Introduction

Compared with the former electronic devices, the current nanodevices are advantageous in smaller feature size, higher integration, more stability, and higher performance, etc. (Berman and Krim 2013) Currently, as for the typical complementary metal oxide-semiconductor (CMOS) fabrication technology, the ‘top-down” nanolithography method has been determined by diffraction limit of light. However, the “bottom-up” approach is increasingly becoming a promising tool to meet the fabrication requirements for next-generation nanoelectronic devices in the future, through rearranging and assembling some fundamental building blocks (Biswas et al. 2012; Chen et al. 2015; Cui et al. 2015; Mehta et al. 2012). Exhilaratingly, Ag nanowires and single-walled carbon nanotubes as the interesting new building blocks, fabricated by physical or/and chemical methods, are viewed as the promising candidates for next-generation interconnects due to their most remarkable electrical, thermal, optical, mechanical, and other properties (Ceyhan and Naeemi 2013; De Volder et al. 2013; Do et al. 2015; Langley et al. 2013; Subash et al. 2013; Toprak and Bayazitoglu 2013; van de Groep et al. 2012; Zabihi and Araghi 2016a, b). Additionally, interconnect technology is essential for fabricating nanostructures and nanodevices in nanoelectromechanical systems (NEMSs), while the axial nanowelding is the key foundation of 2D/3D complex contacts.

In the recent years, many innovative technologies for microelectronics fabrication have been directly applied to nanointerconnect process. Banhart (2001) reported the nanoconnection of crossing multiwalled carbon nanotubes (MWNTs) with the aggregation of hydrocarbons and successive transformation into amorphous carbon at the junction, which is irradiated by a scanning electron microscope (SEM). Duan et al. (2005) performed nanospot welding by using scanning probe microscope (SPM) through the localized electric field inducing oxidation of silicon to SiOx. The nanorobotic spot welding, with controlled metal deposition with Attogram precision from copper-filled carbon nanotubes, was also investigated (Dong et al. 2007). In addition, in nanowelding of metal nanowires, Peng et al. (2008) demonstrated a new nanoscale electrical welding technique by using a sacrificial nanowire, assembling and welding gold nanowires together into complex nanostructures and conductive circuits. Lu et al. (2010) demonstrated that single crystalline gold nanowires can be cold-welded together within seconds by mechanical contact alone and under relatively low applied pressures. Recently, Garnett et al. (2012) has reported a light-induced plasmonic nanowelding technique to assemble metallic nanowires into large interconnected networks. To further explore nanowelding techniques of nanowires and carbon nanotubes, Guo (2010) summarized the various creation methods of nanojunctions, and Cui et al. 2009 summarized the joining and interconnect formation of nanowires and carbon nanotubes for nanoelectronics and nanosystems. Consequently, the nanowelding of nanowires and carbon nanotubes can be well solved experimentally.

In order to obtain better interconnect quality, nanowelding configurations should be performed to find out how interconnect factors affect contact behaviors and subsequent atomic structures. Unfortunately, the experimental procedure and specific details of nanowelding can hardly be observed. However, as for a realistic manner, the molecular dynamics (MDs) method provides a powerful tool for demonstrating the dynamical evolution of atomic configurations (Cui et al. 2014, 2016a; Jang et al. 2004; Pereira and Da Silva 2011; Terrones et al. 2002). With the tight-binding MD method, Terrones et al. simulated molecular junctions of joining SWNTs to analyze the responsible mechanisms for junction formation. Jang et al. performed the MD simulation of carbon nanotube welding under electron beam irradiation, and the junction structure and hydrogen termination of dangling bonds on the mechanical responses of junctions are also considered in their article. Additionally, Pereira et al. carried out an MD study of cold welding of gold and silver nanowires aiming at the experimental research of cold welding published by Lu et al. (2010) However, the evolution, behavior, and configuration in interconnect processes are still lacking, and current MD simulations are mainly about interconnect between the congeneric nanowires or carbon nanotubes (CNTs), while little is known regarding the interfacial contact behavior and configuration between metal nanowires and CNTs with atomistic simulations. Therefore, the atomistic simulations of axial nanowelding configuration and contact behavior between Ag nanowires (AgNWs) and single-walled carbon nanotubes (SWNTs) are demonstrated, and its dominant mechanism and detailed structural characteristics are analyzed and discussed on the basis of a series of the MD simulation results in this article.

