Measuring methods for thermoelectric properties of one-dimensional nanostructural materials

Abstract

Thermoelectric materials and devices have attracted extensive research interests. Great progress has been obtained in improving the thermoelectric figure of merit ZT of several one-dimensional (1D) nanostructural materials. Simultaneously, tremendous efforts have been devoted to characterize thermoelectric performance of nanostructural materials and associated devices. Accurate measurements of the Seebeck coefficient and thermal conductivity of 1D nanostructural materials are still challenging tasks. This review explores the latest research results on measuring methods for thermoelectric properties of 1D nanostructural materials. Five frequently used methods to measure the Seebeck coefficient are presented and twelve popular methods to measure thermal conductivity are described. Device structures, measuring principles, merits and shortcomings, and application examples of each method are discussed in detail. Two potential hot topics in measuring thermoelectric properties of 1D nanostructural materials are proposed.

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Yang Liu

Yang Liu received a B.S. degree in physics from SiChuan University in 2013. He is currently a Master degree candidate at Institute of Semiconductors, Chinese Academy of Science under the guidance of Prof. Xiaodong Wang. His main research interests are the thermoelectric character of silicon nanowires and measurement of thermoelectric parameters.

Mingliang Zhang

Mingliang Zhang received a PhD degree in materials chemistry from City University of Hong Kong in 2007. From 2007 to 2009, he worked as a senior research associate in City University of Hong Kong. From 2009 to 2010, he was a postdoctoral research in ECE department of University of California San Diego. He is an associate professor of Engineering Research Center for Semiconductor Integrated Technology at the Institute of Semiconductors, CAS, from 2010. His research interests focus on technologies for micro-/nano-scale fabrication, nanomaterials for energy conversion and MEMS/NEMS devices for chem/biosensors.

An Ji

An Ji received a B.S degree in Electronic Engineering from Huazhong Science Technolegy University in 1982. Currently, he is a professor of Institute of Semiconductors, CAS. His early research involved photodetector and piezoresistive sensors. His current research interests are focused on MEMS and high efficiency LED devices.

Fuhua Yang

Fuhua Yang received a Ph.D. degree in solid physics from Paul Sabatier University, Toulouse in 1998. Currently, he is a professor/co-director of Institute of Semiconductors, CAS. His early research involved 2DEG transport, semiconductor cavity optical properties, and light storage device. Presently his research interests include single electron transistor and their integration, RTD/HEMT integrated circuits and MEMS.

Xiaodong Wang

Xiaodong Wang received a PhD in condensed matter physics from Institute of semiconductors, Chinese Academy of Sciences (CAS) in 2001. Currently, he is a professor/director of the Engineering Research Center for Semiconductor Integrated Technology at Institute of semiconductors, CAS. His research experience includes In(Ga)As/GaAs quantum dot lasers, GaInNAs/GaAs quantum well lasers and GaN LEDs. His current research interests are focused on high efficiency solar cells, thermoelectric devices at nanoscale and quantum dot field effect transistors.

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1 Introduction

One of the great challenges of modern society is the energy crisis, including energy storage, consumption, and dissipation. Consequently, functional materials and devices, having the ability to reduce power dissipation routes, have attracted enormous interests.^1–4 Among these, thermoelectric materials, which could directly transform thermal and electrical energy in the solid-state, based on Seebeck and Peltier effects,⁵ hold great promise for improving energy conversion and harvesting.^6,7 These materials could be associated with solar power systems,^8–10 sensors¹¹ and related devices.^12–14 For example, the performances of ever-shrinking electronic chips were historically enhanced by increasing power and increasing on-chip power density. Heat generation from the chips, however, is spatially non-uniform, resulting in regions of localized high heat fluxes known as hotspots (>1000 W cm⁻²) which presents a cooling challenge.¹³ Localized, on-chip, solid-state thermoelectric refrigeration was expected to open up the possibility of microelectronic chips with efficient thermal control. However, there has been only modest progress for several years because of the real challenges faced by researchers trying to enhance the thermoelectric performance. Fortunately, low dimensional nanostructures, compared with their bulk counterparts, have been proposed to have better thermoelectric performance due to increased phonon scattering and quantum confinement, as put forward in the early 1990s by Hicks et al.¹⁵ Later, several 1D nanostructures, such as nanowires (NWs)^16–18 and nanotubes (NTs),^19–21 have been extensively investigated. Up to now, a tremendous amount of work has been committed to manufacture 1D materials and characterize their thermoelectric performance.^22–31 Nevertheless, the measuring methods for thermoelectric properties of 1D nanostructure materials are still key issues to obtain materials with improved thermoelectric performance.

1.1 Principles of thermoelectricity

The thermoelectric effect is fundamentally a direct solid-state conversion between thermal and electrical energy by Seebeck and Peltier effects. For conducting or semiconducting materials, the microscopic mechanism of the Seebeck effect mostly depends on the carrier distribution under a temperature gradient. The carriers (electrons or holes) are uniformly distributed without the temperature gradient. However, once a temperature gradient exists, the carriers at the hot end have larger kinetic energy and tend to diffuse to the cold end. As a consequence of the charge carrier diffusion, the accumulation of the electric charge established an internal electric field to prevent the further diffusion of the carriers. Eventually, the diffusion caused by the temperature gradient and the drift of carriers caused by the internal electric field reach dynamic equilibrium. Consequently, the Seebeck potential between the hot and cold extremity of the material is established.

In order to quantify the Seebeck effect of various materials, Seebeck coefficient/thermoelectric power (TEP) was defined as the ratio between the thermoelectric induced voltage and the temperature difference across the material:

where ΔT, ΔV are the temperature difference along the NW and the thermoelectric voltage induced by temperature difference, respectively. The sign depends on characteristics of materials: being positive for p-type semiconductors and negative for n-type semiconductors.

As for the performance of a thermoelectric material, this is tightly correlated with its electronic and phononic transportation characterization and is normally described by the dimensionless thermoelectric figure of merit:^32,33

where T represents the environmental temperature of a working device, S, σ, κ are the Seebeck coefficient, electrical conductivity, and thermal conductivity of the thermoelectric material, respectively. From eqn (1-2), a large power factor, S²σ, implied that the material could output large voltage or current, and a material with low heat conductivity possessed high ZT.

1.2 ZT of 1D nanostructural materials

To enhance the performance of thermoelectric materials, a great effort had been made to reduce their thermal conductivities and increase the Seebeck coefficients. For example, doping had been proved to be a promising approach to improve ZT of nanoscale materials because of its remarkable impact on the thermoelectric properties of nanomaterials.^34–37 Band engineered materials have been proved to have remarkable figure of merits.^38,39 Composites and alloys, due to their relatively low thermal conductivities and high electric conductivities compared with their bulk counterparts, have attracted extensive interests.^40–47 Low dimensional nanostructures have also been confirmed to exhibit good thermoelectric performance.^48–53 These materials provided a promising building block for practical thermoelectric applications in nanoelectronics.¹² Especially, reducing the scale of the material had a huge impact on its thermoelectric property, which could be explained as due to the following:^14,33,54 (i) improvement of the density of states near the Fermi level owing to the quantum effect, and thus the enhancement of Seebeck coefficient compared to the bulk materials; (ii) severe phonon scattering at the interfaces and boundaries, resulting in decreasing thermal conductivity.

From published papers, most thermoelectric materials have ZT value of around 1.0.^55–57 For power generation, an optimistic energy conversion efficiency of the thermoelectric materials at heat source temperature about 750 K was predicted to be 30% when the ZT value reached 4.0, which would be an attractive choice for energy harvesting.⁵⁸ In experimental measurements, the ZT values of 1D nanostructures based on Bi–Sb–Te–Se complexes were in the range of 1.5–2.5.^59–61 Surface rough silicon (Si) NW exhibited a ZT of 0.6 at room temperature, while the ZT value of bulk Si was about 0.01.²⁵ The ZT value of single-crystalline β-SiC NWs was measured to be 0.12, which was around 120 times higher than the reported maximum value of bulk β-SiC.⁶² From theoretical calculation, Bi₂Te₃ 1D quantum wire with width 5 Å square cross section had a ZT up to 14.¹⁵ Based on the quantum confinement effect of electrons and phonons, the ZT of bismuth NT with 10 nm diameter and 2 nm thickness was theoretically predicted up to about 6.⁶³ The ZT of Si_1−xGe_x NWs, oriented along the [110] direction with rectangular cross section area of 2.3 nm², was theoretically predicted to be above 4.⁶⁴ Furthermore, the room-temperature ZT of a 1.1 nm diameter GaAs NW was predicted to reach as high as 1.34, exhibiting more than 100-fold improvement over the bulk counterpart.⁶⁵ The ZT of ZnO NW increased 30 times compared with its bulk, when its diameter decreased to 8 Å.⁶⁶ Therefore, a possible approach to improve thermoelectric performance is by converting bulk materials into 1D nanostructures.

1.3 Methods for measuring thermoelectric properties

Although great progress has been obtained in increasing the thermoelectric figure of merit of 1D nanostructural material,^37,67,68 thermoelectric properties measurements of nanoscale materials and devices are still a severe challenge. This might be attributed to the difficulty in dealing with the fabrication of measuring structures, issues of electrical contacts and the noises from nanostructural devices. Therefore, the measuring methods must be improved and optimized so as to explore high performance thermoelectric materials. Along with the technological development, the properties of thermoelectric materials with scale decreasing to a few microns or even a few nanometers, could be characterized. Hitherto, several methods have been developed to measure the thermal properties of NWs, such as self-heating 3ω method,⁶⁹ thermal flash method,⁷⁰ and using a suspend micro-device^71–73 In addition, a few reviews had been reported involving thermoelectric properties and structures of NWs.^74–80 Only few reviews, however, involved the measuring methods of thermoelectric properties of 1D nanostructural materials.^81–83

This review explores the latest research results on the measuring methods for thermoelectric properties of 1D nanostructural materials. Five often used methods to measure Seebeck coefficient are discussed. Similarly, twelve of the most popular methods to measure thermal conductivity are described. In each method, its principle, applications, merits and shortcomings are presented in order to provide a comprehensive understanding of the method. Furthermore, two potential hot topics in measuring the 1D nanostructure thermoelectric properties are discussed.

2 Measurements of the Seebeck coefficient of 1D nanostructural materials

An accurate measurement of the Seebeck coefficient is essential with the aim to investigate and evaluate thermoelectric properties of new materials. However, measuring the Seebeck coefficient of an individual NW is fraught with difficulty for the requirement to extract the Seebeck voltage, ΔV, and temperature drop, ΔT, across the NW precisely. Therefore, there were at least two challenges associated with the measurement of Seebeck coefficient. One was applying a sufficient temperature difference along the NW, and another was measuring the Seebeck voltage accurately, which is a only a few microvolts.

In this section, five methods for measuring the Seebeck coefficient of NWs are discussed. The methods using mesoscopic or microfabricated suspended devices have been extensively used and various similar devices have been built during the last decade. Methods using thermocouples or reference films were developed to characterize the Seebeck coefficient of NWs, offering other routes to obtain the temperature difference besides temperature coefficient of resistance (TCR = (dR/dT)/R). The last method, using an ac signal, could suppress unwanted noise so to improve the measuring accuracy. The discussions below focus on the principles of these methods. Furthermore, the main advantages and disadvantages of the methods are presented as well as their applications. A summary of these methods is presented in Table 1.

Table 1 Measurement of Seebeck coefficient of 1D nanostructural material

Method	Source	Sensor	Merits	Shortcomings	Ref.
Mesoscopic device	Direct current (DC)	Based on TCR	Simple device	Long thermal stabilization period	16
			Easy sample placement	Extra effort to achieve ohmic contact	21
Microfabricated suspended device	DC	Based on TCR	Thermal stabilization within several seconds	Complex device	73
				Difficult sample placement	110
				Extra effort to achieve electrical contact
Microdevice with thermocouples	DC	Thermocouple	The temperature obtained near the contacts	Difficult noise cancelling and circuit design for thermocouple	114, 115
Measurement with a reference film	DC	Based on a reference film	Without direct temperature measurement	Difficult to achieve electrical contact and extra effort to obtain the SR and SC	117, 118
2ω technique	Alternating current (AC)	Based on TCR	Simple device	Small signal at high frequency	111
			High signal/noise ratio		119

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2.1 Mesoscopic device

2.1.1 Structure. In this method, a schematic layout of a typical structure for the Seebeck coefficient/TEP measurement, as well as its scanning electron microscope (SEM) image, is shown in Fig. 1(a). The NW is placed on a silicon oxide/silicon (SiO₂/Si) substrate and then followed by a deposition of two metallic wires (e.g. Pt) contacting both ends of the NW. These wires, in a four-probe configuration, serve as both electrodes and thermometers. To generate Joule heat, a microfabricated heater was fabricated adjacent to one of the NW-wires contacts. A direct current (DC), I, was applied to this heater and raised the temperature locally around the neighboring contact area. Furthermore, temperature gradient (ΔT) would be obtained from the resistances of the two thermometers, R_n and R_f, based on their TCR which had been previously calibrated. Fig. 1(b) shows another device which was almost the same as the former. However, two zigzag heaters, labeled as H1 and H2, were symmetrically fabricated. Four metallic wires (C1, C2, Th1 and Th2) comprised four-point electrical contacts to characterize the electrical property of the NW. In addition, it is worth noting that Th1 and Th2 also serve as resistive thermometers.

Fig. 1 Mesoscopic devices for measurement of the Seebeck coefficient of individual 1D nanostructures: (a) typical device with platinum (Pt) line heater; (b) scanning electron micrographs of a device used to quantitate the thermopower of the NW. Reprinted with permission from ref. 84 and 16, AIP Publishing LLC and Nature Publishing Group.

2.1.2 Principle. This Seebeck coefficient measurement relies on the heater to provide a temperature difference across the NW. Once a direct current, I, crosses through the heater as schematically illustrated in Fig. 1(a), the temperature around the adjacent contact area would rise as a consequence of Joule heating. Part of the heat flows through the NW and the SiO₂ layer, creating a temperature gradient along the NW. Then, instruments (voltage and current meters) were implemented to read resistances of the thermometers as well as the resultant thermoelectric voltage, ΔV (TEV), simultaneously.⁸⁵ Next, the temperature gradient, ΔT, between the two thermometers was calculated based on the relationship between the thermometers’ resistances and temperatures. The temperature of the thermometer was a function of the TCR, so, the resistance measured could be converted to average temperature of the thermometers direct.²¹ Consequently, the TEP could be obtained from eqn (1-1).

Before carrying out the measurement, it is necessary to determine the relationship between resistance and temperature of the thermometer. In other words, the TCR needed to be determined.⁸⁶ For this purpose, a four-point probe technique was adopted.⁷³ Shin et al.,⁸⁵ for example, used four-probe to assure a significant improvement in accuracy. Compared with two-point-probe technique, the contact contribution and the resistance of wires outside the substrate could be eliminated when the four-point probe technique was used. Therefore, it is possible to obtain accurate signals through the resistances of the thermometers.

