Phase transformations of mono-crystal silicon induced by two-body and three-body abrasion in nanoscale

Computational Materials Science 82 (2014) 140–150

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Phase transformations of mono-crystal silicon induced by two-body and three-body abrasion in nanoscale Jiapeng Sun a,⇑, Liang Fang a,⇑, Jing Han b, Ying Han a, Huwei Chen c, Kun Sun a,⇑ a

State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, Shaanxi Province, PR China School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu Province, PR China c Department of Applied Physics, School of Science, Xi’an Jiaotong University, Xi’an 710049, Shaanxi Province, PR China b

a r t i c l e

i n f o

Article history: Received 3 July 2013 Received in revised form 31 August 2013 Accepted 24 September 2013 Available online 20 October 2013 Keywords: Nanoindentation Two-body abrasion Three-body abrasion Mono-crystalline silicon Molecular dynamics

a b s t r a c t This article is focused on understanding the structural phase transformations of mono-crystalline silicon induced by nanoindentation, two-body and three-body abrasion at the nanoscale using the large-scale molecular dynamics simulation. The evolution and distribution of the possible phases are discussed in terms of coordination number (CN), radial distribution function (RDF), bond angle distribution function (ADF) and atom type tracking. The results show a new phase transformation route that is an initial diamond cubic silicon turns into high density amorphous (HDA) beneath the moving particle and then transforms into low density metastable amorphous (LDMA) behind the particle in both two-body and three-body abrasion. Considering the different phase transformation between nanoindentation and two/three-body abrasion, a stress criterion is proposed to predict the phase transformation, which can be generally applied to hydrostatic pressure experiment, nanoscale uniaxial compression and nanoindentation. For nanoindentation, a common misunderstanding of a metastable phase is clarified, which is also observed in front of the moving particle in two/three-body abrasive. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Motivated by the extensive application in continuously shrinking modern electronic devices, the single crystal silicon has been investigated intensively in the past few decades in order to deeply understand its mechanical behavior at the micro/nanoscale. In particular, the phase transformation mechanisms of the mono-crystalline silicon under various mechanical loadings, led by hydrostatic pressure, nanoindentation, nanoscratching and nanotribology, have been attracting considerable attention. Since the pioneering work of Minomura and Drickamer [1], earlier studies are focused on the high-pressure phase transformation under the hydrostatic pressure using the diamond-anvil cell (DAC) experiments. It has been well known that the bulk silicon undergoes first phase transformation of the diamond cubic phase (Si-I) to the dense body-centered-tetragonal metallic b-tin phase (b-Si or Si-II) at 10–13 GPa [2–4]. Larger hydrostatic pressures, then, lead to a sequence of transitions to other high-pressure phase, such as, Si-V, Si-VI, Si-VII, Si-X and Si-XI. During depressurization process, the highpressure phases do not recover to the ground-state Si-I structure, but to other denser metastable phases with fourfold coordination depending on the pressure release rate. Slow pressure release from ⇑ Corresponding authors. E-mail addresses: [email protected] (J. Sun), [email protected] (L. Fang), [email protected] (K. Sun). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.09.055

the Si-II results in the rhombohedra r8 phase (Si-XII) at 10 GPa, which then transforms into the body-centered-cubic bc8 phase (Si-III) at 2 GPa [5,6]. For fast unloading, the Si-II turns into amorphous silicon on the contrary [7–9]. As a standard tool for probing the nanoscale mechanical behavior of materials, the nanoindentation has been extensively applied to understand the phase transformation mechanism of mono-crystalline silicon. A unique high load by the nanoindentation is applied to a very small local region, which makes it possible to understand the mechanical deformation at the nanoscale. In contrast to the DAC experiments, nanoindentation induces not only hydrostatic pressure but also high shear stress which has been reported to lower the threshold for the onset of the phase transformation [10] and promote a new phase not observed under hydrostatic conditions [11,12]. In situ electrical measurements show that the semiconductor like Si-I transforms into a material with more metallic character during loading [13–15], which is believed to the b-Si recorded by hydrostatic pressure tests. The molecular dynamics simulations, however, indicate that the Si-I transforms into two types of body-centered-tetragonal phase i.e. b-Si and bct5 with fivefold coordination [16–18]. Recently, the in situ Raman microspectroscopy experiment confirms the formation of mixture of b-Si and bct5 during nanoindenation [19]. The only suggested b-Si by the electrical measurements could be attributed to the similar metallic structure between bct5 and b-Si phase. During unloading, the bct5 and b-Si all could be transformed into a

