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Effect of crystallographic orientation on the extrusion of silicon surface during an impact: Molecular dynamics simulation
Nuclear Instruments and Methods in Physics Research B 270 (2012) 133–139
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Effect of crystallographic orientation on the extrusion of silicon surface during an impact: Molecular dynamics simulation Ruling Chen a,⇑, Jianbin Luo b, Dan Guo b, Xiao Hu c, Hong Lei a a
Nano-Science and Nano-Technology Research Center, Shanghai University, Shanghai 200444, China State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China c Sauer-Danfoss (US) Company, Plymouth, MN 55447, USA b
a r t i c l e
i n f o
Article history: Received 14 April 2011 Received in revised form 16 September 2011 Available online 22 September 2011 Keywords: Crystallographic orientation Extrusion Crystalline silicon Impact Molecular dynamics simulation
a b s t r a c t Molecular dynamic simulation was applied in analyzing the effect of crystallographic orientation on the extrusion formation of silicon surface during the impact of a large silica cluster in dry and wet condition, respectively. The crystallographic orientation would have no obvious influence on the cross-section of crater created by the impact in either dry or wet conditions. The cross-section of crater appeared to be trapezoid shape and semicircular shape after the dry and wet impact, respectively. The inner layer of the crater after a wet impact was smoother than that after a dry impact. The extrusion patterns on the surfaces of (0 0 1)-, (0 1 1)- and (1 1 1)-oriented silicon single crystals had four, two, and threefold symmetries, respectively. Moreover, the critical velocity of the extrusion formation on Si(1 1 0) substrate under the dry impact would be the largest, followed by Si(1 1 1) substrate, and Si(0 0 1) substrate was the smallest. The critical velocity reached to its minimum when the impact had an incidence angle of 45°. However, the crystallographic orientation would have no influence on the critical velocity of the extrusion under the wet impact, and the critical velocity reached its minimum at the incidence angle of 30°. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The phenomenon of an extruded silicon surface was at first observed by Pharr et al. in 1991 through indentation experiment [1]. It is meaningful to understand the atomic scale material removal mechanism in the ultra-precision machining processes by studying the mechanism of extrusion of silicon surface under different dynamic loadings including indentation loading and impact loading. Experiments [2,3] and simulations [4,5] have shown that the monocrystal silicon (c-Si) under an indentation load has a localized transformation from a diamond-cubic phase (Si-I) to a metallic phase with a b-Sn structure (Si-II). The phase transformation zone under the indenter is enlarged by the increased load. When the transformed metallic Si-II zone extends to the radius of contact between the indenter and silicon surface, the material under indenter is able to flow plastically resulting in a metal-like extrusion. The formation of extrusion on the silicon surface depends strongly on the settings of the indentation including maximum force, loading and unloading rate, geometry of indenter, and crystallographic orientation of silicon substrate. Gerbig et al. demonstrated that the crystallographic orientation has an influence on
⇑ Corresponding author. E-mail address: [email protected] (R.L. Chen). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.09.013
the critical contact pressure of phase transformation during the indentation of c-Si substrate [6,7]. The critical contact pressure for orientation Si(1 1 0) or Si(1 1 1) is lower than that for Si(0 0 1) at the indentation loading stage. However, it is higher at the indentation unloading stage. Jasinevicius et al. demonstrated that the formation of multiple structure phases on the silicon surface under cyclic microindentation experiment is affected by the crystallographic orientation and number of successive cycles [8]. The molecular dynamics simulation results indicated that the crystallographic orientation of silicon surface has an influence not only on the phase transformation, but also on the distribution and the volume of the transformed region under indentation load [9,10]. In addition, some researchers have studied the effect of crystallographic orientation on the extrusion patterns on the surface of crystalline Au [11], Fe [12], Cu [13], and SiC [14], respectively. Since localized high pressure and high temperature could be induced by an impact, the extrusion of silicon surface could have a different mechanism as compared with the case of indentation loading. In the past two decades, extensive molecular dynamics simulations have been conducted to study the formation of crater for a silicon surface under the impact of a cluster [15–24]. The rim around the crater (namely extrusion) after the impact has indeed been observed. However, the small clusters (with less than 1000 atoms) and ultra-high impact velocities indicate that these studies could be mainly adapted to the process of ion bombardment on the
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silicon surface. During an ion bombardment, the extrusion may result from the sputtering and redepositing of lower energetic atoms in the plastic deformation zone [15]. Two typical studied topics are: the relationship between the depth of crater and the incident energy of impact [21–23]; the evolution of crater shape in case of different types of cluster and crystal orientations of silicon substrate [24]. However, most of these studies emphasize on the formation mechanism of crater rather than its rim. It is well known that the topography of crater after impact should be affected by the momentum transfer during the impact process, which is related to impact velocity, size and type of cluster [16,21]. Based on our previous study [25], it has been suggested that the mechanism of extrusion on silicon surface under the impact of a large silica cluster with a relative low impact velocity is different from that under the ion bombardment or indentation. During the impact of large silica cluster, the silicon surface is extruded by the combinational effects of thermal spread, phase transformation and crystallographic slip. It has been also found that the extrusion on silicon surface is in embryo at impact unloading stage and growing up at the cluster rebounding stage. However, no specific result has been reported so far on the effect of crystallographic orientation on extrusion formation when a large silica cluster impacts on a silicon surface. Though the effect of water on the deformation of silicon under indentation [26] or on the phase transformation of silicon under impact [27] has been studied by molecular dynamics simulations, most of which were limited to the cluster–surface interactions in a condition with no water (namely dry indentation or dry impact) [10,20,21]. However, the water solution is indispensable to the ultra-precision surface machining processes such as chemical mechanical polishing (CMP) [28] and elastic emission machining (EEM) [29]. Molecular dynamic study of the extrusion formation under a wet impact is supposed to provide an atomistic insight into the material removal in the ultra-precision surface machining process. The study reported in this paper is to identify the influence of crystallographic orientation on the extrusion formation of c-Si surface, which is impacted by large silica clusters with relative low velocity as described in our previous researches [25,30]. A set of molecular dynamics simulations for both dry and wet impact have been conducted by varying impact velocity, incidence angle, and crystallographic orientation. 2. Simulation methodology In this study, MD simulations were performed by a modification of the XMD simulation package (Version 2.5.32) from University of Connecticut [31]. Fig. 1 shows the simulation model of the impact of silica clusters toward silicon substrate under the dry and wet impact, respectively. For wet impact, the water layer with a density of 0.997 g/cm3 and a thickness of 10 Å, was over the silicon substrate initially. The c-Si substrates, including Si(0 0 1), Si(1 1 0) and Si(1 1 1), were adopted. The dimensions of these substrates under the dry impact and wet impact are listed in Table 1. The outer
layers (four atomic layers) of the substrate were fixed in space with the exception of the top contact surface. Thermostat layers (eight atomic layers) had been used to ensure reasonable outward heat conduction away from the control volume. The interatomic interaction in the silica cluster–silicon substrate system was modeled by a Stillinger–Weber-like potential [32]. As for the silica cluster surface, the bridging oxygen (BO) atom and the non-bridging oxygen (NBO) atom were separated, and the BO atom was bonded to two adjacent silicon atoms. All NBO atoms with a dangling free bond were saturated with hydrogen atoms. The hydrogen atom was placed at an equilibrium distance (0.95 Å) away from a NBO atom with a Si–O–H angle of 116° [33]. In the simulation, the model TIP4P [34] was used as water molecules. The interaction between the water molecules and the cluster atoms was described as a potential modeled according to Ref. [33], where different Lennard-Jones (LJ) parameters and fractional charges were assumed for BO and NBO. All the pair interactions were truncated at a cutoff radius of 9 Å, and reaction field corrections for TIP4P were applied. The Ewald summation method was not adopted because of the large simulation ensemble in this study. The interaction between the water molecules and the substrate silicon atoms was described as a Lennard-Jones potential modeled according to Ref. [26]. The cutoff radius for the Lennard–Jones interaction was 8.47 Å. In addition, the simulation ensemble will breakdown when the high-energy repulsive parts of the potentials are not solved. In this study, we treated this problem by some simple ways not by ZBL potential. As shown in Eq. (1), the function of M(r) was adopted.
