Nanoscale Mechanical and Mechanically-Induced Electrical Properties of Silicon Nanowires

Abstract

Molecular dynamics (MD) simulation was employed to examine the deformation and phase transformation of mono-crystalline Si nanowire (SiNW) subjected to tensile stress. The techniques of coordination number (CN) and centro-symmetry parameter (CSP) were used to monitor and elucidate the detailed mechanisms of the phase transformation throughout the loading process in which the evolution of structural phase change and the dislocation pattern were identified. Therefore, the relationship between phase transformation and dislocation pattern was established and illustrated. In addition, the electrical resistance and conductivity of SiNW were evaluated by using the concept of virtual electric source during loading and unloading similar to in situ electrical measurements. The effects of temperature on phase transformation of mono-crystalline SiNWs for three different crystallographically oriented surfaces were investigated and discussed. Simulation results show that, with the increase of applied stress, the dislocations are initiated first and then the phase transformation such that the total energy of the system tends to approach a minimum level. Moreover, the electrical resistance of (001)- rather than (011)- and (111)-oriented SiNWs was changed before failure. As the stress level of the (001) SiNW reaches 24 GPa, a significant amount of metallic Si-II and amorphous phases is produced from the semiconducting Si-I phase and leads to a pronounced decrease of electrical resistance. It was also found that as the temperature of the system is higher than 500 K, the electrical resistance of (001) SiNW is significantly reduced through the process of axial elongation.

1. Introduction

The discovery of a number of specific structures and phase transformations in silicon material [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] has attracted great attention in semiconductor industry in the recent decades. The physical properties of silicon materials are significantly affected by stress, which may lead to the evolution of phase transformation and the change of electric conductivity of the material. This stress related process is also called strained-Si. It has been reported that the change of electric conductive property of strained-Si is influenced by the direction of the applied stress [4,5,6,7,8,9,10,11,12,13,14,15]. Complete understanding of the detailed mechanisms of strained-Si may enhance the development of the Si materials in semiconductor science and technology. For instance, high performance nanowire metal-oxide-semiconductor field-effect transistors (nwMOSFETs) are of interest as a potential alternative for planar complementary MOS (CMOS), primarily because of their performance gains derived from one-dimensional transport and their inherent immunity against short channel effects [16]. It was found that the tensile stress (10 GPa) contributes to a significant transconductance enhancement in both n-nwFETs and p-nwFETs devices.

Recently, the effect of side surface orientation on the mechanical properties of silicon nanowires was studied by molecular dynamics simulations [17]. It was found that silicon nanowires with {100} side surfaces have a lower tensile strength but higher compressive strength. In addition, several investigators have observed the phase transformation of mono-crystalline Si in micrometer scale during nanoindentation [18,19,20,21,22]. Most traditional experimental methods are capable of observing the microstructures only after unloading. Some investigators [4,5] have utilized transmission electron microscopy (TEM) to in situ monitor and observe the evolution of structural phase transformation process. However, this technology is extremely difficult and expensive. Numerical simulation, on the other hand, may provide an alternative to investigate detailed mechanism of deformation and phase transformation.

