Nanoscale Mechanical and Mechanically Induced Electrical Properties of Silicon Nanowires

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1 crystals Article Nanoscale Mechanical and Mechanically-Induced Electrical Properties of Silicon Nanowires Yen-Hung Lin and Tei-Chen Chen * Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan; [email protected] * + 886-6-2757575 Correspondence: [email protected]; Tel:    Received: 21 March 2019; Accepted: 6 May 2019; Published: 7 May 2019 Molecular dynamics (MD) simulation was employed to examine the deformation and phase Abstract: 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. ff ff erent The e ects of temperature on phase transformation of mono-crystalline SiNWs for three di 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. Keywords: mono-crystalline SiNWs; molecular dynamics; coordination number; centro-symmetry parameter; phase transformation; dislocation; conductivity; resistance 1. Introduction The discovery of a number of specific structures and phase transformations in silicon material [ 1 – 15 ] has attracted great attention in semiconductor industry in the recent decades. The physical properties of silicon materials are significantly a ected by stress, which may lead to the evolution of phase ff 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 4 – 15 ]. Complete understanding of the detailed is influenced by the direction of the applied stress [ mechanisms of strained-Si may enhance the development of the Si materials in semiconductor science ff and technology. For instance, high performance nanowire metal-oxide-semiconductor field-e ect 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 e ff ects [ 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 e ect of side surface orientation on the mechanical properties of silicon nanowires ff was studied by molecular dynamics simulations [ 17 ]. It was found that silicon nanowires with {100} Crystals 2019 , crystals , 240; doi:10.3390 / cryst9050240 www.mdpi.com / journal / 9

2 Crystals 2019 9 , 240 2 of 20 , 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 – 22 ]. Most traditional experimental methods are capable of observing the during nanoindentation [ 18 , ] have utilized transmission electron 4 microstructures only after unloading. Some investigators [ 5 microscopy (TEM) to in situ monitor and observe the evolution of structural phase transformation ffi process. However, this technology is extremely di cult 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 6 – 11 ]. Only a few work investigated its electric conductive properties [ 8 – 11 Si [ ]. Conductivity of mono-crystalline Si is the key property for various applications of silicon material. It was found that the 12 13 , 15 ]. Silicon conductive properties of the Si material are closely linked to the amount of Si-II phase [ , 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 23 ]. The strain retained in NWs can significantly a of these NWs [ ect their electronic properties by ff 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 e ff ect has also been observed for Si NWs [ 26 ]. Moreover, the optical properties of the Si nanowires were also a ff ected by mechanical strain under the applications of an electric field through giant electro-optical e ff 27 ]. At present, ect [ 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 [ 31 ] have examined either one- (1-D) or 28 – 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 e ects of unloading, temperature and surface orientation were included. Coordination number ff (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 1 − 6 − 10 direction with a strain rate 0.6 fs Z in the . 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 Terso ff [32–36] that considers the e ff ect of bond angle and covalent bonds, has been shown to be

3 Crystals 2019 9 , 240 3 of 20 , covalent bonds, has been shown to be particularly [32–36] that considers the effect of bond angle and th a diamond lattice structure such as C, Si, and reasonable in dealing with IV elements and those wi Ge. Moreover, the accuracy and applicability of this potential have been further verified by particularly reasonable in dealing with IV elements and those with a diamond lattice structure such as simulation and experimental results [37–39]. researchers through good agreements between C, Si, and Ge. Moreover, the accuracy and applicability of this potential have been further verified by Therefore, the Tersoff potential is study to analyze the dynamic function [36] was adopted in th researchers through good agreements between simulation and experimental results [ – 37 ]. Therefore, 39 ep as short as 1 fs was used to ensure solution correlations in Si-Si atoms. In this work, the time st ] was adopted in this study to analyze the dynamic correlations in Si-Si the Terso 36 potential function [ ff methodology was used to incorporate Newton’s equations of accuracy. A modified five-step atoms. In this work, the time step as short as 1 fs was used to ensure solution accuracy. A modified motion, so that the position and velocity of a particle can be effectively evaluated. Moreover, the five-step methodology was used to incorporate Newton’s equations of motion, so that the position mixed neighbor list was applied to enhance computational efficiency. The simulations were ff ectively evaluated. Moreover, the mixed neighbor list was applied and velocity of a particle can be e performed in constant NVT ensemble with velocity-Verlet integrator. The model was first relaxed to enhance computational e ciency. The simulations were performed in constant NVT ensemble ffi for 50,000 steps at 300 K and zero force. Temperature was controlled using a Nosé-Hoover with velocity-Verlet integrator. The model was first relaxed for 50,000 steps at 300 K and zero force. thermostat. -Hoover thermostat. é Temperature was controlled using a Nos The stresses of SiNWs were determined by using the maximum local stress (MLS) [40–42] ] 42 – 40 The stresses of SiNWs were determined by using the maximum local stress (MLS) [ technique. In the method of MLS, the SiNW was divided into one hundred regions along the technique. In the method of MLS, the SiNW was divided into one hundred regions along the loading loading axis at each time step. Initially, the local stresses in each region were determined separately axis at each time step. Initially, the local stresses in each region were determined separately using the using the Miyazaki’s method [43]. Then, the maxi mum of these local stresses was defined as the 43 Miyazaki’s method [ ]. Then, the maximum of these local stresses was defined as the true stress of true stress of the SiNW. Techniques of coordi nation number (CN) [6–10] and centro-symmetry 44 the SiNW. Techniques of coordination number (CN) [ 51 ] 6 – 10 ] and centro-symmetry parameter [ – parameter [44–51] were also used to monitor and elucidate the detailed mechanism of phase were also used to monitor and elucidate the detailed mechanism of phase transformation throughout transformation throughout the whole process in wh ich the evolution of structural phase change and the whole process in which the evolution of structural phase change and the dislocation structure can the dislocation structure can be identified. be identified. Figure 1. MD Simulation model for the SiNW. A DC voltage is supposed to apply at the top and MD Simulation model for the SiNW. A DC voltage is supposed to apply at the top and bottom Figure 1. bottom surfaces from which a circuit is connected. surfaces from which a circuit is connected. 3. Results and Discussion 3. Results and Discussion The original atoms of monocrystalline Si, conventionally labeled as Si-I phase, have a coordination The original atoms of monocrystalline Si, conv entionally labeled as Si-I phase, have a ◦ ◦ number of four. Figure 2 shows that the structure of Si-I is gradually deformed from 90 on to 70 the structure of Si-I is gradually deformed from coordination number of four. Figure 2 shows that the (001)-orientation under the action of tensile stress. The phase with a coordination number of six, of tensile stress. The phase with a coordination 90° to 70° on the (001)-orientation under the action β labeled as -Sn structure (Si-II), is gradually formed due to relative sliding between atoms along the  rmed due to relative sliding between -Sn structure (Si-II), is gradually fo number of six, labeled as ]. The electrical resistance of mono-crystalline Si can be determined by the relation 9 7 – tensile direction [ -crystalline Si can be atoms along the tensile direction [7–9]. The electr ical resistance of mono , and ), where A A ρ denote the specific resistance, the length, and the cross-sectional area of , l of R = ρ ( l / = A ), where ρ determined by the relation of , l , and A denote the specific resistance, the length, R ρ ( l / the β ]. If the cross-sectional area of the 15 -Sn phase, respectively [ -Sn can be evaluated, the electrical β the cross-sectional area of the and the cross-sectional area of the β -Sn phase, respectively [15]. If R resistance, , of the material can then be obtained accordingly. R β -Sn can be evaluated, the electrical resistance, , of the material can then be obtained accordingly.