8 Prototype of potential functionsðUðrÞÞ r > r0 > > > < ðsuch as Wantanabe; LJ; Columb PotentialÞ > Modification of potential functionsðMðrÞÞ r r0 > > : ðMðrÞ ¼ A r2 þ B r þ CÞ:
ð1Þ
And the coefficients of A, B, C were solved by the Eq. (2).
8 MðrÞjr¼r0 ¼ UðrÞjr¼r0 > < MðrÞ0 jr¼r0 ¼ UðrÞ0 jr¼r0 > : MðrÞ0 jr¼0 ¼ 10 MðrÞ0 jr¼r0 ;
ð2Þ
where r is the separation between two atoms. And the selection of the variable r0 was based on some tentative calculations. In this study, the amorphous silica cluster has 1728 silicon atoms and 3456 oxygen atoms. The cluster is a sphere with a diameter of around 54 Å. At the beginning of the simulation, the silica clusters were located 20 Å above the substrate surface. The simulation system was initiated with a temperature of 293 K. After a relaxation of 7000 fs, the initial velocities and incidence angles of the clusters were varied. The duration of one cluster’s impact lasted for 20,000 fs. During the simulation, the temperature of the thermostat atoms was kept at 293 K by using Gauss–Hoover method. And velocity rescaling at every 30 time steps was adopted to maintain the fixed temperature of the thermostat layer. We had performed the simulations with the different time steps (0.5 fs and 1.0 fs) in the wet conditions. The obvious difference between the simulation results by 0.5 fs and 1.0 fs was not noticed. So, the time step of 1.0 fs was adopted in order to improve the computational efficiency. 3. Effect of crystallographic orientation on the shape of crater and pattern of extrusion 3.1. Cross-section of crater
Fig. 1. The schematic diagram of the cluster impact on the crystal silicon substrate under (a) the dry impact, (b) the wet impact.
As shown in Fig. 2, the cross-section of the crater exhibits nearly trapezoid shapes under the dry impact due to the crystallographic
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Table 1 Dimensions of different crystallographic orientation substrates under the dry impact and wet impact. Impact conditions
Impacted substrates
Dimensions of silicon substrates (X Y Z) a0
Number of atoms in the simulation system
Dry impact
Si(0 0 1) Si(1 1 0) Si(1 1 1) 10 Å H2O/Si(0 0 1) 10 Å H2O/Si(1 1 0) 10 Å H2O/Si(1 1 1)
28 38 16 28 38 16 28 37 16 28 38 14 28 38 14 28 37 14
141,376 141,487 134,755 134,828 138,681 130,555
Wet impact
Notes: a0 = 5.43 Å, the lattice constant of c-Si.
Fig. 2. Side cross-section view of the impact zone at 20,000 fs under the normal impact with 7000 m/s. The magenta dots and blue dots present five and threefold silicon atoms, respectively. Cyan dots present silicon atoms with a coordination number under three. The rest of atoms present fourfold silicon atoms. (a, c, e) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the dry impact, respectively. (b, d, f) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the wet impact, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
slip, regardless of the different crystallographic orientation of the substrate. However, the cross-section of crater exhibits a nearly semicircular shape under the wet impact regardless of the different crystallographic orientation of the substrate (Fig. 2). And the inner layer of the crater after a wet impact is obviously smoother than that after a dry impact (Fig. 2). It is speculated that the density of the water film between the cluster and substrate may be increased with the decreasing of the clearance between them at the impact loading stage under the wet impact. In other words, the water film between the cluster and substrate may become the confined liquids. Therefore, the fluidity of the water film will descend. This may be similar to the solidification of the water film. The solidified water film may result in a more uniform distribution of the local pressure and temperature of the impact zone. So, in an ultra-precision surface machining, the water is not only the transfer medium of abrasive and chemical matters, but also is contributing to a better surface quality of the machined surface. Therefore, the crystallographic orientation has no significant influence on the cross-section of the crater on a silicon surface impacted by a large silica cluster in dry or wet condition. The phenomenon is different from an ion bombardment, under which the cross-section of the crater is affected by the crystallographic orientation of the substrate. Allen et al. demonstrated that the cross-section of the crater has a triangular shape when an Ar cluster impacts on a Si(1 0 0) substrate [24]. However, the cross-section of the crater has a round shape when the Ar cluster impacts on a Si(1 1 1) substrate. This difference may be induced by the small
Fig. 3. Top view of the extrusion produced at 20,000 fs under the normal impact of the cluster. Pink atoms are above original impacted silicon surface. The rest of atoms are below the original silicon surface. (a–c) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the dry impact with 6500 m/s, respectively. (d–f) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the wet impact with 7000 m/s, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Ar cluster (about 135 Ar atoms) with the high impact energy (24 eV/atom). 3.2. Distribution pattern of extrusion 1Þ and (1 1 1) Under the dry impact, the primary slip planes ð1 1 0 intersect with the impacted plane (0 0 1) along the [1 1 0] and ½1 1 directions [13,25], resulting in a surface extrusion with a fourfold in-plane symmetry (Fig. 3). For the impacted (1 1 0) surface, the 1Þ and ð1 1 1Þ cross the impacted plane primary slip planes ð1 1 and ½2 1 1 directions, resulting in a surface extrualong the ½2 1 1 sion with a twofold in-plane symmetry [13,35]. For the impacted ð1 1 1Þ and ð1 1 1Þ intersect (1 1 1) surface, the slip planes ð1 1 1Þ; 0; ½0 1 1 and ½1 0 1 directions, and the impacted plane along ½1 1 exhibits a threefold in-plane symmetry [13,35]. Under the wet impact, the distributions of the surface extrusion for impact planes (0 0 1), (1 1 0) and (1 1 1) are similar to that under the dry impact resulting from the same mechanism of crystallographic slip (Fig. 3). Therefore, the distribution pattern of the extrusion under the impact of a large silica cluster is similar to the case of nanoindentation experiment [13] and ion bombardment experiment [24]. Such a coincidence may be related to the residual stress anisotropy in silicon substrate under indentation or impact loading [35]. 4. Effect of crystallographic orientation on the critical velocity of extrusion formation Simulation experiments for impacts with varied crystallographic orientation, impact velocity and incidence angle have been
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performed to further investigate the formation mechanism of surface extrusion. A critical velocity (Vcr) for the extrusion formation is defined when the height of extrusion reaches 5 Å (Fig. 2e). An indepth study on the mechanism of extrusion formation on the silicon surface during the impact process was reported in Ref. [25]. The simulation results showed that the thermal spread, phase transformation and crystallographic slip have an influence on the extrusion formation of silicon surface under the impact of a large silica cluster [25]. Therefore, the relationships between Vcr and the local temperature and pressure of the impact zone, and the crystallographic orientation of the substrate are analyzed as follows.
