First-principles study on structural and electronic properties of copper nanowire encapsulated into GaN nanotube

Physica B 406 (2011) 3502–3507

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First-principles study on structural and electronic properties of copper nanowire encapsulated into GaN nanotube Liang-Cai Ma a,b, Yan Zhang a, Jian-Min Zhang a,n, Ke-Wei Xu c a

College of Physics and Information Technology, Shaanxi Normal University, Xian 710062, Shaanxi, PR China School of Physics and Electrical Information Engineering, Ningxia University, Yinchuan 750021, Ningxia, PR China c State Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, Shaanxi, PR China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 29 November 2010 Received in revised form 6 May 2011 Accepted 13 June 2011 Available online 25 June 2011

We present a systemic study of the structural and electronic properties of Cun nanowires (n ¼ 5, 9 and 13) encapsulated in armchair (8,8) gallium nitride nanotubes (GaNNTs) using the first-principles calculations. We find that the formation processes of these systems are all exothermic. The initial shapes are preserved without any visible changes for the Cu5@(8,8) and Cu9@(8,8) combined systems, but a quadratic-like cross-section shape is formed for the outer nanotube of the Cu13@(8,8) combined system due to the stronger attraction between nanowire and nanotube. The electrons of Ga and N atoms in outer GaN sheath affect the electron conductance of the encapsulated metallic nanowire in the Cu13@(8,8) combined system. But in the Cu5@(8,8) and Cu9@(8,8) combined systems, the conduction electrons are distributed only on the copper atoms, so charge transport will occur only in the inner copper nanowire, which is effectively insulated by the outer GaN nanotube. Considering the maximal metal filling ratio in nanotube, we know that the Cu9@(8,8) combined system is top-priority in the ultra-large-scale integration (ULSI) circuits and micro-electromechanical systems (MEMS) devices that demand steady transport of electrons. & 2011 Elsevier B.V. All rights reserved.

Keywords: Copper nanowire GaN nanotube Electronic structure First-principles calculation

1. Introduction Nanotubes and nanowires, two main groups of the so-called quasi-one-dimensional (1-D) nanostructures, have been proved to be promising materials for nanoelectronic, nanolithography, photocatalysis, microscopy and other fields of modern nanotechnologies [1,2]. Among them, the metallic nanowires are important components for the interconnection of nanoscale electronic elements [3], however, the metallic nanowires are usually unstable chemically and the environment may affect their transport properties [4]. The pristine metal nanowires with about 10 A˚ diameter have been reported to exist only transiently in even ultrahigh vacuum [5,6]. Therefore, the nanocables, i.e. a metallic nanowire protected by an insulating, chemically stable outer sheath (nanotube), are desirable. It is well-known that the electromagnetic nanowires are encapsulated inside carbon nanotubes (CNTs) by capillarity or wet-chemistry methods, which have been carried out successfully for a decade [7–12]. Novel electronic and magnetic properties of metal-filled CNTs have been reported [13–16]. However, the strong coupling between the encapsulated metallic nanowires and the outer CNTs would lead to a degenerations in the electronic properties of the

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nanowires. Moreover, exposure to gases such as O2 and NO2 may affect the electronic properties of carbon nanotubes considerably [17]. Therefore, such combined carbon nanotube/metal nanowire structures do not appear to be as promising as nanocables with conducting properties [18]. Recent successful preparations of novel inorganic nanotubes [19–22] have provided excellent candidate materials for nanocables. Among them, gallium nitride nanotubes (GaNNTs) are of great importance because of their high thermal and mechanical stability. Theoretical studies have shown that the GaNNTs are wide band-gap semiconductors and their gaps ( 2 eV) are independent of their chiralities [23,24]. In addition, the GaNNTs have more extensive inner-cavity than CNTs and boron nitride nanotubes (BNNTs), due to significantly larger Ga–N bond length of ˚ for 1.88 A˚ than the C–C and B–N bond lengths of 1.42 and 1.44 A, material storage and nano-size manipulation, respectively. These advantages make the GaNNTs as a suitable shield for metallic nanowires. However, few theoretical or experimental investigations of metallic nanowires encapsulated into GaNNTs have been reported so far. In fact, it has been achieved experimentally that numerous foreign materials, such as Fe, Co, Ni, Cu, KI or Fe–Ni alloy nanorods/nanowires, have already been encapsulated inside CNTs and BNNTs [9,25–30]. Thus, we believe, the possibility exists, that the 1-D materials, such as copper nanowires, can also be encapsulated into GaNNTs. Before realizing this in experiment, it is