Most of previous studies have focused on structural phase transformation of mono-crystalline Si [6,7,8,9,10,11]. Only a few work investigated its electric conductive properties [8,9,10,11]. Conductivity of mono-crystalline Si is the key property for various applications of silicon material. It was found that the conductive properties of the Si material are closely linked to the amount of Si-II phase [12,13,15]. Silicon nanowires (NWs) are attracting significant attention from the electronics technology and industry due to the urgent drive for ever-smaller electronic devices, from cell phones to computers. The operation of these future devices, and a wide array of additional applications, will depend on the physical properties of these NWs [23]. The strain retained in NWs can significantly affect their electronic properties by perturbing the band structure or changing the Fermi energy of the nanostructures [24]. For instance, the applied strain on carbon nanotubes (CNTs) may introduce a distinct conductance change from semiconductor to metallic [25]. A strain-induced giant piezoresistance effect has also been observed for Si NWs [26]. Moreover, the optical properties of the Si nanowires were also affected by mechanical strain under the applications of an electric field through giant electro-optical effect [27]. At present, for the topics of phase transformation of mono-crystalline Si, most of the researches have concentrated on three-dimensional bulk material. Only a few literatures [28,29,30,31] have examined either one- (1-D) or two-dimensional (2-D) cases. While the global conductive properties of the material can be measured through the traditional experiment, the initiation and propagation of Si-II phase in nanostructured silicon and the relationship between the amount of Si-II phase and the conductive properties are not fully understood and require further studies. Moreover, it appears there is no any discussion in literature about the formation and interaction between dislocation and phase transformation. The objective of this work was to investigate the detailed mechanisms of both phase transformation and dislocation of crystalline SiNWs subjected to tensile stress by using MD simulations, in which the effects of unloading, temperature and surface orientation were included. Coordination number (CN) technique was used to monitor and elucidate the detailed mechanisms of dislocation and phase transformation throughout the loading process. Moreover, the variations of electrical resistance and conductivity of SiNWs during loading and unloading were also evaluated. The simulation results were compared with experimental data performed by Mylvaganam et al. [15].

2. Methodology

This study investigated the mechanical behavior of the SiNW with a perfect diamond crystalline structure under uniaxial tension using MD simulation. The atoms were stretched in the Z-direction by the applied load and free to move along both X and Y directions, as shown in Figure 1. During loading, the top atoms move in longitudinal direction with equal speed. The initial diameter and length of wire are 6 nm and 50 nm, respectively. The number of atoms in simulation models are 70,660, 70,078, and 71,407 along the [001], [011], and [111] directions, respectively. A tensile load was applied in the Z direction with a strain rate 0.6 × 10⁻⁶·fs⁻¹. Moreover, suppose a DC voltage be imaginarily applied on the top and bottom surfaces of the model to induce an imaginary DC current for the convenience of comparison with experimental data. This technique was first proposed and used for nano-indentation [15].

The influences of surface orientation, temperature and unloading on the nanoscale mechanical behavior were investigated individually. The inter-atomic potential function, proposed by Tersoff [32,33,34,35,36] that considers the effect of bond angle and covalent bonds, has been shown to be particularly reasonable in dealing with IV elements and those with a diamond lattice structure such as C, Si, and Ge. Moreover, the accuracy and applicability of this potential have been further verified by researchers through good agreements between simulation and experimental results [37,38,39]. Therefore, the Tersoff potential function [36] was adopted in this study to analyze the dynamic correlations in Si-Si atoms. In this work, the time step as short as 1 fs was used to ensure solution accuracy. A modified five-step methodology was used to incorporate Newton’s equations of motion, so that the position and velocity of a particle can be effectively evaluated. Moreover, the mixed neighbor list was applied to enhance computational efficiency. The simulations were performed in constant NVT ensemble with velocity-Verlet integrator. The model was first relaxed for 50,000 steps at 300 K and zero force. Temperature was controlled using a Nosé-Hoover thermostat.

The stresses of SiNWs were determined by using the maximum local stress (MLS) [40,41,42] technique. In the method of MLS, the SiNW was divided into one hundred regions along the loading axis at each time step. Initially, the local stresses in each region were determined separately using the Miyazaki’s method [43]. Then, the maximum of these local stresses was defined as the true stress of the SiNW. Techniques of coordination number (CN) [6,7,8,9,10] and centro-symmetry parameter [44,45,46,47,48,49,50,51] were also used to monitor and elucidate the detailed mechanism of phase transformation throughout the whole process in which the evolution of structural phase change and the dislocation structure can be identified.

