Silicon Heterojunction Formed by Inserting Carbon

Oct 9, 2012 - Using molecular dynamics (MD) simulations, we report a carbon/silicon (C/Si) heterojunction formed by inserting carbon nanotubes (CNTs) ...
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Carbon/Silicon Heterojunction Formed by Inserting Carbon Nanotubes into Silicon Nanotubes: Molecular Dynamics Simulations Dan Xia,†,‡ Qingzhong Xue,*,† Teng Zhang,† Liangyong Chu,† and Mingdong Dong*,‡ †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao, Shandong 266555, P. R. China Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Aarhus C, DK-8000, Denmark

‡

S Supporting Information *

ABSTRACT: Using molecular dynamics (MD) simulations, we report a carbon/ silicon (C/Si) heterojunction formed by inserting carbon nanotubes (CNTs) into silicon nanotubes (SiNTs). Due to the weak mechanical property of the SiNTs, insertion of CNTs into them can not only reinforce their mechanical stabilities but also form multiwalled C/Si nanotube heterojunctions. The driving force of the coaxial assembly is primarily the intertube van der Waals (vdW) interactions. The coaxial self-assembly process is strongly tube size dependent, and the intertube distance (Δd) for a successful assembly between the two type nanotubes is around 3.5 Å. Simulations suggest possible bottom-up self-assembly routes for fabrication of novel nanomachines and nanodevices in nanomechanical systems. This study also suggests that the possibility of synthesizing SiNTs with fewer walls, even single-walled SiNT in aid of CNTs.

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INTRODUCTION One-dimensional nanomaterials, such as carbon nanotubes (CNTs)1 and silicon nanotubes (SiNTs),2 have attracted particular interest because of their novel properties and potential applications. The extraordinary mechanical,3−11 thermal,12−14 optical,15 and electrical properties16−19 of CNTs have made them fascinating materials in the field of nanoscience and nanotechnology since its discovery in 1991.1 Due to the key role of silicon (Si) in the modern semiconductor industry, one-dimensional SiNTs are of special interest. However, it should be noted that carbon has mainly sp2 hybridization, whereas Si has mainly sp3 hybridization. Therefore, it is difficult to synthesize hollow one-dimensional SiNTs with sp3 Si hybridization. Thus far, much theoretical research and calculations have explored the properties of SiNTs and predicted the existence of one-dimensional SiNTs.20−26 Recently, it has been reported that SiNTs can be successfully synthesized by molecular beam epitaxy,2 chemical vapor deposition,27 hydrothermal method,28 and a lot of other methods.29−32 The thickness of the synthesized SiNT wall can be a few nanometers.28 These SiNTs exhibit much stronger attraction to hydrogen compared to the isodiameter CNTs20 and have a very high reversible charge capacity of 3247 mA h/g with a Coulombic efficiency of 89% and also demonstrate superior retention even at 5C rate (=15 A/g).30 SiNTs with their hollow structures would have better compatibility with the present established Si technology and by filling the hollow space with one type of nanomaterial and/or decorating the outer surface with another type of nanomaterial may open up the exciting possibility for making various kinds of nanosized heterojunctions.33 © 2012 American Chemical Society

Due to the poor mechanical properties of SiNTs under external force, the produced multiwalled SiNTs are unstable, and the single-walled SiNT has not been prepared until now. In this work, we report a carbon/silicon (C/Si) heterojunction formed by inserting CNT into SiNT using molecular dynamics (MD) simulations. It is found that the C/Si tube heterojunctions, produced by inserting CNTs into SiNTs, can maintain the tubular shape of the SiNTs. Besides, the singlewalled SiNT may be prepared using the CNT as a template and coating the SiNT onto it. From MD simulations, we discover that the assembly process of multiwalled C/Si nested nanotubes is driven primarily by the van der Waals (vdW) interaction between the two types of nanotubes and the whole process is largely tube size dependent. To ensure a successful assembly, the diameters of CNT and SiNT should be suited. The formed C/Si multiwalled nanotube (MWNT) holds several advantages and could potentially lead to low-cost and high-efficency solar cells34 and nanosized anodes.30,35 Our results suggest a promising bottom-up approach for building C/Si MWNTs from single CNT and SiNT or multiwalled CNTs and SiNTs with desired structures and properties for specific applications. In this controllable manner, the formed C/Si nanostructures may be used as starting materials for more complex machines and devices in the nanoscience and nanotechnology field. The simulations also suggest the possibility of synthesizing SiNTs with a few walls in assistant of CNTs, even single-walled SiNT. Received: December 15, 2011 Published: October 9, 2012 23181