L.-C. Ma et al. / Physica B 406 (2011) 3502–3507

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inside are fully relaxed to minimize the total energy of the system until a precision of 10  4 eV is reached. The conjugate gradient minimization is used for optimization of the atom coordinates ˚ The until the force acting on each atom is less than 0.02 eV/A. 4s24p1, 2s22p3 and 3d104s1 electrons are taken as the valence electrons for Ga, N and Cu atoms, respectively. Fig. 1 shows the initial geometric structures of Cun nanowires encapsulated into armchair (8,8) GaNNT from the cross section views of (a) Cu5@(8,8), (b) Cu9@(8,8) and (c) Cu13@(8,8), in which the gray, blue and orange balls denote Ga, N and Cu atoms, and the big and small balls denote the atoms on the adjacent A layer and B layers, respectively. The numbers m on the orange balls in (a)–(c) denote the mth Cu shell in the nanowires. The (8,8) GaNNT is chosen here since its eightfold rotation symmetry about its axis is easy to match with the four-fold rotation symmetry of Cu nanowire. Considering the lattice mismatch between the (8,8) GaNNT and the [0 0 1] oriented Cu nanowires which cut from bulk face-centered cubic (FCC) Cu along their common axis direction, we reduce axis direction lattice constant of Cu nanowires from 3.61 to 3.24 A˚ so that the nanotube unit cell in axis length of 3.24 A˚ contains two adjacent Cu layers (one Cu layer is coincident with one GaN layer of outside GaNNT). In the cross section of the Cun@(8,8) (n ¼5, 9 and 13 is the number of the Cu atoms contained in one unit cell) combined systems, we still use the same lattice constant 3.61 A˚ of the bulk FCC Cu for Cu nanowires. The lattice constant of Cu nanowires along tube axis ˚ which corresponds to direction is changed from 3.61 to 3.24 A, about 10% compress strain. Therefore we make a comparison of the electronic structure of Cu nanowire with and without strain. Taking Cu5 nanowire as an example, the band structures and total DOS of nanowire with and without strain have been shown in Fig. 2. We can find that the change in electronic structure of the Cu nanowire is not significant.

highly desirable to study the structure and electronic properties of copper nanowires encapsulated into GaNNTs first. Here we choose copper nanowires for the following reasons: (1) the completely filled 3d electron shell of Cu atoms might result in weaker coupling with the nanotube sheath than the other open-shell transition metals such as Fe, Co and Ni and (2) Cu has been used extensively to replace Al as interconnects in ultra-large-scale integration (ULSI) circuits and micro-electromechanical systems (MEMS). The obvious advantage for using Cu stems from its lower resistivity (rCu ¼1.67 m O cm, rAl ¼ 2.66 m O cm) and higher melting point (TCu ¼1358 K, TAl ¼933 K) than Al. This can lead to lower Joule heat and R–C delay (R and C represent the resistance and capacitance associated with interconnect architecture, respectively), which gives Cu the advantage over Al in electromigration and possibly stress migration as well [31]. In this paper, the structural and electronic properties of Cun (n¼ 5, 9 and 13) nanowires encapsulated inside armchair (8,8) GaNNTs have been investigated using the projector-augmentedwave (PAW) potential approach to the density-functional theory (DFT) within the generalized-gradient approximation (GGA) implemented in Vienna ab initio simulation package (VASP). The rest of the paper is organized as follows. Section 2 gives the details of our DFT calculation method and model of Cun nanowires encapsulated inside the (8,8) GaNNT. In Section 3, we firstly present the structural optimization results and the formation energies of Cun@(8,8) combined systems, then the results for electronic structures mainly include band structures, total density of states (DOS), and projected densities of states (PDOS), charge density distribution. Finally, the conclusions of the work are given in Section 4.

