† Corresponding author. E-mail:
Thermal conductivity of nanowires (NWs) is a crucial criterion to assess the operating performance of NWs-based device applications, such as in the field of heat dissipation, thermal management, and thermoelectrics. Therefore, numerous research interests have been focused on controlling and manipulating thermal conductivity of one-dimensional materials in the past decade. In this review, we summarize the state-of-the-art research status on thermal conductivity of NWs from both experimental and theoretical studies. Various NWs are included, such as Si, Ge, Bi, Ti, Cu, Ag, Bi2Te3, ZnO, AgTe, and their hybrids. First, several important size effects on thermal conductivity of NWs are discussed, such as the length, diameter, orientation, and cross-section. Then, we introduce diverse nanostructuring pathways to control the phonons and thermal transport in NWs, such as alloy, superlattices, core–shell structure, porous structure, resonant structure, and kinked structure. Distinct thermal transport behaviors and the associated underlying physical mechanisms are presented. Finally, we outline the important potential applications of NWs in the fields of thermoelectrics and thermal management, and provide an outlook.
With the improvement of nano-fabrication and engineering technologies, one-dimensional (1D) materials, such as nanowires (NWs), nano-tubes, and quantum wires, have been designed and synthesized in the past decades.[1,2] Due to the unique properties different from bulk materials, 1D materials have attracted growing research interests,[1,3,4] and have vast applications in the fields of electronic, optoelectronic, and energy conversion devices. Among them, crystalline semiconductor NWs are very promising materials in the present miniaturization of devices towards the nanoscale. They cover a wide range of materials, from single element semiconductors (such as Si, Ge, and Bi), the compound semiconductors (such as ZnO, GaN, SiC, Bi2Te3, GaAs, and InP), to the composite systems (such as Si/Ge, SiO2/SiC, and ZnS/Si), in which Si, Ge, and their composite NWs received numerous studies for the promising applications and integrability with current semiconductor electronics industry.[5–7] Moreover, the metal NWs also exhibit important applications in shape memory, heat transfer, and quantum transport.[4,8,9]
Thermal conductivity of nanoscale materials is quite different from that of bulk materials. Understanding and predicting the thermal conductivity of NWs play an important role in promoting the following two most fundamental applications: (i) thermal management, which is of fundamental and technological importance due to its broad applications in heat flow controlling,[10,11] modern phononic computations,[12,13] and novel heat dissipation solutions and materials,[14–23] and (ii) new thermoelectric materials, where the conversion efficiency is captured by the dimensionless figure of merit
On the other hand, the recent advances in nano-fabrication techniques make it possible to control the geometry and dimension of NWs with atomic precision.[31,32] Consequently, various nanostructuring pathways are proposed to construct diverse NWs, such as alloy NWs,[33] superlattice NWs,[34,35] core–shell NWs,[36,37] porous NWs,[38,39] resonant structure,[40] and kinked structure.[41] Various thermal transport behaviors and reduction in thermal conductivity are discovered in these NWs. For example, the coherent phonon, found in both superlattice NWs and core–shell NWs, can be used to reduce thermal conductivity of NWs.[35,36] Moreover, various nanostructuring methods can result in remarkable reduction in thermal conductivity of NWs, while under distinct scattering mechanisms. To date, there is no systematical review on the different nanostructuring methods and thermal transport behaviors in NWs, which would be valuable for providing an overview of the existing studies and guidance to future works.
In this article, we review the recent advances in the study of thermal conductivity of NWs. First, the size effects, including the length, diameter, and orientation, on thermal conductivity of various NWs are presented. The research methods, unique phenomena, and the corresponding underlying mechanisms are also discussed. Moreover, various important impacts on manipulating thermal transport in NWs are presented in detail. Finally, we also summarize the important potential applications of NWs based on the thermal transport properties, such as thermoelectrics and thermal management. Our review would provide the basic and fundamental knowledge of thermal transport in NWs, and the key impacts on thermal conductivity of NWs.