3. Results and Discussion

The original atoms of monocrystalline Si, conventionally labeled as Si-I phase, have a coordination number of four. Figure 2 shows that the structure of Si-I is gradually deformed from 90° to 70° on the (001)-orientation under the action of tensile stress. The phase with a coordination number of six, labeled as β-Sn structure (Si-II), is gradually formed due to relative sliding between atoms along the tensile direction [7,8,9]. The electrical resistance of mono-crystalline Si can be determined by the relation of R = ρ(l/A), where ρ, l, and A denote the specific resistance, the length, and the cross-sectional area of the β-Sn phase, respectively [15]. If the cross-sectional area of the β-Sn can be evaluated, the electrical resistance, R, of the material can then be obtained accordingly.

3.1. Mechanical Behaviors of Nanostructured Si Nano Wire

Both dislocation and phase transformation are produced after the atoms in the material are slipped with each other under the action of external forces. If the microstructure induced by dislocations leads to a stable and physically meaningful phase, it is generally called phase transformation. Otherwise, the microstructure induced by dislocations is just a result of a specific deformation pattern. It is obvious that the variation of stress in material is closely related to the evolution of either dislocation or phase transformation. By utilizing the CN and CSP techniques, the atoms under the evolution of phase transformation and dislocation in (001)-oriented SiNW can be extracted and is shown in Figure 3. It can be seen that at the same strain level the region having dislocation (blue shown by CSP) in is obviously larger than that of phase transformation (cyan shown by CN). The latter is almost completely enclosed by the former. As the strain is gradually increased to a critical value, the atoms start to slip first and then introduce dislocations. As the sliding proceeds further, the nanostructure of material is continuously re-crystallized to form a specific microstructure, called structural phase transformation. The variation of stress corresponding to the evolution of dislocation and phase transformation was shown in Figure 4.

Figure 4a shows the stress-strain curve of (001)-oriented SiNW subjected to tensile stress. Both the tensile stress and the shear stress are presented. It is seen that phase transformation takes place at ε = 6.8%, where a sudden jump of the maximum shear stress, τ_max, appears instead of the tensile stress σ_zz.

To see the propagation of the phase change inside the NW more clearly, the atoms at and near the surface are screened out, and only the average maximum stress for the remaining atoms is computed. The calculated maximum shear stress vs. strain curve was as shown in Figure 4b. The deformation mechanisms within the strain range between 6.6% and 7.3% can be interpreted as follows: As the strain of the material is increased from 6.6% to 6.8%, the shear stress is gradually increased and reaches to the critical value for initiation of dislocations. As the strain is increased from 6.8% to 6.9%, a slight stress drop takes place due to the propagation of dislocations. As the strain is further increased to more than 6.9%, the stress goes up quickly due to the significant evolution of phase change.

Figure 5 shows that the slip directions of atoms on (001)-oriented surface at strain level 7.26% are along both the directions of [1 2 −1] (black) and [2 −1 −1] (red). Moreover, it can also be observed that the slip directions of dislocation and phase change are identical, which shows the close link between them. Simulation results indicate that shear stress distorts the microstructure and induces the dislocations first. The microstructure will then be rearranged and re-crystallized to reduce the total energy. In other words, new phases will continuously be produced with the sequences of Si-I phase, meta-stable phase, Si-II phase, and high-pressure phase as the stress is increased. The ability of different phase to sustain the high stress is then enhanced accordingly.