2. Calculation method and model All the calculations are performed within the DFT using the plane-wave basis VASP code [32–37]. The electron–ionic core interaction is represented by the PAW potentials [38], which are more accurate than the ultrasoft pseudopotentials. To treat electron exchange and correlation, we chose the Perdew–Burke– Ernzerhof [39] formulation of the GGA, which yields the correct ground-state structure of the combined systems. The cutoff energy for the plane-waves is chosen to be 400 eV, and the supercell is large enough to ensure that the vacuum space is 18 A˚ to eliminate the interaction between periodic images. The Brillouin zone integration is performed within the Gamma centered Monkhorst–Pack scheme [40] using 1  1  11 k-points. To avoid the numerical instability due to level crossing and quasidegeneracy near the Fermi level, we use a method of Methfessel– Paxton order N (N ¼1) with a width of 0.2 eV. Geometric structures of both the pristine nanotube and the nanowire wrapped

3. Results and discussion The optimized structures are shown in Fig. 3 (a), (b) and (c) for Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems, respectively. For the Cu5@(8,8) and Cu9@(8,8) combined systems, the initial shapes (quadratic-prismatic Cu wires and cylindrical (8,8) GaNNTs) are preserved without any visible changes after optimization due to weak interaction between the thin Cu nanowires and GaNNTs. However, while a thicker Cu13 nanowire is encapsulated in the (8,8) GaNNT, the strength of both Cu–N (especially) and Cu–Ga bondings increases. Therefore, not only a quadratic-like cross-section shape is formed for the nanotube but also a relative rotation about common axis has taken place for the nanotube with respect to the nanowire. To investigate the stability of Cun@(8,8) combined systems, we have estimated the formation energies Eform of the

3 1

1

Cu5@(8,8)

Cu9@(8,8)

2

1

2

Cu13@(8,8)

Fig. 1. The cross section views for (a) Cu5@(8,8), (b) Cu9@(8,8) and (c) Cu13@(8,8), where the gray, blue and orange balls denote Ga, N and Cu atoms, and the big and small balls denote the three type atoms on the adjacent layers A and B, respectively. The numbers m on the orange balls denote the mth Cu shell in the nanowires. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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c=3.24Å

4

2 Energy (eV)

2 En ergy (eV)

c=3.61Å

4

0 -2 -4

0 -2 -4

-6

-6 Γ

Ζ

10

20

30

Γ

40

Ζ

10

20

30

40

˚ The Fermi level is set to zero energy Fig. 2. Band structures (left panels) and total DOS (right panels) of the free-standing Cu5 nanowire with (a) c¼ 3.24 A˚ and (b) c ¼3.61 A. and indicated by the horizontal red dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Cu5@(8,8)

Cu9@(8,8)

Cu13@(8,8)

Fig. 3. Optimized structures of (a) Cu5@(8,8), (b) Cu9@(8,8) and (c) Cu13@(8,8) combined systems.

Cun@(8,8) combined systems and the results are 0.04,  0.06 and 0.23 eV for Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems, respectively. Here Eform is defined as Eform ¼ fEðGaNNT þCun Þ½EðGaNNTÞ þ EðCun Þg=n

ð1Þ

where EðGaNNTþ Cun Þ, EðGaNNTÞ and EðCun Þ represent the total energies of the Cun@(8,8) combined systems, optimized pristine (8,8) GaNNT and free-standing Cun nanowires, respectively, and n is the number of the Cu atoms in per unit cell. The negative formation energies are obtained for all three Cun@(8,8) combined systems implying that formation processes of these systems are all exothermic. However, Kang et al. found that the inserting processes of Fe13 and even Fe9 body-centered cubic (BCC) metallic nanowires into metallic (8,8) CNT are endothermic [41]. This suggests the semiconducting GaNNTs are preferred to the CNTs to shield thicker metal nanowires. For the Cu5@(8,8) and Cu9@(8,8) combined systems, where the thin nanowires are well separated from the nanotubes, the formation energies are extremely small, indicating the interactions between nanowire and nanotube are very weak. So as mentioned above the GaNNT is not substantially distorted. For the Cu13@(8,8) combined system, the stronger attraction between Cu atom of the outermost shell and its nearest neighboring N atom in the same layer A leads to not only a quadratic-like cross-section shape formed for the outer nanotube but also a relative rotation about common axis has taken place for the outer nanotube with respect to the nanowire. Better insight into the distribution of electrons with energy and the degree of electronic interaction between Cu nanowire and GaNNT can be gained from an analysis of band structures and density of states (DOS). Shown in Fig. 4 are the band structures of the Cu5@(8,8), Cu9@(8,8), and Cu13@(8,8) combined systems. The band structures of the pristine (8,8) GaNNT and three freestanding Cu nanowires are also shown for comparison. The G

