Thermal transport characteristics of supported carbon nanotube: Molecular dynamics simulation and theoretical analysis
Introduction
Carbon nanotube (CNT) has been recognized as one of the promising materials due to their outstanding transport and mechanical properties [1], [2], [3], [4], [5], [6]. To date, CNT-based field-effect transistors [7], micro-scale computer [8] and microprocessor [9] have been realized. This rapid development makes CNT a great option for next-generation beyond-silicon electronic systems [10]. However, as the trend of miniaturization becomes prominent [11], the high heat flux density of local hot spots, up to ~108 W/m2, has severely limited practical applications of microelectronic devices, and the thermal design has become the major concern [12]. Therefore, for bringing CNT-based devices into practice, the thermal transport characteristics of CNT must be studied. More importantly, although CNT possesses ultra-high thermal conductivity [13], [14], [15], [16], [17], the existence of the surrounding medium or substrate in devices can significantly influence the thermal transport performance [18,19]. Thus, the substrate effect on CNT should be systematically researched.
Since the discovery of CNT, tremendous efforts have been devoted to investigating thermal transport properties of free-standing CNT, and studying the dependence with different parameters, such as length, temperature, diameter and chirality [13,14,[20], [21], [22], [23], [24]]. However, over the past decade, theoretical and experimental studies have found a significant reduction of thermal conductivity in nanostructure when supported on a substrate [25], [26], [27], [28], [29], [30], [31]. Moreover, the intrinsic thermal transport characteristics mentioned above with parameters variation can also be changed. Numerical calculations have demonstrated that supported graphene exhibits a much insensitive behavior to length and width variation compared to suspended counterpart [32], [33], [34]. The same phenomenon has also been demonstrated in bismuth telluride quintuple layer [35].
Previous studies on the substrate effect of CNT were carried out by Davide et al. and Alexander et al. based on the assumption that only nearest neighbors interact at the interface [36,37]. However, they obtained quite different characters of length dependence for supported CNT, which may be attributed to the improper interaction potential. Afterwards, Ong et al. employed more accurate van der Waals (vdW) interaction and reported a 33% reduction in thermal conductivity once CNT is supported on the amorphous SiO2 substrate [38]. The similar reduction of 34%-41% was found by Qiu et al. with a chirality dependent phenomenon [39]. However, no further researches are reported and the comprehensive study on the thermal transport characteristics of supported CNT is still lacking.
Here, we systematically investigate the length, temperature and substrate coupling strength dependence of thermal conductivity in supported SWCNT using molecular dynamics (MD) simulation. A theoretical model is built to describe the length dependent thermal conductivity with substrate supported. Moreover, the analysis of spectral energy density (SED) is carried out to reveal the underlying mechanisms behind the temperature and substrate effects. At last, we calculate the stress distribution of CNT atoms to elucidate the influence of CNT-substrate coupling strength on thermal conductivity.
Section snippets
Numerical simulation
We use the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package [40] for molecular dynamics (MD) simulation due to its powerful performance to reproduce thermal transport properties of nanomaterials and excellent parallel characteristic. The schematic diagram of the supported model is shown in Fig. 1(a). The silicon is used as the substrate material due to its practical application in electronic industry. The SWCNT (10, 10) is supported on the Si substrate and the
Length dependence of thermal conductivity
We first study the size effect of both suspended and supported CNT. The calculated thermal conductivity of various system sizes at room temperature is plotted in Fig. 2(a). The thermal conductivity for suspended ones with longitudinal length (L) increasing in the present study (κ = 350~1356 Wm−1K−1 with L = 10~400 nm) is consistent with the previous simulated results (κ ≈ 375~1250 Wm−1K−1 with L = 50~400 nm) [21,43] and can be connected with the experimental data (κ ≈ 1800~2800 Wm−1K−1 with L
Conclusions
In conclusion, we have systematically studied the thermal transport properties in supported CNT by varying the system length, temperature and substrate coupling strength. We at the first time propose a theoretical model with 1/κ ~ (1+α)/L relation to well describe the size effect of supported nanostructure. Meanwhile, κ ~ T−β behavior is verified to be suitable for both suspended and supported CNT to describe the temperature dependence. In addition, thermal conductivity of supported CNT is
Declaration of Competing Interest
The authors declare that there is no conflict of interest.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51636002 and 51827807).
CRediT author statement
Yufeng Zhang: Methodology, Investigation, Writing - Original Draft. Aoran Fan: Investigation, Writing - Original Draft. Meng An: Valiation, Writing - Review & Editing. Weigang Ma: Writing - Review & Editing. Xing Zhang: Supervision, Funding acquisition.
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