Generally, the variation of stress in material due to external loadings can be introduced through structural phase transformation. The stress level necessary to induce phase change is phase-dependent. For instance, the stress level to induce metallic β-Sn phase (Si-II) should be larger than 12 GPa [6,42]. If one can trace the phase change of SiNW and estimate the amount of Si-II atoms, the prediction of its resistance change might become possible. In this work, the technique of CN is used to identify the coordinate number of each atom. By screening out the atoms of original Si-I phase with CN = 4, the new transformed atoms can be displayed. Figure 6 shows the lateral view of the cross-section at various strain stages. The atoms in the deformed zone with different coordination numbers are marked by different colors (CN < 4 incomplete nanostructure as blue, CN = 5 meta-stable phase as cyan, CN = 6 Si-II phase as yellow, and CN > 6 high pressure phase as red). As shown in Figure 6 and Figure 7, when the (001)-oriented SiNW is exerted by tensile stress, some Si-I atoms are converted into meta-stable phases with CN = 5 due to the change of covalent bonds. Figure 6 shows that at the initial tensile stage, the atoms of meta-stable phase are initiated at two sides of SiNW first and then gradually spread to the middle at ε = 9.3%. The amount of meta-stable phase in SiNW is increased with the increase of tensile stress (as shows in ε = 18%). When the increase of meta-stable phase becomes saturated, the nanostructure of the material cannot sustain the stress by means of the formation of meta-stable phase. The evolution of phase change transformed from meta-stable phase to Si-II phase or high-pressure phase will be taken place. Then, the nanostructure of the new phases will keep on sustaining the stress again. At ε = 47%, a large number of Si-II and high-pressure atoms are uniformly distributed within the atoms of meta-stable phase. As the strain is larger than 58%, amorphous phase starts to appear along the slip planes near the middle of SiNW, as shown in Figure 7. As the strain is larger than 62%, small voids appear between the amorphous atoms. These voids are then aggregated together to form bigger micro-cracks as the strain keeps increasing. At ε = 72%, the SiNW finally fails by fracture. Since a large number of Si-II atoms are produced at ε = 47%, the resistivity of SiNW at and above this strain level should reflect a significant change.

Recently, conductivity of SiNW has been investigated [12,13,15]. It was reported that the conductivity of SiNW is closely related to the direction and the magnitude of strain. In other words, the conductivity of the SiNW material might be affected by the phase transformation induced by tensile stress. A dc pseudo-voltage is imagined to be imposed on both top and bottom surfaces of SiNW, as shown in Figure 1, from which a circuit is connected. The change of current is evaluated as the strain is increased. During elongation stage, if the conductivity of material remains the same, the current in the circuit is supposed to be zero. However, as the conductivity of material is increased due to the phase change from semiconducting to metallic, the current flow in the circuit will be increased gradually accordingly. The electrical resistance R of mono-crystalline Si can be determined by using the relation R = ρ(l/A). If the value of l/A for the cross-sectional area of the β-Sn can be calculated, the electrical resistance R of the material can be obtained.

Figure 8a shows the resistance-strain curve (the right side ordinate represents the equivalent electrical resistance). It can be found that the electrical resistance of the SiNW does not show obvious change when the strain is smaller than 37%, since the phase change from Si-I to Si-II is not obvious at this small strain level. As the strain is larger than 37%, some of Si-II atoms are produced due to the plastic deformation of material. Consequently, the electrical resistance of material starts to decrease. As shown in Figure 8b, since the Si-II atoms are not significantly produced at strain larger than 37%, the current is not yet increased dramatically. The electrical resistance of material is reduced continuously with the increase of strain. As the strain is increased further, the number of Si-II atoms gradually becomes saturated. As the strain keeps increasing and larger than 57%, the electrical resistance of the material is not reduced continuously due to the phase change from Si-II to high pressure or amorphous phase. Finally, as the applied stress is larger than the ultimate strength of material (e.g., 57% strain in Figure 8b), the material fails by fracture.

3.2. Effects of Surface Orientation

The effects of three different surface orientations, namely (001), (011), and (111), on the deformation pattern and the electric resistance of SiNWs were investigated individually. It is well-known that the slip systems of the single crystal silicon with distinct surface orientations are different [52,53]. For instance, the (001)- and (011)-oriented single crystalline silicon’s can launch two pairs and one-pair slip systems, respectively. Moreover, the slip system of the latter is perpendicular to the tensile direction. As the material can launch more slip systems, the strain is easily increased through dislocations without a significant increase of stress. Therefore, its modulus of elasticity would be lower. On the contrary, if the material does not have any slip system, its modulus of elasticity should be much higher comparatively. In other words, the modulus of elasticity and conductivity of nanostructure are related to the number of slip systems.