Both the virial pressure and temperature within the impact zone under the cluster were calculated. The impact zone was constructed around the cluster and the distance from the cluster surface is within 12 Å [36]. The local pressure of the impact zone of the substrate (P) is given by [37]
*N l X i¼1
+, mi v 2i
ð3 V l Þ þ
*N l X
*
*
F i ri
+, ð3 V l Þ
4.2. Local temperature affected by crystallographic orientation The local temperature of the cross-section is given by [38,39]
4.1. Local pressure affected by crystallographic orientation
P¼
of the impact zone, and h i denotes a statistical averaging over all simulation times. Fig. 4 illustrates that the local pressure of the impact zone at the impact loading stage is not affected by the crystallographic orientation under either the dry or wet impact, respectively. Moreover, there is no obvious difference in the local pressure in the same impact condition between the dry and wet impact. It indicates that the water film has no obvious influence on the local pressure of the transformation zone at the impact loading stage.
ð3Þ
i¼1
where Nl and Vl are the number of silicon atoms and volume of the impact zone. * mi and vi are the mass and the velocity of the atom i, * respectively. F i and r i are the force and position of the silicon atom i
Tg ¼
*N g X
+, 2
mi ðv i v c Þ
ð3 Ng kB Þ;
ð4Þ
i¼1
where kB is the Boltzmann constant. The cross-section passed through the center of the impact zone and is parallel to the direction of impact and has a thickness of 11 Å. The cross-section is divided into cubic cells of dimensions 11 11 11 Å. Tg and Ng are the average temperature and number of atoms for one cell, respectively. If atom i is one of silicon atoms of the substrate, vc will be the instantaneous velocity for the mass center of the silicon atoms at the cross-section. If atom i is one of atoms of the silica cluster, vc will be the instantaneous velocity for the mass center of the cluster.
Fig. 4. Pressure curves of transformation zone at the impact loading stage under the normal impact with 4313 m/s. (a, c, e) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the dry impact, respectively. (b, d, f) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the wet impact, respectively.
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Fig. 5. Cross section of the temperature distribution in the transformation zone at the different moments under the wet normal impact with 4313 m/s. (a) t = 650 fs, (b) t = 1000 fs, (c) t = 1700 fs, (d) t = 2100 fs, (e) t = 2600 fs, (f) t = 3500 fs, (g) t = 8000 fs, (h) t = 20,000 fs.
Fig. 5 describes the typical changing profile of the local temperature of the impact zone during the wet impact process. The local temperature will increase at the impact loading stage and decrease at the impact unloading stage. Then it will increase again and form the second peak value at the cluster rebounding stage. This is similar to that under the dry impact [25]. As shown in Tables 2–4, the crystallographic orientation has a significant effect on the local temperature of the impact zone under the dry impact. The local temperature of the Si(1 1 0) substrate
Table 2 The local temperatures of impact zone at different moments under the dry impact on the Si(0 0 1) substrate with 4313 m/s. T1, T2, T3, and T4 are the moment of the maximum FZ, the deepest penetration position of the cluster, the second peak value of the local temperature of the impact zone, and the minimum FZ, respectively. FZ is the Z component of resultant forces of cluster atoms [25,27].
Table 3 The local temperatures of impact zone at different moments under the dry impact on the Si(1 1 0) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1200–3500 1200–3900 1200–4300 1200–4300 1200–3700 1200–3600
800–2400 800–2700 750–2700 800–3000 800–3200 800–3000
800–3000 750–3200 800–3500 1000–4200 1000–4300 1000–4300
700–2000 750–2300 700–2700 750–2400 700–2200 700–2100
Table 4 The local temperatures of impact zone at different moments under the dry impact on the Si(1 1 1) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2.
Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1500–4200 1500–4500 1500–4200 1500–4000 1500–4400 1500–4000
1000–2800 1000–2800 1000–2700 1000–3100 1000–3100 1000–3000
1000–3900 1000–4000 1000–4000 1000–4100 1000–4100 1000–4000
700–2400 800–2500 800–2500 800–2300 800–2200 750–2200
0 15 30 45 60 75
1200–3800 1200–4000 1200–4500 1200–4200 1200–4200 1400–3700
800–2600 800–2600 800–2700 800–3200 800–3500 800–3300
800–3000 800–3300 800–3500 1000–4000 1000–4000 1000–4000
700–2100 700–2300 750–2700 650–2200 700–2400 700–2200
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Table 5 The local temperatures of impact zone at different moments under the wet impact on the Si(0 0 1) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1000–3200 1000–3200 1000–3000 850–2500 800–2300 650–1700
700–2200 750–2300 750–2400 700–2200 750–2200 600–1650
800–2600 800–2700 800–2700 800–2700 750–2700 600–1650
600–1800 650–1800 600–1900 600–1800 500–1400 375–550
Table 6 The local temperatures of impact zone at different moments under the wet impact on the Si(1 1 0) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1000–3000 1000–3300 1000–3000 800–2500 750–2200 700–1600
750–2200 750–2100 750–2200 750–2400 750–2300 650–1600
800–2600 800–2800 800–2700 800–2800 800–2700 650–1600
650–1900 600–2000 650–2100 600–2000 550–1400 350–550
[10]. Therefore, it can be speculated that the content of semi-Si-II and semi-bct5-Si in the Si(0 0 1) substrate during the impact could be higher than that in the Si(1 1 1) substrate. The impact zone of Si(0 0 1) substrate could absorb more heat than that of Si(1 1 1) substrate during impact process. This is further validated by the simulation that the local temperature of the Si(0 0 1) substrate is higher than that of the Si(1 1 1) substrate in the same dry impact conditions (Tables 2–4). Furthermore, the speculation might be experimentally validated by an apparatus, which is used to monitor the change of contact resistance during the impact. This apparatus could be similar to the commonly used in situ electrical measurement apparatus under indentation load [3,7]. As shown in Tables 5–7, the local temperature of impact zone under the wet impact is obviously lower than that under the dry impact in the same other conditions. It is speculated that the water film could absorb partial heat and inhibit the temperature rising of the impact zone. Moreover, the crystallographic orientation has no significant effect on the local temperature of the impact zone under the wet impact. It could be supported by a conjecture that the variation of the local temperature of different crystallographic orientation substrates will become less when the temperature itself is in lower level. 4.3. Vcr affected by crystallographic orientation
Table 7 The local temperatures of impact zone at different moments under the wet impact on the Si(1 1 1) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1000–3200 1000–3100 1000–3300 800–2600 750–2300 650–1600
750–2200 750–2000 750–2300 750–2300 750–2300 650–1800
750–2600 800–2500 800–2600 800–2700 800–2600 650–1700
700–2000 650–1800 700–1800 700–1900 600–1500 375–650
is lower than that of the Si(0 0 1) substrate when the cluster impacts on the substrate in the same dry impact conditions. The local temperature of the Si(1 1 1) substrate is closed to that of the Si(1 1 0) substrate. The simulation result shows that c-Si transforms into a locally ordered transient structure during impact loading and later transforms into an amorphous phase during impact unloading [40]. The transient structure seems to be a mixture of semi-Si-II and semibct5-Si, which is metallic and has a good conductor of electricity and heat. Therefore, the higher the content of the mixture in the impact zone, the more heat will be absorbed by the impact zone. The results of previous indentation experiment have shown that Si-II phase and amorphous silicon are prone to be observed on the Si(1 0 0) and Si(1 1 1) substrate under the indenter, respectively
According to above two sections, the local pressure of the impact zone is not affected by the crystallographic orientation under the dry impact, and the local temperature of the Si(1 1 0) substrate is lower than that of the Si(0 0 1) in the same impact conditions. However, the local temperature of the Si(1 1 1) is closed to that of the Si(1 1 0) substrate. This finding coincides with another simulation result, which demonstrates that the Vcr of Si(110) is the largest among three crystallographic orientations, Si(1 1 1) the second, followed by Si(0 0 1) (Fig. 6a). Under the wet impact, the local pressure and temperature of the impact zone are not affected by the crystallographic orientation, as illustrated in Fig. 4 and Tables 5– 7. This finding coincide with the simulation result, which demonstrates that the Vcr of Si(0 0 1) is same to that of Si(1 1 0) or Si(1 1 1) substrates (Fig. 6b). The explanation of these coincidences can be referred to Ref. [25]. 4.4. Vcr affected by incidence angle of the cluster Fig. 6(a) illustrates that Vcr reaches its minimum at the incidence angle of 45° under the dry impact. As previously stated, Vcr is related to local temperature, local pressure and crystallographic slip. Tables 2–4 demonstrates that the local temperature of the impact zone is not affected by the incidence angle under the dry impact. In addition, our previous study shows that the local pressure of the impact zone decreases with the increase of the incidence angle [25]. Moreover, the effect of crystallographic slip on
Fig. 6. Variation of the critical velocity of extrusion formation (Vcr) in different impact conditions at 20,000 fs. (a) The dry impact, (b) the wet dry.