2.1.3 Merits and shortcomings. In order to minimize the heat loss due to air convection, the device was put in a vacuum chamber. Furthermore, the temperature difference along the NW provided by the heater was sufficient to facilitate the Seebeck coefficient measurement. Therefore, a tight control of energy flow in the device was not necessary.⁸⁷ Another merit was that the NW was put on the substrate followed by the deposition of metallic wires which resulted in easy sample placement. However, the Seebeck voltage, ΔV, was small (a few millivolts) and was measured by a nanovoltmeter. Additionally, the major error source in this method would be ΔT due to various interferences, for instance, the fluctuation of ambient temperature and the rectification of TCR. Therefore, low noise configuration is required for an accurate measurement of the Seebeck coefficient, for example, high vacuum and lock-in amplifiers for measuring the resistance of the temperature sensors. It was worth noting that this method required a thermal stabilization period after a heating power change, and cannot avoid uncertainty when reading the temperature owing to the presence of the substrate.⁸⁵ To tackle this, Shin et al., removed the backside Si underlying the SiO₂ layer, and the membrane structure allowed for faster thermal stabilization within several seconds relative to the traditional bulk substrate.⁸⁵

Another difficulty is the formation of ohmic contacts which was historically a challenge for NWs. On the one hand, the contact at the interface of the electrode and NW was mostly non-ideal because of the extremely small contact area (<0.05 μm²) and the unsubstantial contact. On the other hand, the oxide layer existing on the surface of the NWs and Schottky barrier at the contact area increased the experimental difficulty.⁸⁴ It had been reported that a 40 nm Bi NW would consist of a 25 nm crystalline Bi core and a 7 nm thick amorphous oxide coating which resulted in a nearly 1 × 10⁶ Ω electrical contact resistance between the Bi NW and metal electrode.⁸⁸ Nevertheless, in order to accurately obtain the Seebeck coefficient, it is necessary to couple the NW and electrode with an ohmic contact. From published papers, there are several methods to obtain ohmic contacts. In most of the measurements, electrical contacts were formed by depositing noble metals, such as Pt and tungsten (W), or carbon (C) films using focused ion beam (FIB) or Electron Beam Induced Deposition (EBID) due to its high accuracy on the selected region, followed by thermal annealing.⁸⁹ SEM and electrical measurements could be used to ensure the good ohmic contacts. For example, Valentín et al.,⁹⁰ utilized FIB to deposit Pt electrodes on β-silicon carbide NW to obtain electrical contact. Their SEM image showed that part of the NW was exactly covered by the deposited Pt and confirmed that an unsubstantial contact had been formed. It was noteworthy that FIB could also be used to expose the surface of the NW. Murata et al.,^91,92 implemented a FIB processing to remove a selected portion of the quartz covered on bismuth (Bi) NW, and then deposit carbon films on the NW to form electrical contacts. The total contact resistances, however, based on their two-wire and four-wire measuring results, could be more than 2 × 10⁵ Ω. Notably, this approach was time consuming and might contaminate or even damage the NWs.^88,93 An electrothermal annealing process prior to the measurement could also lead to electrical contacts. Shapira et al.⁹⁴ used a staircase sweep of potential with steps of 0.5 V crossing the contact of a 30 nm nickel (Ni) NW and gold (Au) electrode to break down the native oxide until the resistance of the NW dropped from its initial value of ∼10⁸ Ω to <10⁴ Ω, which implied that the dielectrical contact resistance between Ni NW and Au could be approximately 10⁸ Ω. The same process was also found in literature.⁹⁵ A DC voltage pulse of 1.5 V for 0.5 s had been applied across the SiGe NW and aluminium (Al) contact. It was found that part of the NW became welded to the Al lead and was inserted into the metal due to Joule heating. Nevertheless, special attention should be paid to the voltage magnitude when a DC voltage is applied because the NWs are fragile and could be broken due to Joule heating. Additionally, it had been proved that thermal annealing and doping had a significant effect on the metal–NW contact. For example, Yu et al.⁹⁶ found that, after thermal annealing, the measured resistivity could drop from 10³ Ω cm to ∼1 Ω cm for Si NWs with Au contact. The thermal annealing process not only led to improved metal–NW contact but also facilitated NW doping via diffusion and ionization of the metal.⁹⁶ To obtain good ohmic contacts, other techniques have also been developed. Jang et al.⁹⁷ carried out an etching and depositing process of the electrodes without breaking the vacuum so as to prevent the further formation of the oxide layer. An appropriate plasma treatment was also used on the contact area prior to forming the electrical contact by Chul-Ho et al.⁸⁴ Interestingly, Wang et al.⁹⁸ developed a novel method to locally evaporate Pt metal between the NW and the electrodes using a shadow mask process.

2.1.4 Applications. The mesoscopic device is one of the most convenient and useful methods to measure the TEP of a single NW, which could achieve both the temperature difference and measuring the Seebeck voltage. Small et al.,²¹ in 2004, obtained the Seebeck coefficient of single wall CNTs (SWCNTs) using the microdevice and the measured thermoelectric power was ∼200 μV K⁻¹ at room temperature. Boukai et al.¹⁶ fabricated a thermoelectric device platform to quantitate the thermopower and electrical conductivity of Si NW arrays, as shown in Fig. 1(b). The SiNW array was at the central area and under the wires (Th1 and Th2). The heaters were labeled as H1 and H2. Th1 and Th2 were four-point devices which served as resistive thermometers. C1, C2, Th1 and Th2 comprised the four-point electrical contacts to the Si NWs, with C1 and C2 utilized as the current source and drain for those electrical conductivity measurements. With this device, the TEP of Si NWs of cross-sectional area of 20 nm × 20 nm was measured to be about 400 μV K⁻¹. More importantly, they found that the ZT values represent an approximately 100-fold improvement over bulk Si, with values reaching ZT ≈ 1 at 200 K. Lee et al.⁸⁴ investigated the temperature-dependent TEP of individual wide band gap ZnO. The device they used is illustrated in Fig. 1(a). Their result showed that the TEP value of the ZnO NWs was as high as −400 μV K⁻¹ at room temperature. Recently, Xu et al.,⁹⁹ utilizing this method, obtained the Seebeck coefficient of individual single-crystalline SnTe NWs with different diameters ranging from ∼218 to ∼913 nm. The result showed that, when the diameter was decreased to 218 nm, the Seebeck coefficient was −41 μV K⁻¹.

Compared with the line heater, a platinum resistance thermometer (PRT) coil was designed to generate a larger temperature difference between both ends of the NWs (see Fig. 1(b)).^16,99,100 This makes the measurement of TEV easier. To obtain the temperature more accurately, two PRTs was adopted to alternately serve as the heat source.⁷² In addition, scanning thermal microscopy (SThM) or numerical simulations are also used to correct the measured temperature difference.^81,94,101 Furthermore, taking into account the temperature distribution over the structure, infrared image was used to directly obtain the temperature distribution of the device and this method was found to be appropriable to examine thermoelectric characteristics.¹⁰²

Mesoscopic structures have been successfully applied in determination of the thermoelectric properties of various NWs, such as Sb₂Te₃,¹⁰³ InAs,^100,104 GeSn,¹⁰⁵ InSb¹⁰⁶ and Ni,¹⁰⁷ as well as fibres.¹⁰⁸

2.2 Microfabricated suspended device

2.2.1 Structure. The outline of the suspended microstructure device incorporated two adjacent thick ultra-low-stress Si nitride (SiN_x) platforms, each around 15 μm × 25 μm, suspended by several long (200–400 μm) and narrow (2–4 μm) SiN_x beams, as shown in Fig. 2(a). On each platform, a PRT was deposited and acted as not only a heater to achieve a temperature difference but also as a thermometer. Furthermore, two electrodes were lithographically patterned for connecting the NW. Once a NW was placed on the device and bridged on the two electrodes designed on each island, the NW was connected to the outside pads via Pt wires deposited on each SiN_x beam. A SiO₂ film was deposited on top of the thermometers to isolate the NW from PRTs.^73,95 Fig. 2(b) shows another device with a SiC NW suspended over the electrodes with platinum contacts deposited on the NW-electrode contact area using FIB.⁹⁰

Fig. 2 (a) Microfabricated suspended device and (b) SEM image of a SiC NW over the suspended microresistance thermometry device, platinum contacts are deposited on the NW-electrode contact area using ion beam induced deposition. Reprinted with permission from ref. 133 and 90, American Chemical Society and AIP Publishing LLC.

2.2.2 Principle. In this suspended device, when a direct current flows through one of the PRTs, the temperature at one end of the NW is increased by Joule heating. Part of the heat would flow through the NW and create a temperature gradient along the NW. The Seebeck voltage, ΔV, was then induced by the temperature gradient and could be measured through the contact pads which connected the NW. Furthermore, the temperature difference ΔT could be obtained through the PRT’s TCR. The Seebeck coefficient, consequently, can be determined from eqn (1-1).

2.2.3 Merits and shortcomings. The microfabricated suspended device is a powerful tool for the measurement of one-dimensional nanostructures, offering significant advantages such as measuring the Seebeck coefficient, electric conductivity and thermal conductivity of the same NW. One of the main outcomes of this device was that it provided an effective approach to measure the thermal properties of NWs with small diameter down to a few nanometres, for example, 10 nm in ref. 73. Compared with the mesoscopic device, this suspended device allowed for faster thermal stabilization within several seconds after each temperature change due to thermal decoupling of the electrical heaters/sensors from the carrier substrate. However, this method involved additional preparation efforts such as the fabrication of the suspended devices and difficult sample placement. Complex processes and very specific equipments were required to fabricate the suspended structures. For example, more than five process steps and electron beam lithography were involved. Additionally, the devices in this method also ran into inevitable issues with controlled placement of the single NWs exactly between the two Pt electrodes designed on each island due to the small size of the NWs (<100 nm) and the suspended structure. From published papers, there were two main strategies to place the NWs. In the first strategy, the NWs were first dispersed into a volatile solvent by sonication, and then drop-cast onto a wafer containing many suspended devices. After drying the solvent, statistically, some of the NWs were exactly adsorbed on the two Pt electrodes.^73,110 It was worth noting that high density of the devices on a wafer significantly improved the yield of testable NWs since the drop dispense method of NW deposition was inherently a random process.¹¹¹ In the second strategy, individual NWs were picked up by a tip from the hosting bundle, and then a nanomanipulator was used to place the NW at a desired location for characterization. Being highly selective and reproducible, this strategy, provided a reliable way to manipulate a single NW for certain applications.^62,112 Nevertheless, it was a time consuming work and special instruments were required, such as FIB and the nanomanipulator. Another difficulty was the formation of ohmic contacts. To reduce the electrical contact resistance between the NW and the electrodes, FIB, thermal annealing and other novel strategies were adopted, which have been discussed in Section 2.1.3.

2.2.4 Applications. By employing this method, the Seebeck coefficient of individual SWCN bundles as a function of temperature were measured. It showed linear temperature dependence in the temperature range of 30–250 K, and saturated above 250 K.⁷³ To investigate the thermoelectric properties of Bi₂Te₃ NWs, Li et al.,¹¹⁰ using this suspended microdevice, found the Seebeck coefficient of a 391 nm Bi₂Te₃ NW to be ∼50 μV K⁻¹ at room temperature, and the results showed it had the same trend as bulk Bi₂Te₃ material. Valentín et al.,⁹⁰ recently, investigated the thermal properties of β-SiC NWs as shown in Fig. 2(b). The temperature dependence of the Seebeck coefficient was studied, and the largest value for NW in 90 nm turned to be −68 μV K⁻¹ at 370 K. Moreover, Lee et al.¹¹³ simultaneously measured all thermoelectric properties of SiGe NWs which exhibited a large thermoelectric ZT of ∼0.46 at 450 K.

2.3 Microdevice with thermocouples

2.3.1 Structure. A microfabricated device structure with thermocouples for the Seebeck measurement is shown in Fig. 3(a). The device consisted of two outside microfabricated heaters and two microthermocouples fabricated on a Si₃N₄ film. The NW was put under the two electrical contacts.

Fig. 3 (a) A device including two meander heaters and two Ag/Ni thermocouples for measurement of S and σ for NW arrays; (b) plots of Seebeck coefficient against annealing temperature for PbTe NWs; (c) photograph of the suspended microdevice for evaluating thermoelectric properties of the nanomaterial; (d) measurement of the temperature from the two microthermocouples in the short-circuit configuration during heating. Reprinted with permission from ref. 114 and 115, American Chemical Society and IOP Publishing.

2.3.2 Principle. The individual NWs were placed between the two heaters for characterizing thermoelectric properties as shown in Fig. 3(a). In order to evaluate the Seebeck coefficient, the NWs were heated by feeding a current into the heater from either side. Therefore, a temperature gradient was then generated along the NWs. From the two electrical contacts, the Seebeck voltage and temperatures at two ends of the NW were measured individually. More specifically, the temperature difference, ΔT, of the NWs could be obtained from the two microthermocouples (TC₁ and TC₂); the Seebeck voltage, ΔV, could be measured from the two electrical contacts. Finally, from the temperature difference ΔT and the Seebeck voltage ΔV, the Seebeck coefficient at a specific temperature could be approximated as:¹¹⁵where S_metal1 is the Seebeck coefficient of the metal contacted with the NWs.

2.3.3 Merits and shortcomings. It should be noted that the temperature difference of the NW could be obtained from the TCR of the heaters as described in the sections above. However, it was difficult to make precise measurements of the temperature at the end of the NW since the temperature along the heater was non-uniform and the resistance was measured as an average value. As for the temperature sensor involved in this method, it conferred the advantage that the microthermocouple had the ability of precise temperature measurement at a very small area near the electrical contact.¹¹⁴ Additionally, the thermocouple is an ideal simple measurement device, with each temperature being characterized by a precise temperature–voltage curve, independent of any other detail. Nonetheless, in reality, the thermocouple was affected by issues such as ambient temperature fluctuation and circuit design mistakes. Furthermore, the NW had to be placed over/under the same metal, otherwise, the Seebeck voltage could not be accurately detected due to different contacts at two ends of the NW. It should also be pointed out that, before applying this measurement, the thermocouples should be calibrated.

2.3.4 Applications. Yang et al.,¹¹⁴ using a device with two meander heaters and two thermocouples deposited on top of an array of ∼200 PbTe NWs as shown in Fig. 3(a), analyzed the annealing effect of PbTe NWs. Fig. 3(b) showed that the measured Seebeck coefficient was −479 μV K⁻¹ for annealed NWs which was 80% larger in magnitude than the Seebeck coefficient of bulk PbTe. Ono et al.¹¹⁵ developed a platform with built-in microthermocouples to evaluate the thermoelectric properties of low-dimensional materials. As shown in Fig. 3(c), the device consisted of freely suspended heating elements opposite to each other, and a thermocouple integrated into the individual heating element. The temperature was obtained from two microthermocouples with a Cr–Al junction during heating, which is shown in Fig. 3(d). Their obtained Seebeck coefficient of a Bi₂Te₃ bundle was about 19 μV K⁻¹.