4 Crystals 9 , 240 4 of 20 2019 , Figure 2. Microstructure of -Sn phase. β -Sn phase. Figure 2. Microstructure of 3.1. Mechanical Behaviors of Nanostructured Si Nano Wire 3.1. Mechanical Behaviors of Nanostructured Si Nano Wire Microstructure of -Sn phase. Figure 2. Both dislocation and phase transformation are produced after the atom s in the material are Both dislocation and phase transformation are produced after the atoms in the material are slipped 3.1. Mechanical Behaviors of Nanostructured Si Nano Wire slipped with each other under the action of exte rnal forces. If the microstructure induced by with each other under the action of external forces. If the microstructure induced by dislocations leads produced after the atom s in the material are Both dislocation and phase transformation are dislocations leads to a stable and physically meaningful phase, it is generally called phase to a stable and physically meaningful phase, it is generally called phase transformation. Otherwise, slipped with each other under the action of exte rnal forces. If the microstructure induced by transformation. Otherwise, the microstructure induced by dislocations is just a result of a specific the microstructure induced by dislocations is just a result of a specific deformation pattern. It is obvious dislocations leads to a stable and physically meaningful phase, it is generally called phase of stress in material is closely related to the deformation pattern. It is obvious that the variation that the variation of stress in material is closely related to the evolution of either dislocation or phase transformation. Otherwise, the microstructure induced by dislocations is just a result of a specific evolution of either dislocation or phase transforma tion. By utilizing the CN and CSP techniques, the transformation. By utilizing the CN and CSP techniques, the atoms under the evolution of phase of stress in material is closely related to the deformation pattern. It is obvious that the variation atoms under the evolution of phase transformation and dislocation in (001)-oriented SiNW can be transformation and dislocation in (001)-oriented SiNW can be extracted and is shown in Figure 3. tion. By utilizing the CN and CSP techniques, the evolution of either dislocation or phase transforma extracted and is shown in Figure 3. It can be seen that at the same strain level the region having and dislocation in (001)-oriented SiNW can be atoms under the evolution of phase transformation It can be seen that at the same strain level the region having dislocation (blue shown by CSP) in is dislocation (blue shown by CSP) in is obviously larger than that of phase transformation (cyan extracted and is shown in Figure 3. It can be seen that at the same strain level the region having obviously larger than that of phase transformation (cyan shown by CN). The latter is almost completely shown by CN). The latter is almost completely encl osed by the former. As the strain is gradually dislocation (blue shown by CSP) in is obviously larger than that of phase transformation (cyan enclosed by the former. As the strain is gradually increased to a critical value, the atoms start to slip increased to a critical value, the atoms start to slip first and then introduce dislocations. As the shown by CN). The latter is almost completely encl osed by the former. As the strain is gradually first and then introduce dislocations. As the sliding proceeds further, the nanostructure of material is structure of material is continuously re-crystallized to form a sliding proceeds further, the nano increased to a critical value, the atoms start to slip first and then introduce dislocations. As the continuously re-crystallized to form a specific microstructure, called structural phase transformation. specific microstructure, called structural phase tran sformation. The variation of stress corresponding sliding proceeds further, the nano structure of material is continuously re-crystallized to form a The variation of stress corresponding to the evolution of dislocation and phase transformation was to the evolution of dislocation and phase transformation was shown in Figure 4. specific microstructure, called structural phase tran sformation. The variation of stress corresponding shown in Figure 4. to the evolution of dislocation and phase transformation was shown in Figure 4. Figure 3. P and phase transformation (cyan) shown by Evolution of dislocation (blue) shown by CS Figure 3. Evolution of dislocation (blue) shown by CS P and phase transformation (cyan) shown by Figure 3. Evolution of dislocation (blue) shown by CSP and phase transformation (cyan) shown by CN CN at different strains. CN at different strains. at di ff erent strains.

5 Crystals 9 , 2019 , 240 5 of 20 b ) ( ) ( a ) atoms of phase transformation (cyan) in stress-strain curve a Figure 4. ( ) MLS stress-strain curve; ( b Figure 4. b ) atoms of phase transformation (cyan) in stress-strain curve ) MLS stress-strain curve; ( ( a (atoms near the surface are screened out). (atoms near the surface are screened out). Figure 4a shows the stress-strain curve of (001)-oriented SiNW subjected to tensile stress. Both the Figure 4a shows the stress-strain curve of (001)-o riented SiNW subjected to tensile stress. Both tensile stress and the shear stress are presented. It is seen that phase transformation takes place at is seen that phase transformation takes place at the tensile stress and the shear stress are presented. It τ , where a sudden jump of the maximum shear stress, 6.8% = ε , appears instead of the tensile max  max , appears instead of the tensile = 6.8%, where a sudden jump of the maximum shear stress,  σ . stress zz stress . zz  To see the propagation of the phase change inside the NW more clearly, the atoms at and near the To see the propagation of the phase change inside the NW more clearly, the atoms at and near surface are screened out, and only the average maximum stress for the remaining atoms is computed. the remaining atoms is the surface are screened out, and only the av erage maximum stress for The calculated maximum shear stress vs. strain curve was as shown in Figure 4b. The deformation computed. The calculated maximum shear stress vs . strain curve was as shown in Figure 4b. The mechanisms within the strain range between 6.6% and 7.3% can be interpreted as follows: As the strain deformation mechanisms within the strain range between 6.6% and 7.3% can be interpreted as of the material is increased from 6.6% to 6.8%, the shear stress is gradually increased and reaches to the follows: As the strain of the material is increase d from 6.6% to 6.8%, the shear stress is gradually critical value for initiation of dislocations. As the strain is increased from 6.8% to 6.9%, a slight stress increased and reaches to the critical value for initiation of dislocations. As the strain is increased drop takes place due to the propagation of dislocations. As the strain is further increased to more than from 6.8% to 6.9%, a slight stress drop takes place due to the propagation of dislocations. As the 6.9%, the stress goes up quickly due to the significant evolution of phase change. strain is further increased to more than 6.9%, the stress goes up quickly due to the significant Figure 5 shows that the slip directions of atoms on (001)-oriented surface at strain level 7.26% evolution of phase change. 1 − 1] (red). Moreover, it can also be observed − 1] (black) and [2 − are along both the directions of [1 2 s on (001)-oriented surface at strain level 7.26% Figure 5 shows that the slip directions of atom that the slip directions of dislocation and phase change are identical, which shows the close link are along both the directions of [1 2 -1] (black) and [2 -1 -1] (red). Moreover, it can also be observed between them. Simulation results indicate that shear stress distorts the microstructure and induces that the slip directions of dislocation and phase change are identical, which shows the close link the dislocations first. The microstructure will then be rearranged and re-crystallized to reduce the between them. Simulation results indicate that sh ear stress distorts the microstructure and induces total energy. In other words, new phases will continuously be produced with the sequences of Si-I the dislocations first. The microstructure will then be rearranged and re-crystallized to reduce the phase, meta-stable phase, Si-II phase, and high-pressure phase as the stress is increased. The ability of total energy. In other words, new phases will cont inuously be produced with the sequences of Si-I erent phase to sustain the high stress is then enhanced accordingly. ff di phase, meta-stable phase, Si-II phase, and high-pressure phase as the stress is increased. The ability Generally, the variation of stress in material due to external loadings can be introduced through stress is then enhanced accordingly. of different phase to sustain the high structural phase transformation. The stress level necessary to induce phase change is phase-dependent. to external loadings can be introduced through Generally, the variation of stress in material due 6 , 42 ]. For instance, the stress level to induce metallic β -Sn phase (Si-II) should be larger than 12 GPa [ level necessary to induce phase change is structural phase transformation. The stress If one can trace the phase change of SiNW and estimate the amount of Si-II atoms, the prediction of -Sn phase (Si-II) should be larger phase-dependent. For instance, the stress level to induce metallic β its resistance change might become possible. In this work, the technique of CN is used to identify than 12 GPa [6,42]. If one can trace the phase change of SiNW and estimate the amount of Si-II atoms, CN = 4 , the coordinate number of each atom. By screening out the atoms of original Si-I phase with possible. In this work, the technique of CN is the prediction of its resistance change might become the new transformed atoms can be displayed. Figure 6 shows the lateral view of the cross-section atoms of original Si-I atom. By screening out the used to identify the coordinate number of each at various strain stages. The atoms in the deformed zone with di ff erent coordination numbers are phase with CN = 4, the new transformed atoms can be displayed. Figure 6 shows the lateral view of 5 meta-stable phase as = 4 incomplete nanostructure as blue, CN < marked by di ff erent colors (CN e atoms in the deformed zone with different the cross-section at various strain stages. Th 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).