The patterns of deformation and fracture for (001)-, (011)- and (111)-oriented SiNWs were shown in Figure 9, Figure 10 and Figure 11, respectively. It was observed that the dislocations of nanostructure will appear first to facilitate the elongation. Later on the nanostructure of material will be reconstructed to produce phase transformation with the increase of tensile stress. As the strain is increased further, a large amount of amorphous phase is suddenly produced near the slip-plane of the nanostructure and leads to the fracture of SiNW material. As shown in Figure 9, the (001)-oriented SiNW is destroyed along (111)-plane. For the case of (011)-oriented SiNW, a large amount of atoms are slipped along slip-direction of nanostructure. Since this material has only one pair of slip system with an angle of 45° with respect to the tensile direction, more space might be accommodated for the deformation of material. For instance, the shape of cross-section may be changed from circle to ellipse gradually, as shown in Figure 10. Since the number of slip-system in (011) is less than other oriented SiNW, it is difficult to endure the stress through phase transformation. Consequently, a large amount of amorphous phase is produced along slip-plane and leads to the fracture finally. For (111)-oriented SiNW, the angle between the slip system and the tensile direction is just 90°. Consequently, the atoms are difficult to move along the slip plane. Fracture of material needs to have the bonds breaking directly with no any mechanisms of dislocations and phase change. Therefore, as shown in Figure 11, the stress of fracture becomes much higher and the fracture plane is perpendicular to the tensile direction. The modulus of elasticity of the material also depends on the orientation. As indicated in Figure 12, since slip system is more difficult to launch at (111)-oriented SiNW, its modulus of elasticity is the highest. On the other hand, the (001)-oriented SiNW can launch the highest number of slip systems compared to the other two orientations. Its modulus of elasticity is, therefore, the lowest.

As reported in the literature [12,13,15], the direction of the applied stress has an effect on the conductive properties of the material. As shown in Figure 8a, under the action of the tensile stress, the value of l/A of the β-Sn varies in the range 0.027–0.0025. The corresponding electrical resistance R of the material is within the range of 10³–10⁻³. It was estimated that, to change the electricity of SiNW from semiconductor to conductor, the electrical resistance of the material must be reduced to below 10⁻², or the value of l/A for β-Sn approximately 0.0075 (see Figure 8a). In other words, if l/A of β-Sn is higher than the threshold value, the material behaves like a semiconductor and when l/A is reduced to or below the level of 0.0075, the material becomes the conductor.

As discussed above, the ultimate strains of (011)- and (111)- SiNWs are about 30% and 35%, respectively. If the l/A of the materials is reduced to 0.0075, their corresponding strains for (011)- and (111)-oriented SiNWs should be 38% and 43%, respectively, as shown in Figure 13a. In other words, these values have already larger than the ultimate strains of the material. It can be seen in Figure 13b that the electric current of (011)-oriented and (111)-oriented SiNWs can be raised significantly when the material changes from semiconductor to conductive. The relationship between stress and electricity is shown in Figure 14a,b. On the other hand, the stress levels of σ_zz and τ_max required to change the electricity of (001)-oriented SiNW are smaller than (011)- and (111)-oriented SiNWs. The significant change of electricity in (001)-oriented SiNW is realized as the σ_zz is greater than 24 GPa, as shown in Figure 14c. For (011)- and (111)-oriented SiNWs, the required stress levels are 31 and 42 GPa, respectively, and the materials are already fractured at these stress levels. Therefore, it is not possible to change the electrical property of the (011)- and (111)-oriented SiNWs simply by applying a tensile stress. However, for (001)-oriented SiNW, one can change the electrical property by the application of a tensile stress. Further studies along this direction are indeed worthwhile.

3.3. Effects of Unloading

Since the electric property of (001)-oriented SiNW can be changed by stress before failure, the mechanisms of dislocation and phase transformation of this material under the action of tensile stress were investigated further. It has been mentioned that the variation of stress in this material is related to phase change, such as transformed from Si-I phase to meta-stable phase, to Si-II phase, and to the high-pressure phase. The phase change from Si-I to meta-stable phase is within the elastic deformation. However, the phase change from meta-stable to Si-II phase is attributed to plastic deformation. When the phase transformation takes place in the elastic range, after unloading the induced meta-stable phase is recovered to the original Si-I phase and the length of SiNW remains unchanged. It is apparent that the corresponding electric property will also remain unchanged after unloading.