Phonons are the dominant heat carriers in semiconducting solids, and have non-negligible contribution to thermal transport in metals.[42,43] The size of the system is found to have significant impacts on the phonon scatterings and thermal transport behaviors in low dimensional materials,[23,44,45] especially for NWs. On the other hand, the continuous miniaturization of transistors and the consequent increase in power density pose severe thermal management challenges, further complicated by small characteristic device dimensions which also make thermal transport in NWs an important phenomenon to investigate.[44] In the following, the recent studies of size effects, including length effect, diameter effect, and orientation effect, on thermal conductivity of NWs are summarized.
Lattice thermal conductivity of a material has mainly been described in terms of the average mean free path (MFP) of phonons. When the length scale becomes comparable to the MFP of those phonons which make significant contribution to thermal transport, an apparent reduction in thermal conductivity can be observed. Thus the length dependence of thermal conductivity in NWs is so interesting, meaningful, and vital to study. For Si NWs, the length dependence of thermal conductivity is controversial in literature studies. From molecular dynamics (MD) and Green–Kubo calculations, Volz and Chen found that the Si NWs possess weak length dependence.[44] Ohara et al. also reported the phonons MFP of Si NWs is quite short,[46] below 5 nm when the diameter of NWs is smaller than 6.5 nm. These results indicate that the phonon MFP of Si NWs is much shorter than that of bulk Si, in which more than half of thermal conductivity at room temperature is contributed by phonons with MFP longer than
There are also a number of studies that witness the strong length dependence of thermal conductivity and ballistic thermal transport in NWs. Hsiao et al.[53] found that ballistic thermal conduction can persist over
Polyethylene chain is another type of extra-thin NWs and exhibits some intriguing thermal transport behaviors. Bulk polymer materials are generally regarded as thermal insulators for their low thermal conductivities of the order of
In 1D NWs structures, the effective thermal conductivity is a function of both surface (boundary) and internal phonon–phonon scattering, as reported in Si NWs,[50,60] diamond NWs,[61] GaAs NW,[62] and Cu NW.[63] As a consequence of the unique surface scattering in NWs determined by the nature of NWs structure, the thermal conductivity values can be reduced by one order of magnitude, even below the Casimir limit.[52,64,65] The small cross section in NWs implies a more significant reduction of the thermal conductivity due to the surface scattering, compared to that in thin films because of a higher surface to volume ratio (SVR) in NWs.[66,67] For example, early experiments and simulations on Si or Si/Ge NWs verified that the room temperature thermal conductivity is strongly dependent on diameters, exhibiting a decreasing tendency with the increase of surface scatterings.[45,68] Recently, Lee et al.[69] experimentally demonstrated that this dependence is still valid at high temperature up to 700 K. At high temperature, the thermal conductivity of smooth Si NWs also shows the classical diameter dependence from 40 to 120 nm, and there is an increasing contribution of high-frequency phonons (optical phonons) as the diameter decreases and the temperature increases.[69]
On the other hand, other scattering mechanisms, such as phonon–surface scattering and phonon–impurity scattering, would also affect the degree of the diameter dependence. For instance, Hochbaum et al.[24] found in experiment that after surface etching, thermal conductivity of the rough Si NWs not only has lower value but also exhibits weaker diameter dependence. Furthermore, Martin et al.[60] computed the frequency-dependent phonon scattering rate from perturbation theory, and found that thermal conductivity of rough Si NWs shows a quadratic dependence on diameter D and roughness
For other kinds of NWs, similar diameter-dependent thermal conductivity of NWs has also been reported, such as ZnO NWs,[70] PbTe NWs,[71] Bi2Te3 NWs,[72] and Bi NWs.[73] In most NWs, the thermal conductivity usually shows a dramatic reduction by at least an order of magnitude compared to the bulk values, due to the enhanced phonon–surface scattering. Meanwhile, there are also some unique diameter-dependent thermal transport phenomena and phonon activities observed in NWs. Bui et al.[70] experimentally found that in individual ZnO NW thermal conductivity approximately shows a linear dependence on the cross-sectional area of the NWs in the measured diameter range, ∼50–210 nm. In addition, through MD simulations, Chen et al.[67] found a simple universal linear dependence of thermal conductivity on SVR for Si NWs with small diameter, regardless of the cross sectional geometry. We will discuss in detail in the following section. As a high-performance thermoelectric material, the thermal conductivity of Bi2Te3 NWs is experimentally studied by Rojo et al.[72] Basically speaking, a remarkable reduction of thermal conductivity was observed, more than 70% when the diameter of the NW was reduced by one order of magnitude (from 300 nm to 25 nm). More interestingly, the analysis based on kinetic–collective model reveals that the surface scattering has significant impacts on acoustic phonons and largely altered the MFP of the low-frequency phonons.