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mixture of metastable bc8 (Si-III) and r8 (Si-XII) at a slow release rate. But most amorphous silicon is detected in the residual contact impressions for fast unloading rates [19–22]. The presence and distribution of residual phases after nanoindentation could be related to the crystallographic anisotropy and in homogeneity of the stress distribution [22,23]. Comparing with the considerable understanding of the phase transformation induced by the nanoindentation and hydrostatic pressure, the phase transformation and deformation mechanism is still an open question on the nanotribology, including two-body abrasion and three-body abrasion. With the aid of the molecular dynamics, Zhang and Tanaka [24] reports that amorphous phase transformation is the main deformation mechanism during twobody and three-body abrasion. Wu et al. [25] suggest an alternative phase transformation route under the nano-grinding conditions: the initial Si-I phase transforms into amorphous silicon, which is in turn partially transformed into a mixture of metastable bc8 (Si-III) and r8 (Si-XII) embedded in amorphous silicon. Apparently, the phase transformations are related to the loading status and velocity. From the nanoscratching experiments, Huang et al. [26] reports that amorphous silicon is the only phase at a low stress, but the amorphous silicon can be recrystallized into Si-I nanocrystal, metastable bc8 (Si-III) and r8 (Si-XII) embedded in amorphous silicon at a sufficient stress. Gassilloud [27] finds that Si-XII can appear within the amorphous silicon region at a low loading speed, but only amorphous silicon exists at a high loading speed after nanoscratching. At a large load, dislocations can be initiated. The molecular dynamics simulations [28] confirm the amorphous transformation at a relatively small load, and suggest that nanotwins will be emerged at a large load. However, there is no direct evidence that confirms the transformed metastable bc8 (Si-III) and r8 (Si-XII) from the amorphous silicon in the previous experiments or simulations. Two/three-body abrasion induced phase transformation at the nanoscale is not only the basic science, but also related to engineering applications. Besides the Micro-Electro Mechanical Systems (MEMS), the specific applications, where the abrasion at the nanoscale becomes critical, include chemical–mechanical polishing (CMP), probe-based data storage devices and semiconductor processing equipment. From above short review, it follows that the structural phase transformation as well as the mechanism are far less clear in two-body abrasion and three-body abrasion. Even until now, we almost know nothing about three-body abrasion induced phase transformation, compared to abundant research on nanoindentation and DAC experiment. Hence, investigations on the deformation and phase transformation of mono-crystalline silicon induced by two/three-body abrasion are still interesting, and a promote understanding of the possible phase transformation as well as the mechanism is required. This article is intended to evaluate the structural phase transformation and deformation of mono-crystalline silicon induced by nanoindentation, two-body and three-body abrasion at the nanoscale. Large-scale molecular dynamics simulations are carried out on the (1 0 0) surface of mono-crystalline silicon based on Tersoff potential as described in Section 2. The techniques of coordination number (CN), radial distribution function (RDF), bond angle distribution function (ADF) and atom type tracking are used to monitor and elucidate the phase transformation. The detailed phase distributions and structure characteristics in nanoindentation and two/three-body abrasion are described in Section 3. The possible experiment and theoretical evidences are also provided. The phase transformation route in two/three-body abrasion, stress mechanisms and criterion to predict the phase transformation are presented in separate subsections of Section 4. The possible phase transformation in three-body abrasion is also investigation. Finally, generalization and conclusions are presented in Section 5.

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2. Methods Large scale molecular dynamics simulations are performed based on the Tersoff potential [29] for silicon atoms. Because the Tersoff potential gives the correct cohesive energies for the different phase, it has been extensively employed to predict the phase transformation. The interactions between the silicon atoms and the diamond atoms as abrasive particle are modeled by the Morse potential [30]. All of the simulations are performed utilizing the Verlet integration algorithm with a time step of 2.5 fs by LAMMPS [31] molecular dynamics simulation code. A commonly used model of two-body abrasion is adopted as illustrated in Fig. 1(a), where a spherical diamond particle with radius 10.86 nm slides with constant velocity in (1 0 0) silicon substrate surface. Because of the large hardness compared with silicon, the diamond particle is considered as a rigid body. To avoid the boundary effect a large silicon substrate consists of 2, 834, 079 atoms in total with a dimensions of 70.60  16.29  32.59 nm along x-, y-, and z-directions. The sliding is along the x-directions, and the indenting is along the y-directions. Periodic boundary conditions are applied in both x- and z- directions, but free boundary is set along the y-direction. A 1 nm thick layer on the bottom of the substrate is fixed to provide structural stability. To dissipate excessive thermal energy generated by loading and sliding, Langevin thermostat [32] is applied to a 1.6 nm thick layer of atoms adjacent to the rigid layers. All the remaining layers are free moved according the Newton motion equations. The silicon atoms are initially arranged in a diamond cubic structure with a constant lattice parameter of 0.5431 nm and then equilibrated at 300 K for 50 ps using the Nose–Hoover thermostat [33,34]. Subsequently, the particle is moved toward the silicon substrate to the defined indentation depth with a constant velocity of 100 m/s along the y-direction. After 50 ps relaxation, the particle is scratched along the crystal orientation of [1 0 0] in the (0 1 0) crystal plane with a constant sliding velocity of 100 m/s. The normal and lateral force is timely calculated by accumulating all the vertical and horizontal interaction forces where the substrate atoms contact with the particle atoms during simulation. Since the pioneering work of Zhang and Tanaka [24], the existing molecular dynamics simulations of three-body abrasion all utilize the modified two-body abrasion model by adding the

Fig. 1. The atomic model of the (a) two-body abrasion and (b) three-body abrasion.