R.L. Chen et al. / Nuclear Instruments and Methods in Physics Research B 270 (2012) 133–139
the formation of extrusion is the strongest at the incidence angle of 45°, since the glide planes of c-Si are along {1 1 1} planes. Therefore, Vcr shall indeed approximate its minimum at the incidence angle of 45°. However, Fig. 6(b) shows that Vcr reaches its minimum at the incidence angle of 30° under the wet impact. Tables 5–7 show that the local temperature is closely affected by the incidence angle under the wet impact. The local temperature changes insignificantly when the incidence angle varies from 0° to 30°, and it decreases when the angle is above 30°. Meanwhile, the local pressure of the impact zone is decreasing by the increased incidence angle. Considering the relationship between the crystallographic slip and impact angle, Vcr under the wet impact shall indeed approximate its minimum at the incidence angle of 30°. 5. Conclusions The effects of crystallographic orientation on the extrusion of silicon surface by the impact of a large silica cluster are concluded as follows. (1) The crystallographic orientation has no significant influence on the cross-section of the crater when a large silica cluster impacts on a silicon surface in either dry or wet condition. The phenomenon is different from the ion bombardment, under which the cross-section of the crater is affected by the crystallographic orientation. Under the dry impact, the cross-section of crater exhibits a trapezoid shape regardless of the crystallographic orientation. However, the cross-section of crater exhibits a semicircular shape regardless of the crystallographic orientation under the wet impact because of the buffering effect of water film. The inner layer of the crater after a wet impact is obviously smoother than that after a dry impact. (2) The extrusion pattern is largely determined by the crystallographic orientation of the impacted surface in both the dry and wet conditions. The patterns on the surfaces of (0 0 1)-, (0 1 1)- and (1 1 1)-oriented c-Si appear to have four, two, and threefold symmetries, respectively. This phenomenon coincides with that after a nanoindentation or ion bombardment. (3) Under the dry impact, the critical velocity of the extrusion formation on the silicon surface is affected by the crystallographic orientation. Among the substrates with three different crystallographic orientations, the critical velocity of the extrusion on the Si(1 1 0) substrate under the dry impact is the largest, followed by Si(1 1 1) substrate, and Si(0 0 1) substrate is the smallest. However, the crystallographic orientation has no influence on the critical velocity of the extrusion under the wet impact. The critical velocity under the wet impact is obviously higher than that under the dry impact because of the hindrance effect and reduced temperature of water film. (4) The critical velocity of the extrusion reaches its minimum at the incidence angle of 45° under the dry impact. However, the critical velocity reaches its minimum at the incidence angle of 30° under the wet impact.
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Acknowledgements This work is supported by NSFC (Nos. 50905104, 90923016, 91023016), 973 program (No. 2009CB724201), Tribology Science Fund of State Key Laboratory of Tribology (No. SKLTKF09A04), Leading Academic Discipline Project of Shanghai Municipal Education Commission (No. J50102), Specialized Research Fund for Selection and Cultivation of Outstanding Young Teachers in Shanghai Higher Education (No. SHU09060), and Innovative Foundation of Shanghai University. References [1] G.M. Pharr, W.C. Oliver, D.C. Harding, J. Mater. Res. 6 (1991) 1129. [2] J.E. Bradby, J.S. Williams, J.W. Leung, P. Munroe, Appl. Phys. Lett. 77 (2000) 3749. [3] J.E. Bradby, J.S. Williams, M.V. Swain, Phys. Rev. B 67 (2003) 085205. [4] R. Pérez, M.C. Payne, A.D. Simpson, Phys. Rev. Lett. 75 (1995) 4748. [5] K. Mylvaganam, L.C. Zhang, P. Eyben, J. Mody, W. Vandervorst, Nanotechnology 20 (2009) 305705. [6] Y.B. Gerbig, S.J. Stranick, D.J. Morris, M.D. Vaudin, R.F. Cook, J. Mater. Res. 24 (2009) 1172. [7] M.C. Gupta, A.L. Ruoff, J. Appl. Phys. 51 (1980) 1072. [8] R.G. Jasinevicius, J.G. Duduch, P.S. Pizani, Mater. Lett. 62 (2008) 812. [9] Y.H. Lin, T.C. Chen, P.F. Yang, S.R. Jian, Y.S. Lai, Appl. Surf. Sci. 254 (2007) 1415. [10] D.E. Kim, S.I. Oh, Nanotechnology 17 (2006) 2259. [11] J.D. Kiely, J.E. Houston, Phys. Res. B 57 (1998) 12588. [12] R. Smith, D. Christopher, S.D. Kenny, Phys. Res. B 67 (2003) 245405. [13] Y. Wang, D. Raabe, C. Klüber, F. Roters, Acta Mater. 52 (2004) 2229. [14] H.P. Chen, R.K. Kalia, A. Nakano, P. Vashiishata, I. Szlufarska, J. Appl. Phys. 102 (2007) 063514. [15] J. Samela, K. Nordlund, V.N. Popok, E.E.B. Campbell, Phys. Rev. B 77 (2008) 075309. [16] T.J. Colla, R. Aderjan, R. Kissel, H.M. Urbassek, Phys. Rev. B 62 (2000) 8487. [17] T. Diaz de la Rubia, G.H. Gilmer, Phys. Rev. Lett. 74 (1995) 2507. [18] S.J. Carroll, P.D. Nellist, R.E. Palmer, S. Hobday, R. Smith, Phys. Rev. Lett. 84 (2000) 2654. [19] Y. Yamaguchi, J. Gspann, Phys. Rev. B 66 (2002) 155408. [20] T. Aoki, J. Matsuo, Nucl. Instrum. Methods Phys. Res. B 228 (2005) 46. [21] M. Henkel, H.M. Urbassek, Nucl. Instrum. Methods Phys. Res. B 145 (1998) 503. [22] Z. Insepov, I. Yamada, Nucl. Instrum. Methods Phys. Res. B 153 (1999) 199. [23] Z. Insepov, R. Manory, J. Matsuo, I. Yamada, Phys. Rev. B 61 (2000) 8744. [24] L.P. Allen, Z. Insepov, D.B. Fenner, C. Santeufemio, W. Brooks, J. Appl. Phys. 92 (2002) 3671. [25] R.L. Chen, J.B. Luo, D. Guo, X.C. Lu, J. Appl. Phys. 104 (2008) 104907. [26] C.Y. Tang, L.C. Zhang, Nanotechnology 16 (2005) 15. [27] R.L. Chen, J.B. Luo, D. Guo, H. Lei, J. Appl. Phys. 108 (2010) 073521. [28] J.F. Luo, A. David, IEEE Trans. Semicond. Manuf. 14 (2001) 112. [29] A. Kubota, H. Mimura, K. Inagaki, Y. Mori, K. Yamauchi, J. Electrochem. Soc. 153 (2006) G874. [30] F.L. Duan, J.B. Luo, S.Z. Wen, J.X. Wang, Chin. Sci. Bull. 50 (2005) 1661. [31] J.Y. Wang, X.W. Wang, J. Rifkin, D.X. Li, Chin. Phys. Lett. 18 (2001) 1386. [32] T. Watanabe, H. Fujiwara, H. Noguchi, Jpn. J. Appl. Phys. Part 2 38 (1999) L366. [33] M. Rovere, M.A. Ricci, D. Vellati, F. Bruni, J. Chem. Phys. 108 (1998) 9859. [34] W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, M.L. Klein, J. Chem. Phys. 79 (1983) 926. [35] Y.B. Gerbig, S.J. Stranick, R.F. Cook, Scr. Mater. 63 (2010) 512. [36] Q.H. Tang, F.H. Chen, J. Phys. D: Appl. Phys. 39 (2006) 3674. [37] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987. [38] C.L. Cleveland, U. Landman, Science 257 (1992) 355. [39] H. Haberland, Z. Insepov, M. Moseler, Phys. Rev. B 51 (1995) 11061. [40] R.L. Chen, J.B. Luo, D. Guo, X.C. Lu, Nucl. Instrum. Methods Phys. Res. B 266 (2008) 3231.