Computational methodology

As for the MD simulations, the nanowelding process has been performed by DISCOVER module of MATERIALS STUDIO software, which was developed by Accelrys Software Inc. And in the MD simulations, the key of calculation is the selection of interatomic force field, which determines the work load, accuracy of results, and the approximate extent between the calculation model and the real system. Thus, all the MD simulations are implemented by the powerful condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field (Cui et al. 2013a, b; Sun 1994; Sun 2013; Yan et al. 2009; Zhou et al. 2015). It is a parameterized, tested, and validated first ab initio force field, which enables an accurate and simultaneous prediction of structural, conformational, vibrational, and thermophysical properties of condensed matter physics. The total energy (E total) includes potential energy (E potential) and kinetic energy (E kinetic), which can be described as follows:

$$ {E}_{\mathrm{total}}={E}_{\mathrm{potential}}+{E}_{\mathrm{kinetic}} $$
(1)

And, the total potential energy (E potential) can be expressed by the following terms:

$$ {E}_{\mathrm{potential}}={E}_{\mathrm{valence}}+{E}_{\mathrm{cross}-\mathrm{term}}+{E}_{\mathrm{non}-\mathrm{bond}} $$
(2)
$$ {E}_{\mathrm{valence}}={E}_{\mathrm{bond}}+{E}_{\mathrm{angle}}+{E}_{\mathrm{torsion}}+{E}_{\mathrm{oop}}+{E}_{\mathrm{UB}} $$
(3)
$$ \begin{array}{l}{E}_{\mathrm{cross}-\mathrm{term}}={E}_{\mathrm{bond}-\mathrm{bond}}+{E}_{\mathrm{angle}-\mathrm{angle}}+{E}_{\mathrm{bond}-\mathrm{angle}}+\hfill \\ {}{E}_{\mathrm{end}-\mathrm{bond}-\mathrm{torsion}}+{E}_{\mathrm{middle}-\mathrm{bond}-\mathrm{torsion}}+\hfill \\ {}{E}_{\mathrm{angle}-\mathrm{torsion}}+{E}_{\mathrm{angle}-\mathrm{angle}-\mathrm{torsion}}\hfill \end{array} $$
(4)
$$ {E}_{\mathrm{non}-\mathrm{bond}}={E}_{\mathrm{vdW}}+{E}_{\mathrm{Coulomb}}+{E}_{\mathrm{H}-\mathrm{bond}} $$
(5)

Here, the E bond, E angle, E torsion, E oop, and E UB, including the valence energy (E valence), represent the bond stretching term, two-bond angle term, dihedral bond-torsion term, out-of-plane interaction term, Urey-Bradlay term, respectively. The cross-term interacting energy (E cross-term) explains the effects such as bond changes or angle distortions determined by surrounding atoms. And, the different energy terms E bond-bond, E angle-angle, E bond-angle, E end-bond-torsion, E middle-bond-torsion, E angle-torsion, and E angle-angle-torsion, respectively, give the stretch-stretch interaction between two adjacent bonds, bend-bend interaction between two valence angles, stretch-bend interaction between a two-bond angle and one of the bonds, stretch-torsion interaction between a dihedral angle and one of the end bonds, stretch-torsion interaction between a dihedral angle and the middle bond, bend-torsion interaction between a dihedral angle and one of the valence angles, and the bend-bend-torsion interaction between a dihedral angle and its two valence angles. In addition, the non-bond energy (E non-bond), containing the van der Waals interaction term (E vdW), a Coulomb term for electrostatic interaction (E Coulomb), and the hydrogen bond energy (E H-bond), accounts for the interaction between non-bond atoms.

