Molecular dynamics simulations of the tensile and melting behaviours of silicon nanowires

Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học

Molecular dynamics simulations of the tensile and melting behaviours of silicon nanowires Yuhang Jing à , Qingyuan Meng, Wei Zhao Department of Astronautical Science and Mechanics, Harbin Institute of Technology, No.92, West Da-Zhi Street, Harbin 150001, People’s Republic of China article info Article history: Received 29 September 2008 Received in revised form 7 November 2008 Accepted 13 November 2008 Available online 3 December 2008 PACS: 61.46.Km 62.25.Àg 65.80.+n Keywords: Si nanowires Molecular dynamics Tension Melting behaviour abstract The tensile and melting behaviours of single crystalline silicon nanowires (SiNWs) are studied using molecular dynamics simulations. The atomic interactions are described using the Stillinger–Weber potential. The tensile test results show that the tensile behaviour of the SiNWs is strongly dependent on the simulation temperature, strain rate, and diameter of the nanowires. The critical load clearly decreases with increasing temperature and with decreasing strain rate, and increases with increasing diameter. Additionally, the melting test results demonstrate that the melting temperature of the SiNWs decreases with decreasing diameter, due to the increase in surface energy. The structural transition of SiNWs with an increasing temperature is also studied. Crown Copyright & 2009 Published by Elsevier B.V. All rights reserved. 1. Introduction One-dimensional semiconductor nanostructures are attracting great interest for their tremendous technological potential in nanoscale devices [1,2]. Utilizing the structure at the nanometer level is a key technology in the development of electronic devices and elements of nanoelectromechanical systems (NEMS). There- fore, it is important to understand the mechanical properties for engineering usefulness such as design of reliability in service. Silicon nanowires (SiNWs) appear to be an especially appealing choice due to their compatibility with conventional Si-based electronic technology. Recently, SiNWs have been synthesized by solution techniques [3], an oxide-assisted catalyst-free method [4,5], and a metal-catalytic vapour–liquid–solid method [6–8]. High-resolution electron microscopy experiments have shown that the resulting SiNWs carry cores with monocrystalline bulk structures [7,9]. From a theoretical viewpoint, many correlative theoretical predictions have been performed in recent years [10–15]. In most of the work, the Quantum mechanics methods were used, and the attentions were mainly paid on the microstructural and electronic properties of the SiNWs. The mechanical strength of the nanowires plays an important role in maintaining the structural integrity of the structures, devices or systems. However, such calculations are very expensive. Sizedependent and thermodynamical properties of nanowires are still unattainable to such methods. Molecular dynamics (MD) simulations are increasingly being used to study the mechanical behaviour and deformation mechanisms of nanostructures. A number of studies have used the MD simula- tions to analyze the tensile failure modes in metal nanowires [16–19]. Metal nanowires have been found to exhibit unique physical behaviour under tensile loading. However, the studies on the mechanical characters of SiNWs are little reported [20,21]. Although empirical methods carry a considerable simplification of the underlying atomistic processes, they still represent an alternative to access those important nanowire properties [20,22]. In this paper, we report the results of MD simulations on the tensile and melting behaviours of [110]-oriented SiNWs. The effect of temperature, strain rate, and cross-sectional size on the mechanical properties is studied. We also investigate the size effect on the melting temperature of SiNWs. 2. Simulation method Because the exact atomic structure of the SiNWs is unknown in most cases, some theoretical calculations of nanowires with different shapes can be found in the literature. Zhao and Yakobson ARTICLE IN P RESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physe Physica E 1386-9477/$ -see front matter Crown Copyright & 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2008.11.006 à Corresponding author. Tel.: +86 451864 00158. E-mail address: jingyuhang@gmail.com (Y. Jing). Physica E 41 (2009) 685–689 [23] proposed the pentagonal and hexagonal SiNWs along the /110S direction. Justo et al. [24] reported classical molecular dynamic simulations of silicon nanowires of various shapes and orientations. Menon [20] and Ponomareva et al. [22] investigated the tetragonal and clathrate SiNWs. Based on the reported experimental observation [9], the triangular-shaped nanowires have relatively large size (diameter of about 100 nm). As for the triangular-shaped SiNWs, no theoretical study has been reported in the literature. A detailed study of such SiNWs is necessary to understand the properties of SiNWs with different shapes. In this study, we construct [110]-oriented SiNWs with triangular cross sections directly from the bulk silicon by removing the atoms outside a triangle. To save computational time, the NWs are relatively thin with diameter Do10 nm, the top and side views of the optimized structures of single crystalline SiNWs are shown in Fig. 1. The nanowires with triangular cross-sectional shape are enclosed with two {111} side planes and one {10 0} side plane. The atomic interactions are described using the Stillinger– Weber (SW) potential [25]. The empirical SW interatomic potential consists of two- and three-body interaction terms and were originally fitted to describe the crystalline and liquid silicon phases. This potential consists of sums of two- and three-body interaction contributions. The two-body potential describes the formation of a chemical bond between two atoms. The three-body potential favors structures in which the angles between