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SIMULATION METHODS Calculations have been performed with the Materials Studio (MS) software. The force field of the condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) is chosen to model the atomic interaction.36 COMPASS is the first ab initio force field that has been parametrized and validated using condensed-phase properties in addition to various ab initio and empirical data, and it has been shown to be applicable in describing the mechanical properties of CNT37,38 and silicon.39,40 The force field is expressed as a sum of valence (or bond), cross-terms, and nonbond interactions, and for the details one should refer to our former article.41 MD simulations were carried out under a constant volume and constant temperature dynamics (NVT) ensemble, and the dynamics process is conducted to allow the system to exchange heat with environment. The Nosé thermostat is employed to control the temperature and generate the correct statistical ensemble. As a temperature control, the thermodynamic temperature was kept constant by allowing the simulated system to exchange energy with a “heat bath”. The typical model considered in this work is an armchair CNT (10, 10) with a diameter of 13.56 Å and length of 115.60 Å and an armchair SiNT (10, 10) with a diameter of 21.40 Å and length of 116.65 Å (Figure 1a). To avoid the dramatic deformation of

types of nanotubes, the CNT begins to insert into the SiNT. At the same time, the SiNT starts to deform and finally collapses during this time period (Figure 1c). After t = 10 ps, the SiNT collapses totally and the inserting end of the CNT has to transform its circle shape to an oven form to reduce the friction of the two types of nanotubes, which makes the assembly process much more smooth and faster. At t = 38 ps, the CNT inserts through the whole SiNT and the inserting end has recovered to a circular shape again, which completes full encapsulation of the smaller CNT into the larger SiNT. Afterward, the CNT (10, 10) oscillates inside the SiNT (10, 10) because of the inertia forces and the intertube vdW attraction (Figure 1g−j) (see Supplementary Video, Supporting Information). As time goes on, the amplitude of the oscillation becomes smaller and smaller and finally keeps an equilibrium state at t = 500 ps. The structures of the formed double-walled C/Si nanotube after achieving equilibrium are shown in Figure 1k and 1m for a side view and top view, respectively. In order to characterize the geometric structure of the formed double-walled C/Si nanotube clearly, the concentration profiles are shown in Figure 2. The concentration profile is

Figure 1. Snapshots of self-assembling a CNT (10, 10) (gray) and SiNT (10, 10) (yellow) into a double-walled C/Si nanotube at t = 0, 1, 10, 18, 35, 38, 49, 64, 80, 92, and 500 ps, respectively (a−k). (m) Snapshot of the formed double-walled C/Si nanotube in top view.

the SiNT in the initial simulation, the CNT is inserted into the SiNT for a small distance (5 Å). All simulations were carried out at room temperature 300 K, a time step of 1 fs was used, and data were collected in intervals of 1 ps. Then the fullprecision trajectory was recorded, and the results were analyzed.

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RESULTS AND DISCUSSION Our MD simulation setup and the dynamics procedure are described in Figure 1. An armchair CNT (10, 10) and an armchair SiNT (10, 10) with similar lengths (115.60 Å for CNT and 116.65 Å for SiNT) are lined coaxially. To avoid the initial dramatic deformation of the single-walled SiNT, the CNT is inserted into the SiNT for a distance of 5 Å, as shown in Figure 1a. At the beginning of the simulation (t = 1 ps) shown in Figure 1b, the SiNT deforms severely and pushes the CNT to the edge of the opening due to the strong repulsive force. After that, due to the strong attractive force between two

Figure 2. Concentration profiles of the formed double-walled C/Si nanotube along the (a) x and (b) y axes. (Insets) Scheme of the formed double-walled C/Si nanotube.

calculated for 3D periodic structures by computing the profile of atom density within evenly spaced slices parallel to the bc, ca, and ab planes. In practice, this is equivalent to taking the a, b, and c components of the fractional coordinates of each atom and independently generating a plot for each component.42 Here, we only give the concentration profiles along the x and y axes, because the properties along the radial direction are much 23182