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self-rotation to the particle [35–37]. We consider this modified model is not realistic. Generally, the motion of the particle is derived by the moving first body in three-body abrasion. Hence the movement pattern of the particle is not known in advance and should be able to obtain from the simulation. In the present paper, a new model for three-body abrasion is proposed, as shown in Fig. 1(b). In this model, a diamond particle is placed between two single crystal silicon substrates (first body) with a distance of 0.54 nm. The size of the abrasion and substrate, boundary conditions and other parameters are in correspondence with two-body abrasion model as mentioned above. At the first stage of simulation, both substrates are moved toward the particle perpendicularly at a constant velocity 100 m/s. After 50 ps relaxation, one of the two substrates moves horizontally along the [1 0 0] orientation on the (0 1 0) crystal plane at a constant sliding velocity of 200 m/s, but the other substrate remains motionless. Similar to the simulation of two-body abrasion, the normal and lateral force is calculated by adding all the vertical and horizontal interaction forces of the substrate atoms acting on the particle atoms respectively during simulation. In the course of nanoindentation, five phases (Si-I, Si-II, Si-III, Si-XII and bct5 phase) were observed and classified in the previous experiment [11] and simulation results [12,18]. In order to identify these phases, the techniques of coordination number (CN), radial distribution function (RDF) and bond angle distribution function (ADF) are applied jointly in this work. Although RDF and ADF are widely employed to classify the crystal structures, both the techniques become powerless when different phases are mixed together in a small volume as in the nanoindentation. In this work, CN is firstly applied to identify the phase structures and profile the phase region and phase distribution, because CN just consider the surrounding environments of an atom with a radius of 0.35 nm in current work. RDF and ADF are further used to verify and characterize the detailed phase structures within the congregating single-phase region identified by CN. Si-I phase has four nearest neighbors at a distance of 0.235 nm at ambient pressure. Si-II has four nearest neighbors at a distance of 0.242 nm and two at only slightly larger distance of 0.257 nm bct5 phase has one neighbor at a distance of 0.231 nm and four at 0.244 nm. Hence, Si-I, SiII and bct5 phase can be distinguished easily just considering the nearest neighbors with the maximum bond length of 0.28 nm in the present paper. Si-III phase and Si-XII both have four nearest neighbors within the distance of 0.237 nm and 0.239 nm respectively. Hence, Si-III/XII cannot be distinguished from Si-I just considering the nearest neighbors. However, Si-III has a unique non-bonded fifth neighbor at 0.341 nm at 2 GPa, and Si-XII has a unique one at 0.323 nm or 0.336 nm at 2 GPa [6], while Si-I has twelve non-bonded second neighbors at 0.383 nm. Based on this difference, fourfold coordinated silicon atoms, which have unique one non-bonded neighbor in the range from 0.28 nm to 0.35 nm, are assumed as metastable Si-III/XII phase with fourfold coordination. This phase identified method has been successfully used to distinguish the phase structures in the course of nanoindentation [12,6]. When the phases have been classified by CN, RDF and ADF are further used to verify and characterize the detailed phase structures within the congregating single-phase region. The typical dimension of Si-II, bct5 and Si-III/XII region is 1.9  1.4  1.8 nm, 2.2  1.7  2.5 nm and 5.4  3.1  5.4 nm located below the indenter in the current condition respectively. To avoid edge effects, the atoms located in a skin of 0.5 nm surrounding these singlephase region are not considered into the computation of both RDF and ADF, but taken into account the neighbors atoms. This computation region for RDF and ADF is sufficiently large to characterize the phase structure within a cut-off distance of 0.5 nm.