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Effect of crystallographic orientation on the extrusion of silicon surface during an impact: Molecular dynamics simulation Ruling Chen a,⇑, Jianbin Luo b, Dan Guo b, Xiao Hu c, Hong Lei a a
Nano-Science and Nano-Technology Research Center, Shanghai University, Shanghai 200444, China State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China c Sauer-Danfoss (US) Company, Plymouth, MN 55447, USA b
a r t i c l e
i n f o
Article history: Received 14 April 2011 Received in revised form 16 September 2011 Available online 22 September 2011 Keywords: Crystallographic orientation Extrusion Crystalline silicon Impact Molecular dynamics simulation
a b s t r a c t Molecular dynamic simulation was applied in analyzing the effect of crystallographic orientation on the extrusion formation of silicon surface during the impact of a large silica cluster in dry and wet condition, respectively. The crystallographic orientation would have no obvious influence on the cross-section of crater created by the impact in either dry or wet conditions. The cross-section of crater appeared to be trapezoid shape and semicircular shape after the dry and wet impact, respectively. The inner layer of the crater after a wet impact was smoother than that after a dry impact. The extrusion patterns on the surfaces of (0 0 1)-, (0 1 1)- and (1 1 1)-oriented silicon single crystals had four, two, and threefold symmetries, respectively. Moreover, the critical velocity of the extrusion formation on Si(1 1 0) substrate under the dry impact would be the largest, followed by Si(1 1 1) substrate, and Si(0 0 1) substrate was the smallest. The critical velocity reached to its minimum when the impact had an incidence angle of 45°. However, the crystallographic orientation would have no influence on the critical velocity of the extrusion under the wet impact, and the critical velocity reached its minimum at the incidence angle of 30°. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction The phenomenon of an extruded silicon surface was at first observed by Pharr et al. in 1991 through indentation experiment [1]. It is meaningful to understand the atomic scale material removal mechanism in the ultra-precision machining processes by studying the mechanism of extrusion of silicon surface under different dynamic loadings including indentation loading and impact loading. Experiments [2,3] and simulations [4,5] have shown that the monocrystal silicon (c-Si) under an indentation load has a localized transformation from a diamond-cubic phase (Si-I) to a metallic phase with a b-Sn structure (Si-II). The phase transformation zone under the indenter is enlarged by the increased load. When the transformed metallic Si-II zone extends to the radius of contact between the indenter and silicon surface, the material under indenter is able to flow plastically resulting in a metal-like extrusion. The formation of extrusion on the silicon surface depends strongly on the settings of the indentation including maximum force, loading and unloading rate, geometry of indenter, and crystallographic orientation of silicon substrate. Gerbig et al. demonstrated that the crystallographic orientation has an influence on
⇑ Corresponding author. E-mail address: [email protected] (R.L. Chen). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2011.09.013
the critical contact pressure of phase transformation during the indentation of c-Si substrate [6,7]. The critical contact pressure for orientation Si(1 1 0) or Si(1 1 1) is lower than that for Si(0 0 1) at the indentation loading stage. However, it is higher at the indentation unloading stage. Jasinevicius et al. demonstrated that the formation of multiple structure phases on the silicon surface under cyclic microindentation experiment is affected by the crystallographic orientation and number of successive cycles [8]. The molecular dynamics simulation results indicated that the crystallographic orientation of silicon surface has an influence not only on the phase transformation, but also on the distribution and the volume of the transformed region under indentation load [9,10]. In addition, some researchers have studied the effect of crystallographic orientation on the extrusion patterns on the surface of crystalline Au [11], Fe [12], Cu [13], and SiC [14], respectively. Since localized high pressure and high temperature could be induced by an impact, the extrusion of silicon surface could have a different mechanism as compared with the case of indentation loading. In the past two decades, extensive molecular dynamics simulations have been conducted to study the formation of crater for a silicon surface under the impact of a cluster [15–24]. The rim around the crater (namely extrusion) after the impact has indeed been observed. However, the small clusters (with less than 1000 atoms) and ultra-high impact velocities indicate that these studies could be mainly adapted to the process of ion bombardment on the
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silicon surface. During an ion bombardment, the extrusion may result from the sputtering and redepositing of lower energetic atoms in the plastic deformation zone [15]. Two typical studied topics are: the relationship between the depth of crater and the incident energy of impact [21–23]; the evolution of crater shape in case of different types of cluster and crystal orientations of silicon substrate [24]. However, most of these studies emphasize on the formation mechanism of crater rather than its rim. It is well known that the topography of crater after impact should be affected by the momentum transfer during the impact process, which is related to impact velocity, size and type of cluster [16,21]. Based on our previous study [25], it has been suggested that the mechanism of extrusion on silicon surface under the impact of a large silica cluster with a relative low impact velocity is different from that under the