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3a, one can observe that the COMs of the two types of nanotubes get close to each other with increasing simulation time and Dz decreases sharply at the beginning of the simulation. At about t = 38 ps, the two COMs coincide and Dz drops to zero for the first time, which means that the full insertion process is completed. Afterward, the two COMs and Dz oscillate around an equilibrium axis of their own with the amplitude becoming smaller and smaller, and finally, all COMs and Dz reach their own equilibrium value. The total potential energy versus simulation time is also plotted to depict the assembly process more clearly, as shown in Figure 3b. The inset is the amplificatory curve of the total potential energy of the system against time from t = 0 to 200 ps. It is clear that the total potential energy of the system decreases remarkably in the initial 10 ps, which may be caused by fast insertion of the CNT into the SiNT in the initial 10 ps. After the SiNT collapses totally, the slope of the total potential energy decreasing becomes smaller till the full encapsulation process completes at about t = 38 ps, when the total potential energy drops down to the lowest value. Afterward, the total potential energy varies not as the Dz oscillates around an equilibrium axis but every time achieves a wave crest and finally drops down to almost the same lowest value (wave trough). As time goes on, the wave crest of the total potential energy becomes lower and lower and finally almost keeps a constant value (value of the wave trough) when the simulation time reaches 500 ps. It is known that the chirality has a significant effect on the properties of the CNTs. A CNT is of metallic type when it exhibits armchair chirality, whereas the CNT can be the semiconducting type or semimetallic type when its chirality is zigzag or chiral,43 whereas the SiNT has a semiconducting gap, which in contrast to CNT is largely independent of the diameter and chirality.24 Therefore, we can construct different types of nanocomposites by tailoring the composition (metallic versus semiconducting tubes) and thickness of the CNT and SiNT walls to optimize the electronic and optical properties.44,45 To investigate the effect of chirality on the selfassembly process of the composite system, we simulate an armchair CNT (10, 10) inserting into different chiral SiNTs as well as different chiral CNTs encapsulating into an armchair SiNT (10, 10). The parameters of the selected chiral CNTs and chiral SiNTs are given in Table 1. All CNTs and SiNTs have the same lengths and similar diameters, respectively, except for CNT (18, 0), SiNT (16, 2), and SiNT (18, 0), which have larger ΔD compared to the other ones and listed here are not used to research the effect of chirality on the self-assembly process but just for comparison.

more attractive than the ones along the axial direction. Four distances shown in Figure 2 are the distances of two peaks between the CNT and the SiNT concentration profiles, which denote the intertube spacing of the two types of nanotubes along the x and y axes. Analyzing the simulation data, one can obtain that the four distances defined in Figure 2 are 3.776, 3.766, 3.500, and 3.736 Å. All these distances are a little larger than 3.4 Å, which may be caused by a little larger diameter difference (ΔD) between the two types of nanotubes. This will be discussed in the following text. The self-assembly process is also confirmed by the change of the center-of-mass (COM) distance projected in the axial direction (Dz) between the two types of nanotubes as a function of simulation time, as shown in Figure 3. From Figure

Figure 3. Dynamic process of a CNT (10, 10) inserting into a SiNT (10, 10). (a) Dz and COMs of two types of nanotubes as a function of simulation time. Black dash dot line denotes the time when the full encapsulation process completes, while the black arrows denote the curves belong to different y axes. (b) Potential energy of the system versus simulation time. (Inset) Amplificatory curve of the total potential energy of the system against time from t = 0 to 200 ps.

Table 1. Diameters, Number of Atoms, and Difference of Diameters (ΔD) of the Chiral Nanotubes Utilized in MD Simulations SiNTs

CNTs

(m, n) for two NTs

diameter (Å)

atom

diameter (Å)

atom

ΔD (Å) for chiral SiNTs and CNT(10,10)

ΔD (Å) for chiral CNTs and SiNT(10,10)

(10,10) (11,9) (12,8) (13,7) (15,4) (16,3) (17,1) (16,2) (18,0)