Figure 15a shows the stress-strain curves after unloading at strain levels of 7%, 27%, 37%, 57%, and fracture respectively. It is seen that when the unloading started at 7% strain, the SiNW does not possess permanent elongation after complete unloading since there is no phase change during the loading phase. As the unloading started at 27% strain, the SiNW has experienced a large amount of structure phase transformation during loading including most of meta-stable phase and a little Si-II phase, as shown in Figure 16. After unloading, most of meta-stable phase will be reconstructed and converted into original Si-I phase. Since some residual shear stress about 2 GPa exists inside the nanostructure at strain 27%, as shown in Figure 15b, the residual Si-II phase inside the structure induces the re-crystallization of meta-stable phase. Consequently, a residual elongation of 2.2 nm is produced. As the strain is increased further and greater than 27% upon unloading, the residual elongation after complete unloading is also increased. The residual elongation after unloading becomes 4.6 and 12.5 nm at the unloading strains of 37% and 57%, respectively. As shown in Figure 16, when strain is greater than 38% corresponding to a stress of 12 GPa, as shown in Figure 12, a large amount of Si-II atoms are produced inside the nanostructure and cause a large amount of plastic deformation. As reported in the literature [6,54], this stress level is the average stress of Si-II phase and a large amount of Si-II atoms are produced at this moment. As the strain is 57%, the high-pressure phase will be reconstructed and converted into Si-II phase or meta-stable phase after complete unloading. Therefore, the number of Si-II atoms is increased first during loading stage and then gradually dropped down to a steady value after unloading.

When the stress is smaller than 12 GPa, which is just the threshold of plastic deformation, only a small amount of plastic deformation is produced inside the nanostructure. Since only meta-stable phase with a few number of Si-II atoms is remained after unloading, the change of electricity is not significant. When the stress is greater than 12 GPa at a strain of 37%, a large amount of plastic energy accompanied with a large number of Si-II atoms is produced. Since the residual atoms of Si-II and meta-stable phases inside the nanostructure are significant, as shown in Figure 17, the electrical property of the nanostructure is, therefore, changed significantly.

As discussed above, when the strain is large enough to produce a large amount of Si-II atoms inside the nanostructure, a considerable amount of Si-II phase will remain inside the nanostructure after unloading because Si-II phase is the consequence of plastic deformation, which will not be fully recovered after unloading. Therefore, the amount of Si-II phase, produced and remained during loading and unloading, respectively, will play the key role of the variance of electrical property of SiNW. Figure 18 shows the relationship of resistance and current versus strain of SiNW. It can be observed that when the strain reaches to 57% during loading and then unloading is applied, the electrical resistance of the material will be decreased at first and then increased to a steady value gradually. The residual l/A finally reaches a value lower than 0.0075. This result reflects the mechanical phenomenon of nanostructure in loading and unloading and its corresponding electric conductivity is transformed from semiconductor to conductor. When the stress is greater than 24 GPa, a large number of Si-II atoms inside the nanostructure cause the change of electric property. As shown in Figure 18a, at strains of 27% and 37%, the value of residual l/A is returned to the basic point after unloading. In other words, this strain level is too low to change the electric property of the material. As shown in Figure 18b, the current of SiNW maintains at a certain value without returning back to the basic point after unloading. Therefore, appropriate application of tensile stress on (001) SiNW might be beneficial to change the electrical property of the materials even on unloading. Specifically, this nanostructured material behaves like a conductor as a result of the residual Si-II phase on unloading.