3. Results 3.1. Phase transformation during initial nanoindentation Fig. 2 illustrates the distribution of the transformed phases due to nanoindentation on the (1 0 0) silicon surface according to the coordination number with the indent depth 4.50 nm. The Si-II phase with sixfold coordination appears at the center and side of the transformed region along the [1 0 0] and [0 0 1] directions as shown in Fig. 2(a–c). The bct5 phase with fivefold coordination  0 1], [1  0 1]  and are around the Si-II phase along the [1 0 1], [1  directions as shown in Fig. 2(d and e), which is the silicon’s [1 0 1] slip direction. Several atom layers beneath the indenter are partially transformed into a mixture phase of Si-I and Si-III/Si-XII phases as shown in Fig. 2(a), but the initial diamond cubic structure remains in this region under the shallow indentation depth (not shown in the paper). The RDF, CN and ADF of atoms located at Si-II and bct5 region are computed to verify the high pressure phase as shown in Fig. 3. For comparison the RDF peaks of bct5 phase calculated by plane wave pseudopotential method [11] and Si-II phase calculated by Tersoff potential [38] are also shown in figure. Although the RDF peaks have slightly shifted which is attributed to the different calculated method and the severe deformation of the phase, the simulated peaks are agreed with the literatures. The RDF and ADF peaks confirm the formation of Si-II and bct5 phase. And the broadened and shifted RDF and ADF peaks indicate that the Si-II and bct5 phase undergo severe deformation. The observed phase distribution due to nanoindentation maintains consistent with the existing reports [12,18,39,40]. A lot of isolated metastable phase atoms near the periphery of the phase transformation region are observed along the [1 0 0] and [0 0 1] directions. Those metastable phase atoms are identified as Si-III/Si-XII atoms with four nearest neighbors within the distance of 0.28 nm and a unique one within distance of 0.35 nm as shown in Fig. 2 according to the CN [18]. After unloading the resulted metastable phase atoms during loading are changed to the diamond cubic phase (Si-I) in the present simulation, although the Si-III/Si-XII phases are generally observed during the retraction process in the experiments [6,19,22]. This metastable phase atoms is also observed in the Kim’s simulation of nanoindentation [18]. The RDF and ADF of those atoms are present in Fig. 4. For comparison those characteristics of diamond cubic phase are also shown in figure. All the RDF peaks are widely broadened, and the first peak slightly shifts to the left, but the second and third peak slightly shift to the right with respect to those of diamond cubic structure. An added small RDF peak is observed for the metastable atoms, which leads to the increased coordination number at distance of 0.35 nm and is responsible for the identified Si-III/SiXII phase, as shown in Fig. 4(a). In contrast to single sharp peak at 109° of the diamond cubic silicon that is characteristic of a perfect tetrahedral unit, a major peak at 112° and a small peak at 97.2° are examined in ADF for the metastable phase, which is discriminated from the bond angle of 118° and 99° in Si-III phase and 137° in Si-XII phase [5,6]. The splitting ADF peak suggests a distorted tetrahedral atomic arrangement for metastable phase. From above descriptions, the present authors consider that the metastable phase can be identified as the slightly distorted diamond cubic structure (DDS) rather than Si-III /Si-XII phase. In order to ascertain the phase transformation route, we track the alteration of atom type during indentation at the different indent depth as shown in Fig. 5. Kim and Oh [18] have ever suggested that the DDS atoms with fourfold coordination are the intermediate phase prior to the transformation to bct5 and Si-II phases. In the present paper, convincing evidence shows that the DDS atoms cannot transform into bct5 or Si-II phase, but partially turn into

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Fig. 2. Cross-section view of phase distribution induced by nanoindentation at the indent depth 4.50 nm. Silicon atoms in diamond cubic structure (Si-I) are invisible. (a)  0 1) plane. And top view corresponding to labeled depth, (c) T1, (d) T2, (e) T3 in (a). Central cross-section view on the (0 0 1) plane; (b) central cross-section view on the (1 Atoms are colored according to the coordination number. Sky blue, blue, red and golden ones are bct5, Si-II, Si-III/Si-XII atoms, and surface atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. RDF and ADF (g(h)) of the Si-II and bct5 phase.

diamond cubic atoms with increasing the indentation depth, and others are remained as shown in Fig. 5(a). The great majority of new formed bct5 atoms are directly formed by the Si-I atoms, and a fraction of bct5 atoms are derived from Si-II phase with increasing the indentation depth as shown in Fig. 5(b). The new formed Si-II phase is not only derived from Si-I atoms, but also from the bct5 atoms during indentation. It is interesting that the bct5 phase is observed prior to Si-II phase. 3.2. Phase transformation during two-body abrasion During two-body abrasion, four regions, i.e. initial indentation region, scratched region, beneath particle region and cutting chip region, are shed special light to investigate the phase distribution.

