle with crystalline experiments materials and provedprovide the some rationality good theoretical of the simplified and experimental numerical model. references These for studies the evolution about the anisotropyof material ofcracks hard andduring brittle the crystallineprocessing. materials In addition, provide the change some goodin crystal theoretical orientations and experimental also has a significant references effect for theon evolutionthe friction of and material elasticity cracks between during brittle the processing. materials. In addition, the change in crystal orientations also has aAlthough significant these effect researchers on the friction have and conducted elasticity betweenmany studies brittle on materials. the anisotropy of non-porous crystals,Although it is still these necessary researchers to describe have the conducted anisotropy many of porous studies crystalline on the anisotropy materials in of detail. non-porous In this crystals,paper, pores it is stillmake necessary the single to describecrystal silicon the anisotropy workpiece of porousbecome crystalline a non-continuous materials geometry, in detail. Inwhich this paper,has some pores properties make the that single the continuous crystal silicon surface workpiece does not become have. aThe non-continuous influence of anisotropy geometry, on which the hasprocessing some properties of porous thatmaterials the continuous is very easy surface to change does notto some have. extent The influenceowing to ofthe anisotropy heterogeneity on the of processingthe materials. of porousIn order materials to explore is veryhow easythe anisotro to changepy toaffects some the extent pore owing walls, toa molecular the heterogeneity dynamics of themodel materials. is established In order in this to explore paper, howwhich the is anisotropyabout polishing affects the the non-continuous pore walls, a molecularsurface. Laws dynamics about modelthe removal, is established stress, and in this modification paper, which of porous is about ma polishingterials are the revealed non-continuous by changing surface. crystallographic Laws about theorientations. removal, stress,Meanwhile, and modification studies on the of porousdistribution materials of the are materials, revealed displacement, by changing crystallographic polishing force, orientations.and phase transformation Meanwhile, are studies conducted. on the These distribution studies are of very the materials,important for displacement, exploring the polishing effect of force,crystallographic and phase orientations transformation on porous are conducted. material Theses and studiesstudying are the very removal important mechanism for exploring of porous the ematerials.ffect of crystallographic orientations on porous materials and studying the removal mechanism of porous materials. 2. Simulation Method 2. Simulation Method In this paper, a set of three-dimensional molecular dynamics simulation models are established. The schematicIn this paper, diagram a set ofof three-dimensionalthe models is shown molecular in Figure dynamics 1. simulation models are established. The schematic diagram of the models is shown in Figure1.

. Figure 1. Schematic diagram of the diamond abrasive polishing single crystal silicon. Figure 1. Schematic diagram of the diamond abrasive polishing single crystal silicon. The model is mainly composed of the diamond abrasive and the single crystal silicon workpiece. The diamondThe model abrasive is mainly is a spherecomposed with of a radiusthe diamon of 2 nm.d abrasive The workpiece and the is rectangularsingle crystal with silicon two pores,workpiece. whose The dimensions diamond inabrasive the X-direction, is a sphere Y-direction, with a radius and Z-direction of 2 nm. The are 17workpiece nm, 11 nm, is rectangular and 11 nm, respectively.with two pores, Pores whose are positioned dimensions at in the the polishing X-directio distancen, Y-direction, of 4–6 nm and and Z-direction 8–10 nm, and are the17 nm, sizes 11 in nm, the X-direction,and 11 nm, respectively. Y-direction, and Pores Z-direction are positioned are 2 nm,at the 3 nm,polishing and 6 nm,distance respectively. of 4–6 nm For and the 8–10 convenience nm, and ofthe descriptions, sizes in the X-direction, pore walls ofY-direction, the workpiece and Z-direction are marked are in Figure2 nm, 13 b.nm, A and 6 C nm, sides respectively. are pore walls For inthe the convenience entry areas of of descriptions, pores. B and pore D sideswalls areof the pore workpiece walls in are the marked exit areas in ofFigure pores. 1b. Three A and kinds C sides of are pore walls in the entry areas of pores. B and D sides are pore walls in the exit areas of pores.

Micromachines 2020, 11, 742 4 of 16 Micromachines 2020, 11, x 4 of 16 Micromachines 2020, 11, x 4 of 16 Three kinds of crystal surfaces are set in the model, namely, (010), (011), and (111) surfaces. The crystalThree surfaceskinds of are crystal set in surfaces the model, are namely, set in (010),the model, (011), andnamely, (111) (010), surfaces. (011), The and structure (111) ofsurfaces. the crystal The structure of the crystal surface and the atomic spacing ‘d’ of single crystal silicon are shown in surfacestructure and of the the atomic crystal spacing surface ‘d’ and of single the atomic crystal siliconspacing are ‘d’ shown of single in Figure crystal2. Thesilicon maximum are shown value in Figure 2. The maximum value of the atomic spacing ‘d’ determines properties of the crystal. Figure 3 ofFigure the atomic 2. The spacing maximum ‘d’ determinesvalue of the properties atomic spacing of the ‘d’ crystal. determines Figure 3properties shows di ffoferences the crystal. in the Figure shape 3 shows differences in the shape of the first pore under different crystallographic orientations. In this ofshows the first differences pore under in the di ffshapeerent of crystallographic the first pore un orientations.der different In crystallographic this paper, the orientations. polishing depth In this is paper, the polishing depth is expressed by ‘ap’. expressedpaper, the by polishing ‘ap’. depth is expressed by ‘ap’.

Figure 2. Structure and atomic spacing of single crystal silicon. FigureFigure 2. 2.Structure Structure and and atomic atomic spacing spacing of of single single crystal crystal silicon. silicon.