6 Crystals 9 , 240 6 of 20 , 2019 CN = 6 Si-II phase as yellow, and CN > 6 high pressure phase as red). As shown in Figures 6 cyan, and 7, when the (001)-oriented SiNW is exerted by tensile stress, some Si-I atoms are converted into d SiNW is exerted by tensile stress, some Si-I As shown in Figures 6 and 7, when the (001)-oriente meta-stable phases with CN = 5 due to the change of covalent bonds. Figure 6 shows that at the initial CN = 5 due to the change of covalent bonds. atoms are converted into meta-stable phases with the atoms of meta-stable phase are initiated at two Figure 6 shows that at the initial tensile stage, tensile stage, the atoms of meta-stable phase are initiated at two sides of SiNW first and then gradually sides of SiNW first and then gradually spread to the middle at = 9.3%. The amount of meta-stable  spread to the middle at ε 9.3%. The amount of meta-stable phase in SiNW is increased with the = crease of tensile stress (as shows in phase in SiNW is increased with the in  = 18%). When the increase of tensile stress (as shows in ε = 18%). When the increase of meta-stable phase becomes e of the material cannot sustain comes saturated, the nanostructur increase of meta-stable phase be saturated, the nanostructure of the material cannot sustain the stress by means of the formation of the stress by means of the formation of meta-s table phase. The evolution of phase change meta-stable phase. The evolution of phase change transformed from meta-stable phase to Si-II phase high-pressure phase will be taken place. Then, transformed from meta-stable phase to Si-II phase or or high-pressure phase will be taken place. Then, the nanostructure of the new phases will keep on the nanostructure of the new phases will keep on sustaining the stress again. At = 4 7%, a large  ε = 47%, a large number of Si-II and high-pressure atoms are uniformly sustaining the stress again. At number of Si-II and high-pressur e atoms are uniformly distributed within the atoms of meta-stable distributed within the atoms of meta-stable phase. As the strain is larger than 58%, amorphous phase phase. As the strain is larger than 58%, amorphous phase starts to appear along the slip planes near starts to appear along the slip planes near the middle of SiNW, as shown in Figure 7. As the strain is the middle of SiNW, as shown in Figure 7. As the strain is larger than 62%, small voids appear larger than 62%, small voids appear between the amorphous atoms. These voids are then aggregated between the amorphous atoms. These voids are then aggregated together to form bigger = together to form bigger micro-cracks as the strain keeps increasing. At ε 72%, the SiNW finally fails micro-cracks as the strain keeps increasing. At  = 72%, the SiNW finally fails by fracture. Since a by fracture. Since a large number of Si-II atoms are produced at 47%, the resistivity of SiNW at and ε = large number of Si-II atoms are produced at = 47%, the resistivity of SiNW at and above this strain  above this strain level should reflect a significant change. level should reflect a significant change. Figure 5. Slip directions of atoms (cyan) in (001) SiNW (The directions of [1 2 -1]: black; and [2 -1 -1]: − 1]: red). Slip directions of atoms (cyan) in (001) SiNW (The directions of [1 2 − 1]: black; and [2 − 1 Figure 5. red).

7 Crystals 2019 9 , 240 7 of 20 , Figure 6.  = 7.44–18%). (cyan: The lateral view of the cross-section at different strain levels ( = The lateral view of the cross-section at di erent strain levels ( ff Figure 6. 7.44–18%). (cyan: meta-stable ε = 7.44–18%). (cyan:  The lateral view of the cross-section at different strain levels ( Figure 6. meta-stable phase with CN = 5). meta-stable phase with CN = 5). = 5). phase with CN  Figure 7. The lateral view of the cross-section at different strain levels ( = 47–72%). (blue:  The lateral view of the cross-section at different strain levels ( Figure 7. = 47–72%). (blue: ε Figure 7. The lateral view of the cross-section at di ff erent strain levels ( = 47–72%). (blue: incomplete incomplete nanostructure with CN < 4; cyan: CN = 5 meta-stable phase with CN = 5; yellow: Si-II incomplete nanostructure with CN < 4; cyan: CN = 5 meta-stable phase with CN = 5; yellow: Si-II 5; yellow: Si-II phase with = nanostructure with CN < 4; cyan: CN = 5 meta-stable phase with CN pressure phase with CN > 6). phase with CN = 6; red: high pressure phase with CN > 6). phase with CN = 6; red: high CN = 6; red: high pressure phase with CN > 6). 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 a ff ected by the phase transformation induced by tensile