Moreover, some studies[74,75] reported an abnormal diameter-dependent thermal conductivity in ultrathin NWs, that is, thermal conductivity increases with the decrease of diameter, which is different from or even contradictory to our conventional understanding. For example, Ponomareva et al.[75] found in MD simulations that the thermal conductivity increases with the decrease of diameter at very small diameter (
The crystals with different orientations have been synthesized in experiments, and the corresponding thermal transport properties would be varied.[78] For instance, the experimentally synthesized Si NWs are typically oriented in the
Moreover, thermal conductivity of NWs can also be modulated by selecting orientation direction.[83,84] Recently, the anisotropic thermal conductivity of single-crystal Bi NWs was also experimentally observed by HR-TEM and SAED investigations.[83] The thermal conductivity of Bi NWs is strongly orientation-dependent, in which the
To manipulate the surface scatterings and thermal transport in NWs, different cross-section is designed. By using MD simulations, Chen et al.[67] revealed that thermal conductivity of Si NWs varies with different cross sectional geometries (Fig.
In addition to the external surface, the phonon–surface scattering can also be induced to internal of NWs. Chen et al.[87] proposed an idea to reduce the thermal conductivity of Si NWs by introducing a small hole at the center of NW cross-section to construct a Si nanotube (Si NT) structure. A very small hole (only 1% reduction in cross-section area) can induce a 35% reduction in room temperature thermal conductivity. Moreover, with the same cross sectional area, thermal conductivity of Si NT is only about 33% of that of Si NW at room temperature. This is because more localization modes are concentrated on the inner and outer surfaces of Si NTs. By using a highly sensitive measurement system, Wingert et al.[88] found in experiment the sub-amorphous thermal conductivity in ultrathin crystalline Si NTs. The crystalline Si NTs with shell thickness as thin as ∼5 nm have a low thermal conductivity of
Compared to bulk materials, NWs exhibit 100-fold reduction in thermal conductivity because of the strong phonon–boundary scattering. However, as one of the promising applications, thermoelectric performance of NWs is still far from the requirement for industry use. Therefore, it is indispensable to further reduce the thermal conductivity of NWs to optimize thermoelectric performance. Previous studies have shown that one effective way is the construction of alloy or superlattices.[89,90] For example, SixGe1−x NWs is a promising candidate, because both Si and Ge belong to the same group, have the same crystal structure, and display total solubility.
By using MD simulations, Chen et al.[91] demonstrated that the thermal conductivity of SixGe1−x NW depends on the composition remarkably, as shown in Fig.
Constructing superlattice NWs is another way that can effectively reduce the thermal conductivity of pure NWs. With non-equilibrium MD simulations, Hu and Poulikakos[35] found ultralow values of thermal conductivity in Si/Ge superlattice NWs, taking advantage of the combination of surface and interfacial phonon scattering. As shown in Fig.
In order to further reduce the thermal conductivity of superlattice NWs, other approaches are proposed to destroy the coherent phonon. For instance, Mu et al.[95] demonstrated through MD simulations that the already low thermal conductivity of Si/Ge superlattice NWs can be further reduced by introducing hierarchical structure, as shown in Fig.
Thermal transport in another novel superlattice NW, the crystalline/amorphous Si superlattice NWs,[96,97] has also been studied.[98] The cross-plane thermal conductivity of the crystalline/amorphous Si superlattices NW is very low, which is close to that of amorphous bulk Si even for amorphous layer as thin as ∼6 Å. Interestingly, the cross-plane thermal conductivity increases weakly with temperature, which is associated with a decrease of the Kapitza resistance at the crystalline/amorphous interface with temperature.[98]
The most innovative way to further modulate the thermal conductivity of NWs is via the structure engineering, such as core–shell structure, porous structure, resonant structure, and kinked structure. The structure engineering not only induces additional surface scattering, defect scattering, and phonon localization, but also controls the coherent wave-like transport behaviors, and consequently alters the thermal transport properties of NWs.