FigureFigure 3. 3. InfluencesInfluences of of the the anisotropy anisotropy on on pore pore walls. walls. Figure 3. Influences of the anisotropy on pore walls. TheThe workpiece workpiece is is divided divided into into three three parts: parts: Newt Newtonianonian atoms, atoms, thermostatic thermostatic atoms, atoms, and and boundary boundary The workpiece is divided into three parts: Newtonian atoms, thermostatic atoms, and boundary atoms.atoms. Newtonian Newtonian atoms atoms are are atoms atoms in in the the polishing polishing area, area, thermostatic thermostatic atoms atoms keep keep the the temperature temperature atoms. Newtonian atoms are atoms in the polishing area, thermostatic atoms keep the temperature constant,constant, and and boundary boundary atoms atoms are are fixed. fixed. The The micr microcanonicalocanonical ensemble ensemble (NVE) (NVE) is is used, used, the the initial initial constant, and boundary atoms are fixed. The microcanonical ensemble (NVE) is used, the initial temperaturetemperature of of the the simulation simulation is is kept kept in in 293 293 K, K,and and periodic periodic boundary boundary conditions conditions (PBC) (PBC) are set are in set the in temperature of the simulation is kept in 293 K, and periodic boundary conditions (PBC) are set in the Z-direction.the Z-direction. The abrasive The abrasive is set is as set a asrigid a rigid body, body, the interaction the interaction between between C-C C-Catoms atoms is negligible, is negligible, the Z-direction. The abrasive is set as a rigid body, the interaction between C-C atoms is negligible, the interactionthe interaction between between C-Si C-Si atoms atoms is described is described by byMorse Morse potential potential function function [28], [28], and and the the Morse Morse interaction between C-Si atoms is described by Morse potential function [28], and the Morse potentialpotential function function can be expressed by the following equation: potential function can be expressed by the following equation: −−αα −− 2α2((rrrijr00 )) 2(2α rr ij(r )r ) Er()=− D [ e−−2(ααi j rr0 ) 2 e −− 2( rrij ] ) 0 E(rij)ij = D=−0[0e− −ij002e− ij − ] (1)(1) Er()ij D0 [ e− 2 e ] (1) D α wherewhere D00 is is the the binding binding energy, energy,α is theα is gradient the gradient coeffi coefficientcient of the of potential the potential energy energy curve, curve, and r0 andis the where D0 is the binding energy, is the gradient coefficient of the potential energy curve, and distance between the two atoms when the interaction between atoms is equal to zero. r0 is the distance between the two atoms when the interaction between atoms is equal to zero. r0 isThe the interaction distance between between the Si-Si two atoms atoms is when described the interaction by the Terso betweenff potential atoms function is equal [ 29to ],zero. and the The interaction between Si-Si atoms is described by the Tersoff potential function [29], and the TersoffThepotential interaction function between can be Si-Si expressed atoms is by described the following by the equations: Tersoff potential function [29], and the Tersoff potential function can be expressed by the following equations: Tersoff potential function can be expressed by the following equations: X 1 EEU== Uij (2) =21 ij (2) EU2 iij,≠j ij (2) 2 ij≠

Micromachines 2020, 11, 742 5 of 16

Uij = fc(rij)[ fR(rij) + bij fA(rij)] (3) where fc(rij) is the cut-oﬀ function, fR(rij) is the rejection function, fA(rij) is the attraction function, bij is the modulation function, and rij is the distance between atomic i and j. fR(rij), fA(rij) and fc(rij) can be expressed by the following equations:

λijrij fR(rij) = Aije− (4)

µ r f (r ) = B e− ij ij (5) A ij − ij   1  rij Rij  1 1 rij Rij ≤ fc(rij) = + cos( − ) Rij < rij Sij (6)  2 2 Sij Rij  − ≤  0 rij > Sij where Aij is dual binding energy of the rejection function, Bij is dual binding energy of the attraction function, Sij and Rij are cut-off radii, λij is the gradient coefficient of the potential energy curve in the attraction function, and µij is the gradient coefficient of the potential energy curve in the rejection function. bij can be expressed by the following equations:

n n 1 = ( + i i )− 2ni bij xij 1 βi ζij (7) X ζij = fc(rik)ωik g(θijk) (8) k,i,j

2 2 ci ci g(θijk) = 1 + (9) d2 − d2 + (h cos θ ) i i i − ijk where βi is the bond order coeﬃcient; ci, di, and hi are elastic coeﬃcients; ζij is angular potential energy; and θijk is the angle of atoms. The simulation is divided into two parts: system relaxation and the polishing process of the workpiece. The relaxation process is mainly to keep the system energy stable and make the simulation environment close to the actual situation. During the polishing process, the abrasive feeds in the negative direction of the X-axis and rotates with the Z-axis. All MD simulations are based on the large-scale atomic/molecular massively parallel simulator (LAMMPS) [30] and results are visualized by OVITO [31]. Curves are drawn by ORIGIN [32]. Simulation parameters are shown in Table1. Micromachines 2020, 11, 742 6 of 16

Table 1. MD (molecular dynamics) simulation parameters in 3D nano-machining.

Parameters Value Radius of abrasive 2 nm Atom number of abrasive 5899 Size of workpiece 17 11 11 nm3 × × Si(010): 102241 Atom number of workpiece Si(011): 102374 Si(010): 101493 Time step 1 fs Initial temperature 293 K Polishing depth (ap) 0.75 nm, 1 nm, 1.25 nm, 1.5 nm Polishing distance 14.2 nm [-100] on (010) surface Polishing direction [-100] on (011) surface [-11-2] on (111) surface Size of pore 2 3 6 nm3 × × Polishing speed 100 m/s Spinning speed 25 m/s

3. Results and Discussion

3.1. Analysis of the Surface Topography and Displacement Vector

3.1.1. Analysis of the Surface Topography The anisotropy of the crystal is a key parameter that determines the structure and performance of the material, which affects the removal method of materials and has an important impact on the processing efficiency and quality. Figure4 shows three kinds of single crystal silicon workpieces with Si(010), Si(011), and Si(111) surfaces in the Y-direction, and describes the distribution of materials on the surfaces at the end of polishing. It is obvious that the removed materials mainly exist in the following ways: covering the surface of pores, accumulating at the front of the abrasive to be chips, and some of the chips being converted to the side flow. Figure4d describes the conversion process of chips and side flows. When the polishing depth is 0.75 nm, the coverage of pore areas is low. A few chips and side flows are formed. When the polishing depth is 1.5 nm, the coverage of pore areas is very high, and a large amount of chips and side flows are formed. Some reasons can account for these phenomena. When the polishing depth becomes larger, the contact part between the abrasive and the workpiece is improved, and the polishing area is widened, which improves the coverage of materials in pore areas. Meanwhile, the amount of materials removed is increased with increase in the polishing depth, so the increase of chips is more obvious, and there are more chips converted into the side flows. Generally speaking, side flow atoms are less than chip atoms. Comparing the distribution of materials on the three kinds of surfaces at the same polishing depth, it is easy to find that the number of chips gathered on the Si(010) surface is more than that on Si(011) and Si(111) surfaces at the end of polishing, and the number of chips produced on the Si(111) surface is the least, which indicates that the resistance of the unpolished surface to the abrasive is smaller and materials accumulate more easily when polishing the Si(010) surface. In contrast, the Si(111) surface will lead to the less accumulation of materials during the polishing. Micromachines 2020, 11, 742 7 of 16 Micromachines 2020, 11, x 7 of 16