2.4 Measurement with a reference film

2.4.1 Structure. The microchip is shown in Fig. 4, which consisted of two identical pairs of metallic contacts anchored on an SiO₂ layer. A NW was suspended over one pair of them, and a reference film with a known Seebeck coefficient was between the other. To generate a temperature gradient, a thin film heater was also designed beside the sample.

Fig. 4 Schematic diagram of Seebeck coefficient measuring device with a reference film.

2.4.2 Principle. As shown in Fig. 4, a direct current was fed through the thin film heater in order to generate an identical temperature difference, ΔT, on both pairs of the contact film. With the reference film, the temperature difference between two ends of the NW could be determined through the reference voltage U_R of the Seebeck reference film:

U_R = (S_R − S_C)ΔT (2-2)

where S_R and S_C are the known Seebeck coefficient of the reference film and the contact pads, respectively. Therefore, when the Seebeck voltage U_N of the NW was measured, the NW’s Seebeck coefficient S_N could be obtained according to:¹¹⁶

S_N − S_C = U_N/ΔT = U_N(S_R − S_C)/U_R (2-3)

2.4.3 Merits and shortcomings. The main advantage of this method was that it avoided determining the temperature difference between two NWs contacts, when compared with the TCR method. Thus, the influence of non-uniform temperature distribution could be minimized, if the device was properly designed, such as a symmetrical structure. However, more effort is required to investigate the Seebeck coefficient of the reference film and the contact pads at different temperature. Furthermore, to obtain a correct Seebeck voltage, one has to solve the ohmic contact problem before applying this method. The Seebeck voltage could not be obtained if non-ohmic contacts were present.¹¹⁷ Depositing noble metals, such as Pt and Ti, using FIB, or annealing procedure were recommended to guarantee good electrical contacts.^90,91

2.4.4 Applications. Cronin et al.¹¹⁷ used a reference film with known Seebeck coefficient to measure the Seebeck coefficient and resistivity of an individual Bi NW. The Seebeck voltage, however, could not be obtained owing to the high resistance of the non-ohmic contacts. Volklein et al.¹¹⁸ further developed this method and carried out a simulation to demonstrate that temperature differences between two ends of the NW could be obtained. Furthermore, together with a steady-state dc thermal bridge method (DCTBM), this measurement was further developed to investigate the thermoelectric transport coefficient S, κ and σ of NWs, so to obtain the figure of merit ZT.¹¹⁶

2.5 2ω technique

2.5.1 Structure. The related schematic of the device structures for the Seebeck coefficient measurement in a vacuum is shown in Fig. 1(a). The device consists of one microfabricated heater and two thermometers patterned on a Si substrate covered with a thin SiO₂ layer.

2.5.2 Principle. When an ac current at frequency ω is fed into the microheater this results in Joule heating with a frequency 2ω. This heat diffusion caused a temperature oscillation which propagated through the substrate to the NW. Therefore, a temperature difference was established, and both the temperatures associated with the frequency 2ω. T_H(2ω) and T_L(2ω), at two ends of the NW could be determined by measuring the four-probe resistance of the Pt wires. Consequently, the temperature difference ΔT(2ω), could be obtained by:

ΔT(2ω) = T_H(2ω) − T_L(2ω) (2-4)

Employing lock-in amplifiers, both the Seebeck voltage ΔV(2ω) and ΔT(2ω) could be measured. Finally, the Seebeck coefficient, S, of the NW is calculated as (eqn (2-5))¹¹⁹

2.5.3 Merits and shortcomings. The thermoelectric power measurement essentially incorporated reading the voltage generated by a temperature gradient. In order to produce the temperature gradient, the described method used an AC current to heat the heater via Joule heating. By employing a lock-in amplifier to obtain the 2^nd harmonic voltage, the influence of environmental factors, such as temperature and pressure fluctuation, was minimized due to the high signal/noise ratio of the lock-in amplifier. Furthermore, the Seebeck voltage, ΔV(2ω), was clearly proportional to the temperature difference, ΔT(2ω), without any offset, because there was no phase lag between them.¹¹⁹ Nevertheless, it should be noted that, as the frequency increased, the temperature fluctuation amplitude (although the average temperature over time would remain the same) would be decayed, resulting in a reduction of measured thermoelectric voltage.¹¹¹ As a result, the frequency in this method was recommended to be below the inverse of the thermal time constant of the heater. For example, below 1 kHz in ref. 111. Additionally, if a bulk substrate device was adopted, a period of time to reach thermal equilibrium was required. This situation could be improved by the suspended structure.

2.5.4 Applications. Duarte et al.¹¹¹ measured the Seebeck coefficient of an individual NW with this method. In their measurement, the microheater and the NW were suspended to prevent substrate-coupling effects.^73,120 In addition, they also observed thermopower enhancement in “junctioned” gold NWs near room temperature.²³ Kirihara et al.¹¹⁹ recently fabricated a device with Pt microelectrodes and a microheater. It was reported that the Seebeck coefficient of single-crystalline boron nanobelt (20 nm average thickness) was measured to be 174 μV K⁻¹ at 300 K. Furthermore, the thermopower of quantum dots defined in heterostructure NWs were also measured so to obtain a comprehensive understanding of the quantum dot thermopower as a function of the Fermi energy.^121,122

3 Measurement of thermal conductivity of 1D nanostructural materials

In this section, twelve types of measurements of thermal conductivity of 1D nanostructural material are covered. The method with microfabricated suspended device, 3ω method and transient electrothermal method (TET) have been extensively used and the thermal conductivities of various NWs have been measured by these methods.^69,73,123 The T-type nanosensor method was initially developed to characterize the thermal conductivity of a carbon nanotube and was later developed to measure the thermal conductivity of a NW. The DCTBM could be utilized to evaluate both conductive and non-conductive fibers. When compared with the existing techniques, this method appeared to present a reasonable alternative due to its simplicity and a high degree of reliability.¹²⁴ Optical heating and electrical thermal sensing method (OHETS) was developed to characterize the thermal diffusivity of individual non-conductive submicron/nanoscale wires/tubes. Transient photoelectrothermal (TPET) and pulse laser-assisted thermal relaxation (PLTR) techniques were both based on laser irradiation and featured significant signal/noise ratio in millivolts.¹²⁵ Measurements based on Raman thermography or thermoreflectance techniques were methods that could be used to measure absolute temperature. With these non-contact temperature measuring methods, the influence of thermal contact resistances could be eliminated. Thermal flash method could be carried out without calling for any knowledge or estimate of the interfacial/contact resistances.¹²⁶ 3ω-scanning thermal microscopy (SThM) technique which was based on third harmonic voltage at the thermoresistive probe could obtain the thermal conductivities of a wide range of individual NWs embedded in a matrix.

This section briefly introduces the principles of these methods. The main advantages and disadvantages of the methods are presented as well as their applications. A summary of these methods is presented in Table 2.

Table 2 Measurement of thermal conductivity of 1D nanostructural material

Method	Principle	Samples in references	Uncertainty	Merits	Shortcomings	Ref.
Microfabricated suspended device	MEMS	Conductive NWs	>9%^73	Platform for the Seebeck coefficient, electrical and thermal conductivity	Complicated structure	71
	Steady-state method	Minimum diameter 10 nm^73		Measurement sensitivity down to ∼1 pW K^−1 with special configuration^112,140	Difficult sample placement	73
		Thermal conductivity from 1.1 to 3000 W m^−1 K^−1 ^128,129			Extra effort to achieve ohmic contact	140
					Influence of the unknown thermal contact resistance
3ω method	3ω theory	Conductive NWs	9%^191	Simple structure	Exist truncating error and radial heat loss	69
	Dynamic method	Minimum diameter 45 nm^189		Convenient manufacture	Difficult for non-conductive NWs	191
		Thermal conductivity from 0.5 to 830 W m^−1 K^−1 ^159,189		High signal-to-noise ratio	Low signal level (μV)
T-type nanosensor	1D transient conduction theory	Conductive NWs	7%^196	Simple structure	Insufficient sensitivity with small diameters	195
	Steady state method	Minimum diameter 9.8 nm^195		Thermal contact resistance could be theoretically extracted	Considerable influence of the thermal contact resistance	199
		Thermal conductivity from 110 to 2000 W m^−1 K^−1 ^199,195
DCTBM	1D transient conduction theory	Conductive fibers	11%^124	Simple structure	Only larger fibers had been measured	124
	Steady state method	Nonconductive fibers (additional metallic coating)		High degree of reliability	Difficult to evaluate the thermal contact resistance
		Minimum diameter ∼15 μm^205		Both conductive and non-conductive fibers
		Thermal conductivity from 7 to 27 W m^−1 K^−1 ^124,205
OHETS	1D transient conduction theory	Conductive fibers	10%^206	Simple structure	The thermal diffusivity was obtained rather than the thermal conductivity	206
	Dynamic method	Nonconductive fibers (additional metallic coating)		Both conductive and non-conductive sample	Low signal level (μV)	207
		Minimum diameter ∼800 nm^207		Neglectful effect of the laser beam distribution	Complex configurations
		Thermal diffusivity from 1.05 × 10^−7 to 6.54 × 10^−5 m^2 s^−1 ^206,207
TET	1D transient conduction theory	Conductive fibers	10%^123	Simple structure	Only for the thermal diffusivity	123
	Transient method	Nonconductive fibers (additional metallic coating)		Both conductive and non-conductive samples	Nonconstant heating power due to the variation of sample resistance	215
		Minimum diameter ∼324 nm^211		Strong signal level	The results depended on the rising time of the electric current
		Thermal diffusivity from 1.53 × 10^−7 to 6.67 × 10^−5 m^2 s^−1 ^123,211
TPET	1D transient conduction theory	Conductive fibers	—	Simple structure	Only for the thermal diffusivity	218
	Transient method	Nonconductive fibers (additional metallic coating)		Both conductive and non-conductive samples	Only larger fibers had been measured
		Minimum diameter 10.4 μm^218		Strong signal level	The results depended on the rising time of the laser beam
		Thermal diffusivity from 5 × 10^−7 to 2.53 × 10^−5 m^2 s^−1  ^218
PLTR	1D transient conduction theory	Conductive fibers	10%^209	Simple structure	Only for the thermal diffusivity	209
	Transient method	Nonconductive fibers (additional metallic coating)		Both conductive and non-conductive samples	Only larger fibers had been measured	210
		Minimum diameter 23 μm^210		Negligible influence of the laser beam’s rising time
		Thermal diffusivity 1.05 × 10^−5 m^2 s^−1 ^210
Raman thermography	Raman thermography	Conductive NWs	14.41%^227	Simple structure	Limited resolution of the Raman spectrometer	127
	Steady state method	Minimum diameter 1.8 nm^220		Negligible influence of the thermal contact resistance	Raman spectrum should be corrected before measurements	220
		Thermal conductivity from 0.44 to 2630 W m^−1 K^−1 ^127,227
Thermal flash method	Thermal flash	Conductive fibers	—	Both conductive and non-conductive samples	The thermal diffusivity was obtained rather than the thermal conductivity limited by the data acquisition rate	70
	Transient method	Nonconductive fibers		Without concern for thermal contact resistance		126
		Minimum diameter 271 nm^70
		Thermal diffusivity from 5.97 × 10^−8 to 1.78 × 10^−3 m^2 s^−1 ^70,126
Thermoreflectance technique	Thermoreflectance technique	Conductive NWs	—	1.1 °C temperature resolution	Limited by the spatial resolution of the thermoreflectance	238
	Steady state method	Minimum diameter 115 nm^238		Without concern for thermal contact resistance	Thermoreflectance coefficient should be calibrated
		Thermal conductivity 46 W m^−1 K^−1 ^238
SThM technique	3ω-SThM	Conductive NWs	—	Spatial resolution around 100 nm	Consequential effect of the thermal contact resistance	241
	Dynamic method	Minimum diameter 120 nm^247		Non destructive method	Complex theoretical models	244
		Thermal conductivity from 0.5 to 128 W m^−1 K^−1 ^241,247

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3.1 Microfabricated suspended device

3.1.1 Structure. The outline of the suspended structure is shown in Fig. 2(a) which has been described in Section 2.2.1. In this method, the suspended structure was loaded into a cryostat with an ambient pressure less than 1 × 10⁻⁵ Torr to ensure that the heat loss from the NW to the ambient environment by convection was negligible.

3.1.2 Principle. In this typical method, a dc current, I_h, was applied to the suspended heater so that the average temperature of the heater, T_h, was elevated above the ambient temperature, T₀, as shown in Fig. 5(a). With the PRT’s TCR, the temperature, T_h, of the heater could be obtained by measuring the resistance of the heater, R_h, through the standard four-probe method. At the same time, the temperature of the sensor, T_s, was determined using a lock-in amplifier which generated a very small probing current so that the Joule heat of the sensor could be ignored.

Fig. 5 (a) Schematic of energy exchange, for the heater at T_h, and the sensor at T_s; (b) experimental setup of the Wheatstone bridge circuit for NW thermal measurement. Reprinted with permission from ref. 128, American Chemical Society.

To determine the thermal conductivity of the NW, some assumptions were put forward as following:⁷³

(i) The temperature of the heater or sensor was uniform.

(ii) The heat transfers between the two membranes by air conduction, convection and radiation were negligible.

(iii) The temperature at the junction between each beam and the substrate was equal to the substrate temperature which was considered to be a constant, T₀.

With the assumptions above, the energy exchange could be given as Fig. 5(a), where Q_h and 2Q_L are the Joule heat of heater and two Pt wires generated by the current, I_h, respectively. Simultaneously, the Joule heat rose the temperature of the heater by ΔT_h (≡T_h − T₀). Then, a certain part of heat (Q_s) was conducted through the NW from the heater to the sensor which raised the temperature of sensor by ΔT_s (≡T_s − T₀), and it was further transferred to the ambiance through the six beams supporting the sensor (2Q₂). Furthermore, it was noteworthy that Q_s was equal to 2Q₂. Another part of the heat, 2Q₁, was conducted away through the six beams which connected to the heater. Hence, the energy conservation was invoked as:

2Q₁ + 2Q₂ = Q_h + 2Q_L (3-1)

With careful calculation, one could find that the thermal conduction of beams which suspended the sensor, G_b, could be obtained as:

From the thermal resistance circuit shown in Fig. 5(a), the thermal conduction of NW, G_s, could be determined as:⁷³

Thus, the thermal conductivity of NW, κ_s, was obtained by:

where l and A_s are the length, and cross section area of the NW sample, respectively. Additionally, temperature changes in each membrane (ΔT_h and ΔT_s) could be obtained from the measured resistances of the heater and sensor. Q_h and Q_L could be calculated from the direct current passing through the heater and the measured resistance of the heating PRT as well as the Pt wires on the beams.