Core–shell NW is another type of heterostructures with additional interfaces, such as in Si–Ge[99] and III–V core–shell materials, which becomes an important class of nanomaterials because of their remarkable electronic, optical, and thermal properties as well as potential applications in nanoelectronics, nanophotonics, photovoltaics, and thermoelectrics.[100–102] The thermal transport in core–shell NWs also attracted lots of research interests, especially for Si–Ge NWs, due to the fundamental importance and applications in heat dissipation and thermoelectrics.[100,103,104] By using non-equilibrium MD simulations, Hu et al.[105] found that a simple deposition of a very thick Ge shell on a crystalline Si NW can lead to a dramatic 75% decrease of room temperature thermal conductivity compared to an uncoated Si NW, as shown in Fig.
Moreover, Chen et al.[36] found a remarkable oscillation effect in heat current autocorrelation function in core–shell NWs from equilibrium MD simulations, while the same effect is absent in pure Si NWs. This intriguing oscillation is caused by the coherent resonance effect (Fig.
Porous structures, such as porous bulk materials, thin films, and even single crystalline porous NWs, nowadays can be fabricated and have been proposed for different applications, ranging from lithium ion batteries to solar cells. The previous studies have shown that the porosity would induce large reduction in thermal conductivity due to the large reduction in phonon group velocities caused by coherent phononic effects,[109] and strong phonon localizations.[110] Inspired by these suppression phenomena, there are also some attempts to realize porous structures in NWs. Experimentally, Weisse et al.[38] found that in Si NWs with diameters larger than the phonon MFP, as shown in Fig.
More interestingly, recent experimental work by Zhao et al.[112] demonstrates that with high spatial resolution through selective helium ion irradiation with a well-controlled dose, the structure porosity or defects in Si NWs can be optionally tuned. As shown in Fig.
The concept of a locally resonant phonon mode is widely used to optimize the thermoelectric energy conversion efficiency, such as in clathrates, perovskites, and skutterudites,[113–115] leading to a large reduction of lattice thermal conductivity. The resonant/hybridized mode is also a basic concept to construct electron-crystal phonon-glass materials, which have great potential application in thermoelectric field due to the ultra-low thermal conductivity and excellent electric properties. Under this concept, Davis and Hussein[116] proposed a Si resonant configuration, a silicon thin film with a periodic array of pillars on the free surfaces, which can qualitatively alter the phonon spectrum due to a hybridization mechanism between the pillar local resonances and the underlying atomic lattice dispersion. Similarly, for NWs Markussen et al.[117] demonstrated through atomistic calculations that the surface-decorated Si NWs, nanotrees and alkyl functionalized silicon NWs, can have a high ZT value ∼1 due to the significantly reduced phonon conductance. The resonant transmission dips are observed in the nanotrees (Fig.
As a recent advance, Xiong et al.[40] proposed a novel NW structure, the branched alloy NWs. Using atomistic simulations, they found that this structure can combine designed resonant structures with the alloying effect, leading to the extremely low thermal conductivity in such Si NWs. The hybridization between resonant phonons and propagating modes greatly reduces the group velocities and the phonon mean free paths. As shown in Fig.
Structure wrinkling or kinking is another effective way to manipulate thermal conductivity in NWs as the phonon transport channel is distorted. Based on MD simulations, Jiang et al.[41] found that thermal conductivity of kinked Si NW is 70% lower than that of pure NW at room temperature (Fig.