FigureFigure 4.4.E Effectsffects of of anisotropy anisotropy on on the the surface surface morphology morphology at diatff differenterent polishing polishing depths depths (0.75 (0.75 nm, 1nm, nm, 1 1.25nm, nm,1.25 1.5 nm, nm). 1.5 nm). 3.1.2. Effects of Anisotropy on the Deformation of Pores 3.1.2. Effects of Anisotropy on the Deformation of Pores The deformation process of each pore wall (A, B, C, and D sides) is not identical. Generally The deformation process of each pore wall (A, B, C, and D sides) is not identical. Generally speaking, the deformation of A and C sides is basically the same, and the deformation of B and D speaking, the deformation of A and C sides is basically the same, and the deformation of B and D sides is basically the same. In the numerical simulation, the movement direction of A and C sides sides is basically the same. In the numerical simulation, the movement direction of A and C sides points to the pore areas, and the movement direction of B and D sides points to the continuous surface, points to the pore areas, and the movement direction of B and D sides points to the continuous which indicates that the deformation of pore walls is related to the relative movement direction of surface, which indicates that the deformation of pore walls is related to the relative movement the abrasive [33]. In order to study the effects of anisotropy on the deformation of pore walls more direction of the abrasive [33]. In order to study the effects of anisotropy on the deformation of pore reasonably, the deformation of the first pore in different crystallographic orientations is analyzed. walls more reasonably, the deformation of the first pore in different crystallographic orientations is In Figures5 and6, the length of blue arrows represents the size of the displacement, and the direction analyzed. In Figures 5 and 6, the length of blue arrows represents the size of the displacement, and of arrows represents the displacement direction of atoms relative to the initial position. Figure5a–c the direction of arrows represents the displacement direction of atoms relative to the initial position. describes the deformation of the A side in different crystallographic orientations when the polishing Figure 5a–c describes the deformation of the A side in different crystallographic orientations when distance is 4 nm. While Figure6a–c describes the displacement of atoms at the first pore when the the polishing distance is 4 nm. While Figure 6a–c describes the displacement of atoms at the first polishing distance is 14.2 nm. It can be seen from Figure5 that, when the surface in the Y-direction is pore when the polishing distance is 14.2 nm. It can be seen from Figure 5 that, when the surface in (111) surface, the displacement of atoms in the upper part of the A side is relatively large. Blue arrows the Y-direction is (111) surface, the displacement of atoms in the upper part of the A side is relatively are relatively dense and long. The bending deformation with a large angle is obvious in the upper part large. Blue arrows are relatively dense and long. The bending deformation with a large angle is of the A side, but the deformation in the lower part of the A side is not obvious, which is the local obvious in the upper part of the A side, but the deformation in the lower part of the A side is not deformation. When the surface in the Y-direction is (010) surface and (011) surface, the deformation obvious, which is the local deformation. When the surface in the Y-direction is (010) surface and of the A side belongs to the entire deformation. When the surface in the Y-direction is (011) surface, (011) surface, the deformation of the A side belongs to the entire deformation. When the surface in the deformation of the A side is the smallest, and the bending angle is the smallest. It can be seen the Y-direction is (011) surface, the deformation of the A side is the smallest, and the bending angle from the Figure6 that, when the polishing distance is 14.2 nm, the displacement of the upper part is the smallest. It can be seen from the Figure 6 that, when the polishing distance is 14.2 nm, the of the first pore changes with the change of the surface in the Y-direction. When the surface in the displacement of the upper part of the first pore changes with the change of the surface in the Y-direction is (111) surface, the number of blue arrows is large and the atomic displacement near the Y-direction. When the surface in the Y-direction is (111) surface, the number of blue arrows is large pore wall is large as well. This indicates that, when the surface of the workpiece in the Y-direction is and the atomic displacement near the pore wall is large as well. This indicates that, when the surface (111) surface, the deformation of pore walls is large, and the atoms above the pore are prone to the of the workpiece in the Y-direction is (111) surface, the deformation of pore walls is large, and the large displacement. This is mainly because the Si(111) surface is the cleavage surface of single crystal atoms above the pore are prone to the large displacement. This is mainly because the Si(111) surface silicon. The distance parallel to the atomic layer in the cleavage surface is relatively large, which easily is the cleavage surface of single crystal silicon. The distance parallel to the atomic layer in the contributes the atomic layer having cracks owing to the extrusion pressure, so the pore wall easily cleavage surface is relatively large, which easily contributes the atomic layer having cracks owing to produces large deformation, and the atoms nearby are prone to the large displacement. the extrusion pressure, so the pore wall easily produces large deformation, and the atoms nearby are prone to the large displacement.

Micromachines 2020, 11, 742 8 of 16 Micromachines 2020, 11, x 8 of 16

Figure 5. EffectsEﬀects of anisotropy on the deformation of the first ﬁrst pore at the polishing distance of 4 nm.nm.