two bonds made by the same atom are close to the tetrahedral angle. The SW potential has been used in the study of molten Si [25] as well as surfaces of crystalline Si [26]. The SW potential has also been adopted for the study of SiNWs and found to give good results for nanowire properties [20,22]. Therefore, the SW potential should be reliable to study the mechanical properties of SiNWs. The loading state in the present tension simulations is as follows: the relative positions of atoms within the five atomic layers at the top and bottom of NWs are fixed during simulations, forming two rigid borders; the others are set as thermal controlled layers, as illustrated in Fig. 1. The system temperature is controlled by rescaling the atom velocities [27]. The SiNWs are initially annealed at 700 K over a period of 10 6 time-steps, where each step is separated by an interval of 0.5 fs, and then the structures of the nanowires were dynamically relaxed at a given temperature for 50 ps with traction-free boundary conditions, which allows the nanowires to have stable configuration. The strain was then applied along the axial direction to study the mechanical proper- ties of the SiNWs. In order to investigate the relative influences of temperature, strain rate and cross-sectional size on the mechan- ical properties of the current SiNWs under tension loading conditions, this study simulates testing under various tempera- tures in the range of 10–1200 K, with strain rates varying from 2  10 À4 to 2  10 À2 /ps and wire diameter ranging from 4.27 to 6.15 nm. In the melting simulations, the periodic boundary condition is applied in the axial direction. The initial configuration was relaxed for 50ps at 300 K. The heating process is simulated by a temperature increment of T ¼ 100 K. However, a temperature increment of T ¼ 50 K is applied near the melting region. For each temperature interval, the MD cell was relaxed for 50 ps. 3. Results and discussion The generated results of the MD simulation are presented. The deformation characteristics of the nanowire in uniaxial tension are considered at the first stage. The effect of temperature, strain rate, and cross-sectional size on the mechanical properties of the nanowires such as the critical load is studied. Afterwards, the melting properties of the SiNWs are investigated. 3.1. The tensile properties of the SiNWs Fig. 2(a) shows the axial load–strain curve for the SiNW with diameter 4.27 nm, simulated at 300 K, with strain rate of 0.04%/ps. From the figure, it is seen that the load increases up to a maximum value of 141 nN corresponding to strain of 0.124, then the load suddenly decreases to 32 nN where the plastic zone is developed. For low strains ( e o0.05), the load–strain relation is essentially linear in the elastic regime, and Young’s modulus can be directly evaluated in this elastic region. Young’s modulus is ARTICLE IN PRESS Fig. 1. Top and side views of the optimized structures of single crystalline SiNWs. Fig. 2. (a) Load–strain curves of the SiNW with diameter 4.27 nm, simulated at 300 K, with strain rate of 0.04%/ps. (b) Snapshots of atomic configurations at various strains. Y. Jing et al. / Physica E 41 (2009) 685–689686 estimated as 118.4 GPa according to the present model, which is consistent with the experimental result of 93–180 GPa of SiNWs [28,29]. The deformation process can be better understood by the wire evolution presented in Fig. 2(b). For small strains, the bonds of the nanowire are just stretched and preserve their fourfold coordination in the nanowire, and no structural defects appear at this stage. For larger strains, bond breakage in the outmost layer is observed and spreads toward the center as the strain increases. With the strain increasing further more, we find that sliding along the {111} plane happens, and many atoms rearrange in the neck region. When a single crystal is stretched, the fundamental deformation mechanism is a shearing action based on the resolved shear stress on an active slip system. The silicon is a diamond structure and its slip plane is {111} [30], and in the present simulation the load is along the [11 0] orientation and the resolved shear stress on the (111) plane causes the sliding. After the formation of the neck, the plastic deformations have been carried mainly through the reconstruction and rearrangement of the neck region, which was previously reported in other studies [16]. Beyond this region, the nanowire keeps ordered structure and have no significant change. Since buckling occurs as a result of dynamic processes, the mechanisms of material deformation are influenced both by temperature and by strain rate. Therefore, if material deforma- tions in SiNWs are to be fully understood, the influences of these factors must be investigated. Fig. 3 shows the effects of temperature and strain rate on the tension behaviour. Fig. 3(a) shows the axial load–strain curves of SiNWs with diameter 4.27 nm, which were simulated at 10–1200 K with a strain rate of 0.04%/ps. The results clearly demonstrate that the critical buckling load decreases at higher temperature. At higher temperature, the atomic structure has high entropy, and the atoms vibrate about their equilibrium position at much larger amplitude. A greater number of molecules gain sufficient energy to overcome the activation energy barrier, as compared to low temperature, and hence deformation occurs. This result suggests that a thermally activated process plays an activating role in the complete elongation of SiNWs. Fig. 3(b) shows the axial load–strain curves of SiNWs with diameter 4.27 nm, which were simulated at 300 K with strain rate varying from 0.02 to 2%/ps. The strain rate adopted here is very high compared to that in experiment, because only very short period of time can be simulated due to the time scale of molecular dynamics set by the atomic motion. One consequence of the short time scale is that very high strain rates are required to get any reasonable deformation within the available