There are other structural engineering methods in NWs very similar to the structural kinking, such as sawtooth NWs[119] and twinning superlattice NWs,[120] and interesting thermal transport behaviors are observed in these structures. For example, by using Monte Carlo simulations, Moore et al.[119] found that the sawtooth roughness on a NW can also cause phonon backscattering and suppress the thermal conductivity below the diffuse surface limit. The backscattering effect can be accounted for only by a negative specularity parameter if the detail of the surface roughness is ignored. The phonon localization phenomenon in twinning superlattice NWs is studied by Xiong et al.[120] by using non-equilibrium MD simulations, in which they found the disappearance of favored atom polarization directions and large reduction in thermal conductivity.
Because of the important potential applications in the thermoelectric field, there have been tremendous efforts to optimize thermoelectric properties of NWs by reducing the lattice thermal conductivity. As reported in an early experiment in 2008, Hochbaum et al.[24] reported that the rough Si NWs exhibit 100-fold reduction in thermal conductivity compared to bulk counterpart, without much affected Seebeck coefficient and electrical resistivity, thus yielding ZT = 0.6 at room temperature. These findings encouraged the further studies on reducing thermal conductivity of NWs with various mechanisms.[7,26,27,121] For Si NWs, Markussen et al.[117] proposed surface-decorated silicon NWs, nanotrees and alkyl functionalized silicon NWs, to improve thermoelectric performance, showing larger ZT than that in ultrathin Si NWs.[30] Benefitting from the large suppression of thermal transport in porous silicon NW arrays, Zhang et al.[29] experimentally found that the large-area porous silicon NW arrays exhibit a high Seebeck coefficient up to
As mentioned above, the core–shell NWs possess low thermal conductivity, which should result in optimal thermoelectric properties in NWs. As shown in Fig.
Because of the adjustable low lattice thermal conductivity of NWs, there are also other types of NWs which have been investigated in the thermoelectric field, such as SnTe,[123] GaSb,[124] Ag2Te,[125] PbTe,[126] and Bi.[73] For the single crystalline NWs, the diameter-dependent thermoelectric properties of individual Bi NWs and SnTe NWs were recently investigated in experiments by Kim et al.[73] and Xu et al.,[123] respectively. Moreover, the heterostructure NWs for the hybrid materials also show enhanced thermoelectric performance due to the further reduced lattice thermal conductivity in NWs, such as GaSb/InAs core–shell NWs,[124] Bi/Te core–shell NWs,[28] and PbTe/Ag2Te heterostructure.[127]
The controllable thermal conductivity of NWs also provides the ideal platform and materials for thermal management in nanomaterials, not only for heat dissipation application but also for exploring unique thermal transport phenomenon.[128,129] Most importantly, the different scattering mechanisms can only dominate the thermal transport in a certain range of frequency. For example, high frequency phonons are sensitive to impurity/doping[130] and defect/porous scattering[131] in various NWs. In addition, low frequency phonons can be scattered by the interface in superlattices NW,[45] the amorphous disorder in polycrystalline NW,[51] and coherent resonance in core–shell structures.[36] Therefore, in a NW, the thermal conductivity or phonons transport can be managed in a well-controlled fashion. For example, by using atomic simulations, thermal rectification phenomena in NWs are reported by Zhang et al.[128] In a graded Si NW (Fig.
Moreover, recently some works engaged in using NWs to improve the heat-transfer performance and stability of flow boiling system, which is used for the cooling of high-thermal-load systems, such as power plants and integrated electrical devices. For example, Li et al.[134] successfully synthesized Si NWs in situ in parallel silicon micro-channel arrays, and integrated NWs into micro-channel heat sinks. Finally, they found that such setup can significantly enhance the flow boiling heat transfer and suppress the flow boiling instability in the NW which acts as the coatings for the flow boiling system. In addition, Shim et al.[135] found that the aligned silicon NWs exhibit improved heat dissipation properties compared to the conventional random silicon NWs. The alignment can increase the critical heat flux significantly with efficient coolant supply, and ensure high stability in extremely high thermal load systems.