8 has been investigated [12,13,1 5]. It was reported that the Recently, conductivity of SiNW 2019 Crystals 8 of 20 9 , , 240 conductivity of SiNW is closely related to the dire ction and the magnitude of strain. In other words, the conductivity of the SiNW material might be affected by the phase transformation induced by stress. A dc pseudo-voltage is imagined to be imposed on both top and bottom surfaces of SiNW, be imposed on both top and bottom surfaces of tensile stress. A dc pseudo-voltage is imagined to as shown in Figure 1, from which a circuit is connected. The change of current is evaluated as the strain connected. The change of current is evaluated as SiNW, as shown in Figure 1, from which a circuit is is increased. During elongation stage, if the conductivity of material remains the same, the current ongation stage, if the conductivity of material remains the same, the the strain is increased. During el in the circuit is supposed to be zero. However, as the conductivity of material is increased due to of material is increased current in the circuit is supposed to be zero. Howe ver, as the conductivity the phase change from semiconducting to metallic, the current flow in the circuit will be increased due to the phase change from semiconducting to me tallic, the current flow in the circuit will be gradually accordingly. The electrical resistance R of mono-crystalline Si can be determined by using of mono-crystalline Si can be determined R increased gradually accordingly. The electrical resistance / -Sn can be calculated, A / l ). If the value of A for the cross-sectional area of the l ( ρ = R the relation β for the cross-sectional area of the A / A / l l ( ρ = ). If the value of β by using the relation R -Sn can be of the material can be obtained. R the electrical resistance 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 esents the equivalent right side ordinate repr Figure 8a shows the resistance-strain curve (the electrical resistance). It can be found that the electrical resistance of the SiNW does not show obvious trical resistance of the SiNW does not show obvious electrical resistance). It can be found that the elec change when the strain is smaller than 37%, since the phase change from Si-I to Si-II is not obvious at this change when the strain is smaller than 37%, since the phase change from Si-I to Si-II is not obvious at small strain level. As the strain is larger than 37%, some of Si-II atoms are produced due to the plastic this small strain level. As the strain is larger th an 37%, some of Si-II atoms are produced due to the deformation of material. Consequently, the electrical resistance of material starts to decrease. As shown plastic deformation of material. Consequently, the elec trical resistance of material starts to decrease. in Figure 8b, since the Si-II atoms are not significantly produced at strain larger than 37%, the current As shown in Figure 8b, since the Si-II atoms are not significantly produced at strain larger than 37%, is not yet increased dramatically. The electrical resistance of material is reduced continuously with the current is not yet increased dramatically. The electrical resistance of material is reduced the increase of strain. As the strain is increased further, the number of Si-II atoms gradually becomes continuously with the increase of strain. As the strain is increased further, the number of Si-II atoms saturated. As the strain keeps increasing and larger than 57%, the electrical resistance of the material is gradually becomes saturated. As the strain keeps increasing and larger than 57%, the electrical not reduced continuously due to the phase change from Si-II to high pressure or amorphous phase. resistance of the material is not reduced continuo usly due to the phase change from Si-II to high Finally, as the applied stress is larger than the ultimate strength of material (e.g., 57% strain in Figure 8b), pressure or amorphous phase. Finally, as the applied stress is larger than the ultimate strength of the material fails by fracture. material (e.g., 57% strain in Figure 8b), the material fails by fracture. a ) ( b ( ) ) resistance-strain curves; a Resistance and current versus tensile strain of SiNW ( Figure 8. ) Figure 8. Resistance and current versus tensile strain of SiNW ( a ) resistance-strain curves; ( b b 5 meta-stable phase = 4; cyan: CN < ) current-strain curves (blue: incomplete nanostructure with CN ( current-strain curves (blue: incomplete nanostruct ure with CN < 4; cyan: CN = 5 meta-stable phase 6). = with CN 5; yellow: Si-II phase with CN = 6; red: high-pressure phase with CN > with CN = 5; yellow: Si-II phase with CN = 6; red: high-pressure phase with CN > 6). ects of Surface Orientation 3.2. E ff 3.2. Effects of Surface Orientation The e ff ects of three di ff erent surface orientations, namely (001), (011), and (111), on the deformation The effects of three different surface orientat ions, namely (001), (011), and (111), on the pattern and the electric resistance of SiNWs were investigated individually. It is well-known that deformation pattern and the electric resistance of SiNWs were investigated individually. It is 52 erent [ ]. 53 , ff the slip systems of the single crystal silicon with distinct surface orientations are di well-known that the slip systems of the single crystal silicon with distinct surface orientations are For instance, the (001)- and (011)-oriented single crystalline silicon’s can launch two pairs and one-pair different [52,53]. For instance, the (001)- and (011)-oriented single crystalline silicon’s can launch two slip systems, respectively. Moreover, the slip system of the latter is perpendicular to the tensile direction. pairs and one-pair slip systems, respectively. Moreov er, the slip system of the latter is perpendicular As the material can launch more slip systems, the strain is easily increased through dislocations without to the tensile direction. As the material can launch more slip systems, the strain is easily increased a significant increase of stress. Therefore, its modulus of elasticity would be lower. On the contrary, if the of stress. Therefore, its modulus of elasticity through dislocations without a significant increase material does not have any slip system, its modulus of elasticity should be much higher comparatively.

9 Crystals 9 , 240 9 of 20 , 2019 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 In other words, the modulus of elasticity and conductivity of nanostructure are related to the number conductivity of nanostructure are related to the number of slip systems. of slip systems. The patterns of deformation and fracture for (001)-, (011)- and (111)-oriented SiNWs were The patterns of deformation and fracture for (001)-, (011)- and (111)-oriented SiNWs were shown ed that the dislocations of nanostructure will shown in Figures 9–11, respectively. It was observ in Figures 9–11, respectively. It was observed that the dislocations of nanostructure will appear first appear first to facilitate the elongation. Later on the nanostructure of material will be reconstructed to facilitate the elongation. Later on the nanostructure of material will be reconstructed to produce to produce phase transformation with the increase of tensile stress. As the strain is increased further, phase transformation with the increase of tensile stress. As the strain is increased further, a large a large amount of amorphous phase is suddenly produced near the slip-plane of the nanostructure amount of amorphous phase is suddenly produced near the slip-plane of the nanostructure and and leads to the fracture of SiNW material. As shown in Figure 9, the (001)-oriented SiNW is leads to the fracture of SiNW material. As shown in Figure 9, the (001)-oriented SiNW is destroyed destroyed along (111)-plane. For the case of (011)-oriented SiNW, a large amount of atoms are along (111)-plane. For the case of (011)-oriented SiNW, a large amount of atoms are slipped along slipped along slip-direction of nanostructure. Since this material has only one pair of slip system slip-direction of nanostructure. Since this material has only one pair of slip system with an angle t be accommodated for the with an angle of 45° with respect to the tensile direction, more space migh ◦ with respect to the tensile direction, more space might be accommodated for the deformation of 45 cross-section may be changed from circle to deformation of material. For instance, the shape of of material. For instance, the shape of cross-section may be changed from circle to ellipse gradually, ellipse gradually, as shown in Figu re 10. Since the number of slip-system in (011) is less than other as shown in Figure 10. Since the number of slip-system in (011) is less than other oriented SiNW, ress through phase transformation. Consequently, a oriented SiNW, it is difficult to endure the st ffi cult to endure the stress through phase transformation. Consequently, a large amount of it is di large amount of amorphous phase is produced along slip-plane and leads to the fracture finally. For amorphous phase is produced along slip-plane and leads to the fracture finally. For (111)-oriented system and the tensile direction is just 90°. (111)-oriented SiNW, the angle between the slip ◦ . Consequently, the atoms 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 cult to move along the slip plane. Fracture of material needs to have the bonds breaking ffi are di have the bonds breaking directly with no any mechanisms of dislocations and phase change. directly with no any mechanisms of dislocations and phase change. Therefore, as shown in Figure 11, Therefore, as shown in Figure 11, the stress of fracture becomes much higher and the fracture plane the stress of fracture becomes much higher and the fracture plane is perpendicular to the tensile is perpendicular to the tensile direction. The modulu s of elasticity of the material also depends on direction. The modulus of elasticity of the material also depends on the orientation. As indicated in the orientation. As indicated in Figure 12, since slip system is more difficult to launch at cult to launch at (111)-oriented SiNW, its modulus of elasticity Figure 12, since slip system is more di ffi (111)-oriented SiNW, its modulus of elasticity is the highest. On the other hand, the (001)-oriented is the highest. On the other hand, the (001)-oriented SiNW can launch the highest number of slip SiNW can launch the highest number of slip syst ems compared to the other two orientations. Its systems compared to the other two orientations. Its modulus of elasticity is, therefore, the lowest. modulus of elasticity is, therefore, the lowest. Figure 9. Fracture pattern of (001)-oriented SiNW by tensile stress. (blue: incomplete nanostructure Fracture pattern of (001)-oriented SiNW by te nsile stress. (blue: incomplete nanostructure Figure 9. 5; yellow: Si-II phase with CN = < 6; red: with CN = 4; cyan: CN = 5 meta-stable phase with CN with CN = 6; red: high = 5; yellow: Si-II phase with CN < 4; cyan: CN = 5 meta-stable phase with CN high pressure phase with CN > 6). pressure phase with CN > 6).