In order to study the axial nanowelding configuration and contact behavior between AgNW and SWNT in Fig. 1a, the corresponding atomic schematic diagram is presented in Fig. 1b. Combining the actual situation, the AgNW of cylindrical structure including 1380 atoms was built with an 8-nm length and 2-nm diameter based on the 3D cubic structure lattice with the same lattice length of 4.0857 Å. In addition, the typical size of SWNT diameter is about 0.75∼3 nm. However, SWNTs with larger diameter are easier to collapse, and the SWNTs with diameter of ∼2 nm can keep good rigidity and cylindricity. As for the unmodified SWNT, the hybrid orbital of each carbon atom is sp 2 with the same 1.42 C–C bond length. The AgNW and SWNT are placed on the Si substrate with a 3D size of 192.004 Å × 76.802 Å × 15.057 Å in the x, y, and z directions based on the 3D cubic lattice type with the lattice parameter of 5.4307 Å × 5.4307 Å × 5.4307 Å.

Fig. 1
figure 1

a The schematic of axial nanowelding between AgNW and SWNT and b the corresponding atomic structural image

Full size image

In the following MD simulations of nanowelding, because the atomic configuration and contact behavior between AgNW and SWNT are the main research targets, the motions of all the Si atoms were constrained in the x, y, and z directions, combining with the characteristics of bulk Si substrate. Then, taking the nanometer-size effects of AgNW and SWNT into account, the x, y, and z directions of the simulation box was imposed by the non-periodic boundary conditions. Considering the disorderly movement of the atoms under the normal circumstances, the initial random velocities of all atoms were given in accordance with the Maxwell-Boltzmann distribution, while the Andersen thermostat condition was selected for maintaining a constant temperature. And, the temperature of any physical systems is composed of the motion of the molecules and atoms. These particles have a range of different speeds, and the speed of any single particle is constantly changed with the collisions subjected by other particles. As for a large number of particles, if the system is at or near equilibrium, it is almost the same proportion in a specific speed range. So, the Maxwell-Boltzmann distribution, as the probability distribution in the field of statistical mechanics, explains the proportion for any speed range well as the temperature functions of the system. It also shows that it is reliable for simulating the nanowelding process with the random initial velocities according to the Maxwell-Boltzmann distribution. Thus, the nanowelding process was simulated under the constant NVT (N represents the number of atoms, V gives the volume, and T is the temperature) ensemble based on the integration method of Velocity Verlet. Based on our previous researches about the energy-equilibrated process before nanowelding process (Cui et al. 2016a, b), in order to obtain the stable and accurate physical data, the total simulation time was set to 500 ps with 2-fs fixed time step and 250,000 steps, and the trajectories of all the atoms were stored and the frame was output every 5000 steps.

Results and discussion

As for the nanowelding process, although the diameter of SWNT depends on the spiral vector parameters with the discontinuous values, keeping the similar diameter between AgNW and SWNT should be firstly considered. And, the size of (15, 15) metallic armchair SWNT, with 2.034-nm diameter and 8.116-nm length, is close to AgNW. Simultaneously, the AgNW and SWNT are arranged coaxially as one of the actual situations in Fig. 1b, and the initial atomic configuration is given in Fig. 2a. And, the distances of AgNW-SWNT, AgNW-Si surface, and SWNT-Si surface are set to 3, 2, and 1.8 Å, respectively.

Fig. 2
figure 2

Snapshots for instantaneous nanowelding configurations between AgNW and (15, 15) SWNT with the head-to-head structural style on the Si surface in the x-z plane at the temperature of 500 K