3.1.3 Merits and shortcomings. One of the main merits of these suspended devices was that they could access not only to the thermal conductivity but also to the Seebeck coefficient and the electric conductivity of the same individual NW. Hence, these nanostructures offered a convenient route to obtain the figure of merits of the NWs. Furthermore, the influence of the substrate could be minimized by the suspended geometry. Heat transfer between the two membranes via radiation and air conduction were well below the measurement sensitivity (∼1 nW K⁻¹) at 300 K and were negligible when the suspended structure was enclosed in a cryostat with a vacuum level better than 1 × 10⁻⁵ Torr.⁷³

Ever since this method was introduced,¹²⁹ various approaches had been developed to improve the accuracy of the measurement, such as estimation of the thermal contact resistances,^130–132 and using a Wheatstone bridge to cancel the temperature fluctuation.¹²⁸ The measurement sensitivity of the standard devices had been demonstrated to be ∼1 nW K⁻¹.⁷³ However, consider the case of a NW with very small diameter (e.g. 10 nm) and thermal conductivity as low as 1 W m⁻¹ K⁻¹, the thermal conductance would be 10 times lower than the sensitivity. Consequently, this method was feasible only when the thermal conductances of the NWs were larger than the sensitivity of the device. For instance, NTs¹³³ and NWs with the thermal conductances larger than 1 nW K⁻¹.^134,135 This limitation may be attributed to several reasons, including temperature noise of the device, parasitic heat loss, etc.^82,136 Therefore, highly sensitive, micro-fabricated suspended devices are required to obtain thermal conductivities of single NWs with smaller diameter NWs, which may exhibit an ultra-high figure of merit due to quantum size effects.^137–139 To this end, noise-canceling schemes have been exploited to cancel the temperature fluctuation in the sample environment, and, consequently, significantly enhanced this thermal bridge method to be capable of measuring thermal conductance values down to ∼1 pW K⁻¹.^140,141 Very recently, careful calculation and measurement had been also carried out to measure NW samples with a low thermal conductance of the order of 10⁻¹⁰ W K⁻¹.^71,112

The presence of an unknown thermal contact resistance between the NW and the contact electrodes was also a critical issue. There have been a few reports on molecular dynamic (MD) simulations and experimental investigations of the thermal contact resistance of the NW and CNT. For example, the thermal contact resistances of ZnTe NW with a diameter of 145.6 nm were obtained through MD simulation, which were around 20 and 5% of the total measured thermal resistance before and after Pt contact deposition, respectively.¹⁴² While another simulation implied that the thermal contact resistance of ZnTe NW with the same diameter was about 10% of the total measured thermal resistance and reduced to 3% after the Pt contact deposition.¹⁴³ The different results might be attributable to different simulation parameters. Shi et al.⁷³ estimated the contribution of thermal contacts with Pt deposition to be less than 15% for 100 nm SiNW. Additionally, for a 66 nm diameter multiwalled carbon nanotube, experimental results showed that thermal contact resistance could contribute up to 50% of the total measured thermal contact resistance.¹³⁰ In practice, the thermal contact resistance could be much larger than that used by simulation or estimated due to non-ideal contact.¹⁴⁴ There were two main reasons that make this thermal contact resistance a challenge for measuring the thermoelectric properties of the NWs. First, when the contact area between the NW and the contact material becomes comparable to the mean free path of phonons or electrons, the thermal contact resistance would consist of an additional ballistic or interface resistance component besides the diffusive component given by Fourier’s law.¹⁴⁴ Second, the contact at the interface is non-ideal for extremely small contact area (<0.05 μm²). A conventional method to decrease the thermal contact resistance was by depositing metallic material, such as Pt and W, on top of the contact using FIB so that the NW was sandwiched between two metallic layers, since metals are good conductors of heat through electrons.¹⁴⁵ Furthermore, careful examination of the contact condition was recommended so as to ensure that the obtained thermal conductivity did not deviate significantly from the intrinsic thermal conductivity of the NW.

3.1.4 Applications. To date, this method had been utilized to determine a number of NWs with various characteristics,^146–151 and various materials. For example, CNTs,¹⁰⁹ SiGe,¹¹³ Bi,^152,153 Bi₂Te₃,¹⁵⁴ PbTe,^155,156 InAs,^53,157 and ZnTe,^142,143 have been investigated using this suspended microdevice for the measurement of their thermal properties.

Kim et al.¹²⁹ measured the thermal conductivity of an individual MWNT of a diameter 14 nm using a microfabricated suspended device. The observed thermal conductivity was more than 3000 W K⁻¹ m⁻¹ at room temperature. The measurements were also performed with 10 nm and 148 nm SWCN bundles by Shi et al.⁷³ The observed thermal conductivities were low compared to that of an individual MWCN, and for the 148 nm bundle, the thermal conductivity exhibited a T^1.5 dependence in the temperature range of 20–100 K. More recently, Wingert et al.,¹²⁸ using their suspended device with a Wheatstone bridge circuit (see Fig. 5(b)), obtained the thermal conductivities of Ge and Ge–Si core–shell NWs with diameters less than 20 nm. The measured thermal conductivity for the 15 and 19 nm Ge NWs were (1.54 + 0.59/−0.30) and (2.26 + 0.60/−0.39) W m⁻¹ K⁻¹, respectively, and the thermal conductivities of the Ge–Si core–shell NWs were in the range of 1.1–2.6 W m⁻¹ K⁻¹ at 108–388 K.

3.2 3ω method

3.2.1 Structure. The NW sample is freely suspended across four electrodes in a four-probe configuration on a dielectric substrate. As shown in Fig. 6(a), the two outside electrodes, A and D, were used for feeding a sinusoidal electrical current, I₀ sin(ωt), and the two inside ones, B and C, were utilized for measuring the voltage across the sample.

Fig. 6 (a) Illustration of the four-probe configuration for measuring the specific heat and thermal conductivity of NW; (b) a SEM image showing the nanoscale four-point probe for the 3ω measurement. Reprinted with permission from ref. 62, Springer.

3.2.2 Principle. The NW sample was freely suspended across four electrodes in a four-probe configuration and fed by a sinusoidal electrical current, I₀ sin(ωt), through the two outside electrodes, A and D, as shown in Fig. 6(a). As long as the current passed through the NW, the temperature fluctuation would be at frequency 2ω due to that the Joule heat was proportional to [I₀ sin(ωt)]². Taking into account the NW’s TCR, the evoked harmonic resistance of the sample would fluctuate at frequency 2ω as well. Therefore, a small 3ω voltage signal between the two inside electrodes (B and C), V_3ω,RMS, could be detected by a lock-in amplifier, from which the specific heat and thermal conductivity could be determined. In addition, the sample was put in a vacuum chamber to prevent heat loss from the NW to the ambient environment by air convection.

No external heater was required since most of the thermoelectric NWs were semiconductors, and themselves could serve as not only heaters but also sensors. However, the samples needed to be suspended in a high vacuum so as to allow the temperature fluctuation and avoid heat loss into the environment. Also, the electrodes had to be highly thermally conductive, so to heat sink the energy at these four points to substrate.⁶⁹ In such a case, the temperatures at the four electrodes were assumed to be stable at ambient temperature, T₀. The heat was considered to diffuse along the NW and the one-dimensional transient conduction equation along the sample suspended between two inside electrodes can be written as:⁶⁹

where ρ, C_p, κ and R₀ are mass density, specific heat, thermal conductivity and electric resistance of the NW, respectively. R′[−(dR/dT)_T0] is the temperature gradient of the resistance at ambient temperature, T₀, L is the length of the NW between the two inside contacts, t is time, and A_s is the cross section of the NW.

From eqn (3-5), the 3ω signal generated in the NW, V_3ω = IR = I(R₀ + δR), was expressed as:

where γ is a constant. When the measurement was performed at the low-frequency limit ωγ → 0, V_3ω was nearly frequency independent. Therefore, eqn (3-6) could be expressed as a simpler expression,⁶⁹

Consequently,

According to eqn (3-6), as the frequency decreased, the magnitude of V_3ω,RMS would gradually increase and eventually reach a frequency-independent value. This has been verified in a number of experiments.^158,159 For this reason, one could obtain the thermal conductivity κ of a NW by fitting the experimental V_3ω data to eqn (3-6) with the measured frequency. Another strategy ​to obtain κ, by taking advantage of the relationship, V_3ω,RMS ∼ I_RMS³, was measuring the V_3ω,RMS values with different ac electrical currents at a low angular modulation frequency.^160–162

3.2.3 Merits and shortcomings. The 3ω method had become a common method to determine the thermal physical properties because of its relatively simple structure and convenient manufacture. Furthermore, it has better signal-to-noise ratio (SNR) compared with the suspended device by employing a narrow-band detection technology, which has an advantage of eliminating spurious signals. The thermal contact resistance was negligible in this method, because they could only shift the amplitude of the signal, but not the frequency. However, the analytical expression deducted by Lu et al.⁶⁹ would introduce errors due to oversimplification and approximation, for instance, truncating part of terms of the infinite series and, furthermore, neglecting the radial heat loss. Special care is required when using this approach considering the truncating error and radial heat loss. Therefore, several improved models for measuring the thermal conductivities of the NWs accurately as well as experimental studies have been carried out.^163,164 Hou et al.¹⁶⁵ developed a comprehensive analytical solution including the NW–substrate interaction and radiation heat loss. Their study showed that for NWs with a diameter around 100 nm or thinner, the radiation heat loss from the wire surface would have a strong effect on the amplitude and phase shift of the 3ω signal.¹⁶⁵ This influence became stronger for thinner NWs. More importantly, from the mechanism of this 3ω method, the samples were required to be electrically conductive and have linear I–V behaviors within the source range. Besides, the TCR of the NW have to be known, which needed to be measured separately.

3.2.4 Applications. The 3ω method, coined by Corbino et al.¹⁶⁶ in 1910, was based on the discovered small third-harmonic voltage component while applying an ac current with angular modulation frequency, ω, through a heater. Later, this method was systematic investigated and became practical.^167–170 Theoretical analysis showed that the thermal parameters could be obtained by measuring the third harmonic component (3ω) of the voltage along a heating wire.¹⁷¹ Lu et al.⁶⁹ further extended the 3ω method to simultaneously measure the specific heat and thermal conductivity of suspended fiber samples across two heat sinks, and, therefore, gave a relatively better SNR. Previously, it was mainly used to study the thermophysical properties of thin films,^{167,172–178} superlattices,^179,180 and even liquid materials.^170,181,182

As for 1D nanostructural materials, this method had also been utilized to investigate the thermal properties of NWs^62,183–188 CNTs,^189,190 and fibers.^159,191 Lee et al.⁶² fabricated a measurement platform with nanoscale four-point setup, as shown in Fig. 6(b), for characterizing the thermoelectric properties of individual β-SiC NW and utilized the 3ω method to obtain the thermal conductivity of the NW. The 3ω voltage as a function of current at 1 kHz was measured, from which the thermal conductivity of 86.5 ± 3.5 W m⁻¹ K⁻¹ was obtained at room temperature. Similarly, Choi et al.¹⁸⁹ found the thermal conductivity of individual MWCNTs (outer diameter of 45 nm), by employing the 3ω method, to be 650–830 W m⁻¹ K⁻¹ at room temperature. Furthermore, Finefrock et al.¹⁵⁹ measured the thermal conductivity of PbTe nanocrystal coated glass fibers using the self-heated 3ω method at low frequency. They also performed a simulation to correct the thermal radiation effect and extract the thermal conductivities of glass fibers which were in the range of 0.50–0.93 W m⁻¹ K⁻¹ near room temperature.

Recently, Dames et al.¹⁶⁴ pointed out that, with an additional dc offset, the thermal conductivity could also be determined from 1ω and 2ω voltages. Feng et al.¹⁹² based on the numerical solution of heat conduction equation, presented an approach to measure the thermal properties of NWs with 2ω or 3ω voltage. This approach was also used to investigate a single Pt NW and carbon fiber and the result had a relative derivation within 4% using either 2ω or 3ω method. However, the 3ω measurement was still superior, despite that the 2ω method was able to yield a larger harmonic signal, relatively, than 2ω method.^164,192 Recently, Xing et al.¹⁹³ presented a complete model for characterizing the thermal properties of the NWs. With this 3ω technique, they also carried out a measurement of Pt NW as a reference sample using both voltage and current sources for sample excitation.¹⁹¹ In particular, a first harmonic (1ω) cancellation technique was developed, in their work, to measure all the relevant thermal properties independently and also improved the measurement precision. It was also observed that the mesoscopic device, which was mentioned in Section 2.1 and employed to measure the Seebeck coefficient, had a similar structure with the structure in the 3ω method. Therefore, the mesoscopic device could be also used to perform the 3ω measurement, and thus obtain the figure of merit ZT. For example, Lee et al.¹⁹⁴ provided a platform with built-in heaters and electrodes to measure electrical resistivity, thermal conductivity, and Seebeck coefficient simultaneously. The result showed that the thermal conductivity of a single crystalline Bi_1.75Sb_0.25Te_2.02 NW of 250 nm in diameter increased from 0.5 W m⁻¹ K⁻¹ at 10 K to 1.2 W m⁻¹ K⁻¹ at 120 K, then followed by a slight increase to 1.4 W m⁻¹ K⁻¹ at 300 K. In literature,¹⁸⁵ the thermoelectric properties of Bi₂Te₃ NWs were also successfully measured using this versatile microfabrication approach.

3.3 T-type nanosensor

3.3.1 Structure. Zhang et al.¹⁹⁶ developed a steady-state short-hot-wire method, in which a sample-attached T-type nanosensor was fabricated to measure the thermal conductivity of a single NW. The measuring system is schematically shown in Fig. 7(a). The hot wire of length l_h, radius r_h and thermal conductivity κ_h was suspended by two electric contacts, F_h1 and F_h2, which also served as heat sinks, at each end. The sample of length l_s and radius r_s was supported with a another electric contact, (F_s) at one end, and the other end was attached to the hot wire in the mid-point. The lengths between the attached point and left/right (F_h1/F_h2) heat sinks were l_h1 and l_h2, respectively.

Fig. 7 (a) Schematic diagram of T-type nanosensor, in which the NW is attached a hot wire at one end and a heat sink at another end; (b) SEM image of the T-type nanosensor with suspended hot wire. Reprinted with permission from ref. 195, John Wiley and Sons.