and Z represent two highly symmetric points in the Brillouin zone of the supercell, that is (0 0 0) and (0 0 0.5), respectively. The Fermi level is set to zero energy and indicated by the horizontal red dashed lines. From Fig. 4 one can see that, the band gap of about 2 eV shows pristine GaNNT to be semiconductor, whereas free-standing Cu nanowires show metallic characteristics, since there are several bands crossing the Fermi level. For the Cu5@(8,8) and Cu9@(8,8) combined systems, we can see that the band structures near the Fermi level are nearly a superposition of the band structures of their components, consistent with the weak interaction between the outer GaNNTs and the inner Cu nanowires in the above interpretation. Thus, the bands crossing the Fermi level in the Cu5@(8,8) and Cu9@(8,8) combined systems originate from the inner Cu nanowires. Furthermore we examine the distribution of valence charge densities of these two systems and find almost no interactions between the Cu and Ga or N atoms. In the case of Cu13@(8,8) combined system, because the third shell Cu atoms of the thicker Cu13 nanowire are close to the tube wall of (8,8) GaNNT and are thus enhanced in the hybridization between p orbitals of the N aotms and d orbitals of Cu atoms, the band structures of the Cu13@(8,8) combined system are not simply a superposition of those of their components. This is similar to the case of potassium iodide (KI) chain intercalated (10,10) CNT studied theoretically by Yam et al. [42], where the band structures of the combined system near the Fermi level alters upon the KI intercalation. The total density of states (DOS) of Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems are given in Fig. 5(a), (b) and (c), respectively. The Fermi level is set to zero energy and indicated by the vertical red dashed lines. Firstly, all three Cun@(8,8) combined systems have a metallic behavior compared with the semiconductor (8,8) GaNNT as is shown in Fig. 5(d). Secondly, the DOS value near the Fermi level and the integration area increase for

L.-C. Ma et al. / Physica B 406 (2011) 3502–3507

Cu5

(8,8)

4

Cu5@(8,8)

3505

Cu9@(8,8)

Cu9

Cu13

Cu13@(8,8)

Energy (eV)

2

0

-2

-4

Γ

Ζ

Γ

Ζ

Γ

Ζ

Γ

Ζ

Γ

Ζ

Γ

Ζ

Ζ

Γ

Fig. 4. Band structures of the pristine (8,8) GaNNT, the free-standing Cu5, Cu9 and Cu13 nanowires, as well as the Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems. The Fermi level is set to zero energy and indicated by the horizontal red dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Cu9@(8,8)

Cu5@(8,8)

Cu13@(8,8)

(8,8)

DOS (arb.unit)

80 60 40 20 0 -8

-6

-4

-2

0

2

4

6 -8

-6

-4

-2

0

2

4 6 -8 -6 Energy (eV)