time [31]. For all strain rates, the load increases linearly with strain up to 0.11. Below this value, the load–strain curves are almost completely overlapped for all of strain rates applied, indicating that in the linear elastic region no plastic deformation occurs and the elastic properties of a nanowire is insensitive to strain rate. However, a slower strain rate results in a lower critical buckling load. Regarding the strain rate influence, the strain or deformation tends not to be uniformly distributed within the material, particularly when a large strain is applied. Hence, some regions of the nanowire are subjected to larger stresses or strains than others, and it is within these regions that defects will first become evident. When a lower strain rate is applied, the SiNWs have more time to induce adequate local deformation, and hence the onset of plastic deformation is accelerated. Therefore, a slower strain rate results in a lower critical load. The present results clearly demonstrate that the mechanical properties of SiNWs are sensitive to the strain rate and temperature conditions. An important factor in evaluating the mechanical properties of nanowire is the size effect. Physical and chemical properties of materials are expected to exhibit some dependencies on dimen- sionality and cross-sectional size. We describe the scaling proper- ties of nanowires as a function of their diameters (as shown in Fig. 1). As for the triangular-shaped SiNWs in the present study, the method to estimate an effective wire size is similar to Ref. [24], where the perimeter of SiNWs were used to estimate an effective wire size. To investigate the effect of the SW potential on the scaling properties of SiNWs, the critical loads are also computed using the Tersoff potential [32] and EDIP model [33,34]. The simulation results show that the SW potential seems to be more reasonable to describe silicon nanowires. Fig. 4(a) shows the axial load–strain curves for nanowires with diameter 4.27 nm, which were simulated at 300 K with a strain rate of 0.04%/ps. From the picture, it can be seen that the Tersoff potential shows the highest critical load and critical strain. The SW potential shows somewhat higher critical load than the EDIP model, however, the EDIP model shows somewhat higher critical strain than the SW potential. The critical strain (0.124) computed using the SW potential is in good agreement with experiment result (0.104) [35]. The critical loads computed using the three different interatomic potentials are higher than the experimental estimates [35]. It should be noted, however, that experimental samples almost always contain defects and impurities that can reduce the critical strength. Fig. 4(b) shows the variation in critical load with diameter of SiNWs. The result clearly demonstrates that ARTICLE IN P RESS Fig. 3. Load–strain curves for the SiNWs under tensile loading. Effects of (a) temperature and (b) strain rate on the tension behaviour of the SiNWs. Y. Jing et al. / Physica E 41 (2009) 685–689 687 the critical load decreases with decreasing the diameter of the nanowires. Specifically, as the diameters increase from 4.27 to 6.15 nm, decreases of about 50% in the critical load computed using the three different interatomic potentials. The reason for this behaviour may be the small atomic-coordination number and weak cohesion of the atoms near the surface, as compared with those in the bulk, and the increasing dominance of the surface would decrease the strength of the structure. 3.2. The melting properties of the SiNWs The variation of potential energies as a function of temperature is shown in Fig. 5. As can be seen from the results in the picture, the energy generally increases with decreasing diameter of SiNWs at a given temperature, which indicates that surface energy increases with decreasing diameter. The potential energies also increase linearly with increasing temperature and change abruptly near the melting region. The melting temperature T m is defined as the point of an abrupt change in the potential energies for the heating process. From Fig. 5, it is found that the melting temperature of SiNWs increases with increasing diameter, which is consistent with the fact that the melting behaviour of nanostructure materials is strongly dependent on size. In general, the thermodynamic property of nanostructures is different from bulk materials [36]. The change of the melting temperature of nanostructures depends on their surface. This indicates that the unstable surface of free-standing nanowires leads to a decrease in the melting temperature. To understand the melting behaviour of SiNWs, the structural evolution of the nanowire with the diameter of 3.32 nm at different temperatures in the heating process is shown in Fig. 6. Before the melting behaviour starts, the atoms of the SiNW oscillate at their equilibrium position. As the melting behaviour starts, the unstable atoms on the edge move to the facet of the SiNW. It should be also noted that at 1450 K, which is 150 K below the melting point, several atoms in the central region of the nanowires are still in the crystalline configurations. However, when the temperature is increased to 1600 K, none of the atoms are in their lattice configurations, and the atomic positions are ARTICLE IN PRESS Fig. 4. (a) Load–strain curves for SiNWs with diameter 4.27 nm, which were simulated at 300 K with strain rate of 0.04%/ps. (b) The variation in critical load with the diameter of SiNWs. Fig. 5. Potential energy as a function of temperature for SiNWs. Fig. 6. Structural transition of the SiNW with a diameter of 3.32nm at different temperatures. Y. Jing et al. / Physica E 41 (2009) 685–689688 disordered. The nanowire finally collapses, which indicates the melting of the nanowire. 4. Conclusions In this paper, molecular dynamics simulations with Stillin- ger–Weber potentials are used to simulate the tensile and melting behaviours of the SiNWs. 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