3.3.2 Principle. Once a constant direct current, I_dc, passed through the hot wire, a uniform Joule heat was generated, and during the entire measurement, all the ends connected with the heat sinks were maintained at the initial temperature, T₀. Furthermore, the temperature of the hot wire and the sample depended on their thermal properties and the heat generation rate of the hot wire. With the measurement of the one-dimensional steady-state heat conduction along the hot wire and the sample, one could obtain the thermal conductivity of the sample by measuring the average temperature of the hot wire and calculating the heat generation rate. This method is theoretically applicable to any kind of individual nanofiber and NW.^197,198

The heat loss is assumed to be neglected when the measurement is carried out in a vacuum, and the effect of radiation can also be neglected because of the small temperature gradient along the hot wire. Furthermore, the thermal resistance of the contact can also be ignored in order to simplify this model. Then, the relevant one-dimensional heat conduction equations of a hot wire can be expressed as:¹⁹⁹

where T_h1(x_h1) and T_h2(x_h2) are the temperature at x_h1 and x_h2, respectively. κ_h is the thermal conductivity of the hot wire, and q_v, defined as IV/(A_hl_h), is the volumetric heat generation rate, where I, V and A_h are the supplied electrical current, the voltage and the cross area of hot wire, respectively.

As for the sample, the equation of heat conduction could be written as:

where T_s(x_s) is the temperature of the sample at x_s, and κ_s is the thermal conductivity of the sample.

Under the boundary condition, with temperatures of the heat sinks the same as the surrounding temperature, T₀, and the temperature of the contact point between the hot wire and the sample is T_c, eqn (3-9) and (3-10) can be solved. Then, the average temperature rise of the hot wire could be calculated as:

Next, the heat flow through the NW was obtained as:

where A_s is the cross-sectional area of the sample. Considering the temperature gradient of the sample, the heat flux of NW could be also expressed as:

Combining (3-11), (3-12) and (3-13), the thermal conductivity of the NW is:¹⁹⁹

In principle, steady state was reached within several seconds when a constant direct current passes through the hot wire. As long as the ΔT_h and q_v were measured, one could obtain the thermal conductivity κ_s.

3.3.3 Merits and shortcomings. This method was, in principle, able to characterize the thermal properties of any single nanofiber, NW, and even SWCNTs. It is regarded as having the advantages of simplicity as well as high accuracy. For example, uncertainty analysis was calculated, including uncertainty of hot wire thermal conductivity, thermal contact resistance and etc., to be within 7%, which was accepted as of high accuracy.^196,199 In addition, the junction thermal contact resistance could be theoretically extracted through changing the length of the sample.¹⁹⁵ However, it was difficult to be applied in experiments at the nanoscale. The error caused by thermal contact resistance was depending on the contact length and can be as large as 20%, which indicated that the thermal contact resistance had a significant effect on this measurement and, to a large extent, limited its reliability and accuracy.¹⁹⁹ Furthermore, the hot wire must be fabricated at nanoscale to acquire sufficient sensitivity when measuring NWs. The connection between the hot wire and NW also became one of the fundamental points of this measurement which had been verified by Ito et al.^195,199 By bonding the Pt hot wire and the NW to make the contact length equal to the width of the Pt hot wire, the deviation of the measured thermal conductivities with and without considering the thermal resistance was reduced.

3.3.4 Applications. This method had been successfully applied to measure the thermal conductivity of CNTs^197,198 and other NWs.^199,200 Fujii et al.,¹⁹⁵ fabricated suspended platinum nanofilm and lead terminals using a micro-electro-mechanical system (MEMS) technology. As illustrated in Fig. 7(b), the dimensions of the nanofilm were 27.5–40.0 nm in thickness, 330–600 nm in width, and 5.3–5.7 μm in length, respectively. The nanofilm was suspended about 6 μm above the silicon substrate and served as the hot wire. With this platform, it was found that the thermal conductivity of a CNT with a diameter of 9.8 nm exceeded 2000 W m⁻¹ K⁻¹ at room temperature. In addition, they also found that the thermal conductivity increased as its diameter decreased, which was contrary to many other 1D nanostructural thermoelectric materials.^99,103 Ito et al.¹⁹⁹ characterized the thermal conductivity of SiC NW with a diameter of 141 nm. The measurement result was obtained, in which the thermal conductivity turned out to be approximately 110 W m⁻¹ K⁻¹ at 300 K. Furthermore, a 3ω-T type probe was proposed to measure the thermal properties of NWs and the thermal contact resistance of the junction.^201,202 More interestingly, a T-type probe composed of Wollaston wire was further developed in both 1ω and 3ω configurations for thermal conductivity measurements,^203,204 which is conceptually very similar to that of Fujii et al.¹⁹⁸

3.4 Steady-state dc thermal bridge method (DCTBM)

3.4.1 Structure. The structural scheme of DCTBM is shown in Fig. 8, where the NW was suspended between two electrodes, A and B, which also served as heat sinks.

Fig. 8 Structure of the DCTBM for 1D nanostructure thermal conductivity measurement.

3.4.2 Principle. The sample, suspended over the two heat sinks, was heated at a steady state when a dc current passed through. Then, the resistance changed correspondingly, which was recorded using a four-probe technology. The temperature distribution could be determined according to one-dimensional heat conduction and the boundary conditions T(x = 0) = T(x = L) = T₀, in which T₀ was the ambient temperature,¹²⁴where κ, V, I, L and A_s are the thermal conductivity, the voltage, the current, the effective length and the cross section of the sample, respectively. The average temperature rise, then, was expressed as:¹²⁴

Therefore, the thermal conductivity could be determined as long as the heating power, the corresponding temperature rise and NW’s geometric parameters were acquired.

To measure the thermal conductivity accurately, the sample had to be placed in a vacuum chamber in order to reduce the heat loss due to air convection. In addition, the resistance–temperature relationship, which was used to determine the temperature, needed to be calibrated before the measurement of thermal conductivity.

3.4.3 Merits and shortcomings. This method could be utilized to evaluate both conductive and non-conductive samples. For conductive materials, the sample could serve as both a heater and a thermometer; for non-conductive samples, one might deposit an additional metallic coating on the sample to act as the heater and thermometer. For example, Pt was selected as the coating layer on individual poly(ether ketone) (PEK)/CNT fibers because of its stable temperature–resistance relationship and lower thermal conductivity (compared with Au).¹²⁴ However, it was necessary to extract the real thermal conductivity of the sample from the results with metallic coating, and the effect of the metallic coating should also be considered. Additionally, up to now, only large fibers (>15 μm) had been measured by this method. When applying to NWs, the effect of the thermal contact resistance and radiation heat loss are needed to be evaluated before the measurement.

3.4.4 Applications. Moon et al.¹²⁴ developed the DCTBM and measured the thermal conductivity of individual poly(ether ketone) (PEK)/CNT composite fibers over a temperature range of 295–400 K. The thermal conductivities of these fibers at 390 K were found to be about 27 W m⁻¹ K⁻¹, which was comparable to some engineering alloys. Moreover, the thermal conductivity of multi-wall CNTs (MWCNTs) containing Bi-component fibers were also measured, using this measuring method, to be approximately 7 W m⁻¹ K⁻¹.²⁰⁵

3.5 Optical heating and electrical thermal sensing (OHETS)

3.5.1 Structure. In this method, the sample was suspended over two electrodes, A and B, as shown in Fig. 8. Furthermore, a periodically modulated laser beam was employed to irradiate the sample.

3.5.2 Principle. When the sample was irradiated using a periodically modulated laser beam, it would experience a periodical temperature change with time owing to the periodical laser heating, which, as a result, would lead to a periodical change in its electrical resistance.

A small dc current was applied through the electrodes, A and B, to detect the voltage variation which had the same frequency with the modulated laser beam. Additionally, the voltage variation was strongly affected by the heat conduction along the NW. Therefore, the thermophysical properties of the sample could be determined through the phase shift of the voltage variation relative to the laser beam.

The NW was assumed to have a uniform temperature distribution in its cross-section, as long as the thermal diffusion length, μ = √(2α/ω) (α: thermal diffusivity of the wire; ω: modulation frequency), was much larger than the sample diameter D. Furthermore, to enhance the effect of the heat sinks, dimensions of the heat sinks need to be much larger than the diameter of the sample. This will result in negligible temperature variation at the heat sinks due to the laser heating.

When the laser heating power had the form of I = I₀(1 + cos(ωt)/2), the heat transfer equation along the axial direction of the NW could be written as:²⁰⁶

where Q₀ = E/LA_s, E and A_s are laser beam energy absorbed by the sample and cross-sectional area of the wire, respectively; c_p, κ and ρ are the specific heat, the thermal conductivity and the density of the sample, respectively. Moreover, the laser beam was assumed to be uniform over the sample. Thus the effect of non-uniform distribution of the laser beam can be neglected.²⁰⁶

In this method, a lock-in amplifier could only detect the temperature component that periodically varied with time (T̃_s), which was in the form of T̃_s = θe^iωt, in which θ is the temperature of the NW. Then, the average temperature variation along the wire was expressed as:

where [small theta, Greek, macron]₀ and ϕ are the amplitude and phase of [small theta, Greek, macron], respectively. Therefore, using the real part of the ω voltage across the NW was:²⁰⁶

Eqn (3-19) implied that, in this method, the phase shift of the voltage variation over the NW should be measured and be used for data fitting. In other words, once the phase shift as a function of the modulation frequency for the sample was measured, the thermal diffusivity could be determined by data fitting.

3.5.3 Merits and shortcomings. The OHETS method could be used to characterize the thermal properties of 1D conductive and non-conductive NWs. It was also noted that the non-uniformity of the laser beam distribution and the radiation heat loss from the sample, which was housed in a vacuum chamber, had negligible effect on the measured phase shift.²⁰⁷ However, an additional metallic coating needed to be deposited on the sample for non-conductive NWs. As the diameter of the wire was reduced in this method, the metallic coating would have a considerable contribution to the heat conduction.²⁰⁶ The effect of metallic coating should be considered and the real thermal property of the sample needs to be extracted. Besides, the thermal diffusivity of the sample was measured rather than the thermal conductivity. The material’s density and specific heat are thus required to calculate the thermal conductivity. Yet, these two parameters are generally extracted from the bulk counterpart. Furthermore, the system time delay had to be calibrated, before carrying out this method, by detecting the phase shift between the synchronizing signal of the function generator and the modulated laser beam.²⁰⁶

3.5.4 Applications. Hou et al.²⁰⁶ developed this OHETS method and measured the thermal diffusivity of conductive SWCNTs bundles. By fitting the measured phase shift of the voltage variation over the NW, the measured thermal diffusivities of the SWCNT bundles were obtained in the range of 2.98–6.54 × 10⁻⁵ m² s⁻¹. In addition, applying this method, the thermal diffusivity of single non-conductive polyacrylonitrile (PAN) fibers (∼800 nm) were characterized to be 1.05–1.14 × 10⁻⁵ m² s⁻¹.²⁰⁷

3.6 Transient electrothermal method (TET)

3.6.1 Structure. The schematic structure of the TET method is illustrated in Fig. 8, in which the NW was suspended between two electrodes, A and B.

3.6.2 Principle. In this method, the to-be-measured NW is suspended over two electrodes as shown in Fig. 8. When the sample was fed with a dc current which introduced electrical heating from electrodes A, B, the temperature change of the sample would lead to its resistance change, which could be detected by measuring the voltage change of the sample. In addition, the temperature increasing history of the sample was strongly affected by the heat transfer along it. Therefore, the thermal diffusivity of the sample could be measured by fitting the temperature change curve against time.

When the heating power was generated due to the dc current, the heat transfer equation in the NW along the x direction at time t > 0 was written as:

where q₀, κ, c_p and ρ are the electrical heating power per unit volume, the thermal conductivity, specific heat and density of the sample, respectively.

Considering the initial condition, T(x, t = 0) = T₀, and the boundary conditions, T(x = 0, t) = T(x = L, t) = T₀, where T₀ and L are the ambient temperature and the length of the wire, the average temperature of the wire can be written as:

where α is the thermal diffusivity of the sample.

The temperature distribution would finally reach the steady state and the average temperature of the sample was:

Therefore, the normalized temperature rise could be expressed as:¹²³

where α, T₀, T(t), T(t → ∞) are the thermal diffusivity of the sample, ambient temperature, average temperature of the NW at time t and steady state, respectively.

It was noted that, from eqn (3-23), the shape of the normalized temperature rise was only related to the Fourier number, which defined as F₀ = αt/L², for any kind of materials.

There are three methods for data analysis to determine the thermal diffusivity:¹²³

(i) Linear fitting at the initial stage of electrical heating.

At the beginning of the electrical heating, 0 < t < Δt, the corresponding normalized temperature rise can be written as:

T* = 12α/L²Δt (3-24)

Using the NW’s length, the thermal diffusivity, α, could be determined from the slope of the normalized temperature increasing curve.

(ii) Characteristic point method.

One best characteristic point of the T–t curve, could be used to obtain the thermal diffusivity directly, when T* = 0.8665, and the corresponding Fourier number was 0.2026. Therefore, the thermal diffusivity of the sample was expressed as:

α = 0.2026L²/Δt_c (3-25)

(iii) Least square fitting method.

Using different trial values of the thermal diffusivity, the best thermal diffusivity could be found by employing global fitting of the experimental data.

3.6.3 Merits and shortcomings. The TET method was a rapid technique (within a few seconds) that could be applied to non-conductive samples. Compared with the 3ω and OHETS methods, this method featured much reduced measurement time and much stronger signal level. Another merit was that an estimation of the thermal contact resistance in this method was unnecessary.⁷⁰ However, when this method was applied to a non-conductive NW by applying a thin metallic coating on the top of the sample, it added significant complexity to the measurement. More importantly, the additional metallic coating on the sample would undoubtedly increase the measurement difficulty when applying this method to NW with small diameter (e.g. 10 nm). Besides, the analytical expression of the normalized temperature evolution was only suitable with a constant heating power.²⁰⁸ Potential errors would be introduced with non-constant heating power due to the variation of sample resistance. For example, supposing that a constant voltage was supplied and the resistance of the sample increased as a result of self-heating, the current through it would decrease, leading to unstable heating power over the sample. The deviation for thermal conductivity, originating from the heating power variation had been accounted to be around 10% for 10 μm thick Pt wire.²⁰⁸ However, connecting a resistor with the same resistance as the sample in series or parallel would decrease the heating power fluctuation to less than 4%. Another issue in this method was that it was difficult to implement the measurement when the characteristic time of heat transfer of the sample was comparable to or less than the rising time of the electric current.^209,210 Consider a NW with thermal diffusivity of ∼5 × 10⁻⁵ m² s⁻¹ (e.g. CNTs) and length ∼1 μm, the characteristic time of heat transfer would be 2 × 10⁻² μs. Yet, the rising time of the electric current was ∼2 μs in ref. 211, which was much greater than the given characteristic time of heat transfer. Consequently, this method was limited by the rising time of the electric current. It is also worth noting that this method was aimed at measuring the thermal diffusivity. To obtain the thermal conductivity, one has to estimate or measure the density and the heat capacity of the sample, thus the actual thermal conductivity must be calculated.