21.40 21.47 21.58 21.76 21.47

1200 1202 1216 1208 1196 1218 1176 1260

1820 1840 1836 1859 1840 1881 1861

7.84 7.91 8.02 8.20 7.91

21.69 21.15 22.28

13.56 13.58 13.65 13.76 13.58 13.85 13.72

7.84 7.82 7.75 7.74 7.82 7.55 7.68

14.09

1908

8.13 7.59 8.72 23183

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SiNTs, as shown in Figure 4b. All trends of the potential energies versus simulation time almost coincide, which means that the chirality of the SiNTs has little effect on the assembly process. Moreover, the average potential energies after the CNT/SiNT systems reach the equilibrium do not have significant differences. It is evident that three curves in Figure 4a and 4b have larger energy differences compared to the other ones. This may be because the ΔD of the two types of nanotubes are smaller (for higher potential energy level) or larger (for lower potential energy level) than the other cases, which can be found in Table 1. Therefore, we can conclude that this assembly process may be largely dependent on ΔD. The intertube distances (Δd) between the SiNT (10, 10) and different chiral CNTs and between the CNT (10, 10) and various chiral SiNTs are listed in Table 2. Here, Δd denotes the average distance of four

The curves of the total potential energies as a function of simulation time are plotted in Figure 4. Figure 4a shows the

Table 2. Intertube Distances (Δd)a between the Chiral CNTs and the Chiral SiNTs SiNT(n,m) and CNT(10,10)

Δd

(10,10) and (10,10) (11,9) and (10,10) (12,8) and (10,10) (13,7) and (10,10) (15,4) and (10,10) (16,2) and (10,10) (17,1) and (10,10) (18, 0) and (10,10)

3.697 3.687 3.468 3.608 3.536 3.560 3.605 3.605

SiNT(10,10) and CNT(n,m) (10,10) (10,10) (10,10) (10,10) (10,10) (10,10) (10,10) (10,10)

and and and and and and and and

(10,10) (11,9) (12,8) (13,7) (15,4) (16,3) (17,1) (18, 0)

Δd 3.697 3.537 3.479 3.537 3.559 3.548 3.356 3.548

Δd denotes the average distances of four distances (d1−d4) defined in Figure 2. a

distances (d1−d4) defined in Figure 2. From Table 2, one can observe that almost all distances are around 3.35−3.60 Å, which indicates that the CNTs and SiNTs have almost formed strong adhesive binding. Thus, we can conclude that it will form stable multiwalled CNT/SiNT structures when Δd is about 3.5 Å. To confirm the assembly process is strongly tube size dependent, we designed a set of simulations by varying CNT diameters, as described in Figure 1. The parameters of the chosen CNTs are listed in Table 3. The final configurations of

Figure 4. Total potential energies of (a) the chiral CNTs inserting into an armchair SiNT (10, 10) and (b) an armchair CNT (10, 10) inserting into the chiral SiNTs versus simulation time. (Insets) Average potential energies after the CNT/SiNT systems reach equilibrium.

Table 3. Diameters and ΔD between Different CNTs and SiNT (10, 10) Used in MD Simulations

potential energies of the CNTs with different chiralities inserting into an armchair SiNT (10, 10), while the potential energies of an armchair CNT (10, 10) encapsulating into various chiral SiNTs are illustrated in Figure 4b. Due to the differences of atom numbers of the CNTs or SiNTs, with various chiralities, all potential energies are normalized to the atom numbers of CNTs or SiNTs. The insets in Figure 4a and 4b are the average normalized potential energies after the CNT/SiNT systems reach equilibrium. From Figure 4a, one can observe that the curves of the potential energies as a function of simulation time are very similar (except for the modena line CNT (18, 0) and SiNT (10, 10)), although there exists relatively larger oscillations for CNT (11, 9), CNT (13, 7), and CNT (15, 4). Furthermore, the inset in Figure 4a demonstrates that the average potential energies after the CNT/SiNT systems reach equilibrium have little differences, which illustrates that the chirality of the CNT has little effect on the insertion process. A similar situation has happened for the armchair CNT (10, 10) encapsulating into different chiral

(m, n) for two NTs (10,10) (10,10) (10,10) (10,10) (10,10) (10,10) (10,10)

and and and and and and and

(18,1) (18,0) (10,10) (9,9) (8,8) (6,6) (5,5)

SiNT diameter (Å)

CNT diameter (Å)

ΔD (Å)