ion bombardment or indentation. During the impact of large silica cluster, the silicon surface is extruded by the combinational effects of thermal spread, phase transformation and crystallographic slip. It has been also found that the extrusion on silicon surface is in embryo at impact unloading stage and growing up at the cluster rebounding stage. However, no specific result has been reported so far on the effect of crystallographic orientation on extrusion formation when a large silica cluster impacts on a silicon surface. Though the effect of water on the deformation of silicon under indentation [26] or on the phase transformation of silicon under impact [27] has been studied by molecular dynamics simulations, most of which were limited to the cluster–surface interactions in a condition with no water (namely dry indentation or dry impact) [10,20,21]. However, the water solution is indispensable to the ultra-precision surface machining processes such as chemical mechanical polishing (CMP) [28] and elastic emission machining (EEM) [29]. Molecular dynamic study of the extrusion formation under a wet impact is supposed to provide an atomistic insight into the material removal in the ultra-precision surface machining process. The study reported in this paper is to identify the influence of crystallographic orientation on the extrusion formation of c-Si surface, which is impacted by large silica clusters with relative low velocity as described in our previous researches [25,30]. A set of molecular dynamics simulations for both dry and wet impact have been conducted by varying impact velocity, incidence angle, and crystallographic orientation. 2. Simulation methodology In this study, MD simulations were performed by a modification of the XMD simulation package (Version 2.5.32) from University of Connecticut [31]. Fig. 1 shows the simulation model of the impact of silica clusters toward silicon substrate under the dry and wet impact, respectively. For wet impact, the water layer with a density of 0.997 g/cm3 and a thickness of 10 Å, was over the silicon substrate initially. The c-Si substrates, including Si(0 0 1), Si(1 1 0) and Si(1 1 1), were adopted. The dimensions of these substrates under the dry impact and wet impact are listed in Table 1. The outer
layers (four atomic layers) of the substrate were fixed in space with the exception of the top contact surface. Thermostat layers (eight atomic layers) had been used to ensure reasonable outward heat conduction away from the control volume. The interatomic interaction in the silica cluster–silicon substrate system was modeled by a Stillinger–Weber-like potential [32]. As for the silica cluster surface, the bridging oxygen (BO) atom and the non-bridging oxygen (NBO) atom were separated, and the BO atom was bonded to two adjacent silicon atoms. All NBO atoms with a dangling free bond were saturated with hydrogen atoms. The hydrogen atom was placed at an equilibrium distance (0.95 Å) away from a NBO atom with a Si–O–H angle of 116° [33]. In the simulation, the model TIP4P [34] was used as water molecules. The interaction between the water molecules and the cluster atoms was described as a potential modeled according to Ref. [33], where different Lennard-Jones (LJ) parameters and fractional charges were assumed for BO and NBO. All the pair interactions were truncated at a cutoff radius of 9 Å, and reaction field corrections for TIP4P were applied. The Ewald summation method was not adopted because of the large simulation ensemble in this study. The interaction between the water molecules and the substrate silicon atoms was described as a Lennard-Jones potential modeled according to Ref. [26]. The cutoff radius for the Lennard–Jones interaction was 8.47 Å. In addition, the simulation ensemble will breakdown when the high-energy repulsive parts of the potentials are not solved. In this study, we treated this problem by some simple ways not by ZBL potential. As shown in Eq. (1), the function of M(r) was adopted.
8 Prototype of potential functionsðUðrÞÞ r > r0 > > > < ðsuch as Wantanabe; LJ; Columb PotentialÞ > Modification of potential functionsðMðrÞÞ r r0 > > : ðMðrÞ ¼ A r2 þ B r þ CÞ:
ð1Þ
And the coefficients of A, B, C were solved by the Eq. (2).
8 MðrÞjr¼r0 ¼ UðrÞjr¼r0 > < MðrÞ0 jr¼r0 ¼ UðrÞ0 jr¼r0 > : MðrÞ0 jr¼0 ¼ 10 MðrÞ0 jr¼r0 ;
ð2Þ
where r is the separation between two atoms. And the selection of the variable r0 was based on some tentative calculations. In this study, the amorphous silica cluster has 1728 silicon atoms and 3456 oxygen atoms. The cluster is a sphere with a diameter of around 54 Å. At the beginning of the simulation, the silica clusters were located 20 Å above the substrate surface. The simulation system was initiated with a temperature of 293 K. After a relaxation of 7000 fs, the initial velocities and incidence angles of the clusters were varied. The duration of one cluster’s impact lasted for 20,000 fs. During the simulation, the temperature of the thermostat atoms was kept at 293 K by using Gauss–Hoover method. And velocity rescaling at every 30 time steps was adopted to maintain the fixed temperature of the thermostat layer. We had performed the simulations with the different time steps (0.5 fs and 1.0 fs) in the wet conditions. The obvious difference between the simulation results by 0.5 fs and 1.0 fs was not noticed. So, the time step of 1.0 fs was adopted in order to improve the computational efficiency. 3. Effect of crystallographic orientation on the shape of crater and pattern of extrusion 3.1. Cross-section of crater
Fig. 1. The schematic diagram of the cluster impact on the crystal silicon substrate under (a) the dry impact, (b) the wet impact.
As shown in Fig. 2, the cross-section of the crater exhibits nearly trapezoid shapes under the dry impact due to the crystallographic
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Table 1 Dimensions of different crystallographic orientation substrates under the dry impact and wet impact. Impact conditions
Impacted substrates
Dimensions of silicon substrates (X Y Z) a0
Number of atoms in the simulation system
Dry impact
Si(0 0 1) Si(1 1 0) Si(1 1 1) 10 Å H2O/Si(0 0 1) 10 Å H2O/Si(1 1 0) 10 Å H2O/Si(1 1 1)
28 38 16 28 38 16 28 37 16 28 38 14 28 38 14 28 37 14
141,376 141,487 134,755 134,828 138,681 130,555
Wet impact
Notes: a0 = 5.43 Å, the lattice constant of c-Si.