10 Crystals 2019 9 , 240 10 of 20 , Figure 10. Fracture pattern of (011)-oriented SiNW by te nsile stress. (blue: incomplete nanostructure Fracture pattern of (011)-oriented SiNW by tensile stress. (blue: incomplete nanostructure Figure 10. Figure 10. Fracture pattern of (011)-oriented SiNW by te nsile stress. (blue: incomplete nanostructure = 5; yellow: Si-II phase with CN = 6; red: high with CN < 4; cyan: CN = 5 meta-stable phase with CN < 6; red: with CN 4; cyan: CN = 5 meta-stable phase with CN = 5; yellow: Si-II phase with CN = with CN < 4; cyan: CN = 5 meta-stable phase with CN = 5; yellow: Si-II phase with CN = 6; red: high pressure phase with CN > 6). high pressure phase with CN 6). > pressure phase with CN > 6). Fracture pattern of (111)-oriented SiNW by tensile stress. (blue: incomplete nanostructure Figure 11. Figure 11. Fracture pattern of (111)-oriented SiNW by te complete nanostructure nsile stress. (blue: in Figure 11. complete nanostructure Fracture pattern of (111)-oriented SiNW by te nsile stress. (blue: in 5; yellow: Si-II phase with CN = = 6; red: with CN < 4; cyan: CN = 5 meta-stable phase with CN with CN = 6; red: high = 5; yellow: Si-II phase with CN < 4; cyan: CN = 5 meta-stable phase with CN with CN = 6; red: high = 5; yellow: Si-II phase with CN < 4; cyan: CN = 5 meta-stable phase with CN > 6). high pressure phase with CN pressure phase with CN > 6). pressure phase with CN > 6).

11 Crystals 2019 , 9 , 240 11 of 20 Figure 12. MLS stress-strain curves. Figure 12. MLS stress-strain curves. , ff ], the direction of the applied stress has an e As reported in the literature [ 12 15 ect on the 13 , ion of the applied stress has an effect on the As reported in the literature [12,13,15], the direct conductive properties of the material. As shown in Figure 8a, under the action of the tensile stress, Figure 8a, under the action of the tensile stress, conductive properties of the material. As shown in -Sn varies in the range 0.027–0.0025. The corresponding electrical resistance the value of R β of the A / l of the / β -Sn varies in the range 0.027–0.0025. The corresponding electrical resistance the value of l A − 3 3 3 − 3 of the material is within the range of 10 –10 . It was estimated that, to change the electricity of SiNW R of the material is within the range of 10 . It was estimated that, to change the electricity of –10 from semiconductor to conductor, the electrical resistance of the material must be reduced to below resistance of the material must be reduced to SiNW from semiconductor to conductor, the electrical 2 − − 2 -Sn approximately 0.0075 (see Figure 8a). In other words, if 10 β for A / l -Sn is , or the value of β of A / l below 10 for , or the value of l / A / β -Sn approximately 0.0075 (see Figure 8a). In other words, if l of A higher than the threshold value, the material behaves like a semiconductor and when l A / is reduced to -Sn is higher than the threshold value, the ma terial behaves like a semiconductor and when l / A is β or below the level of 0.0075, the material becomes the conductor. 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%, As discussed above, the ultimate strains of (011)- and (111)- SiNWs are about 30% and 35%, respectively. If the A of the materials is reduced to 0.0075, their corresponding strains for (011)- and / l A of the materials is reduced to 0.0075, l / their corresponding strains for (011)- and respectively. If the (111)-oriented SiNWs should be 38% and 43%, respectively, as shown in Figure 13a. In other words, (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 rains of the material. It can be seen in Figure 13b these values have already larger than the ultimate st that the electric current of (011)-oriented and (111)-oriented SiNWs can be raised significantly when the that the electric current of (011)-oriented and (111 )-oriented SiNWs can be raised significantly when material changes from semiconductor to conductive. The relationship between stress and electricity is the material changes from semiconductor to conductive. The relationship between stress and shown in Figure 14a,b. On the other hand, the stress levels of required to change the τ and σ zz max electricity is shown in Figure 14a,b. On the other hand, the stress levels of  max  and zz required to electricity of (001)-oriented SiNW are smaller than (011)- and (111)-oriented SiNWs. The significant change the electricity of (001)-oriented SiNW are smaller than (011)- and (111)-oriented SiNWs. The is greater than 24 GPa, as shown σ change of electricity in (001)-oriented SiNW is realized as the zz zz is greater than 24 GPa,  significant change of electricity in (001)-oriented SiNW is realized as the in Figure 14c. For (011)- and (111)-oriented SiNWs, the required stress levels are 31 and 42 GPa, as shown in Figure 14c. For (011)- and (111)-oriented SiNWs, the required stress levels are 31 and 42 respectively, and the materials are already fractured at these stress levels. Therefore, it is not possible GPa, respectively, and the materials are already fractured at these stress levels. Therefore, it is not to change the electrical property of the (011)- and (111)-oriented SiNWs simply by applying a tensile possible to change the electrical property of the (0 11)- and (111)-oriented SiNWs simply by applying stress. However, for (001)-oriented SiNW, one can change the electrical property by the application of )-oriented SiNW, one can change the electrical property by the a tensile stress. However, for (001 a tensile stress. Further studies along this direction are indeed worthwhile. application of a tensile stress. Further studies along this direction are indeed worthwhile.

12 Crystals 9 , 240 12 of 20 2019 , a ) ( b ) ( b ) ( a ( ) Resistance and current versus tensile strain of SiNW ( ) b ) resistance-strain curves; ( Figure 13. a ) resistance-strain curves; a Resistance and current versus tensile strain of SiNW ( Figure 13. ) Figure 13. Resistance and current versus tensile strain of SiNW ( a ) resistance-strain curves; ( b current-strain curves. ( b ) current-strain curves. current-strain curves. ) resistance vs. axial l/A ( Figure 14. a Relationship between stress and resistance represented by stress; ( b ) resistance vs. maximum shear stress; ( ) comparison of stress at l/A = 0.0075 between (001), c l/A Relationship between stress and resistance represented by Figure 14. ) resistance vs. axial a ( Figure 14. Relationship between stress and resistance represented by ) resistance vs. axial stress; a ( A / l (011), and (111) orientation surfaces. ) resistance vs. maximum shear stress; ( ) comparison of stress at l/A = 0.0075 between (001), c stress; ( b ( / l 0.0075 between (001), (011), = ) comparison of stress at c ) resistance vs. maximum shear stress; ( b A (011), and (111) orientation surfaces. 3.3. Effects of Unloading and (111) orientation surfaces. by stress before failure, the Since the electric property of ( 001)-oriented SiNW can be changed ff 3.3. E ects of Unloading 3.3. Effects of Unloading mechanisms of dislocation and phase transformation of this material under the action of tensile Since the electric property of (001)-oriented SiNW can be changed by stress before failure, by stress before failure, the Since the electric property of ( 001)-oriented SiNW can be changed stress were investigated further. It has been mentioned that the variation of stress in this material is the mechanisms of dislocation and phase transformation of this material under the action of tensile 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