The distribution of the transformed phases due to two-body and three-body abrasion within different region is illustrated in Fig. 6 in different cross-section at the indent depth 4.50 nm. For comparison the phase distribution during nanoindentation is also shown in Fig. 6(i–k) at the same indent depth and cross-section. In the initial indentation region, the Si-II phase due to indentation has totally vanished when the particle departs from this region as shown in Fig. 6(a) and (c–e). Comparing the phase distribution in initial nanoindentation region (Fig. 6(i–k)) and scratched region (Fig. 6(a) and (c–e)), it is shown that nanoindentation induced Si-II phase and bct5 phase are mostly transformed into amorphous phase which is a mixture of atoms with coordination number equal to 4, 5 and 6. A small part of bct5 phase is still remained beneath the transformation region. After scratching the isolated DDS atoms

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particle, and thin bct5 phase locates at the bottom of the phase transformation region. The isolated DDS atoms can also be observed in front of the particle. This phase transformation in two-body abrasion is very different from the phase transformation induced by nanoindentation. After two-body abrasion, the amorphous phase is remained. A part of bct5 phase transforms into amorphous phase, and other part is remained as shown in Fig. 6(a) and (l–n). The transformation of atom type near the cross-section T4 in Fig. 6 is illustrated in Fig. 7(b). A similar transformation is found to that in the initial indentation region. In the cutting chip region, the amorphous phase is still the dominant phase. 3.3. Phase transformation during three-body abrasion The similar phase transformation phenomena are observed in three-body abrasion to two-body abrasion. In the initial indentation region, the major part of bct5 phase transforms into amorphous phase, and just a fraction of bct5 phase region is distributed around the edge of the phase transformation region as shown in Fig. 6(b), and (f–h). No distinct discrimination on the transformation of atom type between two-body and three-body abrasion is probed as shown in Fig. 7(a) and (c). Beneath the moving particle, a large bct5 phase region exists at the bottom of the thick amorphous phase region surrounding the indenter as shown in Fig. 6(p) and (q). After scratching, a thick amorphous phase and major part of bct5 phase is remained as shown in Fig. 6(b) and (o). Comparing with the two-body abrasion, much more bct5 atoms are generated by the indenter and remained after three-body abrasion as shown in Fig. 7(d). All these results indicate that the three-body abrasion can promote the phase transformation comparing to two-body abrasion, which is resulted by the special stress state as discussed below.

Fig. 4. (a) RDF and (b)ADF (g(h)) of the metastable atoms and Si-I phase.

3.4. Depth understanding of the two/three-body abrasion induced amorphous

Fig. 5. Atom type (b) 3.75–4.50 nm.

tracking

from

indent

depth

(a)

2.25–2.50 nm

and

are almost disappeared. The phase transformation is also probed by evaluating the alteration of atom type as shown in Fig. 7(a). After scratching, almost all the Si-II atoms during the indentation are transformed into Si-I and bct5 atoms, a part of bct5 atoms are transformed into Si-I atoms and the other atoms are still remained, and almost all the DDS atoms are transformed into Si-I atoms. Beneath the moving particle, only massive amorphous phase and a small amount of bct5 phase are observed as shown in Fig. 6(a), (m) and (n). The amorphous phase is around the moving

Although we have shown that the amorphization of the crystalline diamond silicon is the governed phase transformation mechanism in two-body and three-body abrasion, further investigation indicates the network structure of resultant amorphous phase in the scratched region and beneath particle region is different. A careful calculation shows that the volume per atom of amorphous phase is 0.76 relative to the zero-temperature diamond structure beneath the abrasion region both in two-body and three-body abrasion, which becomes consistent with the value of the high density amorphous (HDA) [41] phase from the ab initio calculations [42]. Hence, the amorphous phase beneath the abrasion region is identified as the HDA. After scratching, the HDA phase transforms into a low density metastable amorphous (LDMA) [41] phase with volume per atom 0.90 in two-body abrasion and 0.94 in threebody abrasion. The average coordination number (coordination radius 0.302 nm) of the HDA phase is 6.27, which agrees well with the experimental value of 6.40 [43] and CP simulation result of 6.5 [44,45] for liquid silicon using the ab initio simulation, in contrast to LDMA phase of 5.02 in three-body abrasion. In addition, the proportion of 5- and 6-coordinate silicon atoms approaches 83.40% in HDA phase and 61.3% in LDMA phase, which becomes in accordance with Dominik’s reports [46]. Those results verify the HDA and LDMA, and indicate that the HDA phase has a tighter packing of the network than the LDMA phase. The RDF and ADF of the HDA and LDMA are both shown in Fig. 8. The disappeared third RDF peak confirms the amorphous characteristic for HDA and LDMA phase. The intensity of the first RDF peak increases, and the second peak position is shifted to longer distances when the HDA phase transforms into LDMA phase as shown in

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Fig. 6. Cross-section view of phase distribution induced by (a) two-body abrasion; (b) three-body abrasion. (c–h) and (l–q) is the cross-section view corresponding to labeled location in (a) and (b) for two-body and three-body abrasion; (i–k) is the cross-section view of phase distribution induced by nanoindentation corresponding to labeled location T1–T3 in (a and b). All the figures are at the same depth 4.50 nm. Atoms are colored according to the coordination number. Blue, sky blue, red and golden ones are Si-I, bct5, DDS and surface atoms respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 7. Atom type tracking on the (a) initial indentation region; (b) scratched region in two-body abrasion; (c) initial indentation region; (d) scratched region in three-body abrasion.