Fig. 2. Side cross-section view of the impact zone at 20,000 fs under the normal impact with 7000 m/s. The magenta dots and blue dots present five and threefold silicon atoms, respectively. Cyan dots present silicon atoms with a coordination number under three. The rest of atoms present fourfold silicon atoms. (a, c, e) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the dry impact, respectively. (b, d, f) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the wet impact, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
slip, regardless of the different crystallographic orientation of the substrate. However, the cross-section of crater exhibits a nearly semicircular shape under the wet impact regardless of the different crystallographic orientation of the substrate (Fig. 2). And the inner layer of the crater after a wet impact is obviously smoother than that after a dry impact (Fig. 2). It is speculated that the density of the water film between the cluster and substrate may be increased with the decreasing of the clearance between them at the impact loading stage under the wet impact. In other words, the water film between the cluster and substrate may become the confined liquids. Therefore, the fluidity of the water film will descend. This may be similar to the solidification of the water film. The solidified water film may result in a more uniform distribution of the local pressure and temperature of the impact zone. So, in an ultra-precision surface machining, the water is not only the transfer medium of abrasive and chemical matters, but also is contributing to a better surface quality of the machined surface. Therefore, the crystallographic orientation has no significant influence on the cross-section of the crater on a silicon surface impacted by a large silica cluster in dry or wet condition. The phenomenon is different from an ion bombardment, under which the cross-section of the crater is affected by the crystallographic orientation of the substrate. Allen et al. demonstrated that the cross-section of the crater has a triangular shape when an Ar cluster impacts on a Si(1 0 0) substrate [24]. However, the cross-section of the crater has a round shape when the Ar cluster impacts on a Si(1 1 1) substrate. This difference may be induced by the small
Fig. 3. Top view of the extrusion produced at 20,000 fs under the normal impact of the cluster. Pink atoms are above original impacted silicon surface. The rest of atoms are below the original silicon surface. (a–c) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the dry impact with 6500 m/s, respectively. (d–f) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the wet impact with 7000 m/s, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Ar cluster (about 135 Ar atoms) with the high impact energy (24 eV/atom). 3.2. Distribution pattern of extrusion 1Þ and (1 1 1) Under the dry impact, the primary slip planes ð1 1 0 intersect with the impacted plane (0 0 1) along the [1 1 0] and ½1 1 directions [13,25], resulting in a surface extrusion with a fourfold in-plane symmetry (Fig. 3). For the impacted (1 1 0) surface, the 1Þ and ð1 1 1Þ cross the impacted plane primary slip planes ð1 1 and ½2 1 1 directions, resulting in a surface extrualong the ½2 1 1 sion with a twofold in-plane symmetry [13,35]. For the impacted ð1 1 1Þ and ð1 1 1Þ intersect (1 1 1) surface, the slip planes ð1 1 1Þ; 0; ½0 1 1 and ½1 0 1 directions, and the impacted plane along ½1 1 exhibits a threefold in-plane symmetry [13,35]. Under the wet impact, the distributions of the surface extrusion for impact planes (0 0 1), (1 1 0) and (1 1 1) are similar to that under the dry impact resulting from the same mechanism of crystallographic slip (Fig. 3). Therefore, the distribution pattern of the extrusion under the impact of a large silica cluster is similar to the case of nanoindentation experiment [13] and ion bombardment experiment [24]. Such a coincidence may be related to the residual stress anisotropy in silicon substrate under indentation or impact loading [35]. 4. Effect of crystallographic orientation on the critical velocity of extrusion formation Simulation experiments for impacts with varied crystallographic orientation, impact velocity and incidence angle have been
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performed to further investigate the formation mechanism of surface extrusion. A critical velocity (Vcr) for the extrusion formation is defined when the height of extrusion reaches 5 Å (Fig. 2e). An indepth study on the mechanism of extrusion formation on the silicon surface during the impact process was reported in Ref. [25]. The simulation results showed that the thermal spread, phase transformation and crystallographic slip have an influence on the extrusion formation of silicon surface under the impact of a large silica cluster [25]. Therefore, the relationships between Vcr and the local temperature and pressure of the impact zone, and the crystallographic orientation of the substrate are analyzed as follows.
Both the virial pressure and temperature within the impact zone under the cluster were calculated. The impact zone was constructed around the cluster and the distance from the cluster surface is within 12 Å [36]. The local pressure of the impact zone of the substrate (P) is given by [37]
*N l X i¼1
+, mi v 2i
ð3 V l Þ þ
*N l X
*
*
F i ri
+, ð3 V l Þ
4.2. Local temperature affected by crystallographic orientation The local temperature of the cross-section is given by [38,39]
4.1. Local pressure affected by crystallographic orientation
P¼
of the impact zone, and h i denotes a statistical averaging over all simulation times. Fig. 4 illustrates that the local pressure of the impact zone at the impact loading stage is not affected by the crystallographic orientation under either the dry or wet impact, respectively. Moreover, there is no obvious difference in the local pressure in the same impact condition between the dry and wet impact. It indicates that the water film has no obvious influence on the local pressure of the transformation zone at the impact loading stage.
ð3Þ
i¼1
where Nl and Vl are the number of silicon atoms and volume of the impact zone. * mi and vi are the mass and the velocity of the atom i, * respectively. F i and r i are the force and position of the silicon atom i
Tg ¼
*N g X
+, 2
mi ðv i v c Þ
ð3 Ng kB Þ;
ð4Þ
i¼1
where kB is the Boltzmann constant. The cross-section passed through the center of the impact zone and is parallel to the direction of impact and has a thickness of 11 Å. The cross-section is divided into cubic cells of dimensions 11 11 11 Å. Tg and Ng are the average temperature and number of atoms for one cell, respectively. If atom i is one of silicon atoms of the substrate, vc will be the instantaneous velocity for the mass center of the silicon atoms at the cross-section. If atom i is one of atoms of the silica cluster, vc will be the instantaneous velocity for the mass center of the cluster.
Fig. 4. Pressure curves of transformation zone at the impact loading stage under the normal impact with 4313 m/s. (a, c, e) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the dry impact, respectively. (b, d, f) Are the Si(0 0 1), Si(1 1 0) and Si(1 1 1) substrate under the wet impact, respectively.
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Fig. 5. Cross section of the temperature distribution in the transformation zone at the different moments under the wet normal impact with 4313 m/s. (a) t = 650 fs, (b) t = 1000 fs, (c) t = 1700 fs, (d) t = 2100 fs, (e) t = 2600 fs, (f) t = 3500 fs, (g) t = 8000 fs, (h) t = 20,000 fs.
Fig. 5 describes the typical changing profile of the local temperature of the impact zone during the wet impact process. The local temperature will increase at the impact loading stage and decrease at the impact unloading stage. Then it will increase again and form the second peak value at the cluster rebounding stage. This is similar to that under the dry impact [25]. As shown in Tables 2–4, the crystallographic orientation has a significant effect on the local temperature of the impact zone under the dry impact. The local temperature of the Si(1 1 0) substrate
Table 2 The local temperatures of impact zone at different moments under the dry impact on the Si(0 0 1) substrate with 4313 m/s. T1, T2, T3, and T4 are the moment of the maximum FZ, the deepest penetration position of the cluster, the second peak value of the local temperature of the impact zone, and the minimum FZ, respectively. FZ is the Z component of resultant forces of cluster atoms [25,27].
Table 3 The local temperatures of impact zone at different moments under the dry impact on the Si(1 1 0) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1200–3500 1200–3900 1200–4300 1200–4300 1200–3700 1200–3600
800–2400 800–2700 750–2700 800–3000 800–3200 800–3000
800–3000 750–3200 800–3500 1000–4200 1000–4300 1000–4300
700–2000 750–2300 700–2700 750–2400 700–2200 700–2100
Table 4 The local temperatures of impact zone at different moments under the dry impact on the Si(1 1 1) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2.
Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1500–4200 1500–4500 1500–4200 1500–4000 1500–4400 1500–4000
1000–2800 1000–2800 1000–2700 1000–3100 1000–3100 1000–3000
1000–3900 1000–4000 1000–4000 1000–4100 1000–4100 1000–4000
700–2400 800–2500 800–2500 800–2300 800–2200 750–2200
0 15 30 45 60 75
1200–3800 1200–4000 1200–4500 1200–4200 1200–4200 1400–3700
800–2600 800–2600 800–2700 800–3200 800–3500 800–3300
800–3000 800–3300 800–3500 1000–4000 1000–4000 1000–4000
700–2100 700–2300 750–2700 650–2200 700–2400 700–2200
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Table 5 The local temperatures of impact zone at different moments under the wet impact on the Si(0 0 1) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1000–3200 1000–3200 1000–3000 850–2500 800–2300 650–1700
700–2200 750–2300 750–2400 700–2200 750–2200 600–1650
800–2600 800–2700 800–2700 800–2700 750–2700 600–1650
600–1800 650–1800 600–1900 600–1800 500–1400 375–550
Table 6 The local temperatures of impact zone at different moments under the wet impact on the Si(1 1 0) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1000–3000 1000–3300 1000–3000 800–2500 750–2200 700–1600
750–2200 750–2100 750–2200 750–2400 750–2300 650–1600
800–2600 800–2800 800–2700 800–2800 800–2700 650–1600
650–1900 600–2000 650–2100 600–2000 550–1400 350–550
[10]. Therefore, it can be speculated that the content of semi-Si-II and semi-bct5-Si in the Si(0 0 1) substrate during the impact could be higher than that in the Si(1 1 1) substrate. The impact zone of Si(0 0 1) substrate could absorb more heat than that of Si(1 1 1) substrate during impact process. This is further validated by the simulation that the local temperature of the Si(0 0 1) substrate is higher than that of the Si(1 1 1) substrate in the same dry impact conditions (Tables 2–4). Furthermore, the speculation might be experimentally validated by an apparatus, which is used to monitor the change of contact resistance during the impact. This apparatus could be similar to the commonly used in situ electrical measurement apparatus under indentation load [3,7]. As shown in Tables 5–7, the local temperature of impact zone under the wet impact is obviously lower than that under the dry impact in the same other conditions. It is speculated that the water film could absorb partial heat and inhibit the temperature rising of the impact zone. Moreover, the crystallographic orientation has no significant effect on the local temperature of the impact zone under the wet impact. It could be supported by a conjecture that the variation of the local temperature of different crystallographic orientation substrates will become less when the temperature itself is in lower level. 4.3. Vcr affected by crystallographic orientation
Table 7 The local temperatures of impact zone at different moments under the wet impact on the Si(1 1 1) substrate with 4313 m/s. The meanings of T1, T2, T3, and T4 are the same as in Table 2. Incidence angle (°)
T1 (K)
T2 (K)
T3 (K)
T4 (K)
0 15 30 45 60 75
1000–3200 1000–3100 1000–3300 800–2600 750–2300 650–1600
750–2200 750–2000 750–2300 750–2300 750–2300 650–1800
750–2600 800–2500 800–2600 800–2700 800–2600 650–1700
700–2000 650–1800 700–1800 700–1900 600–1500 375–650
is lower than that of the Si(0 0 1) substrate when the cluster impacts on the substrate in the same dry impact conditions. The local temperature of the Si(1 1 1) substrate is closed to that of the Si(1 1 0) substrate. The simulation result shows that c-Si transforms into a locally ordered transient structure during impact loading and later transforms into an amorphous phase during impact unloading [40]. The transient structure seems to be a mixture of semi-Si-II and semibct5-Si, which is metallic and has a good conductor of electricity and heat. Therefore, the higher the content of the mixture in the impact zone, the more heat will be absorbed by the impact zone. The results of previous indentation experiment have shown that Si-II phase and amorphous silicon are prone to be observed on the Si(1 0 0) and Si(1 1 1) substrate under the indenter, respectively
According to above two sections, the local pressure of the impact zone is not affected by the crystallographic orientation under the dry impact, and the local temperature of the Si(1 1 0) substrate is lower than that of the Si(0 0 1) in the same impact conditions. However, the local temperature of the Si(1 1 1) is closed to that of the Si(1 1 0) substrate. This finding coincides with another simulation result, which demonstrates that the Vcr of Si(110) is the largest among three crystallographic orientations, Si(1 1 1) the second, followed by Si(0 0 1) (Fig. 6a). Under the wet impact, the local pressure and temperature of the impact zone are not affected by the crystallographic orientation, as illustrated in Fig. 4 and Tables 5– 7. This finding coincide with the simulation result, which demonstrates that the Vcr of Si(0 0 1) is same to that of Si(1 1 0) or Si(1 1 1) substrates (Fig. 6b). The explanation of these coincidences can be referred to Ref. [25]. 4.4. Vcr affected by incidence angle of the cluster Fig. 6(a) illustrates that Vcr reaches its minimum at the incidence angle of 45° under the dry impact. As previously stated, Vcr is related to local temperature, local pressure and crystallographic slip. Tables 2–4 demonstrates that the local temperature of the impact zone is not affected by the incidence angle under the dry impact. In addition, our previous study shows that the local pressure of the impact zone decreases with the increase of the incidence angle [25]. Moreover, the effect of crystallographic slip on
Fig. 6. Variation of the critical velocity of extrusion formation (Vcr) in different impact conditions at 20,000 fs. (a) The dry impact, (b) the wet dry.
R.L. Chen et al. / Nuclear Instruments and Methods in Physics Research B 270 (2012) 133–139
the formation of extrusion is the strongest at the incidence angle of 45°, since the glide planes of c-Si are along {1 1 1} planes. Therefore, Vcr shall indeed approximate its minimum at the incidence angle of 45°. However, Fig. 6(b) shows that Vcr reaches its minimum at the incidence angle of 30° under the wet impact. Tables 5–7 show that the local temperature is closely affected by the incidence angle under the wet impact. The local temperature changes insignificantly when the incidence angle varies from 0° to 30°, and it decreases when the angle is above 30°. Meanwhile, the local pressure of the impact zone is decreasing by the increased incidence angle. Considering the relationship between the crystallographic slip and impact angle, Vcr under the wet impact shall indeed approximate its minimum at the incidence angle of 30°. 5. Conclusions The effects of crystallographic orientation on the extrusion of silicon surface by the impact of a large silica cluster are concluded as follows. (1) The crystallographic orientation has no significant influence on the cross-section of the crater when a large silica cluster impacts on a silicon surface in either dry or wet condition. The phenomenon is different from the ion bombardment, under which the cross-section of the crater is affected by the crystallographic orientation. Under the dry impact, the cross-section of crater exhibits a trapezoid shape regardless of the crystallographic orientation. However, the cross-section of crater exhibits a semicircular shape regardless of the crystallographic orientation under the wet impact because of the buffering effect of water film. The inner layer of the crater after a wet impact is obviously smoother than that after a dry impact. (2) The extrusion pattern is largely determined by the crystallographic orientation of the impacted surface in both the dry and wet conditions. The patterns on the surfaces of (0 0 1)-, (0 1 1)- and (1 1 1)-oriented c-Si appear to have four, two, and threefold symmetries, respectively. This phenomenon coincides with that after a nanoindentation or ion bombardment. (3) Under the dry impact, the critical velocity of the extrusion formation on the silicon surface is affected by the crystallographic orientation. Among the substrates with three different crystallographic orientations, the critical velocity of the extrusion on the Si(1 1 0) substrate under the dry impact is the largest, followed by Si(1 1 1) substrate, and Si(0 0 1) substrate is the smallest. However, the crystallographic orientation has no influence on the critical velocity of the extrusion under the wet impact. The critical velocity under the wet impact is obviously higher than that under the dry impact because of the hindrance effect and reduced temperature of water film. (4) The critical velocity of the extrusion reaches its minimum at the incidence angle of 45° under the dry impact. However, the critical velocity reaches its minimum at the incidence angle of 30° under the wet impact.
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