21.40 21.40 21.40 21.40 21.40 21.40 21.40

14.50 14.09 13.56 12.20 10.85 8.14 6.78

6.90 7.31 7.84 9.20 10.55 13.26 14.62

different CNTs inserting into an armchair SiNT (10, 10) are shown in Figure 5. The final structure of a CNT (18, 1) inserting into the SiNT (10, 10) is not shown in Figure 5, because they cannot assemble successfully and form the doublewalled tubular structure, which means that the insertion process has a ΔD limit. From Figure 5, one can observe that CNT (18, 0) and CNT (10, 10) can swim into the SiNT (10, 10) successfully and form perfect double-walled tubes. It can be 23184

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form a perfect tubular C/Si bitube, whereas with a little further increasing the ΔD the whole encapsulation process will be much faster, as shown in the curve of the CNT (10, 10) inserting into SiNT (10, 10) in Figure 6 (red line). Further increasing the ΔD, the assembly process will attain a maximum insertion velocity (pink line). Then, the velocity of the assembly process will decrease with a continuous increasing ΔD (green and dark blue line). The corresponding velocity value can be found from the inset in Figure 6. From the analysis above, we can conclude that the assembly process is strongly dependent on the tube size. Similar encapsulation processes can also be found to form multiwalled C/Si nanotubes by the shell-by-shell assembly method. Figure 7a and 7b shows a CNT (16, 3) inserting into a

Figure 5. Snapshots of the bitubes formed by encapsulating various CNTs into an armchair SiNT (10, 10).

found that the interaction between the CNT (18, 0) and the SiNT (10, 10) is stronger than that between the CNT (10, 10) and the SiNT (10, 10), which can be exhibited in the energy curve of Figure 4a and Δd in Table 2. However, a little smaller diameter CNT (9, 9) encapsulating into the SiNT (10, 10) can only form an oven-shaped bitube because of the larger ΔD. Further increasing ΔD (CNT (8, 8), CNT (6, 6), and CNT (5, 5)), the insertion pathway of the small CNTs will depart from the original coaxial trajectory instead by assembling along the interior tube wall. Finally, the much larger SiNT shell forms a key-shaped structure as shown in Figure 5. The oscillation time after all CNTs inserting into SiNT (10, 10) increases with increasing ΔD; the relative curves are not given here. The COM distances of two types of nanotubes changing with simulation time till the insertion process completed are plotted in Figure 6. The red dash−dot line denotes the representative fit line, and its slope demonstrates the velocity of the insertion process. The inset shows the insertion velocity of the assembly process as a function of ΔD. From Figure 6 one can observe that the insertion velocity of the assembly process will be very slow when the ΔD of two types of nanotubes is 7.31 Å. However, this will lead to a successful assembly and

Figure 7. Snapshots of stepwise assembly of CNT and SiNT into C/Si nested MWNT. Snapshots of the initial and final configurations of (a and b) assembling a CNT (16, 3) and an armchair SiNT (10, 10) into a double-walled C/Si nanotube, (c and d) assembling the formed CNT (16, 3) and SiNT (10, 10) and a CNT (22, 20) into a triplewalled C/Si/C nanotube, and (e and f) assembling the resulting CNT (16, 3) and SiNT (10, 10) and CNT (22, 20) and a SiNT (17, 17) into a tetrawalled C/Si/C/Si nested nanotube.

SiNT (10, 10) to form a double-walled C/Si nanotube, and then the formed CNT (16, 3) and SiNT (10, 10) and a CNT (22, 20) assemble into a triple-walled C/Si/C nanotube (Figure 7c and 7d). The resulting triple-walled C/Si/C nanotube and a SiNT (17, 17) further assemble into a tetrawalled C/Si/C/Si nanotube (Figure 7e and 7f). For a set of given single-walled CNTs or SiNTs, this consecutive shell-by-shell assembly can offer a possible approach to fabricate C/Si/C/Si... nested MWNTs with desired properties under controllable processing steps. Further simulations have also been designed to investigate the assembly process of the single-walled CNT inserting into multiwalled SiNT and multiwalled CNT inserting into multiwalled SiNT, as shown in Figure 8. Figure 8a shows a CNT (10, 10) and a double-walled SiNT (inner SiNT (10, 10)) assembling into a triple-walled C/Si nested nanotube, while the configuration of a CNT (10, 10) and a triple-walled SiNT (inner SiNT (10, 10)) assembling into a tetrawalled C/Si nested nanotube is shown in Figure 8b. The configurations of