Fig. 8(a). The ADF for LDMA phase shows a single broad peak centered at the tetrahedral angle, and a small shoulder near 60°. The centered peak is shifted to near 78°, a small peak but not a shoulder is present near 60°, and a shoulder appears near 155° for the HDA. The discrepancy of the ADF between the HDA and LDMA phase reflects a different networks. It should be stated that the present LDMA is not a normal amorphous silicon (the low-density amorphous silicon, LDA), but a metallic amorphous phase which is also found on decompression of pressure-induced HAD [47]. The present results show a phase transformation from crystalline diamond silicon to HDA phase both in two-body and three-body abrasion. Although there is no direct experimental evi-

dence of two-body and three-body abrasion-induced HDA phase, some existing researches have confirmed the transformation from crystalline diamond silicon to HDA phase under the other different load conditions. Durandurdu [42] has reported the pressure-induced phase transition from crystalline diamond silicon to the HDA phase at 15 GPa using the ab initio calculations. Deb et al. [48] have shown that the crystalline portion of the porous silicon transforms to a HDA phase upon compression using the DAC experiment. Behind the moving abrasive particle, the present molecular dynamics shows that the HDA phase transforms into the LDMA phase. Employing the DAC experiment, Mcmillan et al. [49] have reported a density-driven phase transition occurring from LDA to HDA phase under compression, and the HDA phase reverts to LDA phase upon decompression. Deb et al. [48] have also observed that the pressure-induced HDA phase transforms to LDA phase in porous silicon. All these researches verify the probability of transformation from crystalline diamond silicon to HDA phase and from HDA to LMDA phase, and provide some collateral evidences of the phase transformation in two-body and three-body abrasion, but the direct evidence is still lacking. In summary, the present results suggest a possibly phase transformation route in two-body and three-body abrasion, which is the initial Si-I transforms into the HDA phase beneath the moving abrasive particle and then turns into the LDMA phase covered the surface of the substrate. 4. Discussion 4.1. Phase transformation route

Fig. 8. (a) RDF, CN; (b) ADF (g(h)) of HDA and LDMA phase.

The experimental results have shown that the amorphous silicon is the dominant phase after scratching whatever the load conditions are [26,27,50,51], and some small crystalline structure, such as, Si-I nanocrystals, metastable BC8 (Si-III) and R8 (Si-XII) are embedded in amorphous silicon at a high stress [26] or low speed [27] in two-body abrasion. Therefore, there are two possible transformation paths during two-body abrasion. In the first path, the moving particle can lead to direct amorphization of the crystalline diamond silicon. The resultant amorphous silicon can be retained or undergoes a polymorphous transition. The second

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possible transition path involves the formation of a metallic crystalline phase beneath the moving particle, such as, Si-II and bct5 phase. After scratching, the resulted metallic crystalline phase transforms into amorphous phase. Unfortunately, it has been difficult to identify a specific deformation pathway by the experiments until now. In order to examine the phase transformation route, Fig. 9 illustrates the atom snapshots of two-body abrasion process. It can be seen that the crystalline diamond silicon are transformed into amorphous phase beneath the moving particle. After scratching, the resultant amorphous phase is retained. The similar phase transformation can also be observed in three-body abrasion. The present molecular dynamics simulations not only support the experimental result of the residual amorphous phase after scratching, but also make clear that the first transformation route governs the phase transformation in two-body and three-body abrasion under the present condition. The simulation results effectively support Wang and Huang’s experiment reports [25]. 4.2. Stress mechanism and criterion It is surprised that the transformation of crystalline diamond silicon to the HDA and few bct5 phase occurs beneath the moving particle in two-body and three-body abrasion, but not to the Si-II and bct5 phase as in the nanoindentation, It is now generally accepted that it is the flattening the tetrahedral structure that causes the transformation of Si-I to Si-II by the compressive loading along the [0 0 1] direction [17] and this transformation is stimulated by the hydrostatic stress. It is unfortunate that the transformation mechanism of the amorphous is still an open issue. Early researches [52,53] have related the formation of amorphous to the hydrostatic stress component in nanoindentation. It is suggested that the high volumetric strain is responsible for the transformation of diamond cubic silicon to amorphous. Subsequent researches point out the role of the deviatoric stress cannot be ignored. Minowa and Sumino [54] have indicated that the very high shear stress produced by the scratching causes the amorphization of diamond cubic silicon. Zhang and Tanka [24,55]

Fig. 9. Atom snapshots of two-body abrasion process.