13 Crystals 9 , 240 13 of 20 2019 , 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 related to phase change, such as transformed from Si-I phase to meta-stable phase, to Si-II phase, deformation. When the phase transformation takes place in the elastic range, after unloading the and to the high-pressure phase. The phase change from Si-I to meta-stable phase is within the elastic induced meta-stable phase is recovered to the original Si-I phase and the length of SiNW remains deformation. However, the phase change from meta -stable to Si-II phase is attributed to plastic unchanged. It is apparent that the corresponding electric property will also remain unchanged place in the elastic range, after unloading the deformation. When the phase transformation takes after unloading. induced meta-stable phase is recovered to the orig inal Si-I phase and the length of SiNW remains unchanged. It is apparent that the corresponding electric property will also remain unchanged after Figure 15a shows the stress-strain curves after unloading at strain levels of 7%, 27%, 37%, 57%, unloading. and fracture respectively. It is seen that when the unloading started at 7% strain, the SiNW does not loading at strain levels of 7%, 27%, 37%, 57%, Figure 15a shows the stress-strain curves after un possess permanent elongation after complete unloading since there is no phase change during the loading and fracture respectively. It is seen that when the unloading started at 7% strain, the SiNW does not phase. As the unloading started at 27% strain, the SiNW has experienced a large amount of structure ing since there is no phase change during the possess permanent elongation after complete unload phase transformation during loading including most of meta-stable phase and a little Si-II phase, as shown loading phase. As the unloading started at 27% strain, the SiNW has experienced a large amount of in Figure 16. After unloading, most of meta-stable phase will be reconstructed and converted into original structure phase transformation during loading including most of meta-stable phase and a little Si-II Si-I phase. Since some residual shear stress about 2 GPa exists inside the nanostructure at strain 27%, phase, as shown in Figure 16. After unloading, most of meta-stable phase will be reconstructed and as shown in Figure 15b, the residual Si-II phase inside the structure induces the re-crystallization of converted into original Si-I phase. Since some residual shear stress about 2 GPa exists inside the meta-stable phase. Consequently, a residual elongation of 2.2 nm is produced. As the strain is increased nanostructure at strain 27%, as shown in Figure 15 b, the residual Si-II phase inside the structure induces the re-crystallization of meta-stable phase. Consequently, a re sidual elongation of 2.2 nm is further and greater than 27% upon unloading, the residual elongation after complete unloading is also produced. As the strain is increased further and greater than 27% upon unloading, the residual increased. The residual elongation after unloading becomes 4.6 and 12.5 nm at the unloading strains of 37% elongation after complete unloading is also incr eased. The residual elongation after unloading and 57%, respectively. As shown in Figure 16, when strain is greater than 38% corresponding to a stress of becomes 4.6 and 12.5 nm at the unloading strains of 37% and 57%, respectively. As shown in Figure 12 GPa, as shown in Figure 12, a large amount of Si-II atoms are produced inside the nanostructure and 16, when strain is greater than 38% corresponding to a stress of 12 GPa, as shown in Figure 12, a , 6 cause a large amount of plastic deformation. As reported in the literature [ 54 ], this stress level is the the nanostructure and cause a large amount of large amount of Si-II atoms are produced inside average stress of Si-II phase and a large amount of Si-II atoms are produced at this moment. As the strain plastic deformation. As reported in the literature [6,54], this stress level is the average stress of Si-II is 57%, the high-pressure phase will be reconstructed and converted into Si-II phase or meta-stable phase phase and a large amount of Si-II atoms are produced at this moment. As the strain is 57%, the after complete unloading. Therefore, the number of Si-II atoms is increased first during loading stage and tructed and converted into Si-II phase or meta-stable phase after high-pressure phase will be recons then gradually dropped down to a steady value after unloading. 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, just the threshold of plastic deformation, only a When the stress is smaller than 12 GPa, which is only a small amount of plastic deformation is produced inside the nanostructure. Since only meta-stable 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 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 eater than 12 GPa at a strain of 37%, a large amount of plastic energy significant. When the stress is gr energy accompanied with a large number of Si-II atoms is produced. Since the residual atoms of Si-II accompanied with a large number of Si-II atoms is produced. Since the residual atoms of Si-II and and meta-stable phases inside the nanostructure are significant, as shown in Figure 17, the electrical meta-stable phases inside the nanostructure are sign ificant, as shown in Figure 17, the electrical property of the nanostructure is, therefore, changed significantly. property of the nanostructure is, therefore, changed significantly. ( a ) ( b ) Figure 15. ( a ) Axial stress-strain curves; ( b ) maximum shear stress-strain curves (unloading at strain Figure 15. ( a ) Axial stress-strain curves; ( b ) maximum shear stress-strain curves (unloading at strain of of 7%: cyan; 27%: red; 37%: green; 57%: blue; without unloading: black). 7%: cyan; 27%: red; 37%: green; 57%: blue; without unloading: black).

14 Crystals 2019 , 240 14 of 20 , 9 Figure 16. Number of Si-II atoms versus strain curve (u nloading at strain of 27%: red; 37%: green; Figure 16. Number of Si-II atoms versus strain curve (u nloading at strain of 27%: red; 37%: green; Number of Si-II atoms versus strain curve (unloading at strain of 27%: red; 37%: green; 57%: Figure 16. 57%: blue; without unloading: black). 57%: blue; without unloading: black). blue; without unloading: black). Residual length and residual phases after Figure 17. unloading. (blue: incomplete nanostructure with CN = 6; red: high = 5; yellow: Si-II phase with CN < 4; cyan: CN = 5 meta-stable phase with CN pressure phase with CN > 6). Figure 17. Residual length and residual phases after unloading. (blue: incomplete nanostructure Residual length and residual phases after unloading. (blue: incomplete nanostructure Figure 17. with CN = 6; red: high with CN < 4; cyan: CN = 5 meta-stable phase with CN = 5; yellow: Si-II phase = 5; yellow: Si-II phase with CN with CN 6; red: < 4; cyan: CN = 5 meta-stable phase with CN = As discussed above, when the st rain is large enough to produce a large amount of Si-II atoms pressure phase with CN > 6). high pressure phase with CN > 6). inside the nanostructure, a considerable amount of Si-II phase will remain inside the nanostructure after unloading because Si-II phase is the conseque , which will not be fully nce of plastic deformation As discussed above, when the strain is large enough to produce a large amount of Si-II atoms As discussed above, when the st rain is large enough to produce a large amount of Si-II atoms recovered after unloading. Therefore, the amount of Si-II phase, produced and remained during inside the nanostructure, a considerable amount of Si-II phase will remain inside the nanostructure inside the nanostructure, a considerable amount of Si-II phase will remain inside the nanostructure loading and unloading, respectively, will play the key role of the variance of electrical property of after unloading because Si-II phase is the consequence of plastic deformation, which will not be fully ce and current versus strain of SiNW. It can be SiNW. Figure 18 shows the relationship of resistan , which will not be fully nce of plastic deformation after unloading because Si-II phase is the conseque observed that when the strain reaches to 57% du ring loading and then unloading is applied, the recovered after unloading. Therefore, the amount of Si-II phase, produced and remained during 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. loading and unloading, respectively, will play the key role of the variance of electrical property of Figure 18 shows the relationship of resistance and current versus strain of SiNW. It can be observed that ce and current versus strain of SiNW. It can be SiNW. Figure 18 shows the relationship of resistan when the strain reaches to 57% during loading and then unloading is applied, the electrical resistance ring loading and then unloading is applied, the observed that when the strain reaches to 57% du