Full size image

As for the nanowelding temperature, the stand soldering temperature is about 580 K, and low-temperature welding is becoming more and more important in the nanointerconnect and electronic packaging. So, the MD simulations of nanowelding process were performed at the temperature of 500 K, which is slightly lower than the standard soldering temperature. From the snapshots of instantaneous configurations, the SWNT collapses incompletely with a larger degree of deformation when the simulation time is 10 ps, which may be subjected to larger comprehensive interatomic forces from the Si and Ag atoms at the left part. And, when the time is 50 ps, the SWNT moves toward the head of AgNW with slip phenomenon, achieving good contact with the head-to-head contact configuration and possessing the similar deformation of the whole SWNT. It depends on that the C atoms of the SWNT head are affected by the attraction of Ag atoms at the head of nanowire, while the binding force between Ag atoms and Si surface is larger than that between C atoms and Si atoms through the different distances between Si surface and AgNW or SWNT. In addition, as the simulation time goes on, the Ag atoms of AgNW can be gradually captured into the nanotube because of the terminal suspended C atoms of SWNT being in a state of force imbalance with strong attraction. But, not many Ag atoms are dragged into SWNT, which mainly depends on that the Ag atoms possess stronger metal bond effect with the weak thermal dynamic performance at the lower temperature. Simultaneously, with simulation time increasing from 50 to 500 ps, the left part of SWNT with larger collapse deformation is subsequently recovered and becomes larger in order to swallow AgNW. And, as for the final atomic configuration in Fig. 2f, the diameter size of continuous atomic chain encapsulated in nanotube is slightly smaller than the SWNT diameter. However, only a slight contact, with final configuration of the core-filling Ag atom chain structure of two to three atoms in length, exists at the junction between AgNW and SWNT, which may be related to the nanowelding temperature through affecting the thermal dynamic performance of AgNW.

To further explore how the temperature affects the thermodynamic performance of AgNW and the final nanowelding effect, the final nanowelding atomic configurations are shown in Fig. 3 at different temperature. If the nanowelding process is achieved at the lower cold welding temperature of 300 K, the SWNT will also move toward the AgNW head without Ag atoms entering into nanotube. The reason lies in the stronger metal bond effect of AgNW in the solid state at the lower temperature. With the temperature increasing, the metal bond effect of AgNW will become increasingly weak with stronger thermal dynamic performance. So, the Ag atoms have a great chance to be captured into nanotube. When the atoms enter into the nanotube, the Ag atoms compose the chain structure such as in Fig. 3c due to the binding effect of metal bonds. Based on our previous researches about the melting characteristics and thermal dynamic properties of nanomaterials (Cui et al. 2013c), according to the irregular atomic morphology of AgNW surface, the AgNW is only in the slight surface melting state without changing the AgNW structure. When the temperature is sequentially increased to 1000 K, the AgNW is in the serious melting state while becoming a similar nanodroplet structure and seriously changing its structure of nanowire. Meanwhile, the binding effect of metal bonds will be weakened further. Thus, more Ag atoms are encapsulated in the SWNT and the atomic chain also becomes longer while still keeping the effect of metal bonds, which is given in Fig. 3d. So, the statistical result of the atomic motion for Ag atoms migrating into the nanotube is the capillarity phenomenon, which is similar to the simulation results between SWNT and metal interface published by Song et al. (2009). However, when the temperature is 1250 and 1500 K, respectively, the chain length of the core-filling Ag atoms no longer becomes longer with increasing temperature. At high temperature, the AgNW will soon melt in the liquid state, and the melting nanowire aggregates to the middle position of AgNW by forming a nanodroplet with the effect of metal bonds, which is also a manifestation of the surface tension effect. So, the distance between Ag atoms at the right head of AgNW and the C atoms at the left head of SWNT becomes larger while departing from the scope of interaction between Ag and C atoms, and the Ag atoms are not dragged into SWNT. In addition, several Ag atoms, marked in red circles in Fig. 3e, move to the distant location while getting rid of the shackles of other Ag atoms. Likewise, when the temperature is as high as 1500 K, the thermal motion of Ag atoms becomes very strong. More atoms are emancipated from the melting nanowire and some of which move toward the direction of SWNT still in existence of interacting effect between C atoms. Under the continued weak interaction, the SWNT can slowly move to the Ag nanodroplet and contact with the right part of the nanodroplet. Although the distance becomes smaller between the left SWNT head and the melting nanowire, the Ag atoms are difficult to be captured into the nanotube due to the strong atomic motion, which is similar to that the Ag atoms are easy to rid of the shackles of the metal bond effect. So, at high temperature of 1500 K, the final nanowelding atomic configuration is shown in Fig. 3f. Therefore, high temperatures such as 1000 1250, and 1500 K, are not suitable for nanowelding based on the contact configuration and nanowire self-morphology.