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have suggested the octahedral shear stress is responsible for the amorphourize in the nanoindentation, two-body and three-body contact sliding. Kim and Oh [18] have emphasized the effect of the deviatoric stress on the structural transformation of diamond cubic silicon to Si-II in nanoindentation. Recently, Chrobak et al. [56] have also reported that a high averaged ratio of hydrostatic and von Misses stress lead to the amorphous transformation for the bulk silicon, but low ratio leads to dislocation-controlled plastic deformation for silicon nanoparticle in nanoindentation. A great deal of nanoindentation experiments show that the structure transformation cannot be individually interpreted by the hydrostatic stress, such as, phase transformation anisotropy [22], low transformation pressure [10], and appearance of the new phase (bct5 phase) not observed in DAC experiments [19], which indicates that the shape deformation stimulated by the shear stress and the deviatoric stress plays an important role in the phase transformation of mono-crystal silicon. And the role of individual shear stress cannot be used to explain the different phase transformations between nanoindentation and abrasion in nanoscale. It is, therefore, accepted that neither the hydrostatic pressure, nor the von Mises stress or the octahedral shear stress accountable for shape evolution can individually be able to evaluate the structural phase transformation under the different load conditions. It is, then, interested in which combine of the hydrostatic pressure and von Mises could lead to the amorphous transformation and which to the transformation of Si-I to Si-II phase. To estimate the local stress, the virial theorem is borrowed to calculate atomic stresses. An average atomic stresses locally over a spherical region is used that has a cutoff radius slightly larger than the nearest neighbor distance (0.284 nm). Fig. 10 is the cross-section view of the distribution of hydrostatic stresses and von Misses stress at just prior to the phase transformation in nanoindentation, and two/three-body abrasion. Both the hydrostatic pressure and von Misses stress are concentrated to a tiny volume near the surface beneath the abrasive particle for all the samples. Although, slightly larger von Misses stress can be observed beneath the particle in nanoindentation than in two-body and three-body abrasion, there is no notable distinction in hydrostatic stress distribution. On the face of it, this result implies the different von Misses stress is responsible for the different phase transformation between abrasion and nanoindentation. But, neither the hydrostatic pressure nor the von Misses stress distribution becomes consistent with the phase distribution (not shown in paper). Hence, we consider that neither the hydrostatic pressure nor the von Mises stress is individually able to evaluate the different structural transformation. Further insight on the effect of stress state is provided by observing the discrepancy in the averaged hydrostatic pressure (rh) and von Mises stress (rvon) over the stress concentration zone beneath the moving abrasive particle. The averaged hydrostatic pressure and von Mises stress at just prior to the transformation of Si-I to Si-II in nanoindentation, and Si-I to HDA phase in two-body and three-body abrasion are calculated as listed in Table 1. The ratio of rh and rvon is also calculated, which has proved capable of detecting the dominant deformation for semiconductors. In the nanoindentation, the averaged hydrostatic pressure is 10.15 GPa and therefore it is in excellent agreement with the value of 11– 12.5 GPa predicted from the experiment. In contrast, the average hydrostatic pressure is only 6.93 and 8.55 GPa in two-body and three-body abrasion respectively. This value is far lower than the phase transformation pressure of Si-I to Si-II, therefore the formation of Si-II phase is hindered. If we consider shear stress or von Missess stress is individually responsible for the amorphourization, the amorphous should be present in nanodindenation but not in two/three-body abrasion because much large von Mises stress is lay in nanoindentation rather than two/three-body abrasion. This viewpoint is deviated from the present simulation results and exist-

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Fig. 10. Hydrostatic pressure and von Mises stress contour for (a and b) nanoindentation; (c and d) two-body abrasion; (e and f) three-body abrasion.

ing experimental fact. Although the different in the ratio of rh and rvon is also found, it is inappropriate as a criterion to evaluate the phase transformation because we cannot believe that the rh/rvon of 0.57 and rh of 5 GPa can lead to the phase transformation. Based on the present results, a criterion considering the integrated effect of hydrostatic pressure and von Mises stress on the phase transformation is proposed. If the hydrostatic pressure is larger than the critical value (rch) of 10–12.5 GPa, the phase transformation of Si-I to Si-II occurs whatever the von Mises stress is. And if the hydrostatic pressure is less than 10–12.5 GPa, the critical value (rcvon) 16.0 GPa is suggested for the amorphourization of Si-I. This criterion can be summarized as follows:



rh P rch rh < rch and rv on P rcv on rch  10  12:5 GPa rcv on  16:0 GPa Si  I ! Si  II

Si  I ! a  Si

ð1Þ

where a-Si is amorphous silicon. This criterion can be also applied to the DAC experiment and nanoscale uniaxial compression of mono-crystalline silicon, in which the phase transformation of Si-I to Si-II occurs because of the zero shear stress. 4.3. Possible phase transformation in three-body abrasion The average value of hydrostatic pressure and von Mises stress in nanoindentation and three-body abrasion is very approximate Table 1 Average hydrostatic pressure rh and von Mises rvon.