Meanwhile, the metal NWs coatings for the flow boiling system have also been experimentally investigated. Morshed et al.[136] found that the Cu NWs coatings can enhance the single-phase heat transfer rate by up to ∼25%, whereas in the flow boiling regime, the enhancement was up to ∼56% with a pressure drop increased by ∼20% in the single-phase regime. Moreover, Wang et al.[137] found that Cu NWs as filling materials can enhance the interfacial thermal transport. The high-aspect-ratio is beneficial to achieve low percolation threshold for nano-composites, and thermal conductivity value of
In this review, we present the state-of-the-art studies on the topics of manipulation and fundamental understanding of the thermal conductivity of NWs, including Si, Ge, Bi, Ti, Cu, Ag, Bi2Te3, ZnO, AgTe, and their hybrids. Various important size effects on thermal transport in NWs are discussed, such as length, diameter, orientation, and cross-section effects. We also review the diverse influencing factors and effective pathways to engineer the thermal transport in NWs, such as alloy, superlattices, core–shell structure, porous structure, resonant structure, and kinked structure. Correspondingly, several important thermal transport behaviors and unique underlying physical mechanisms are presented. Based on the understanding and effective manipulation of thermal transport in NWs, we also summarize the important potential applications of NWs from the aspects of thermal conductivity of NWs, including thermoelectric field and thermal management. It should be noted that although this review mainly focuses on thermal transport related fields, NWs also possess exotic properties and many applications in other fields, such as optics and electronics.
In this review, we have clearly presented that there has been significant progress in the understanding and manipulation of the thermal conductivity in various NWs in the past decade. Yet further systematical investigations from both experimental and theoretical efforts are still needed in this research direction. For example, although various methods and pathways are proposed to reduce the thermal conductivity for optimizing thermoelectric properties in NWs, the explored figure of merit in NWs is still behind the requirement for practical industry use. Therefore, further improvements on these materials are expected by combining experimental and theoretical efforts together.
Generally speaking, only a limited portion of phonons, particularly high-frequency phonons, is efficiently suppressed or scattered in NWs. However, long wavelength or low-frequency phonons still possess a significant contribution to thermal conductivities. Therefore, novel strategies that can alter phonons in a wide or full range of frequency, especially for the low-frequency spectrum, are highly desirable to obtain an even lower thermal conductivity. Besides, it is important to incorporate different mechanisms together to achieve optimized ZT, as a single scattering mechanism alone only affects phonons with certain frequencies.
Finally, there are some unique phonon transport behaviors where a comprehensive understanding is still lacking, such as the coherent phonon/wave effect on the thermal transport in NWs. In the superlattice NWs, the coherent scattering and interference of thermal phonons could happen at the atomically smooth interfaces with perfect periodicity. This phenomenon is related to many practical applications, such as waveguides or cloaking. To conclude, we believe that thermal transport in NWs is still an active research topic worth exploring for future study.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] | |
[35] | |
[36] | |
[37] | |
[38] | |
[39] | |
[40] | |
[41] | |
[42] | |
[43] | |
[44] | |
[45] | |
[46] | |
[47] | |
[48] | |
[49] | |
[50] | |
[51] | |
[52] | |
[53] | |
[54] | |
[55] | |
[56] | |
[57] | |
[58] | |
[59] | |
[60] | |
[61] | |
[62] | |
[63] | |
[64] | |
[65] | |
[66] | |
[67] | |
[68] | |
[69] | |
[70] | |
[71] | |
[72] | |
[73] | |
[74] | |
[75] | |
[76] | |
[77] | |
[78] | |
[79] | |
[80] | |
[81] | |
[82] | |
[83] | |
[84] | |
[85] | |
[86] | |
[87] | |
[88] | |
[89] | |
[90] | |
[91] | |
[92] | |
[93] | |
[94] | |
[95] | |
[96] | |
[97] | |
[98] | |
[99] | |
[100] | |
[101] | |
[102] | |
[103] | |
[104] | |
[105] | |
[106] | |
[107] | |
[108] | |
[109] | |
[110] | |
[111] | |
[112] | |
[113] | |
[114] | |
[115] | |
[116] | |
[117] | |
[118] | |
[119] | |
[120] | |
[121] | |
[122] | |
[123] | |
[124] | |
[125] | |
[126] | |
[127] | |
[128] | |
[129] | |
[130] | |
[131] | |
[132] | |
[133] | |
[134] | |
[135] | |
[136] | |
[137] | |
[138] |