Fig. 3
figure 3

Snapshots for instantaneous nanowelding atomic configurations between AgNW and (15, 15) SWNT with the head-to-head structural style on the Si surface in the x-z plane at different temperatures

Full size image

In order to further explore the above atomic configurations and contact behaviors, the corresponding MD simulation results are analyzed from an energetic standpoint. Figure 4a gives the initial total, potential, and kinetic energy and the main components of potential energy during nanowelding process, which is also the final energetic state for getting the optimized atomic configurations in the period of energy minimization. It shows that total energy is mainly occupied by the potential energy with relatively very small kinetic energy of 3003 kcal/mol. Simultaneously, the main components of valence energy and van der Waals interaction energy are also provided with obvious torsion energy, the repulsive and dispersive parts of the van der Waals interaction energy. Because the value of the coulomb energy E Coulomb and the hydrogen bond energy E H-bond is respectively zero in the simulations, the non-bond energy E non-bond in Fig. 4 completely equals to the van der Waals interaction energy E vdW according to Eq. (5). However, the decision of the final configurations does not depend on the initial energy or the final energy but the energy difference between the initial and final state. So, Fig. 4b shows the difference of total, potential, and kinetic energy between the initial and final state during nanowelding process, respectively. There into, the difference of kinetic energy is close to zero at the different nanowelding temperature and the very slight difference is caused by the initial random atomic motion and not very accurate initial and final temperature within the margin of error of approximately 1 K. The difference of the potential energy is very obvious, which increases rapidly at the high temperature of 1250 and 1500 K, respectively. In order to further find out the main potential energy parameters, the main components of valence energy and vdW (non-bond) energy are also given in Fig. 4c, d, respectively. Comparing the energy difference in Fig. 4c, d, the repulsive and dispersive difference of the vdW energy is an order of magnitude higher than the main components of the valence energy, which indicates that the vdW force mainly affects the final nanowelding atomic configurations. The main E bond, E angle, E torsion, and E oop are mainly related with the SWNT deformation. In addition, as the temperature increases, the energy difference in Fig. 4c, d also increases due to the larger SWNT deformation and the average atomic volume, respectively. Consequently, the van der Waals force, including the repulsive and dispersive force, becomes the dominant factor of coaxial nanowelding between SWNT and AgNW.

Fig. 4
figure 4

a Total, potential, and kinetic energy and the main components of potential energy for the initial state during nanowelding process. b The difference of total, potential, and kinetic energy. c The difference of the main components of valence energy (E bond, E angle, E torsion, E oop). d The difference of the van der Waals interaction energy and its components between the initial and final state, respectively

Full size image

In order to further investigate the effect of other factors on nanowelding configurations, the diameter factor is considered based on facing with the inconsistent diameter case of nanowire and nanotube in the actual situation. So, the initial atomic configuration with the ration value between AgNW diameter and SWNT diameter greater than 1 should be also simulated. Then, the metallic armchair (8, 8) SWNT with 1.085-nm diameter and the same 8.116-nm length was selected while keeping the same size of AgNW in Fig. 5a, and the nanowelding process was performed at 500 K in Fig. 5. The corresponding nanowelding behaviors are similar to that in Fig. 2, and the SWNT also moves toward AgNW and contacts with the right head of AgNW over time. Separately, only two Ag atoms are captured into the nanotube with the smaller diameter by the smaller attractive force from C atoms of the left head of SWNT based on our previous research (Cui et al. 2014), in the case of AgNW possessing the same thermodynamics performance at the same nanowelding temperature. And, the SWNT with slight deformation always maintains good consistency with the perfect stiffness in the x direction during the nanowelding process, which is different from the (15, 15) SWNT with a certain conical degree in Fig. 2.