Figure 6.6. EEffectsffects ofof anisotropyanisotropy on on the the deformation deformation of of the th firste first pore pore at theat the polishing polishing distance distance of 14.2 of 14.2 nm. nm. In order to study numerical characteristics of the atomic displacement in pore walls more intuitively,In order the to pore study wall numerical is sliced andcharacteristics the average of displacement the atomic displacement is extracted. Thein pore size walls of the more slice isintuitively,0.5 3 4thenm pore3 (0.5 wall nm is in sliced the X-direction, and the average 3 nm displacement in the Y-direction, is extracted. and 4 nm The in size the of Z-direction). the slice is intuitively,× × the pore wall is sliced and the average displacement is extracted. The size of the slice is Because0.5×× 3 the 4 nm deformation3 (0.5 nm in laws the ofX-direction, A and C sides 3 nm are in thethesame, Y-direction, and the and deformation 4 nm in the laws Z-direction). of B and D sidesBecause are the the deformation same, this paper laws only of A discusses and C sides the numericalare the same, changes and the of Adeformation and B sides. laws Figure of 7B showsand D thesides average are the displacement same, this paper of A only and discusses B sides under the numerical different crystallographic changes of A and orientations. B sides. Figure The 7 average shows displacementthe average displacement of the A side of increases A and B firstsides and under then di decreases.fferent crystallographic The average displacement orientations. ofThe the average B side increasesdisplacement and of then the gradually A side increases flattens. first This and shows then thatdecreases. there is The a recovery averageprocess displacement in the deformationof the B side ofincreases the Aside, and then and itgradually can be known flattens. that This the shows deformation that there mechanism is a recovery of theprocess A side in isthe elastic–plastic deformation mixedof the A deformation. side, and it There can be is known no recovery that processthe defor inmation the B side, mechanism so it can beof knownthe A side that is the elastic–plastic deformation mechanismmixed deformation. of the B side There is plastic is no deformation. recovery process In the samein the way, B side, the deformation so it can be mechanism known that of the the C sidedeformation is elastic–plastic mechanism mixed of deformation,the B side is and plastic that ofde theformation. D side is In plastic the same deformation. way, the As deformation is shown in Figuremechanism7a, when of the the polishingC side is distanceelastic–plastic is 4 nm, mixed the average deformation, displacements and that of theof the A side D side in the is Si(010),plastic Si(011),deformation. and Si(111) As is workpieces shown in areFigure 0.76 nm,7a, 0.68when nm, the and polishing 0.76 nm, respectively.distance is 4 When nm, thethe polishing average distancedisplacements is 4 nm, of the the deformation A side in the of Si(010), the A side Si(011), under and diff Si(111)erent crystallographic workpieces are orientations 0.76 nm, 0.68 is thenm, same and as0.76 that nm, shown respectively. in Figure When5. It is the easy polishing to find that distance the average is 4 nm, displacement the deformation of the Aof sidethe A in side the Si(111) under workpiecedifferent crystallographic is always greater orientations than that inis the other same workpieces as that shown as the in polishing Figure 5. continues. It is easy to Although find that the average displacementdisplacement ofof thethe A A side side in in the the Si(010) Si(111) workpiece workpiece is slightlyis always higher greater than than that that in the in Si(011) other workpieceworkpieces at as the the polishing polishing distance continues. of 4 nm. Although As the polishingthe average continues, displacement the average of the displacement A side in the of theSi(010) A side workpiece in the Si(010) is slightly workpiece higher is than lower that than in thatthe Si(011) in other workpiece workpieces. at the The polishing average displacementdistance of 4 ofnm. the As A the side polishing in the three continues, kinds of workpiecesthe average basicallydisplacement changes of withthe A the side same in the trend, Si(010) which workpiece reaches the is maximumlower thanvalue that in at other the polishing workpieces. distance The ofaverage 6 nm. Whendisplacement the polishing of the distanceA side in is the 6 nm, three the kinds average of displacementsworkpieces basically of the A changes side in Si(111), with Si(011),the same and tr Si(010)end, which workpieces reaches are the 1.01 maximum nm, 0.9 nm, value and 0.93 at nm,the respectively.polishing distance The average of 6 nm. displacements When the polishing of the A dist sideance are is 0.83 6 nm, nm, the 0.58 average nm, and displacements 0.66 nm, respectively, of the A atside the in polishing Si(111), Si(011), distance and of 14.2Si(010) nm. workpieces The recovery are values1.01 nm, of 0.9 the nm, displacement and 0.93 nm, are 0.18respectively. nm, 0.32 The nm, average displacements of the A side are 0.83 nm, 0.58 nm, and 0.66 nm, respectively, at the polishing distance of 14.2 nm. The recovery values of the displacement are 0.18 nm, 0.32 nm, and 0.27 nm,

Micromachines 2020, 11, 742 9 of 16 Micromachines 2020, 11, x 9 of 16 and 0.27 nm, respectively, which indicates that the Si(011) workpiece has the largest elastic recovery respectively, which indicates that the Si(011) workpiece has the largest elastic recovery value after value after the polishing, that is, the elastic deformation of the A side in the Si(011) workpiece is larger the polishing, that is, the elastic deformation of the A side in the Si(011) workpiece is larger than that than that of other workpieces. The average displacement of the B side in the three kinds of workpieces of other workpieces. The average displacement of the B side in the three kinds of workpieces basically changes with the same trend. The displacement increases obviously in the polishing distance basically changes with the same trend. The displacement increases obviously in the polishing from 6 nm to 10 nm, but it increases slowly after the polishing distance of 10 nm. When the polishing distance from 6 nm to 10 nm, but it increases slowly after the polishing distance of 10 nm. When the distance is 10 nm, the average displacements of the B side in the Si(111), Si(011), and Si(010) workpieces polishing distance is 10 nm, the average displacements of the B side in the Si(111), Si(011), and are 1.0 nm, 0.85 nm, and 0.86 nm, respectively. At the end of polishing, the average displacements of Si(010) workpieces are 1.0 nm, 0.85 nm, and 0.86 nm, respectively. At the end of polishing, the the B side in the Si(111), Si(011), and Si(010) workpieces are 1.22 nm, 1.03 nm, and 1.01 nm, respectively. average displacements of the B side in the Si(111), Si(011), and Si(010) workpieces are 1.22 nm, 1.03 Generally speaking, the average displacement of the B side in the Si(111) workpiece is always greater nm, and 1.01 nm, respectively. Generally speaking, the average displacement of the B side in the than that in the other two workpieces. Si(111) workpiece is always greater than that in the other two workpieces.