15 Crystals 2019 , 240 15 of 20 , 9 electrical resistance of the material will be decr eased at first and then increased to a steady value of the material will be decreased at first and then increased to a steady value gradually. The residual A gradually. The residual finally reaches a value lower than 0.0075. This result reflects the l / finally reaches a value lower than 0.0075. This result reflects the mechanical phenomenon of l A / mechanical phenomenon of nanostructure in load ing and unloading and its corresponding electric nanostructure in loading and unloading and its corresponding electric conductivity is transformed conductivity is transformed from semiconductor to conductor. When the stress is greater than 24 from semiconductor to conductor. When the stress is greater than 24 GPa, a large number of Si-II atoms GPa, a large number of Si-II atoms inside the nanost ructure cause the change of electric property. As inside the nanostructure cause the change of electric property. As shown in Figure 18a, at strains of 27% and 37%, the value of residual shown in Figure 18a, at strains of is returned to the basic A / l 27% and 37%, the value of residual / A is returned to the basic point after unloading. In other words, l point after unloading. In other words, this strain level is too low to change the electric property of this strain level is too low to change the electric property of the material. As shown in Figure 18b, the material. As shown in Figure 18b, the current of SiNW maintains at a certain value without the current of SiNW maintains at a certain value without returning back to the basic point after ation of tensile stress returning back to the basic point after unloading. Th erefore, appropriate applic unloading. Therefore, appropriate application of tensile stress on (001) SiNW might be beneficial to e electrical property of the materials even on on (001) SiNW might be beneficial to change th change the electrical property of the materials even on unloading. Specifically, this nanostructured unloading. Specifically, this nanostructured material behaves like a conductor as a result of the material behaves like a conductor as a result of the residual Si-II phase on unloading. residual Si-II phase on unloading. a ) ( b ) ( Resistance and current versus strain of SiNW ( a ) resistance-strain curves; ( b ) current-strain Figure 18. Figure 18. Resistance and current versus strain of SiNW ( a ) resistance-strain curves; ( b ) curves (unloading at strain of 27%: red; 37%: green; 57%: blue; without unloading: black). at strain of 27%: red; 37%: green; 57%: blue; without unloading: current-strain curves (unloading black). ects of Temperature ff 3.4. E 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 It is well known that the variation of temperature might have a significant influence on the SiNWs subjected to tensile stress at di ff erent temperatures are shown in Figure 19. It can be seen that the phenomena of melting, microstructure and physical properties of materials. Stress-strain curves of ultimate strength of the material is decreased as the temperature is increased. Since the bonds between mperatures are shown in Figure 19. It can be seen the SiNWs subjected to tensile stress at different te molecules are more easily to break at higher temperature due to higher kinetic energy of molecules, that the ultimate strength of the material is de creased as the temperature is increased. Since the the ultimate strength is, therefore, decreased. Consequently, the stress level required to produce the bonds between molecules are more easily to break at higher temperature due to higher kinetic phase change may be decreased with the increase of temperature. Additionally, the electrical property energy of molecules, the ultimate strength is, th erefore, decreased. Consequently, the stress level of the material can also be altered more easily at higher temperature. ease of temperature. required to produce the phase change may be decreased with the incr Figure 20 shows the resistance and current versus strain of SiNW. It can be seen that the strain level al can also be altered more easily at higher Additionally, the electrical property of the materi necessary to change the electrical property of the materials is decreased with increasing temperature. temperature. At temperature 700 K, the strain of 46% is required to obtain the result of l A = 0.0075. As the system / Figure 20 shows the resistance and current versus st rain of SiNW. It can be seen that the strain temperature is 300 K, the required strain is increased to 52%. As shown in Figure 20b, the strain of the materials is decreased with increasing level necessary to change the electrical property required to increase the current to a specific value is decreased with the increase of temperature. temperature. At temperature 700 K, the strain A of 46% is required to obtain the result of l / = 0.0075. In other words, the conductivity of the material is enhanced at higher temperature. As the system temperature is 300 K, the required st rain is increased to 52%. As shown in Figure 20b, are as shown in ff at three di A / σ l and τ The values of erent temperatures subjected to max zz the strain required to increase the current to a specific value is decreased with the increase of A Figure 21a,b, respectively. It is seen that the ( / ) at 700 K decreases the fastest, while at 300 K it is the l the material is enhanced at higher temperature. temperature. In other words, the conductivity of slowest. As shown in Figure 20a, the curves of at temperatures of 700 and 500 K are intersected A / l / A at three different temperatures subjected to l The values of  zz and  max are as shown in ) at 700 K decreases the fastes Figure 21a,b, respectively. It is seen that the ( l / t, while at 300 K it is the A

16 Crystals 9 16 of 20 , 2019 , 240 l slowest. As shown in Figure 20a, the curves of A at temperatures of 700 and 500 K are intersected / A at 500K is slower than with each other at the stress level near 23–27 GPa. The decreasing rate of l / slowest. As shown in Figure 20a, the curves of l at temperatures of 700 and 500 K are intersected A / / l at 500K is slower than A with each other at the stress level near 23–27 GPa. The decreasing rate of that at 700 K as the stress is smaller than 23 GPa and it is opposite when the stress is greater than 27 A / with each other at the stress level near 23–27 GPa. The decreasing rate of l 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 GPa. It is probably because as the temperature becomes higher than 700 K, the phase change from that at 700 K as the stress is smaller than 23 GPa and it is opposite when the stress is greater than 27 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, 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 Si-II to high pressure or amorphous phase is already taken place at lower stress level and, therefore, l gives less contribution for further decrease of . As the strain is greater than 47%, the current at / A K will be greater than at 700 K, as shown in Figure 20b. Therefore, further higher temperature might / gives less contribution for further decrease of l A . As the strain is greater than 47%, the current at 500 500 K will be greater than at 700 K, as shown in Figure 20b. Therefore, further higher temperature continuously change the conductivity of the materi al. As shown in Figure 21c, if the change of K will be greater than at 700 K, as shown in Figure 20b. Therefore, further higher temperature might might continuously change the conductivity of the material. As shown in Figure 21c, if the change material conductivity is performed at 700 K, the axial stress  zz should be greater than 21 GPa. continuously change the conductivity of the materi al. As shown in Figure 21c, if the change of should be greater than 21 GPa. σ of material conductivity is performed at 700 K, the axial stress However, stresses of 22.5 GPa and 24 GPa are required at temperatures of 500 K and 300 K, zz material conductivity is performed at 700 K, the axial stress  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. might be the most suitable temperature to change respectively. In addition, it was found that 500 K However, stresses of 22.5 GPa and 24 GPa are required at temperatures of 500 K and 300 K, In addition, it was found that 500 K might be the most suitable temperature to change the electrical the electrical property of the materials. might be the most suitable temperature to change respectively. In addition, it was found that 500 K property of the materials. the electrical property of the materials. Axial stress-strain curves. Figure 19. Figure 19. Axial stress-strain curves. Axial stress-strain curves. Figure 19. ) ) ( a ( b ( a ) ( b ) ) resistance-strain curves; a Resistance and current versus tensile strain of SiNW ( Figure 20. ) resistance-strain curves; ( Figure 20. Resistance and current versus tensile strain of SiNW ( a b ) ) current-strain curves. b ( current-strain curves. ) Figure 20. Resistance and current versus tensile strain of SiNW ( a ) resistance-strain curves; ( b current-strain curves.