3.6.4 Applications. The TET technique is an effective method to assess the thermal diffusivity of materials, including conductive, semiconductive and non-conductive low-dimensional structures. This technique has been successfully used for measuring the thermal diffusivity of thin films composed of anatase TiO₂ nanofibers,²¹² free-standing micrometer-thick poly(3-hexylthiophene) films,²¹³ SWCNTs²¹⁴ and micro/submicroscale polyacrylonitrile wires.²¹¹

Guo et al.¹²³ outlined this measurement to measure the thermophysical properties of one-dimensional conductive and non-conductive NWs. Their uncertainty analysis showed that the experiment had an uncertainty more than 10%. Moreover, the average thermal diffusivities of SWCNT bundles was obtained from Fig. 9, which was found to be 1.15 × 10⁻⁵ m² s⁻¹. Using this method, the thermal diffusivity of SWCNT bundles was also found at the 10⁻⁵ level which was the same as that in literature.²¹⁴ In addition, development and analysis of this method had been also carried out. Feng et al.²⁰⁸ developed this method to simultaneously measure the specific heat and the thermal conductivity of individual samples, and the accuracies of both the measurements were within 6%. Very recently, Liu et al.²¹⁵ analyzed the TET technique and found the TET technique was an effective approach to measuring the thermal properties of various materials. Computational models were also developed for the anisotropic thermal characterization of multi-scale wires.²¹⁶ In addition, a full theoretical model of the TET method has also been derived to include the effects of radiation heat transfer and non-constant heating.²¹⁷

Fig. 9 The normalized temperature vs. the theoretical fitting for an SWCNT bundle. Reprinted with permission from ref. 123, AIP Publishing LLC.

3.7 Transient photoelectrothermal (TPET) technique

3.7.1 Structure. In this measurement, the measuring NW was suspended over two metallic electrodes, as shown in Fig. 8, and irradiated with a step cw laser beam.

3.7.2 Principle. The NW was suspended over two metallic electrodes, as shown in Fig. 8. Furthermore, it was irradiated by a step cw laser beam, and the laser spot should be large enough so as to cover the entire NW and a portion of the electrodes. The laser beam would induce a transient temperature rise in the NW, and then resulted in a transient variation of the electrical resistance of the sample. The temperature variation amplitude of the electrodes (also as huge heat sinks), was much smaller than that of the NW. This ensured that the resistance variation of the electrodes was negligible compared with that of the sample. To extract the thermophysical properties of the NW, a dc current needed to be applied from the two electrodes, A and B, and the transient voltage variation of the NW should be detected.

Assuming that the temperature distribution in the cross section of the NW was uniform, therefore, only the heat transfer in the axial direction of the sample needed to be considered. If the output power of the laser was maintained constant, the heat transfer equation along the NW was:²¹⁸

where ġ and g′, defined as heating power per cubic meter, are the heat generated by the laser beam and the direct current passing through the sample, respectively; κ, c_p, ρ and T are the thermal conductivity, specific heat, density and temperature of the sample, respectively.

Following the same derivation process of the TET method, the normalized average temperature rise could be expressed as:²¹⁸

Considering the temperature, resistance change and voltage variation relationship of the wire, the measured voltage variation could represent the evolution of the normalized temperature. Consequently, according to the normalized temperature evolution, the thermal diffusivity could be determined by the data analysis methods which have been previously mentioned in the TET method.

3.7.3 Merits and shortcomings. The TPET method was developed to measure the thermal diffusivity of materials, including conductive, semiconductive and non-conductive low-dimensional structures based on step laser heating and electrical thermal sensing. It featured a strong signal and took only few seconds. In the experiment, only the information about how fast the voltage increased to reach steady state was needed. No knowledge about the real temperature rise was required.²¹⁸ However, noting that this method had only been applied to wires with diameter about 10 μm, several essential issues deserve careful technical consideration when the NWs were measured. First, just as for the TET method, this method faced the issue that the rising time of the laser beam might be comparable to or greater than the time taken for the sample to reach a steady state. To make the effect of rising time of the laser beam negligible, fast optical switches to control the laser beam might be used.²¹⁸ Second, for non-conductive NWs, the thickness of the metallic coating would be comparable to the NW thickness, which could introduce considerable errors. Other technologies, such as Raman spectra, might be required to solve this problem. Third, theoretical analysis for the effect of radiation heat loss was recommended when NW was measured. Furthermore, this method could only measure the thermal diffusivity. The material’s density and specific heat are needed to be known to calculate the thermal conductivity.

3.7.4 Applications. Wang et al.²¹⁸ developed this measurement to measure the thermophysical properties of conductive and non-conductive wires. They had successfully characterized the thermal diffusivities of a SWCNT bundle and microscale non-conductive wires. As a result, the thermal diffusivity of the SWCNT bundle was measured to be 2.53 × 10⁻⁵ m² s⁻¹, which was much smaller than that of graphite in the layer direction.

3.8 Pulse laser-assisted thermal relaxation (PLTR) technique

3.8.1 Structure. The measuring NW was suspended over two metallic electrodes, A and B, which acted as both contacts and heat sinks, as illustrated in Fig. 8, and irradiated by a fast pulsed laser.

3.8.2 Principle. Upon fast (nanosecond) pulsed laser irradiation, the temperature of the sample would suddenly increase to a high level and then decrease gradually. Such temperature relaxation is strongly affected by the thermal diffusivity and the length of the NW. In order to record this temperature relaxation history, a small direct current was fed through the electrodes, A and B, to obtain its resistance change which corresponded with the temperature change. Consequently, the shape of the normalized ΔV–t cure, which shared the same shape as the ΔT–t cure, could be used to obtain the thermal diffusivity of the sample.

The heat transfer equation in the NW along the x direction at time t > 0 was the same as eqn (3-20). However, here q₀ is sum of the Joule heating and the laser pulse heating. Since temperature evolution was caused by the pulsed laser heating, the effect of the Joule heating was not considered. With homogeneous boundary conditions, T(x = 0, t) = T(x = L, t) = T₀, and initial conditions, T(x, t = 0) = T₀, where T₀ and L are the ambient temperature and the length of the NW, and following the same derivation process of TET method, the simplified and normalized temperature relaxation could be written as:²⁰⁹

Eqn (3-28) showed that the shape of the normalized temperature relaxation was only effected by the Fourier number F₀ = αt/L².

To determine the thermal diffusivity, two approaches were involved: characteristic point method and global data fitting of the temperature relaxation curve, which have been previously mentioned in the TET method.

3.8.3 Merits and shortcomings. This method could be employed to characterize the thermal properties of one-dimensional micro-conductive and non-conductive wires. It was noted that this PLTR technique was the development of the TET and TPET method. The laser heating time could be as short as ∼10⁻⁹ s which was much less than the characteristic time of heat transfer of most samples. Consequently, it could be used to determine the thermal diffusivities of wires which had relatively short characteristic times of heat transfer (e.g. 10⁻⁸ s) and surmounted the drawbacks of the TET and TPET techniques while providing comparable reduced experimental time and high signal/noise ratio.²⁰⁹ Nevertheless, this method had been only applied to wires with diameter about 20 μm, and careful technical considerations were needed when the NWs were measured, such as the radiation heat transfer and the influence of metallic coating, which have been discussed previously. Additionally, another issue was that, when the thermal conductivity of the sample was much higher than that of the electrodes, the temperature at the wire/electrode contacts might not be actually fixed at the ambient temperature.²⁰⁹ Additional deposition of other metallic material on the contact area might be required.

3.8.4 Applications. This method overcame the drawbacks of the TET and TPET techniques and the analyzed uncertainty of this measurement was less than 10%.¹²⁵ Guo et al.,²⁰⁹ using this method, measured the thermal diffusivity of a MWCNT which was calculated to be 1.46 × 10⁻⁵ m² s⁻¹, and the measured average thermal diffusivity of carbon fibers was 9.9 × 10⁻⁵ m² s⁻¹. Recently, a theoretical analysis of the PLTR technique based on a finite difference model, which involved anisotropic heat transfer and radiation heat lost to the surroundings, has been developed.²¹⁰ Using this validated model, the heat transfer characteristics of multiscale wires including CNT had been studied.

3.9 Measurements by Raman thermography

3.9.1 Structure. In this method the sample is suspended over a trench, and the four electrodes (A, B, C and D) worked as both contacts and heat sinks, which is shown in Fig. 6(a).

3.9.2 Principle. It was worth mentioning that there are several models involving Raman thermography. One of the measurements adopting Raman thermography was steady-state Joule heating and optical sensing.^219,220 When there was a direct current passing through the NW, the sample heated itself and the temperature gradient between the middle and each end of the NW was strongly affected by its intrinsic heat transfer capability. Therefore, the thermal conductivity could be determined by figuring out the relationship between the heating power and the temperature difference over the middle and the two ends of the NW.

The heat power, P, generated on the section could be calculated as the volume integral on heat power density (W m⁻³), ρ_h,

where U and V are the voltage and the volume of the effect section of the sample, respectively.

When the sample was in a vacuum, the infrared radiation was neglected. The majority of the generated heat was conducted through the suspended NW to the substrates which acted as heat sinks. When the system reached its steady state, the whole generated heat was equal to the heat conducted away, that is:

where q⃑ is heat flux density in the unit of W m⁻², and A_s is cross section of NW.

From eqn (3-29) and (3-30), and Fourier thermal transfer law, the following equation could be obtained:

where κ is the thermal conductivity of the sample. The thermal power density ρ_h was approximately equal to UI/V, and V could be calculated as V = A_sL, where L is the length of the NW. Assuming the temperature of the heat sinks was the ambient temperature, T₀, and that the temperature at the midpoint of the NW was T_h, which was the highest temperature along the wire, then the thermal conductivity was determined as:²²⁰

Therefore, when the heat power, the geometric parameters of the sample and the temperature difference between the middle and end point of the NW were obtained, one could calculate the thermal conductivity. In addition, the temperature difference could be determined by the Raman spectra shift method.^221,222

3.9.3 Merits and shortcomings. As described above, the thermal contact resistance is an unsolved key issue in determining the intrinsic thermal conductivity in most electrical measurements. Furthermore, it was difficult to obtain the concrete value of thermal contact resistance.^144,198,223 Comparing with that, Raman thermography was a non-contact temperature technology. It could avoid determining the temperature by the relationship between the temperature and resistance of the sample so to eliminate the influence of the thermal contact resistance. Yet, several issues should be considered in the experiment. On the one hand, a shift existed between the laser focus position of the Raman spectrometer and the midpoint of the sample due to the limited resolution of the Raman spectrometer. Supposing that the location shift was 10% of the total length, it would give about 4% uncertainty in the middle point temperature measurement.²¹⁹ On the other hand, the probing laser of the Raman spectrometer would heat the sample when measuring and induce a resistance variation of the sample. However, this variation was demonstrated to be negligible.²²⁰ Another concern was that the temperature dependence of the Raman spectrum should be characterized and treated differently when different samples were analyzed.²¹⁹

3.9.4 Applications. To date, several models had been developed using the Raman-thermal technique, to measure the thermal conductivity of fibers,²²⁴ CNTs,²²⁵ NWs,^226–228 and graphenes.^229,230 Yue et al.²¹⁹ measured the thermal conductivity of individual SWCNTs and MWNTs using the temperature-induced shifts of D-band Raman spectra, and the value was measured to be 2400 and 1400 W m⁻¹ K⁻¹, respectively. Using the same model mentioned in this review, the thermal conductivities of MWCNT bundles were determined based on the temperature dependence intensity of the D-band Raman shift peak, which was more sensitive than the shift of the G band.²²⁵ Combining laser heating and Raman spectroscopy, Soini et al.²²⁶ investigated the thermal properties of freely suspended GaAs NWs. The thermal conductivities of single 170 nm NWs were found to lie in the range of 8–36 W m⁻¹ K⁻¹. Hsu et al.²³¹ developed a model using optical heating and temperature detecting by temperature-induced shifts in the G-band Raman frequency. But, owing to the fact that it was difficult to ascertain the heat power generated by the laser, they did not give the concrete thermal conductivity. Doerk et al.²²⁸ presented a model to measure the thermal conductivities of cantilevered NWs by heating with a focused laser locally, while simultaneously measuring the temperature of the same spot through Raman spectrometry. Very recently, combining Raman and electrical measurements, Wang et al.²³² developed a model to determine the optical absorption and heat transfer coefficients simultaneously. More interestingly, Li et al.²³³ combining T-type with Raman measurements, successfully developed a non-contact T-type Raman spectroscopy method to measure the thermal conductivities of fibers which could easily eliminate the thermal contact resistance.

3.10 Thermal flash method

3.10.1 Structure. In this method, a test NW was positioned between the thermal sensor and a metallic prop acting as a heat sink which aimed to keep the sample suspended in vacuum (see Fig. 10(a)). When implementing this method, a heat pulse would be sent into the sample from a micromanipulator based heater and then into the sensor.

Fig. 10 (a) Schematic of the thermal flash method, in which the NW is suspended between the thermal sensor and a metallic prop; (b) a SEM image of the thermal flash measurement for a polyimide micro/nanofiber. Reprinted with permission from ref. 70, AIP Publishing LLC.

3.10.2 Principle. This method was based on the thermal flash principle, which could directly characterize the thermal diffusivities of nanofibers without being influenced by the presence of interfacial or contact resistances.⁷⁰ In this method, a micromanipulator based heater was used to send a heat pulse through the NW and into the sensor. When the micromanipulator, which was wrapped with metal wire to sever as heater, contacted with the sample, heat would pass through the NW and then into the sensor. As a result, the resistance of the sensor would change and the transient voltage could be monitored while the sensor was maintained under a constant current.

The micromanipulator was modeled as a high-temperature reservoir due to its relatively large size and high thermal conductivity compared with the sample. Thus, from the heat transfer equation, an analytical solution could be derived and applied to obtain the thermal diffusivity of the sample from the data measured. The normalized temporal variation of the temperature at the contact point between the sample and the sensor was derived as:⁷⁰

where α_f and l_f are thermal diffusivity and the length of the sample, respectively.

When applying this method, the time, t, was assumed to be equal to zero when the micromanipulator touched the sample. The sensor and the NW were modeled as being in perfect contact. Furthermore, eqn (3-33) was a simplified expression due to the following equations:

where κ, α and l are thermal conductivity, thermal diffusivity and length, respectively; and subscripts f and s refer to the sample and the sensor, respectively. Eqn (3-34) implied that the measured sample should have low thermal conductivity and sufficiently long length.

To obtain the thermal diffusivity, eqn (3-33), the expression for the transient temperature rise of the sensor, could be utilized in a curve fitting routine as applied to the collected data. The thermal diffusivity of the sample could be determined from the best fitting between the analytical and experimental temperature profiles.