rh (GPa) rvon (GPa) rh/rvon

Nanoindentation

Two-body abrasion

Three-body abrasion

10.15 17.85 0.57

6.93 16.89 0.41

8.55 16.08 0.53

compared with two-body abrasion. This different stress state should be attributed to the movement pattern of abrasive particle in three-body abrasion. In three-body abrasion, the movement pattern of abrasive particle can be formulated using the centre-of-mass velocity and rotational velocity. Considering a simple model of three-body abrasion in which the substrates and the particle are all regarded as rigid body, the centre-of-mass of particle velocity is equal to half of translational velocity of substrate when the particle is in rolling, while it equals to the translational velocity of substrate when the particle is in sliding. In the present model, it is difficult to predict the movement pattern of a particle because of the area contact induced by the elastic–plastic deformation of substrate. Hence, a careful molecular dynamics simulation is essential to investigate the movement patterns of particle. Two typical centre-of-mass velocity–time and self-rotation velocity–time curve of the particle with radius of 5.43 nm and 10.86 nm is shown in Fig. 11(a and b). It can be seen that the centre-of-mass velocity persistently oscillates around 100 m/s which is just the centre-of-mass velocity in rolling. And the oscillation amplitude is extremely large at the beginning and gradually tends to a stable value. The similar characteristics can also be examined from the self-rotation velocity. The velocity oscillation is usually caused by the atomic steps of the particle and the substrate surface. The atomic steps lead the profile of the particle and the substrate to deviate from the ideal sphere and the ideal smooth plane, respectively. The smaller the abrasive is, the more notable the effect of the atomic steps is. Thus, the oscillation for the small abrasive is more violent than the lager abrasive. It can, therefore, be concluded that the particle will have a predominant tendency to roll with an oscillated velocity under the present conditions, and the velocity oscillation becomes small with increasing the particle size.

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whatever the von Mises stress is. And if the hydrostatic pressure is less than 10–12.5 GPa, the critical value 16.0 GPa is suggested for the amorphourize of Si-I. This criterion can be generally applied to evaluate the phase transformation of mono-crystalline silicon in hydrostatic pressure experiment, nanoscale uniaxial compression, nanoindentation, nanoscratching or two-body abrasion, and three-body abrasion. In addition, the possible phase transformation of Si-I to Si-II is predicted in three-body abrasion at a low velocity. For nanoindentation, a metastable phase atoms surrounding the transformation region along the [1 0 0] and [0 0 1] directions is observed as a slightly distorted diamond cubic structure, but not the Si-III/Si-XII phase according to the coordination number, which is also observed in front of the moving particle in two-body and three-body abrasion. By track the alteration of atom type during nanoindentation, it is confirmed that the DDS can be recovered back to a diamond cubic structure in further loading or unloading, but not transformed to other phases. Acknowledgments The authors acknowledge support by the National Natural Science Foundation of China (51075318), and Natural Science Foundation of Shannxi Province, China (2010JM6011). Fig. 11. (a) The centre-of-mass velocity; (b) self-rotation velocity vs. time curve of the particle.

The rolling of particle induces large hydrostatic pressure in samples in three-body abrasion compared with two-body abrasion. This effect can be enhanced with the decreasing of sliding velocity of samples and the interface adhesion. So the phase transformation of Si-I to Si-II can be possible in three-body abrasion at the nanoscale. It is unfortunate that the three-body abrasion at the low velocity cannot be performed under the present simulation conditions which is limited by the intrinsic restrict of molecular dynamics simulation.

5. Conclusions

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Large-scale molecular dynamics simulations are performed to study the phase transformations of mono-crystalline silicon induced by the nanoindentation, two-body and three-body abrasion. A new model of three-body abrasion is proposed to evaluate the phase transformations. The results indicate that the transformation from Si-I to Si-II and bct5 is the dominant phase transformation mechanism in nanoindentation. But a different phase transformation route in two-body and three-body abrasion is suggested. The initial Si-I turns into HDA phase beneath the moving abrasive particle and then transforms to a thick and slightly compact LDMA phase which overlays the surface. No obvious distinction is observed in phase transformation between the two-body and threebody abrasion. But a possible phase transformation of Si-I to Si-II is predicted in three-body abrasion at a low velocity. After scratching, some dispersive bct5 phases are adjacent to the thick LDMA phase in three-body abrasion. In contrast, the surface of substrate is clearly covered by a thin LDMA phase accompanied by sparse bct5 phase sheets in two-body abrasion. The different phase transformation in nanoindentation and two/three-body abrasion indicates that neither the hydrostatic pressure nor the von Mises stress can individually evaluate the phase transformation. Based on the present results, a criterion considering the integrated effect of hydrostatic pressure and von Mises stress on the phase transformation is proposed. Namely, if the hydrostatic pressure is larger than the critical value of 10–12.5 GPa, the phase transformation of Si-I to Si-II occurs

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