Fig. 5
figure 5

Snapshots for instantaneous nanowelding configurations between AgNW and (8, 8) SWNT with the head-to-head structural style on the Si surface in the x-z plane at the temperature of 500 K

Full size image

Additionally, for comprehensive comparison, the above (15, 15) SWNT in Fig. 2 is replaced by the metallic armchair (30, 30) SWNT which has 4.068-nm diameter and 8.116-nm length as the initial atomic configuration, shown in Fig. 6a, b, respectively. And, the nanowelding process was also simulated at 500 K. According to the snapshots for instantaneous nanowelding configurations in Fig. 6a, although the SWNT has the larger diameter, the SWNT cannot swallow the whole AgNW or drag some Ag atoms into the nanotube to form the core-filling nanowire structure. When the simulation time is 10 ps, the SWNT maintains the similar structure with initial configuration from the diameter and cylindricity. However, when the time becomes 50 ps, the SWNT greatly collapses with diminishing size close to the diameter of AgNW in the z direction, and the SWNT further becomes a saddle-like structure at 100 ps in Fig. 6b. And, the collapse deformation of the SWNT becomes more serious at 200 ps. Additionally, the contact behavior between AgNW and SWNT has not occurred while keeping a distance. It is related with the weak interaction force between Ag atoms of the right AgNW head and the left suspended C atoms of SWNT, which mainly depends on that many C atoms cannot interact with the Ag atoms due to that the interaction goes out of scope with larger diameter of SWNT. At the same time, the number of C atoms at the left SWNT head interacting with the Ag atoms at the right head of AgNW gradually increases due to the degree of the SWNT collapse. Thereupon, with increasing of the interaction, the SWNT moves toward AgNW and contacts with the right head of AgNW at the time of 500 ps. Because the left part of SWNT is affected by the strong van der Waals force from AgNW, its self-structure becomes smaller at the left part due to the tight contact with AgNW and larger at the right part due to that there is no interference from other atoms besides Si atoms. Consequently, when the diameter of SWNT is larger than that of AgNW, the contact behavior occurs after the collapse deformation of SWNT for obtaining the final atomic configuration during the nanowelding process.

Fig. 6
figure 6

Snapshots for instantaneous nanowelding configurations between AgNW and (30, 30) SWNT with the head-to-head structural style on the Si surface in a the x-z plane and b the y-z plane at the temperature of 500 K

Full size image

After studying the nanowelding configuration and behavior between AgNW and SWNT in the coaxial direction, the nanojoining situation between AgNW and SWNT, without being coaxial atomic configuration, should be explored with the common initial side to side structural style in Fig. 7.

Fig. 7
figure 7

The atomic configuration of axial nanowelding between AgNW and SWNT with the side to side structural style

Full size image

In the simulations, the metallic armchair SWNTs of (8, 8), (15, 15), and (20, 20), with the same 8.116-nm length and different diameters of 1.085, 2.034, and 2.712 nm, were selected. Figure 8 gives the corresponding initial atomic configurations with about 1.4-nm contact length between the left head of SWNT and the right head of AgNW.

Fig. 8
figure 8

The initial nanowelding configurations between AgNW and (8, 8), (15, 15), and (20, 20) SWNTs with the side-to-side structural style on the Si surface in a the x-y plane and b the y-z plane

Full size image

Then, with the longer simulation time of 1 ns at the temperature of 500 K, the nanowelding simulations were carried out for observing contact behaviors and obtaining the final atomic contact configurations in Fig. 9. Observing them in the x-y plane, the AgNW position almost remains the same, but the SWNT moves along the nanowire surface with different contact configurations. Obviously, in the (15, 15) SWNT-AgNW system, the SWNT does not eventually catch up with the AgNW being neck and neck. For in-depth studying of the contact behavior, Fig. 10 shows the evolution of atomic configuration. With increasing time, the SWNT slowly moves along the AgNW surface with increasing contact length. From the atomic configurations at times 10 and 100 ps, the SWNT almost always moves horizontally in the x direction, and the atomic structure of AgNW is substantially unchanged based on the regular arrangement of atoms from length to diameter. However, when the time is increased to 300 ps, there is a serious twist in the SWNT structure due to the strong attraction by the Ag atoms at the right part of AgNW. Simultaneously, the AgNW structure affected by the reaction from C atoms becomes relatively loose at the right part of AgNW. Subsequently, with the forward movement of SWNT, the distortion angle also becomes smaller. But, because the AgNW can be gradually affected by the C atoms at the head and sidewall of SWNT, the atomic structure of AgNW also gradually becomes loose with larger diameter and smaller length as the final atomic configuration.