Figure 7. Average displacement of A and B. Figure 7. Average displacement of A and B. 3.2. Analysis of the Polishing Force 3.2. Analysis of the Polishing Force 3.2.1. Calculation Method of the Polishing Force 3.2.1. Calculation Method of the Polishing Force The polishing force directly reflects the material removal process and is an important parameter to understandThe polishing the processing force process.directly reflects The polishing the material forcementioned removal process in this and paper is an refers important to the real-time parameter averageto understand force of the the workpiece processing on process. the abrasive Theduring polishing the polishingforce mentioned process. in In this general, paper the refers polishing to the forcereal-time in the macroaverage scale force comes of the from workpiece the deformation on the abrasi of theve workpiece during the and polishing the friction process. between In general, the tool the andpolishing chips, while force in in the the micro macro scale, scale the comes polishing from forcethe deformation mainly comes of fromthe workpiece the interaction and the between friction workpiecebetween atomsthe tool and and tool chips, atoms. while This in section the micro mainly scale, studies the polishing the relationship force mainly between comes the normalfrom the polishinginteraction force between (Y-direction) workpiece and the atoms tangential and polishingtool atoms. force This (X-direction) section mainly with thestudies polishing the relationship distance, aimingbetween to explain the normal the influence polishing of force different (Y-direction) crystallographic and the orientationstangential polishing on the polishing force (X-direction) force of non-continuouswith the polishing surfaces. distance, The tangential aiming to force explain is recorded the influence as Ft, of and different the normal crystallographic force is recorded orientations as Fn. on the polishing force of non-continuous surfaces. The tangential force is recorded as Ft, and the 3.2.2.normal Changes force of is therecorded Polishing as Fn. Force Figure8 shows the change of the polishing force (tangential force and normal force) in three diff3.2.2.erent Changes crystallographic of the Polishing orientations Force when the polishing depth is 1 nm. It is obvious that there are differencesFigure in the8 shows polishing the change force under of the di polishingfferent crystallographic force (tangential orientations. force and normal However, force) in termsin three ofdifferent the overall crystallographic trend, the polishing orientations force in when the threethe polishing kinds of depth crystallographic is 1 nm. It is orientations obvious that basically there are changesdifferences with thein the same polishing trend, so force this paperunder selectsdifferent Si(010) crystallographic surface in the orientations. Y-direction to However, describe thein terms effect of of poresthe overall on the trend, polishing the force,polishing as shown force inin Figurethe three8a. Itkinds can beof seencrystallographic from Figure8 aorientations that the position basically ofchanges pores is atwith the the polishing same trend, distance so this of 4–6paper nm selects and 8–10 Si(010) nm, surface but the in position the Y-direction where the to polishingdescribe the forceeffect reaches of pores the maximumon the polishing and minimum force, as valuesshown doesin Figure not coincide 8a. It can with be theseen boundary from Figure of the 8a pores.that the Inposition the vicinity of pores of the is first at pore,the polishing the maximum distance value of 4–6 of thenm tangential and 8–10 forcenm, but appears the position at the polishing where the distancepolishing of 3 force nm, thereaches minimum the maximu value appearsm and minimum at the polishing values distancedoes not ofco 5.2incide nm, with and the tangentialboundary of forcethe decreases pores. In aboutthe vicinity 18 nN. of In the the first vicinity pore, of the the ma secondximum pore, value the of maximum the tangential value force of the appears tangential at the forcepolishing appears distance at the polishing of 3 nm, distancethe minimum of 7 nm, value the appears minimum at valuethe polishing appears distance at the polishing of 5.2 nm, distance and the tangential force decreases about 18 nN. In the vicinity of the second pore, the maximum value of the tangential force appears at the polishing distance of 7 nm, the minimum value appears at the

Micromachines 2020, 11, 742 10 of 16

Micromachines 2020, 11, x 10 of 16 of 9 nm, and the tangential force decreases about 29 nN. Generally speaking, the ﬂuctuation of the polishing distance of 9 nm, and the tangential force decreases about 29 nN. Generally speaking, the tangential force is relatively small. This is mainly because the source of the tangential force is mainly fluctuation of the tangential force is relatively small. This is mainly because the source of the divided into two parts: one is the reaction force acting on the abrasive when atoms of the workpiece tangential force is mainly divided into two parts: one is the reaction force acting on the abrasive are sheared and the other is the movement of chips in front of the abrasive, which is an important when atoms of the workpiece are sheared and the other is the movement of chips in front of the component of the tangential force. For non-continuous surfaces, although the tangential force tends to abrasive, which is an important component of the tangential force. For non-continuous surfaces, decrease owing to the lack of atoms in pore areas, the ﬂuctuation amplitude will be relatively weak although the tangential force tends to decrease owing to the lack of atoms in pore areas, the owing to the existence of chips in front of the abrasive. fluctuation amplitude will be relatively weak owing to the existence of chips in front of the abrasive.

FigureFigure 8.8. EEffectsﬀects ofof anisotropyanisotropy onon thethe polishingpolishing forceforce atat thethe polishingpolishing depth depth of of 1.0 1.0 nm. nm.