-4

-2

0

2

4

6 -8

-6

-4

-2

0

2

4

6

Fig. 5. The total DOS of (a) Cu5@(8,8), (b) Cu9@(8,8), (c) Cu13@(8,8) combined systems and (d) pristine (8,8) GaNNT. The Fermi level is set to zero energy and indicated by the vertical red dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems successively due to the increasing number of the metal Cu atoms. The projected densities of states (PDOS) onto different shell Cu atoms of the inner wire, onto the Ga and N atoms of the outside tube are shown in Fig. 6(a), (b) and (c) for Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems, respectively. Following features can be seen by comparing the PDOS of these three systems. Firstly, the PDOS of the Cu5@(8,8) combined system onto the core Cu atom (black line) lying on the axis exhibits two well-separated peaks at two sides of the central two smaller peaks, which represent the bonding and antibonding d states [43]. These peaks are broadened with increases the number n of the Cu atoms in per unit cell due to the enhanced interactions with additional peripheral Cu atoms. The bonding and antibonding d states are all located below the Fermi level (vertical dashed line) implying these two states are fully occupied. Secondly, the separation between the bonding and antibonding states is reduced as going from the core Cu atom to the outermost shell Cu atom. This is because the coordination number is reduced and thus the hybridization of the d orbitals is weakened as going from the core Cu atom to the outermost shell Cu atom. So we conclude that the less the coordination number, the weaker the hybridization for the d orbitals of the Cu atoms, the shorter the separation between the bonding and antibonding d states. Thirdly, as can be seen from the inset figures, for Cu5@(8,8) and Cu9@(8,8) combined systems, the PDOS values near the Fermi level are only provided by Cu atoms and the contributions from Ga and N atoms are all zero. This is not the case for the Cu13@(8,8) system, besides the contributions from the Cu atoms, both Ga and N atoms also

have the small contributions. The properties of this and especially the coincidence of the highest peaks of N atom and Cu-3 atom at  2.5 eV in Fig. 6(c) also confirm the strong interaction between outmost shell Cu-3 atom and its nearest N atom. It is known that the number of conduction channels for the ballistic electron transport of metallic nanowires is directly associated with the number of electron bands crossing the Fermi level [3]. Hence, the quantum conductance would not be modified when Cu5 or Cu9 nanowire is filled inside the (8,8) GaNNT to form nanocable. Moreover, such ballistic quantum conductance is rather robust and is not easily disrupted by the local structural defect on the nanowires [3]. The electronic and transport properties of the Cun@(8,8) combined systems can be assessed further by analyzing the charge density distribution. Fig. 7(a), (b) and (c) represents the contour plots of charge density distributions on layer A (upper panels) and layer B (lower panels) for Cu5@(8,8), Cu9@(8,8) and Cu13@(8,8) combined systems, respectively. For the Cu5@(8,8) or Cu9@(8,8) combined system, there is no overlap of the charges between inner Cu nanowire and outer GaNNT indicating a negligible interaction between them, so the conduction electrons are localized on the inner Cu wire region. Thus, electron transport will occur only through the encapsulated Cu nanowire and the inert outer GaNNT serves well as insulating cable sheath. This feature is very important for the applications of nanocables in future nanoscale devices. While for the Cu13@(8,8) combined system, just as can be seen from Fig. 7(c), a large overlap of the charges between the outermost shell Cu atoms of the nanowire and their nearest neighbor N (especially) or Ga atoms of nanotube at the

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Cu5@(8,8)

8 6

0.3

Cu-core Cu-1 Ga N

0.2

4

0.1 0.0

2

-0.2 -0.1

0.0

0.1

0.2

0 Cu9@(8,8)

PDOS (arb.unit)

8 6

Cu-core Cu-1 Cu-2 Ga N

0.3 0.2

4

0.1 0.0

2

-0.2 -0.1

0.0

0.1

0.2

0 Cu13@(8,8)

8 6

0.3 0.2

4

0.1 0.0

2

-0.2 -0.1

0.0

0.1

0.2

Cu-core Cu-1 Cu-2 Cu-3 Ga N

0 -5

-4

-3

-2

-1 Energy (eV)

0

1

2

3

Fig. 6. The PDOS onto different shell Cu atoms of the inner wire, and Ga and N atoms of the outside tube for (a) Cu5@(8,8), (b) Cu9@(8,8) and (c) Cu13@(8,8) combined systems. Black, red, blue and dark cyan as well as magenta and dark yellow lines denote the PDOS onto the core, the first, the second and the third shell Cu atoms of the nanowires as well as the Ga and N atoms of the nanotubes, respectively. The inset figure is the PDOS near the Fermi level (from  0.2 to 0.2 eV). The vertical black dashed lines denote the Fermi level shifted to zero energy. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Cu5@(8,8)

Cu9@(8,8)

Cu13@(8,8)