17 Crystals , 9 2019 , 240 17 of 20 l/A Relationship between stress and resistance represented by a ) at different temperatures ( Figure 21. ff Figure 21. Relationship between stress and resistance represented by l / A at di erent temperatures c axial stress; ( resistance vs. b = l/A ) comparison of stress at ) resistance vs. maximum shear stress; ( b ) resistance vs. axial stress; ( a ( ) comparison of stress at c ) resistance vs. maximum shear stress; ( 0.0075 at different temperatures. 0.0075 at di = A erent temperatures. / l ff 4. Conclusions 4. Conclusion A molecular dynamics (MD) simulation was adopted to examine the deformation and phase 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 ected to tensile stress. While the size of SiNWs transformation of mono-crystalline Si nanowire subj considered in this study is quite small, this phenomenon also appears in the cases with larger sizes, 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 od, the variation of stress in the material can be as reported in the reference. During the loading peri ase transformation. It was found by using the experienced as the result of dislocation or ph 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 techniques of CN and CSP that as SiNW is deformed, the dislocation will appear first and then phase transformation. The nanostructure of the material is forced to deform by the maximum shear the phase transformation. The nanostructure of the material is forced to deform by the maximum stress max  and results in dislocations. The dislocations then introduce the re-crystallization of and results in dislocations. The dislocations then introduce the re-crystallization of τ shear stress max microstructure and lead to the ph ase change such that the total energy of the system is minimized. ff microstructure and lead to the phase change such that the total energy of the system is minimized. E ect Effect of surface-orientations of the material on the change of a material’s electrical property under of surface-orientations of the material on the change of a material’s electrical property under tensile tensile stress is also investigated in this work. It was found that the ultimate tensile strength of the stress is also investigated in this work. It was found that the ultimate tensile strength of the material material in both (011)- and (111)-oriented SiNWs is lo l of stress to cause the wer than the critical leve in both (011)- and (111)-oriented SiNWs is lower than the critical level of stress to cause the sudden seems to be impossible to change the electrical sudden change of conductivity. In other words, it change of conductivity. In other words, it seems to be impossible to change the electrical property of property of these materials without failure. Howeve r, for (001)-oriented SiNW, the stress needed to these materials without failure. However, for (001)-oriented SiNW, the stress needed to induce sudden induce sudden change of conductivity is lower than the ultimate strength of the material. change of conductivity is lower than the ultimate strength of the material. Consequently, it is feasible Consequently, it is feasible to change the electrical property of (001)-oriented SiNW by applying a to change the electrical property of (001)-oriented SiNW by applying a tensile stress. In addition, tensile stress. In addition, phase transformation during unloading also has effect on the phase transformation during unloading also has e ff ect on the conductivity of the material. At lower the stress in the material can be endured through conductivity of the material. At lower stress level, stress level, the stress in the material can be endured through the introduction of a meta-stable phase. loading, the meta-stable phase is recovered to the introduction of a meta-stable phase. After un After unloading, the meta-stable phase is recovered to original Si-I phase with no residual elongation. original Si-I phase with no residual elongation. However, at higher stress level, a large amount of However, at higher stress level, a large amount of Si-II and amorphous phases accompanied with Si-II and amorphous phases accompanied with the significant plastic deformation were produced. the significant plastic deformation were produced. Consequently, a significant residual elongation

18 Crystals 2019 9 , 240 18 of 20 , 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. Y.-H.L. and T.-C.C. conceived and designed the study; Y.-H.L. performed the simulations Author Contributions: and drew the figures; Y.-H.L. and T.-C.C. analyzed the results and wrote the paper. Funding: The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for the financial support of this study under Contract No. MOST 107-2221-E-006-122-. The authors declare no conflict of interest. Conflicts of Interest: References ect of dynamic adjustment of diamond tools on nano-cutting ff Wang, M.H.; You, S.Y.; Wang, F.N.; Liu, Q. E 1. behavior of single-crystal silicon. , 125 , 1–13. [CrossRef] Appl. Phys. A 2019 2. Wang, J.; Zhang, X.; Fang, F.; Chen, R. A numerical study on the material removal and phase transformation 2018 , in the nanometric cutting of silicon. , 608–615. [CrossRef] Appl. Surf. Sci. 455 3. Jelenkovi ́c, E.V.; To, S. Suppression of nanoindentation-induced phase transformation in crystalline silicon Electron. Mater. Lett. 2017 , implanted with hydrogen. , 393–397. [CrossRef] 13 4. Stach, E.A.; Freeman, T.; Minor, A.M.; Owen, D.K.; Cumings, J.; Wall, M.A.; Chraska, T.; Hull, R.; Morris, J.W.; Microsc. Zettl, A., Jr.; et al. Development of a nanoindenter for in situ transmission electron microscopy. , 7 , 507–517. Microanal. 2001 Bobji, M.S.; Ramanujan, C.S.; Pethica, J.B.; Inkson, B.J. A miniaturized TEM nanoindenter for studying 5. material deformation in situ. 2006 , 17 , 1324–1329. [CrossRef] Meas. Sci. Technol. 6. Cheong, W.C.D.; Zhang, L.C. Molecular dynamics simulation of phase transformation in silicon monocrystals Nanotechnology due to nano-indentation. , 11 , 173–180. [CrossRef] 2000 Lin, Y.H.; Chen, T.C.; Yang, P.F.; Jian, S.R.; Lai, Y.S. Atomic-level simulations of nanoindentation-induced 7. phase transformation in monocrystalline silicon. 2007 , 254 , 1415–1422. [CrossRef] Appl. Surf. Sci. 8. Lin, Y.H.; Chen, T.C. A molecular dynamics study of phase transformation in monocrystalline Si under nanoindentation. Appl. Phys. A 2008 , 92 , 571–578. 9. Lin, Y.H.; Jian, S.R.; Lai, Y.S.; Yang, P.F. Molecular dynamics simulation of nanoindentation-induced Nanoscale Res. Lett. 2008 3 , mechanical deformation and phase transformation in monocrystalline silicon. , 71–75. [CrossRef] Kim, D.E.; Oh, S.I. Atomistic simulation of structural phase transformations in monocrystalline silicon 10. Nanotechnology 2006 , 17 , 2259–2263. [CrossRef] induced by nanoindentation. Kim, D.E.; Oh, S.I. Deformation pathway to high-pressure phases of silicon during nanoindentation. J. Appl. 11. 2008 Phys. 104 , 013502. [CrossRef] , 12. Bradby, J.E.; Williams, J.S. In situ electrical characterization of phase transformations in Si during indentation. 2003 , 67 Phys. Rev. B , 085205. [CrossRef] 13. Haberl, B.; Bradby, J.E.; Ru ff ell, S.; Williams, J.S. Phase transformations induced by spherical indentation in ion-implanted amorphous silicon. J. Appl. Phys. 2006 , 100 , 013520. [CrossRef] 14. Ru ell, S.; Bradby, J.E.; Williams, J.S. An in situ electrical measurement technique via a conducting diamond ff J. Mater. Res. , 22 , 578–586. [CrossRef] tip for nanoindentation in silicon. 2007 Mylvaganam, K.; Zhang, L.C.; Eyben, P.; Mody, J.; Vandervorst, W. Evolution of metastable phases in silicon 15. Nanotechnology 2009 , 20 , 305705. during nanoindentation: Mechanism analysis and experimental verification. [CrossRef] 16. Seike, A.; Tange, T.; Sugiura, Y.; Tsuchida, I.; Ohta, H.; Watanabe, T.; Kosemura, D.; Ogura, A. Strain-induced transconductance enhancement by pattern dependent oxidation in silicon nanowire field-e ect transistors. ff Appl. Phys. Lett. 2007 , 91 , 202117. [CrossRef] 17. Zhuo, X.R.; Beom, H.G. E ff ect of side surface orientation on the mechanical properties of silicon nanowires: A molecular dynamics study. Crystals 2019 , 9 , 102. [CrossRef]

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