3.10.3 Merits and shortcomings. Since the transient variation was required to extract the thermal diffusivity rather than the magnitude of temperature, an offset due to thermal contact resistance, commonly a barrier to accurate thermal measurement, would not influence the final result.⁷⁰ However, since the measurement result was dependent on the sample thermal diffusivity and length, two main issues deserve careful technical consideration. On the one hand, the sample should have low thermal conductivity and sufficiently long length to satisfy eqn (3-34). Otherwise, more complex theoretical analysis should be implemented to solve this issue. On the other hand, the time taken to reach steady state was only few microseconds for fibers with relatively high thermal diffusivity, such as CNTs, since the exponential rise time was a function of both the thermal diffusivity and the length of the sample. For example, the time taken to reach steady state for MWNT clusters was approximately 8 μs.¹²⁶ Therefore, instrumentation with a fast data acquisition rate, such as a value in excess of 1 × 10⁶ samples s⁻¹, are required. To solve this problem, up to 1 centimeter samples or digital oscilloscopes offering a maximum data acquisition rate of 1 × 10⁶ samples s⁻¹ were selected to meet the above requirements.^126,234 Additionally, this method measured thermal diffusivity rather than the thermal conductivity. The specific heat and density of the sample thus have to be known in order to properly report thermal conductivity values.

3.10.4 Applications. Demko et al.⁷⁰ developed this thermal flash method to characterize the low thermal diffusivity of nanofibers, as shown in Fig. 10(b). Their result showed that polyimide fibers of diameters 570 and 271 nm exhibited diffusivities of 5.97 × 10⁻⁸ and 6.28 × 10⁻⁸ m² s⁻¹, respectively. In addition, a comprehensive mathematical treatment and analysis of this thermal flash theory was also presented to measure the thermal diffusivity of nanostructures.^126,235 The analysis showed that this method can be carried out without calling for any knowledge or estimate of the interfacial/contact resistances. Recently, this method had also been utilized to measure the thermal conductivity of carbon nanofibers and graphene nanoplatelets^236,237 as well as polyimide-mesophase pitch nanofibers.²³⁴

3.11 Thermoreflectance technique

3.11.1 Structure. The device, as shown in Fig. 2(a), consisted of two adjacent low-stress SiN_x membranes suspended with several beams. To prevent air convection influence on the thermal conductivity measurements, the sample was put in a cryostat chamber and kept in a high vacuum.

3.11.2 Principle. In this typical approach,²³⁸ a direct current was applied to one of the suspended heater so that the heating power was generated and heater’s average temperature was elevated above the ambient temperature. This power could be divided into two parts: heating up the active PRT, defined as Q_active and passing through the NW to heat up the inactive PRT, defined as Q_inactive. Furthermore, the heat conducted through the NW was assumed all to pass to the inactive PRT side to heat it up. Thus, the following equation could be obtained:²³⁸

IV = Q_active + Q_inactive (3-35)

At the same time, the heating power (Q) generated by PRT was expressed as:

Q = G_lΔT (3-36)

where G_l and ΔT are the PRT thermal conductance and its temperature increase, respectively.

From eqn (3-35) and (3-36), one could derive:

IV = G_l(ΔT_h + ΔT_s) (3-37)

where ΔT_h and ΔT_s are the temperature increase on the active and inactive PRT, respectively.

Then, the heat conducted through the NW was obtained as:²³⁸

Consequently, the thermal conductivity could be calculated as:

where G_N, A_s, l and ΔT_N are thermal conductance, cross section, length and temperature difference of the NW, respectively.

To obtain ΔT, the thermoreflectance imaging technique was utilized, which was based on temperature dependence of the materials’ reflection coefficient, and is able to provide lateral resolution of 0.3–0.5 μm and temperature resolution of 0.1 °C. In other words, a reflected light intensity change resulting from the temperature change was detected and turned into a small electric signal. Therefore, the temperature increase and distribution could be obtained.

3.11.3 Merits and shortcomings. The thermoreflectance measurement was a non-contact temperature measuring method, which could achieve submicrometer spatial resolution and 0.1 °C temperature resolution.^238,239 In the experiment, the actual temperature distribution between the two electrodes where the NW bridged was directly measured, instead of the average temperature of the heater/sensor. No knowledge about the TCR of the heater was needed. Thus, an estimation of the thermal contact resistance in this method was unnecessary. Nonetheless, it was notable that the resolution of the thermoreflectance imaging technique was at submicrometer level. Consequently, it was difficult to apply this method to short NWs, the length of which was comparable to the spatial resolution. Another issue should be considered was that the thermoreflectance coefficient of the sample should be calibrated before the measurement, which was a time consuming process.

3.11.4 Applications. Zhang et al.²³⁸ developed this method to characterize the heat transfer along a SiNW. They obtained a thermoreflectance image of the NW and device and then calculated the thermal conductivity of the SiNW (115 nm in width and 3.9 μm in length) which was 46 W m⁻¹ K⁻¹. This value corresponded to the electrical measuring result, 40 W m⁻¹ K⁻¹, made by Li et al.²⁴⁰

3.12 3ω-Scanning thermal microscopy (SThM) techniques

3.12.1 Structure. The schematic of SThM method for NW thermal conductivity measurement is shown in Fig. 11(a), where the tip was made of SiO₂ with a thin layer of palladium (Pd) deposited on the surface (top left of Fig. 11(a)). The Pd strip played the role of a heater and a thermometer when this probe was in contact with the NW (middle of Fig. 11(a)).

Fig. 11 (a) Schematic of SThM method for NW thermal conductivity measurement; (b) SEM pictures of the Si NWs array; (c) SThM thermal imaging of Si NWs embedded in a silica matrix; (d) Si NWs equivalent thermal resistance as a function of the ratio LNW/SNW: circles are used for experimental data and lines for the fits. Reprinted with permission from ref. 241, AIP Publishing LLC.

3.12.2 Principle. Thermal measurements have been investigated using a 3ω SThM method in earlier years, which was able to obtain both thermal images and contact mode topographical images.^242,243

For the 3ω SThM measurement, a sinusoidal current I(t) = I₀ sin(ωt) passed through the thermoresistive probe, generating a Joule heat at pulsation 2ω. The resulting temperature variation T_2ω at the same pulsation then modulated the thermoresistive probe resistance at 2ω. Finally, according to Ohm’s law, the voltage variation at the tip end was a function of 3ω. Then the temperature increase could be expressed as:

where, V_3ω, R₀ and α_R are the third harmonic voltage, electrical resistance at ambient temperature and the temperature coefficient of the tip, respectively.

Therefore, a lock-in measurement of the 3ω output voltage gives insight on the temperature increase of the tip. When the tip contacted with the NW, the heat generated at the tip passed to the sample, and this flow depended on the thermal conductance of the sample (middle of Fig. 11(a)). In other words, the tip temperature variation ΔT_2ω was related with the equivalent thermal resistance R_eq between the tip and the sample. Experimentally, the tip scanned the sample, and, then, the ΔT_2ω tip temperature variation map and the equivalent tip-sample thermal resistance R_eq image could be obtained.²⁴¹

From the equivalent thermal resistance values, the mean thermal conductivity of the NWs could be evaluated. Since the tip was on the top of the NW, the NW equivalent thermal resistance (R_eq)_NW was considered as four thermal resistances in series (shown at right side of Fig. 11(a)),

(R_eq)_NW = R_Tip-NW + R_c + R_NW + R_NW-Sub (3-41)

where R_Tip-NW, R_NW-Sub, R_c and R_NW are the constriction resistance of the heat flux between the tip and the NW, the constriction resistance of the heat flux between the NW and the substrate, the tip–sample contact thermal resistance and the sample intrinsic thermal resistance, respectively.

Fortunately, R_Tip-NW was negligible since the thermal exchange surface was bigger than the NW section. Additionally, both R_NW-Sub and R_c could be estimated.^241,244 As a consequence, the mean NW thermal conductivity could be extracted from the intrinsic thermal resistance R_NW,

where l and A_s are the length and cross section of the NW, respectively.

3.12.3 Merits and shortcomings. This method was able to thermally probe, with a thermal spatial resolution around 100 nm, a wide range of individual NWs embedded in a matrix and it took only a few minutes. Additionally, this method did not require pulling the NWs out from the matrix and suspending it. The intrinsic thermal conductivity of the sample, therefore, could be obtained since it prevented the degradation of the NWs when exposed to air or dissolved in a solution. To obtain reliable thermal conductivities of the NWs, however, both the tip–sample thermal contact resistances, R_c, and the constriction resistance of the heat flux between the NW and the substrate, R_NW-Sub, require careful consideration. For instance, the tip–sample thermal contact resistance has been evaluated as 5.5 × 10⁴ K W⁻¹ which was comparable to the intrinsic thermal resistance of each imaged SiNW.²⁴¹ The value of R_c mostly depended on the experimental conditions, especially on the NW diameter and the thermal exchange diameter between the tip and sample.²⁴⁵ New calibrations of these two resistances and the thermal probe were required for each new sample in order to obtain the thermal conductivities of the NWs accurately.

3.12.4 Applications. The mean thermal conductivity of individual Si NWs, with diameters ranging from 200 to 380 nm embedded in a matrix, as shown in Fig. 11(b), had been measured using SThM method within the 3ω mode by Puyoo et al.²⁴¹ Their SThM thermal imaging of Si NWs embedded in a silica matrix are shown in Fig. 11(c). However, from their results (Fig. 11(d)), no significant thermal conductivity reduction of NWs was observed compared with that of bulk Si. Muñoz Rojo et al.²⁴⁴ had evaluated the mean thermal conductivity of Bi₂Te₃ NWs around 200 nm in diameter using SThM in a 3ω experimental configuration. The estimated mean thermal conductivity of the NWs was (1.37 ± 0.20) W m⁻¹ K⁻¹, showing a slight thermal conductivity reduction. Recently, this method had also been successfully utilized to measure the mean thermal conductivity of SiGe NWs,²⁴⁶ Sb₂Te₃ phase change NWs^245,246 and polymeric P3HT NWs.²⁴⁷

4 Prospects and conclusions

In the past decades, various methods for measuring the 1D nanostructure thermoelectric properties have shown remarkable developments. For practical application of thermoelectric materials, further increasing accuracy and reliability of the measurements is still the main goal. Therefore, the difficulties of the measuring methods, such as the electrical and thermal contact resistances and the noise of the measurements, must be overcome before a universal thermoelectric device can be fabricated. Through reading of papers, analysis and writing of this manuscript, to our knowledge, the following two topics in measuring the 1D nanostructure thermoelectric properties might be increasingly important in the near future. The first involves utilizing specific suspended microstructures to access not only to the thermal conductivity but also to the Seebeck coefficient.^146–150 Hence, these microfabricated structures will offer a route to obtain the figure of merits of the NWs. The second topic is using SThM in a 3ω experimental configuration.^241,244 In this setup, this does not require pulling the NW out from the matrix and suspending it so to prevent the surface modification of the NW. Therefore, the intrinsic thermal conductivity of the NW could be obtained.

In summary, a comprehensive revision of different methods to measure thermoelectric properties of 1D nanostructural materials have been presented. Five frequently used methods to measure the Seebeck coefficient have been reviewed, and twelve of the most popular methods to measure the thermal conductivity have been discussed in detail. In each method, its principle, applications, merits and shortcomings have been presented. Two potential hot topics in measuring the 1D nanostructure thermoelectric properties have been proposed based on a large number of published papers.

Acknowledgements

The authors gratefully acknowledge the support from the National Natural Science Foundation of China under grant numbers 61474115, 61404128, 61372059 and 61274066, and the National High Technology Research and Development Program of China (863 Program) under the grant number 2014AA032302.