ThereThere isis aa big difference difference between between the the normal normal forc forcee and and the the tangential tangential force. force. In pore In pore areas, areas, the thefluctuation fluctuation range range of the of thenormal normal force force is larger is larger than than that thatof the of tangential the tangential force. force. In the In vicinity the vicinity of the offirst the pore, first pore,the maximu the maximumm value value of the of normal the normal force force appears appears at the at polishing the polishing distance distance of 3 ofnm, 3 nm, the theminimum minimum value value appears appears at atthe the polishing polishing distance distance of of 6.3 6.3 nm, nm, and and the the normal normal force decreasesdecreases aboutabout 100100 nN.nN. InIn thethe vicinityvicinity ofof thethe secondsecond pore,pore, thethe maximummaximum valuevalue ofof thethe normalnormal forceforce appearsappears atat thethe polishingpolishing distance distance of of 8.3 8.3 nm, nm, the the minimum minimum value value appears appears at theat the polishing polishing distance distance of 10.2 of 10.2 nm, nm, and and the normalthe normal force force decreases decreases about about 70 nN. 70 This nN. is This because is beca theuse normal the normal force is providedforce is provided by the normal by the reaction normal forcereaction when force the workpiecewhen the isworkpiece extruded. is The extruded. lack of atomsThe lack in the of poreatoms areas in reducesthe pore the areas normal reduces reaction the forcenormal provided reaction by force the workpiece,provided by resulting the workpiece, in the suddenresulting drop in the of sudden the normal drop force of the in normal the pore force areas. in Bythe comparing pore areas. the Bywave comparing amplitude the wave of the amplitude normal force of the and normal tangential force force, and tangential it can be concluded force, it can that be theconcluded wave amplitude that the wave of normal amplitude force is of much normal larger force than is much that of larger the tangential than that force, of the which tangential shows force, that thewhich effect shows of pores that onthe the effect normal of pores force on is the larger normal than thatforce of is thelarger tangential than that force. of the tangential force. ItIt cancan bebe seenseen fromfrom FigureFigure8 a–c8a–c that that the the change change of of crystallographic crystallographic orientations orientations will will bring bring some some locallocal changeschanges toto thethe polishingpolishing force.force. ForFor thethe tangentialtangential force,force, crystallographiccrystallographic orientationsorientations mainlymainly aaffectffect thethe positionposition wherewhere thethe tangentialtangential forceforce reachesreaches thethe maximummaximum andand minimumminimum valuesvalues andand thethe decreasedecrease of of the the tangential tangential force force in in the the pore pore areas. areas. In In the the vicinity vicinity of of the the first first pore, pore, the the maximum maximum value value of theof tangentialthe tangential force force on the on Si(011) the Si(011) surface surface appears appears at the polishing at the polishing distance ofdistance 4.5 nm, of the 4.5 minimum nm, the valueminimum appears value at appears the polishing at the distancepolishing of distance 5.3 nm, of and 5.3 thenm, tangentialand the tangential force decreases force decreases about 30 about nN. 30 nN. The maximum value of the tangential force on the Si(111) surface appears at the polishing distance of 3.2 nm, the minimum value appears at the polishing distance of 5.8 nm, and the

Micromachines 2020, 11, 742 11 of 16

The maximum value of the tangential force on the Si(111) surface appears at the polishing distance of 3.2 nm, the minimum value appears at the polishing distance of 5.8 nm, and the tangential force decreases about 40 nN. In the vicinity of the second pore, the maximum value of the tangential force on the Si(011) surface appears at the polishing distance of 6.8 nm, the minimum value appears at the polishing distance of 9.5 nm, and the tangential force decreases about 25 nN. The maximum value of the tangential force on the Si(111) surface appears at the polishing distance of 7.5 nm, the minimum value appears at the polishing distance of 9.2 nm, and the tangential force decreases about 27 nN. The decrease of the tangential force caused by different orientations is mainly related to the accumulation of chips in front of the abrasive. It can be seen from Figure4 that chips on the Si(010) surface accumulate easily, and the tangential reaction force given by chips is relatively large, so the tangential force near the first pore on the Si(010) surface decreases the least. However, there is less chips accumulation on the Si(111) surface, and the tangential reaction force given by chips is relatively small, so the tangential force near the first pore on the Si(111) surface decreases the most. Because of the small distance between the first pore and the second pore, the effect of chips on tangential force near the second pore is not obvious, and the difference between the tangential force of different workpieces is only 4 nN. For the normal force, the position where the normal force reaches the maximum and the minimum values near the pores is basically same. In the vicinity of the first pore, the normal force of the Si(011) workpiece decreases about 100 nN, and the normal force of the Si(111) workpiece decreases about 105 nN. In the vicinity of the second pore, the normal force of the Si(011) workpiece decreases about 57 nN, and the normal force of the Si(111) workpiece decreases about 60 nN. It can be seen that different crystallographic orientations have no obvious effect on the drop of normal force near the first pore, and the difference in the decrease of the normal force near the second pore under different crystallographic orientations is only 13 nN. Those phenomena indicate that the drop of the normal force is mainly affected by the geometry of the workpiece. Besides, when the normal force reaches the peak value near the first pore at the first time, the peak value of the normal force on the Si(010) and Si(011) surfaces is greater than 100 nN, while the peak value of the normal force on the Si(111) surface is lower than 100 nN, which is mainly because (111) surface is the cleavage surface of single crystal silicon, the atomic layer bonding force parallel to the cleavage surface is weak, and the extrusion pressure required for extrusion failure is relatively small.

3.3. Phase Transformation Analysis

3.3.1. Principle of Phase Transformation Phase transformation analysis is a common method to analyze crystal structure. In this paper, the coordination number is used to study phase transformation. At the beginning, the coordination number of single crystal silicon is 4, and there are four neighboring atoms. When the pressure of the abrasive on the workpiece reaches the critical value, the crystal structure with coordination number 5 and 6 will appear. Figure9 shows the cross-section of the Si(010) workpiece at the polishing depth of 1 nm. It can be seen from Figure9 that there will be a large number of atoms under the abrasive, but phase transformation atoms are in an unstable state. When the abrasive leaves, the β-Si loses its crystal order and becomes an amorphous phase. The amorphous phase is mainly composed of disordered covalent bond and a small amount of β-Si. The whole transformation process follows the high pressure transformation principle. ‘CN’ in the Figure9 represents the coordination number. Micromachines 2020, 11, 742 12 of 16 Micromachines 2020, 11, x 12 of 16

Figure 9.9. A diagram of the cross-sectionalcross-sectional views of the atomicatomic positionspositions with variousvarious views at thethe polishingpolishing distancedistance ofof 14.214.2 nm.nm. CN, coordination number.number.