Figure 6. Evolution of the COM distances between the different CNTs and an armchair SiNT (10, 10) as a function of simulation time. (Inset) Velocity of different CNTs inserting into the armchair SiNT (10, 10). 23185

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Figure 8. Snapshots of the single-walled CNT/multiwalled SiNT nested MWNTs and the multiwalled CNT/multiwalled SiNT nested MWNTs.

targeted properties from a set of given nanostructures. In addition, the formed C/Si MWNT-based nanostructures may be used as starting materials for more complex machines and devices in the nanoscience and nanotechnology field. Our simulations also suggest the possibility of synthesizing SiNTs with fewer walls using the CNTs as a template and coating the SiNTs onto the outer surface of CNTs, even single-walled SiNT.

various multiwalled CNTs encapsulating into multiwalled SiNTs (inner SiNT (17, 17)) with different walls are illustrated in Figure 8c (double-walled CNT (inner CNT (15, 15)), 8d (triple-walled CNT (inner CNT (9, 10)), and 8e (tetrawalled CNT (inner CNT (3, 4)). All assembly processes are successful and ultimately form these perfect C/Si nested MWNTs shown in Figure 8. The rest can be done in the same manner. This is much more practical because it can be implemented by experiment using the synthesized multiwalled CNTs and multiwalled SiNTs. Combining Figures 7 and 8, we can conclude that the multiwalled CNT/multiwalled SiNT/multiwalled CNT/multiwalled SiNT... nested MWNTs can also be formed by this shell-by-shell assembly approach. Even other kinds of tubular heterostructures may also be formed using this assembly method, such as CNT/SiC nanotube heterojunction, CNT/BN nanotue heterojunction, or other inorganic nanotubes heterojunctions, and so on. These formed MWNT heterojunctions may hold great potential in fabricating robust and efficient nanomachines and nanodevices in future nanoelectromechanical systems, such as nanobearings, oscillators, and nanorotors.46

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ASSOCIATED CONTENT

S Supporting Information *

Movie showing details of the small CNT (10, 10) encapsulating into the large SiNT (10, 10) from t = 0 to 80 ps. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 86-546-8392836 (Q.X.); +45 8942 3690 (M.D.). Fax: 86-546-8397900 (Q.X.); +45 8942 3711 (M.D.). E-mail: [email protected] (Q.X.); [email protected] (M.D.).

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CONCLUSIONS In summary, using MD simulations we demonstrate that the single-walled CNTs and SiNTs with different chiralities and diameters can coaxially assemble into C/Si nested heterojunction nanotubes by inserting the smaller diameter CNTs into the larger diameter SiNTs. The intertube vdW interaction plays a significant role in forming C/Si heterojunction nanotubes. The self-assembly process is strongly dependent on the diameters of the two types of nanotubes. In order to obtain a successful assembly process, the intertube distance Δd should be around 3.5 Å. For a given size of large SiNT, the diameter of the small CNT should be properly chosen to ensure a successful and perfect assembly and vice versa. The velocity of the whole insertion process is largely dependent on ΔD. When ΔD is about 7 Å, the whole insertion is very slow but forms the best C/Si tubular heterojunction. Further increasing ΔD, the inserting velocity will be largely faster and achieve a maximum value and then decease subsequently. The chiralities of the CNTs and SiNTs do not have a significant effect on the assembly process. However, we can design different types of C/Si heterojunctions with desired properties by tailoring the CNT’s chirality and the thickness of the CNT or SiNT walls in a controllable manner. Through the stepwise shell-by-shell insertion process, we can also conduct multiwalled C/Si/C/Si... nested heterojunction nanotubes, multiwalled CNT/multiwalled SiNT heterojunction nanotubes, and even multiwalled CNT/multiwalled SiNT/multiwalled CNT/multiwalled SiNT... nested heterojunction nanotubes. This vdW-driven assembly approach provides a fascinating and an efficient way to fabricate the complex structures with

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Fundamental Research Funds for the Central Universities (11CX05002A, 11CX0460A), the Natural Science Foundation of Shandong Province (ZR2010AL009, ZR2011AL023), and the Qingdao Science & Technology Program (12-1-4-7-(1)-jch).

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REFERENCES

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