3.4. Effects of Temperature

It is well known that the variation of temperature might have a significant influence on the phenomena of melting, microstructure and physical properties of materials. Stress-strain curves of the SiNWs subjected to tensile stress at different temperatures are shown in Figure 19. It can be seen that the ultimate strength of the material is decreased as the temperature is increased. Since the bonds between molecules are more easily to break at higher temperature due to higher kinetic energy of molecules, the ultimate strength is, therefore, decreased. Consequently, the stress level required to produce the phase change may be decreased with the increase of temperature. Additionally, the electrical property of the material can also be altered more easily at higher temperature.

Figure 20 shows the resistance and current versus strain of SiNW. It can be seen that the strain level necessary to change the electrical property of the materials is decreased with increasing temperature. At temperature 700 K, the strain of 46% is required to obtain the result of l/A = 0.0075. As the system temperature is 300 K, the required strain is increased to 52%. As shown in Figure 20b, the strain required to increase the current to a specific value is decreased with the increase of temperature. In other words, the conductivity of the material is enhanced at higher temperature.

The values of l/A at three different temperatures subjected to σ_zz and τ_max are as shown in Figure 21a,b, respectively. It is seen that the (l/A) at 700 K decreases the fastest, while at 300 K it is the slowest. As shown in Figure 20a, the curves of l/A at temperatures of 700 and 500 K are intersected with each other at the stress level near 23–27 GPa. The decreasing rate of l/A at 500K is slower than that at 700 K as the stress is smaller than 23 GPa and it is opposite when the stress is greater than 27 GPa. It is probably because as the temperature becomes higher than 700 K, the phase change from Si-II to high pressure or amorphous phase is already taken place at lower stress level and, therefore, gives less contribution for further decrease of l/A. As the strain is greater than 47%, the current at 500 K will be greater than at 700 K, as shown in Figure 20b. Therefore, further higher temperature might continuously change the conductivity of the material. As shown in Figure 21c, if the change of material conductivity is performed at 700 K, the axial stress σ_zz should be greater than 21 GPa. However, stresses of 22.5 GPa and 24 GPa are required at temperatures of 500 K and 300 K, respectively. In addition, it was found that 500 K might be the most suitable temperature to change the electrical property of the materials.

4. Conclusions

A molecular dynamics (MD) simulation was adopted to examine the deformation and phase transformation of mono-crystalline Si nanowire subjected to tensile stress. While the size of SiNWs considered in this study is quite small, this phenomenon also appears in the cases with larger sizes, as reported in the reference. During the loading period, the variation of stress in the material can be experienced as the result of dislocation or phase transformation. It was found by using the techniques of CN and CSP that as SiNW is deformed, the dislocation will appear first and then the phase transformation. The nanostructure of the material is forced to deform by the maximum shear stress τ_max and results in dislocations. The dislocations then introduce the re-crystallization of microstructure and lead to the phase change such that the total energy of the system is minimized. Effect of surface-orientations of the material on the change of a material’s electrical property under tensile stress is also investigated in this work. It was found that the ultimate tensile strength of the material in both (011)- and (111)-oriented SiNWs is lower than the critical level of stress to cause the sudden change of conductivity. In other words, it seems to be impossible to change the electrical property of these materials without failure. However, for (001)-oriented SiNW, the stress needed to induce sudden change of conductivity is lower than the ultimate strength of the material. Consequently, it is feasible to change the electrical property of (001)-oriented SiNW by applying a tensile stress. In addition, phase transformation during unloading also has effect on the conductivity of the material. At lower stress level, the stress in the material can be endured through the introduction of a meta-stable phase. After unloading, the meta-stable phase is recovered to original Si-I phase with no residual elongation. However, at higher stress level, a large amount of Si-II and amorphous phases accompanied with the significant plastic deformation were produced. Consequently, a significant residual elongation remains after unloading. More specifically, as the applied tensile stress is greater than 24 GPa, a large amount of Si-II atoms are remained after unloading and introduce the change of the material from semiconductor to conductor. In other words, an appropriate application of tensile stress can realize the change and benefit of the electrical property. The change of the electrical property of the materials can be accomplished easier at high temperature, especially at 500 K.