3.3.2. EEffectsffects of Anisotropy onon PhasePhase TransformationTransformation Figure 1010 shows shows the analysisthe analysis of the mainof the phase main transformation phase transformation atoms in diff erentatoms crystallographic in different orientations.crystallographic In order orientations. to increase In the order reliability to increase of the the research reliability results, of thisthe sectionresearch conducts results, comparative this section simulationsconducts comparative by changing simulations the polishing by depthschanging (0.75 the nm, polishing 1.0 nm, depths 1.25 nm, (0.75 1.5 nm).nm, 1.0 As cannm, be1.25 seen nm, from 1.5 Figurenm). As 10 cana, for be the seen amorphous from Figure atoms 10a, with for athe coordination amorphous number atoms with of 5, a when coordination the polishing number depth of is5, 0.75when nm, the 1.0 polishing nm, 1.25 nm,depth and is 1.5 0.75 nm, nm, the number1.0 nm, of 1.25 phase nm, transformation and 1.5 nm, atoms the number with coordination of phase numbertransformation of 5 on atoms the Si(111) with surfacecoordination is 985, number 1167, 1656 of 5 and on 2023,the Si(111) respectively. surface Itis can985, be 1167, seen 1656 that and the number2023, respectively. of atoms with It can the be coordination seen that the number number of of 5 onatoms the with Si(111) the surface coordination is the most number at all of polishing 5 on the depths.Si(111) surface The number is the of most atoms at with all thepolishing coordination depths. number The number of 5 on theof Si(011)atoms surfacewith the is slightlycoordination more thannumber that of on 5 theon the Si(010) Si(011) surface surface in most is slightly conditions, more than or maintains that on the a small Si(010) di ffsurfaceerence. in Figure most 10conditions,b shows thator maintains the number a small of atoms difference. with the Figure coordination 10b shows number that of the 6 isnumber far less of than atoms that with with the the coordination number ofof 56 atis thefar less same than polishing that with depth, the andcoordina the efftionect number of crystallographic of 5 at the same orientations polishing on itdepth, is similar and tothe that effect of crystallographicof crystallographic orientations orientations on on atoms it is withsimilar coordination to that of crystallographic number 5. However, orientations when theon polishingatoms with depth coordination is 0.75 nm, number the number 5. However, of atoms when with the the polishing coordination depth number is 0.75 nm, of 6 the on thenumber Si(111) of surfaceatoms with is the the least coordination among the number three kinds of 6 on of the workpieces, Si(111) surface which isis the only least 208. among The numberthe three of kinds atoms of withworkpieces, the coordination which is only number 208. of The 6 on number the Si(010) of at andoms Si(011)with the surfaces coordination is 217 and number 221, respectively.of 6 on the ThisSi(010) shows and thatSi(011) the numbersurfaces ofis atoms217 and with 221, the respectively. coordination This number shows of 6that on thethe Si(111)number surface of atoms does with not increasethe coordination obviously number when the of polishing6 on the Si(111) depth issurfac small.e does Only not when increase the polishing obviously depth when reaches the polishing a certain degree,depth is the small. number Only of when atoms the with polishing the coordination depth reaches number a certain of 6 on degree, the Si(111) the number surface of is atoms larger thanwith thatthe coordination on other surfaces. number Besides, of 6 on it canthe beSi(111) seen surface from the is Figure larger 10 thanc that that the on total other number surfaces. of main Besides, phase it transformationcan be seen from atoms the onFigure the Si(111) 10c that surface the total is the nu largestmber amongof main the phase three transformation types of crystal atoms surfaces on andthe theSi(111) total surface number is ofthe main largest phase among transformation the three types atoms of oncrystal the Si(010) surfaces surface and th ise the total smallest. number The of main total numberphase transformation of main phase atoms transformation on the Si(010) atoms surface on the is Si(011) the smallest. surface The is slightly total number more than of main that onphase the Si(010)transformation surface. Thisatoms is mainlyon the becauseSi(011) surface the Si(111) is slightly surface more is the than cleavage that surfaceon the Si(010) of single surface. crystal silicon,This is whichmainly is because modified the more Si(111) easily surface than is other the cleavage surfaces. su Therface Si(011) of single surface crystal also silicon, has weak which cleavage is modified owing tomore its largeeasily atomic than layerother spacing surfaces. in theThe Y-direction, Si(011) surface but its also cleavage has weak is smaller cleavage than owing Si(111) surface.to its large atomic layer spacing in the Y-direction, but its cleavage is smaller than Si(111) surface.

Micromachines 2020, 11, 742 13 of 16 Micromachines 2020, 11, x 13 of 16

FigureFigure 10. EEffectsﬀects ofof anisotropy anisotropy on on the the number number of atoms of atoms with with coordination coordination numbers numbers 5 and 65 at and diﬀ erent6 at differentpolishing polishing depths. depths.

FigureFigure 1111 shows the phase transformation under under different different crystallographic orientations orientations at at the the polishingpolishing depth depth of of 1.0 1.0 nm. From From Figure Figure 11a–c,11a–c, it it can can be be seen seen that that the the phase phase transformation transformation at at the the A A andand CC sidessides is alwaysis always greater greater than thatthan at that B and at DB sides. and FigureD sides. 11a,b Figure shows 11a,b the phase shows transformation the phase transformationat the pore walls at the of Si(010)pore walls and of Si(011) Si(010) workpieces. and Si(011) Itworkpieces. is easy to It find is easy that to there find is that amorphous there is amorphousphase transformation phase transformation extending toextending the bottom to the at Abottom and C at sides. A and Figure C sides. 11c Figure shows 11c that shows the phase that thetransformation phase transformation at A and Cat sides A and of C the sides Si(111) of the workpiece Si(111) workpiece is basically is concentrated basically concentrated in the upper in partthe upperof the porepart walls,of the andpore does walls, not and extend does to not the exte bottom.nd to However, the bottom. the numberHowever, of the phase number transformation of phase transformationatoms at A and atoms C sides at in A the and Si(111) C sides workpiece in the Si(111) is more workpiece than that inis Si(010)more than and that Si(011) in workpieces.Si(010) and Si(011)This is basicallyworkpieces. consistent This is basically with the aboveconsistent analysis with results the above of the analysis displacement results of vector the displacement at pore walls; vectorthat is, at the pore entire walls; deterioration that is, the of entire A and deterioration C sides occurs of A in and the Si(010)C sides and occurs Si(011) in the workpieces, Si(010) and while Si(011) the workpieces,deterioration while of A andthe deterioration C sides occurs of locally A and in C the sides Si(111) occurs workpiece, locally in but the the Si(111) deterioration workpiece, is relatively but the deteriorationserious. The mainis relatively reason for serious. the diff erencesThe main of phasereason transformation for the differences between of A phase and C transformation sides is that the betweenatomic layer A and spacing C sides on is the that Si(111) the atomic surface layer in the spacing Y-direction on the is tooSi(111) large, surface and the in bindingthe Y-direction force between is too large,atoms and is relatively the binding weak. force The atomicbetween layer atoms spacing is relatively on the Si(010) weak. and The Si(011) atomic surfaces layer in spacing the Y-direction on the Si(010)is smaller and than Si(011) that surfaces on the Si(111) in the surface,Y-direction and theis smaller binding than force that between on the atoms Si(111) is relativelysurface, and strong. the bindingThe atomic force bond between does notatoms break is easilyrelatively during strong. extrusion, The atomic so the entirebond deformationdoes not break occurs. easily When during the extrusion,pressure reaches so the theentire critical deformation value, the occurs. whole poreWhen wall the willpressure have phasereaches transformation, the critical value, but thethe scalewhole of porephase wall transformation will have phase is relatively transformation, small. but the scale of phase transformation is relatively small.