Fig. 9
figure 9

Snapshots for instantaneous nanowelding configurations between AgNW and (8, 8), (15, 15), and (20, 20) SWNTs with the side-to-side structural style on the Si surface in a the x-y plane and b the y-z plane at the temperature of 500 K

Full size image
Fig. 10
figure 10

Snapshots for instantaneous nanowelding configurations between AgNW and (15, 15) SWNT with the side-to-side structural style on the Si surface in the x-y plane at the temperature 500 K

Full size image

By contrast, when the SWNT diameter is smaller or larger than that of AgNW, the left head of SWNT can eventually catch up with the AgNW and flush with the left head of AgNW with the similar contact length in Fig. 9a, c, respectively. For comparing the contact behavior in Fig. 10, the corresponding evolution of configurations in the (8, 8) SWNT-AgNW system and the (20, 20) SWNT-AgNW system is shown in Fig. 11. In Fig. 11a, the SWNT almost always moves horizontally in the x direction, except for the slight deflection at 100 ps. And, the similar contact behavior occurs in the (20, 20) SWNT-AgNW system in Fig. 11b. But, obviously, before SWNT caught up with the AgNW, the radial size of the right part of the SWNT in the y direction is larger than that of the left part of the SWNT. This is because the interaction only occurs between the right C atoms of SWNT and the Si atoms when the right C atoms of SWNT are far apart from the Ag atoms. So, the corresponding collapse deformation in the z direction can occur subsequently, and the extent of deformation depends on the degree of influence from radial interaction between C and Ag atoms, which is related with the distance between the C atoms and Ag atoms. When the C atoms at the right head of SWNT are distant from the AgNW, the larger deformation appears at the right head of SWNT, and vice versa. To better observe the deformation, Fig. 12 shows the snapshots for instantaneous atomic configurations in the y-z plane. Combining Figs. 11b and 12, when the simulation time is 10 ps, the SWNT keeps good cylindricity without obvious size discrepancy between the left part and the right part, which mainly depends on insufficient interaction time between SWNT and Si substrate. Then, with sufficient interaction time of 100 ps, the large collapse deformation appears at the right part of SWNT. With the forward movement of SWNT, the degree of deformation decreases subsequently while the distance between the right head of AgNW and the right part of SWNT gradually becomes small with increasing interaction. When the SWNT catches up with the AgNW being neck and neck, overall, the SWNT subjected to similar interaction from the Ag atoms and Si atoms has consistent deformation. And, the situation described above also occurs in the (8, 8) SWNT-AgNW system and (15, 15) SWNT-AgNW system, respectively. Due to the better rigidity of SWNT with smaller diameter, the deformation is not too obvious during the nanowelding process. So, from the final side-to-side contact configurations in the y-z plane of Fig. 9, when the SWNT is relatively small such as in Fig. 9a, the SWNT configuration is substantially unchanged with pristine structure in Fig. 8a. When SWNT, with similar diameter to AgNW, is the (15, 15) structure, only slight deformation occurs with relatively good cylindricity. However, when the SWNT diameter is relatively larger than the AgNW diameter in Fig. 9c, the SWNT with larger deformation can be tightly affixed to the AgNW surface with larger contact area; the phenomenon is consistent with the published research about carbon nanotubes self-scrolling onto copper nanowires (Yan et al. 2009). At the same time, the adhesion between AgNW and Si substrate, in a similar situation between SWNT and AgNW, is larger than that between SWNT and Si substrate because of the smaller contact gap. So, under the larger adhesion between SWNT and AgNW, the SWNT will move along the AgNW, which will not be constrained in situ by the smaller adhesion effect between SWNT and the Si substrate surface.