Fig. 7. Contour plots of charge density distribution on layer A (upper panels) and layer B (lower panels) for (a) Cu5@(8,8), (b) Cu9@(8,8) and (c) Cu13@(8,8) combined systems, where the gray, blue and orange points represent the Ga, N and Cu atoms. All isodensity curves are drawn with an increment of 0.007 (elections/A˚ 3) from 0.007 to 1 (elections/A˚ 3). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

L.-C. Ma et al. / Physica B 406 (2011) 3502–3507

Table 1 Charge distributions in pristine (8,8) GaNNT, free-standing Cun nanowires and Cun@(8,8) combined systems. Systems

Total

Tube

Wire

(8,8) GaNNT Cu5 nanowire Cu9 nanowire Cu13 nanowire Cu5@(8,8) Cu9@(8,8) Cu13@(8,8)

128 55 99 143 183 227 271

128 – – – 128 128 128.54

– 55 99 143 55 99 142.46

same layer indicates a strong interaction between them and thus weakens the transport properties of the Cu nanowire. In order to quantify the charge transfer between Cu nanowire and GaNNT, we determined the charge distributions based on the criteria of Bader by decomposing the electron density using a finer mesh [44]. The charge distributions of the pristine (8,8) GaNNT, the free-standing Cun nanowires and the Cun@(8,8) combined systems are shown in Table 1. For the Cu5@(8,8) and Cu9@(8,8) combined systems, there is no charge transfer between GaNNT and Cu nanowire, the outer tube and inner wire have the same amount of charges as those of their pristine counterparts. But for Cu13@(8,8) combined system there is a small quantity of electron transfer from the Cu nanowire to the GaNNT, the numbers of electrons in the inner Cu nanowire are 142.46, while those of outer GaNNT are increased to 128.54. There are 0.54 electrons per unit cell transferred from Cu13 nanowire to the tube, especially to the N atoms. As compared to the theoretical studies of KI chain intercalated (10,10) CNT, where a substantial amount of electron transfers from the KI chain to the CNT and the increasing portion of the density is most around the wall of the tube, the small quantity of electron transfer in Cu13@(8,8) combined system maybe the result of the complete filled 3d electron shell of Cu atoms, which result in weaker coupling with the nanotube sheath.

4. Conclusion In summary, the structural and electronic properties of Cun nanowires (n¼5, 9 and 13) encapsulated into the semiconducting (8,8) GaNNT have been investigated systematically using the firstprinciples PAW potential within DFT framework under GGA. For both Cu5@(8,8) and Cu9@(8,8) combined systems, the initial shapes are preserved without any visible changes after optimization, while for the Cu13@(8,8) combined system not only a quadraticlike cross-section shape is formed for the nanotube but also a relative rotation about common axis has taken place for the nanotube with respect to the nanowire. The negative formation energies implying the formation processes are all exothermic, but the extremely small (larger) formation energies indicating that the interactions between nanowire and nanotube are very weak (stronger) for the Cu5@(8,8) and Cu9@(8,8) (Cu13@(8,8)) combined systems (system). For the Cu5@(8,8) and Cu9@(8,8) combined systems, the band structures are nearly a superposition of the band structures of their components. Both projected densities of states (PDOS) and charge density analyses show that in Cu13@(8,8) combined system the electrons of Ga and N atoms in outer GaN sheath affect the electron conductance of the encapsulated metallic nanowire. While in Cu9@(8,8) combined system there is no overlap of the charges between Cu9 nanowire and GaNNT, the conduction electrons are localized in the inner Cu

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wire region, therefore, the electronic transport will occur in the inner Cu nanowire and the outer GaN nanotube, which only functions as an insulating sheath. So taking into account the minimization of the formation energy and wire–tube interaction in the nanocable, we know that both Cu5@(8,8) and Cu9@(8,8) combined systems are the idea nanocables, which can be applied to the ULSI circuits and MEMS that demand steady transport of electrons. But considering the maximal metal filling ratio in nanotube, we know that the Cu9@(8,8) combined system is toppriority.

Acknowledgments The authors would like to acknowledge the National Natural Science Foundation of China (Grant no 51071098) for providing financial support for this research.

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