Micromachines 2020, 11, 742 14 of 16 Micromachines 2020, 11, x 14 of 16

Figure 11. EffectsEﬀects of anisotropy on pore wallswalls at polishing depth of 1.0 nm.

4. Summary and Conclusions 4. Summary and Conclusions In this paper, the molecular dynamics model of the single crystal silicon with non-continuous In this paper, the molecular dynamics model of the single crystal silicon with non-continuous surface isis studied. studied. Influences Influences of di fferentof different crystallographic crystallographic orientations orientations on polishing theon non-continuouspolishing the surfacenon-continuous are explored, surface and are the explored, following and conclusions the following can beconclusions drawn: can be drawn: (1) ItIt can can be be found found that, that, when when the the surface surface in in the the Y-direction Y-direction is (010) and (011) surfaces, the bending deformationdeformation ofof thethe A A side side belongs belongs to the to entire the deformation.entire deformation. When theWhen surface the in surface the Y-direction in the Y-directionis (111) surface, is (111) the surface, deformation the deformation of the A side of the belongs A side to belong the larges to localthe large deformation. local deformation. It is also Itfound is also that found the elasticthat the deformation elastic deformation of A side of in A the side Si(011) in the workpiece Si(011) workpiec is largere is than larger that than in other that inworkpieces. other workpieces. The average The average displacement displacement of the B of side the in B theside Si(111) in the workpieceSi(111) workpiece is always is greateralways greaterthan the than other the two other workpieces. two workpieces. The fluctuation The fluctuat ofion the of tangential the tangential force force is relatively is relatively small small and andthat ofthat the of normal the normal force is force relatively is relatively large. For la therge. tangential For the force,tangential crystallographic force, crystallographic orientations orientationsmainly affect mainly the position affect where the position the tangential where forcethe tangential reaches the force maximum reaches and the minimum maximum values and minimumand the decrease values and of the the tangential decrease of force the intangential pore areas. force For in thepore normal areas. force,For the the normal position force, of the positionnormal forceof the reaching normal the force maximum reaching and the minimum maximum values and minimum near the pores values is basicallynear the the pores same, is basicallyand different the crystallographicsame, and different orientations crystallographic have no obvious orientations effect have on the no drop obvious of the effect normal on force, the dropexcept of forthe a normal slight fluctuation force, except in thefor a value. slight fluctuation in the value. (2) ForFor thethe amorphousamorphous atoms atoms with with the the coordination coordination number number of 5, atomsof 5, atoms with the with coordination the coordination number numberof 5 on the of Si(111)5 on the surface Si(111) are surface the most are at the all polishingmost at all depths. polishing For depths. the atoms For with the the atoms coordination with the coordinationnumber of 6, number effects of of crystallographic 6, effects of crystallographic orientations orientations on it are similar on it to are that similar on the to atomsthat on with the atomsthe coordination with the coordination number of 5.number When of the 5. polishingWhen the depth polishing is 1 nm,depth A andis 1 nm, C sides A and in theC sides Si(010) in theand Si(010) Si(011) and workpieces Si(011) workpiec show overalles show deterioration, overall deterioration, and the transformation and the transformation extends to the extends bottom toof the pores.bottom A of and the C pores. sides inA theand Si(111) C sides workpiece in the Si(111) show workpiece local deterioration, show local which deterioration, is serious, whichbut does is serious, not extend but todoes the not bottom extend of theto the pores. bottom of the pores.

Author Contributions: Conceptualization, Conceptualization,G.W. Guilian and Wang Q.Z.; and Data Qingch curation,un Zheng; J.L.; Formal Data curation, analysis, Jie G.W. Liu; and Formal Z.F.; Funding acquisition, G.W.; Investigation, Y.H.; Methodology, Z.F.; Project administration, Q.Z.; Resources, Q.Z.; Software,analysis, Guilian Z.F.; Supervision, Wang and Q.Z.; Zhijian Validation, Feng; Funding Y.H.; Visualization, acquisition, J.L.; Guilian Writing—original Wang; Investigation, draft, G.W. Yahui and Z.F.;Hu; Writing—reviewMethodology, Zhijian & editing, Feng; Z.F. Project All authors administration, have read Qing andchun agreed Zheng; to the Resources, published versionQingchun of theZheng; manuscript. Software, Zhijian Feng; Supervision, Qingchun Zheng; Validation, Yahui Hu; Visualization, Jie Liu; Writing – original Funding: This work was supported by National Key R&D Program of China (2018YFB1308900), National Natural Sciencedraft, Guilian Foundation Wang of and China Zhijian (51405196), Feng; Writ Naturaling – Science review Foundation& editing, Zhijian of Tianjin Feng. (18JCYBJC20100, 17JCQNJC04700). ConﬂictsFunding: ofThis Interest: work Thewasauthors supported declare by noNational conﬂict Key of interest. R&D Program of China (2018YFB1308900), National Natural Science Foundation of China (51405196), Natural Science Foundation of Tianjin (18JCYBJC20100, 17JCQNJC04700).

Conflicts of Interest: The authors declare no conflict of interest.

References

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