Fig. 11
figure 11

Snapshots for instantaneous nanowelding configurations between AgNW and a the (8, 8) SWNT/b the (20, 20) SWNT with the side-to-side structural style on the Si surface in the x-y plane at the temperature of 500 K

Full size image
Fig. 12
figure 12

Snapshots for instantaneous nanowelding configurations between AgNW and (20, 20) SWNT with the side-to-side structural style on the Si surface in the y-z plane at the temperature of 500 K

Full size image

To further reveal the dominant mechanism for contact configurations in Fig. 9, Table 1 shows the different energy components and their difference. Because the SWNT-AgNW systems are different based on the different SWNT structures, the different energy components also change with the increase of SWNT structural size. And, for exploring the critical influence on the changes of the atomic configurations, the difference of energy is also given in Table 1. Due to the unified temperature of 500 K from the initial state to the final state, the kinetic energy difference is almost unchanged. And, the difference of the total energy, potential energy, and valence energy also tends to be increasingly obvious respectively with increasing size of SWNT. However, the minimum of the van der Waals energy difference appears in the (15, 15) SWNT-AgNW system with the 840 kcal/mol, which may be related to the smaller number of interacting Ag and C atoms under the situation of smaller contact area and larger diameter. By contrast, in the (8, 8) SWNT-AgNW system, there is larger contact length between SWNT and AgNW and the smaller SWNT diameter, which can increase the number of interacting atoms with maximum of E vdW difference. If the SWNT is arranged abreast without any deformation, there will be a small number of interacting atoms. But, the deformation increases the contact area between SWNT and AgNW, which enables the van der Waals energy to achieve a relatively high value of 898 kcal/mol as the (20, 20) SWNT-AgNW system. So, the relatively small van der Waals force, affected by the number of interacting atoms, becomes the dominant factor as the evolution behavior and final atomic configuration in Fig. 9b.

Table 1 Different energy components and differences of the SWNT-AgNW systems in Fig. 9 from the initial state to the final state at the temperature of 500 K
Full size table

Conclusions

In summary, the atomistic simulation of axial nanowelding process is performed with the molecular dynamic method. When the SWNT and AgNW are arranged coaxially with the similar diameter, the SWNT will move toward the AgNW and contact with the head of AgNW. And, the Ag can be dragged into the nanotube while forming core-filling Ag atom chain structure at relatively low temperature, which is related to the thermal dynamic performance of AgNW. When the temperature is very high, the SWNT and AgNW cannot be connected together. The Ag atoms are difficult to be captured into the SWNT due to the strong atomic motion, which is similar to that it is easy to get rid of the shackles of the metal bond effect of AgNW at high temperature. And, the AgNW is in serious melting state, becoming a similar nanodroplet structure and seriously changing its self-structure of nanowire. In addition, when the SWNT has a smaller or larger diameter than the AgNW does, the SWNT cannot drag some Ag atoms into the nanotube or swallow the whole AgNW to form the core-filling Ag atom chain structure, with a slight contact between the heads of SWNT and AgNW. For obtaining better nanowelding effect, the situation, the SWNT possessing strong interactive van der Waals force with AgNW and no serious collapse deformation, can be selected in the nanowelding process, which can be performed at a slightly high temperature for the longer core-filling Ag atom chain encapsulated in the nanotube. In addition, if the nanojoining situation between AgNW and SWNT is not coaxial with the common initial side-to-side structural style, and the SWNT can move along the AgNW surface. Whether the different SWNTs are able to eventually catch up with the AgNW while being neck and neck mainly depends on the size of van der Waals force affected by the number of interacting atoms between the SWNT and AgNW. Hopefully, there may be a way of driving carbon nanotubes, which needs to be studied further. And, the interconnect research affected by SWNT chemical modification and the electrical, thermal, and mechanical properties are also investigated with the theoretical or/and experimental methods for providing meaningful guidance in nanoelectronics fabrication, etc.