References

1. L. E. Bell, Science, 2008, 321, 1457–1461.
2. C. Wu, F. Feng and Y. Xie, Chem. Soc. Rev., 2013, 42, 5157–5183.
3. K. Singh, J. Nowotny and V. Thangadurai, Chem. Soc. Rev., 2013, 42, 1961–1972.
4. N. Linares, A. M. Silvestre-Albero, E. Serrano, J. Silvestre-Albero and J. Garcia-Martinez, Chem. Soc. Rev., 2014, 43, 7681–7717.
5. T. J. Seebeck, Abhandlungen der Deustchen Akademi der Wissenschaften zu Berlin, 1823, pp. 265–373.
6. A. V. Shevelkov, Dalton Trans., 2010, 39, 977.
7. J. H. Bahk, H. Y. Fang, K. Yazawa and A. Shakouri, J. Mater. Chem. C, 2015, 3, 10362–10374.
8. P. Sundarraj, D. Maity, S. S. Roy and R. A. Taylor, RSC Adv., 2014, 4, 46860–46874.
9. J. Wei, Z. B. Nie, G. P. He, L. Hao, L. L. Zhao and Q. Zhang, RSC Adv., 2014, 4, 48128–48134.
10. L. L. Baranowski, G. J. Snyder and E. S. Toberer, Energy Environ. Sci., 2012, 5, 9055–9067.
11. Z. Wang, M. Kroener and P. Woias, TRANSDUCERS 2011-2011 16th International Solid-State Sensors, Actuators and Microsystems Conference, 2011, pp. 1867–1870.
12. M. Arun, Nat. Nanotechnol., 2009, 4, 214–215.
13. I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, D. Koester, R. Alley and R. Venkatasubramanian, Nat. Nanotechnol., 2009, 4, 235–238.
14. J. P. Heremans, M. S. Dresselhaus, L. E. Bell and D. T. Morelli, Nat. Nanotechnol., 2013, 8, 471–473.
15. L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 16631–16634.
16. A. I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J. K. Yu, W. A. Goddard 3rd and J. R. Heath, Nature, 2008, 451, 168–171.
17. A. I. Hochbaum and P. D. Yang, Chem. Rev., 2010, 110, 527–546.
18. V. Varshney, A. K. Roy, D. S. Dudis, J. Lee and B. L. Farmer, Nanoscale, 2012, 4, 5009–5016.
19. W. Shi, S. Song and H. Zhang, Chem. Soc. Rev., 2013, 42, 5714–5743.
20. V. N. Popov, Mater. Sci. Eng., R, 2004, 43, 61–102.
21. J. P. Small and P. Kim, Microscale Thermophys. Eng., 2004, 8, 1–5.
22. A. Druzhinin, I. Ostrovskii, I. Kogut, S. Nichkalo and T. Shkumbatyuk, Phys. Status Solidi C, 2011, 8, 867–870.
23. N. B. Duarte, G. D. Mahan and S. Tadigadapa, Nano Lett., 2009, 9, 617–622.
24. J. P. Feser, J. S. Sadhu, B. P. Azeredo, K. H. Hsu, J. Ma, J. Kim, M. Seong, N. X. Fang, X. Li, P. M. Ferreira, S. Sinha and D. G. Cahill, J. Appl. Phys., 2012, 112, 114306.
25. A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar and P. Yang, Nature, 2008, 451, 163–167.
26. M. Jang, Y. Park, M. Jun, Y. Hyun, S. J. Choi and T. Zyung, Nanoscale Res. Lett., 2010, 5, 1654–1657.
27. F. Y. Ma, Y. Ou, Y. Yang, Y. M. Liu, S. H. Xie, J. F. Li, G. Z. Cao, R. Proksch and J. Y. Li, J. Phys. Chem. C, 2010, 114, 22038–22043.
28. J. Maire and M. Nomura, Jpn. J. Appl. Phys., 2014, 53, 06JE09.
29. Y. Y. Qi, Z. Wang, M. L. Zhang, F. H. Yang and X. D. Wang, J. Phys. Chem. C, 2013, 117, 25090–25096.
30. J. W. Jiang, H. S. Park and T. Rabczuk, Nanoscale, 2013, 5, 11035–11043.
31. G. G. Yadav, G. Zhang, B. Qiu, J. A. Susoreny, X. Ruan and Y. Wu, Nanoscale, 2011, 3, 4078–4081.
32. F. J. DiSalvo, Science, 1999, 285, 703–706.
33. P. Pichanusakorn and P. Bandaru, Mater. Sci. Eng., R, 2010, 67, 19–63.
34. C. Wang, Y. Wang, G. Zhang, C. Peng and G. Yang, Phys. Chem. Chem. Phys., 2014, 16, 3771–3776.
35. J. Li, J. Sui, Y. Pei, X. Meng, D. Berardan, N. Dragoe, W. Cai and L.-D. Zhao, J. Mater. Chem. A, 2014, 2, 4903–4906.
36. W. Zhou, W. Zhao, Z. Lu, J. Zhu, S. Fan, J. Ma, H. H. Hng and Q. Yan, Nanoscale, 2012, 4, 3926–3931.
37. G. Zhang and B. Li, Nanoscale, 2010, 2, 1058–1068.
38. C. H. Will, M. T. Elm, P. J. Klar, B. Landschreiber, E. Güneş and S. Schlecht, J. Appl. Phys., 2013, 114, 193707.
39. Y. Liu, J. Lan, W. Xu, Y. Liu, Y.-L. Pei, B. Cheng, D.-B. Liu, Y.-H. Lin and L. D. Zhao, Chem. Commun., 2013, 49, 8075–8077.
40. T. Zhang, J. Jiang, Y. Xiao, Y. Zhai, S. Yang and G. Xu, J. Mater. Chem. A, 2013, 1, 966–969.
41. A. Yusufu, K. Kurosaki, Y. Miyazaki, M. Ishimaru, A. Kosuga, Y. Ohishi, H. Muta and S. Yamanaka, Nanoscale, 2014, 6, 13921–13927.
42. T. Souier, G. Li, S. Santos, M. Stefancich and M. Chiesa, Nanoscale, 2012, 4, 600–606.
43. J. Liu, J. Sun and L. Gao, Nanoscale, 2011, 3, 3616–3619.
44. Y. Jiang, Z. Wang, M. Shang, Z. Zhang and S. Zhang, Nanoscale, 2015, 7, 10950–10953.
45. H. C. Chang, M. H. Chiang, T. C. Tsai, T. H. Chen, W. T. Whang and C. H. Chen, Nanoscale, 2014, 6, 14280–14288.
46. H. T. Chang, S. Y. Wang and S. W. Lee, Nanoscale, 2014, 6, 3593–3598.
47. S. Bathula, M. Jayasimhadri, B. Gahtori, N. K. Singh, K. Tyagi, A. K. Srivastava and A. Dhar, Nanoscale, 2015, 7, 12474–12483.
48. K. Wang, H.-W. Liang, W.-T. Yao and S.-H. Yu, J. Mater. Chem., 2011, 21, 15057–15062.
49. G. G. Yadav, A. David, T. Favaloro, H. Yang, A. Shakouri, J. Caruthers and Y. Wu, J. Mater. Chem. A, 2013, 1, 11901–11908.
50. E. O. Wrasse, A. Torres, R. J. Baierle, A. Fazzio and T. M. Schmidt, Phys. Chem. Chem. Phys., 2014, 16, 8114–8118.
51. P. Vaqueiro and A. V. Powell, J. Mater. Chem., 2010, 20, 9577–9584.
52. D. Liang, R. Ma, S. Jiao, G. Pang and S. Feng, Nanoscale, 2012, 4, 6265–6268.
53. F. Zhou, A. L. Moore, J. Bolinsson, A. Persson, L. Froberg, M. T. Pettes, H. J. Kong, L. Rabenberg, P. Caroff, D. A. Stewart, N. Mingo, K. A. Dick, L. Samuelson, H. Linke and L. Shi, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 205416.
54. X. Wang and Z. M. Wang, Nanoscale Thermoelectrics, Springer, 2014, p. 16.
55. J. R. Sootsman, D. Y. Chung and M. G. Kanatzidis, Angew. Chem., 2009, 48, 8616–8639.
56. J. R. Szczech, J. M. Higgins and S. Jin, J. Mater. Chem., 2011, 21, 4037–4055.
57. W. Liang, O. Rabin, A. I. Hochbaum, M. Fardy, M. Zhang and P. Yang, Nano Res., 2010, 2, 394–399.
58. C. B. Vining, Nat. Mater., 2009, 8, 83–85.
59. K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis and M. G. Kanatzidis, Science, 2004, 303, 818–821.
60. T. C. Harman, P. J. Taylor, M. P. Walsh and B. E. LaForge, Science, 2002, 297, 2229–2232.
61. R. Venkatasubramanian, E. Siivola, T. Colpitts and B. O’Quinn, Nature, 2001, 413, 597–602.
62. K.-M. Lee, S.-K. Lee and T.-Y. Choi, Appl. Phys. A: Mater. Sci. Process., 2011, 106, 955–960.
63. G. Zhou, L. Li and G. H. Li, Appl. Phys. Lett., 2010, 97, 023112.
64. L. Shi, D. Yao, G. Zhang and B. Li, Appl. Phys. Lett., 2010, 96, 173108.
65. X. Zou, X. Chen, H. Huang, Y. Xu and W. Duan, Nanoscale, 2015, 7, 8776–8781.
66. D. Demchenko, P. Heinz and B. Lee, Nanoscale Res. Lett., 2011, 6, 1–6.
67. Q. Zhang, T. Sun, F. Cao, M. Li, M. Hong, J. Yuan, Q. Yan, H. H. Hng, N. Wu and X. Liu, Nanoscale, 2010, 2, 1256–1259.
68. G. Balasubramanian, I. K. Puri, M. C. Bohm and F. Leroy, Nanoscale, 2011, 3, 3714–3720.
69. L. Lu, W. Yi and D. L. Zhang, Rev. Sci. Instrum., 2001, 72, 2996–3003.
70. M. T. Demko, Z. Dai, H. Yan, W. P. King, M. Cakmak and A. R. Abramson, Rev. Sci. Instrum., 2009, 80, 036103.
71. A. Weathers, K. Bi, M. T. Pettes and L. Shi, Rev. Sci. Instrum., 2013, 84, 084903.
72. A. Boukai, K. Xu and J. R. Heath, Adv. Mater., 2006, 18, 864–869.
73. L. Shi, D. Li, C. Yu, W. Jang, D. Kim, Z. Yao, P. Kim and A. Majumdar, J. Heat Transfer, 2003, 125, 881–888.
74. N. Akhtar and D. Vashaee, 2012 IEEE Green Technologies Conference, 2012, pp. 1–4.
75. G. G. Yadav, J. A. Susoreny, G. Zhang, H. Yang and Y. Wu, Nanoscale, 2011, 3, 3555–3562.
76. A. Bulusu and D. G. Walker, Superlattices Microstruct., 2008, 44, 1–36.
77. Y. Y. Qi, Z. Wang, M. L. Zhang, F. H. Yang and X. D. Wang, J. Mater. Chem. A, 2013, 1, 6110–6124.
78. G. Pennelli, Beilstein J. Nanotechnol., 2014, 5, 1268–1284.
79. S. B. Riffat and X. Ma, Appl. Therm. Eng., 2003, 23, 913–935.
80. C. J. Vineis, A. Shakouri, A. Majumdar and M. G. Kanatzidis, Adv. Mater., 2010, 22, 3970–3980.
81. H. Younghoon, P. Youngsam, C. Wonchul, Z. Taehyoung and J. Moongyu, Nanotechnology Materials and Devices Conference, IEEE, 2011, pp. 194–195.
82. M. M. Rojo, O. C. Calero, A. F. Lopeandia, J. Rodriguez-Viejo and M. Martin-Gonzalez, Nanoscale, 2013, 5, 11526–11544.
83. A. Weathers and L. Shi, Annu. Rev. Heat Transfer, 2013, 16, 101–134.
84. C. H. Lee, G. C. Yi, Y. M. Zuev and P. Kim, Appl. Phys. Lett., 2009, 94, 022106.
85. H. S. Shin, J. S. Lee, S. G. Jeon, J. Yu and J. Y. Song, Measurement, 2014, 51, 470–475.
86. S. Karg, P. Mensch, B. Gotsmann, H. Schmid, P. Das Kanungo, H. Ghoneim, V. Schmidt, M. T. Bjork, V. Troncale and H. Riel, J. Electron. Mater., 2013, 42, 2409–2414.
87. J. P. Small, L. Shi and P. Kim, Solid State Commun., 2003, 127, 181–186.
88. B. C. Stephen, L. Yu-Ming, R. Oded, R. B. Marcie, Y. Y. Jackie, S. D. Mildred, L. G. Pratibha, M. Jean-Paul and I. Jean-Paul, Nanotechnology, 2002, 13, 653–658.
89. A. Mavrokefalos, A. L. Moore, M. T. Pettes, S. Li, W. Wang and X. Li, J. Appl. Phys., 2009, 105, 104318.
90. L. A. Valentín, J. Betancourt, L. F. Fonseca, M. T. Pettes, L. Shi, M. Soszyński and A. Huczko, J. Appl. Phys., 2013, 114, 184301.
91. M. Murata and Y. Hasegawa, Nanoscale Res. Lett., 2013, 8, 400–410.
92. M. Murata, H. Yamamoto, F. Tsunemi, Y. Hasegawa and T. Komine, J. Electron. Mater., 2012, 41, 1442–1449.
93. C. Guthy, C. Y. Nam and J. E. Fischer, J. Appl. Phys., 2008, 103, 064319.
94. E. Shapira, A. Tsukernik and Y. Selzer, Nanotechnology, 2007, 18, 485703.
95. J. A. Martinez, P. P. Provencio, S. T. Picraux, J. P. Sullivan and B. S. Swartzentruber, J. Appl. Phys., 2011, 110, 074317.
96. J.-Y. Yu, S. W. Chung and J. R. Heath, J. Phys. Chem. B, 2000, 104, 11864–11870.
97. S. Y. Jang, H. S. Kim, J. Park, M. Jung, J. Kim, S. H. Lee, J. W. Roh and W. Lee, Nanotechnology, 2009, 20, 415204.
98. Z. Wang, S. S. Adhikari, M. Kroener, D. Kojda, R. Mitdank, S. F. Fischer, W. Toellner, K. Nielsch, P. Woias and Ieee, in 26th Ieee International Conference on Micro Electro Mechanical Systems, 2013, pp. 508–511.
99. E. Z. Xu, Z. Li, J. A. Martinez, N. Sinitsyn, H. Htoon, N. Li, B. Swartzentruber, J. A. Hollingsworth, J. Wang and S. X. Zhang, Nanoscale, 2015, 7, 2869–2876.
100. V. Schmidt, P. F. J. Mensch, S. F. Karg, B. Gotsmann, P. Das Kanungo, H. Schmid and H. Riel, Appl. Phys. Lett., 2014, 104, 012113.
101. H. Younghoon, P. Youngsam, C. Wonchul, K. Jaehyeon, Z. Taehyoung and J. Moongyu, Nanotechnology, 2012, 23, 405707.
102. J. Choi, K. Cho and S. Kim, Microelectron. Eng., 2013, 111, 126–129.
103. Y. M. Zuev, J. S. Lee, C. Galloy, H. Park and P. Kim, Nano Lett., 2010, 10, 3037–3040.
104. P. Mensch, S. Karg, B. Gotsmann, P. Das Kanungo, V. Schmidt, V. Troncale, H. Schmid and H. Riel, 2013 43rd European Solid-State Device Research Conference (ESSDERC). Proceedings, 2013, pp. 252–255.
105. M. Noroozi, B. Hamawandi, M. S. Toprak and H. H. Radamson, International Conference on Ultimate Integration on Silicon, 2014, pp. 125–128.
106. S. Jae Hun, A. L. Moore, S. K. Saha, Z. Feng, S. Li, Q. L. Ye, R. Scheffler, N. Mingo and T. Yamada, J. Appl. Phys., 2007, 101, 023706.
107. H. T. Huang, T. R. Ger, J. W. Chiang, Z. Y. Huang and M. F. Lai, IEEE Trans. Magn., 2014, 50, 1–4.
108. W. Xu, Y. Shi and H. Hadim, Nanotechnology, 2010, 21, 395303.
109. C. Yu, S. Saha, J. Zhou, L. Shi, A. M. Cassell, B. A. Cruden, Q. Ngo and J. Li, J. Heat Transfer, 2006, 128, 234–239.
110. D. Li, A. L. Prieto, W. Yiying, M. S. Martin-Gonzalez, A. Stacy, T. Sands, R. Gronsky, P. Yang and A. Majumdar, 21st International Conference on Thermoelectronics, 2002, pp. 333–336.
111. N. B. Duarte and S. A. Tadigadapa, MEMS/MOEMS Components and Their Applications V. Special Focus Topics: Transducers at the Micro-Nano Interface, 2008, vol. 6885, p. 68850G.
112. S. F. Karg, V. Troncale, U. Drechsler, P. Mensch, P. Das Kanungo, H. Schmid, V. Schmidt, L. Gignac, H. Riel and B. Gotsmann, Nanotechnology, 2014, 25, 305702.
113. E. K. Lee, L. Yin, Y. Lee, J. W. Lee, S. J. Lee, J. Lee, S. N. Cha, D. Whang, G. S. Hwang, K. Hippalgaonkar, A. Majumdar, C. Yu, B. L. Choi, J. M. Kim and K. Kim, Nano Lett., 2012, 12, 2918–2923.
114. Y. Yang, D. K. Taggart, M. H. Cheng, J. C. Hemminger and R. M. Penner, J. Phys. Chem. Lett., 2010, 1, 3004–3011.
115. T. Ono, C. C. Fan and M. Esashi, J. Micromech. Microeng., 2005, 15, 1–5.
116. F. Völklein, H. Reith, M. C. Schmitt, M. Huth, M. Rauber and R. Neumann, J. Electron. Mater., 2009, 39, 1950–1956.
117. S. B. Cronin, Y. M. Lin, M. R. Black, O. Rabin and M. S. Dresselhaus, Xxi International Conference on Thermoelectrics, Proceedings Ict ’02, 2002, pp. 243–248.
118. F. Volklein, M. Schmitt, T. W. Cornelius, O. Picht, S. Muller and R. Neumann, J. Electron. Mater., 2009, 38, 1109–1115.
119. K. Kirihara, T. Sasaki, N. Koshizaki and K. Kimura, Appl. Phys. Express, 2011, 4, 041201.
120. A. Potts, M. J. Kelly, D. G. Hasko, C. G. Smith, J. R. A. Cleaver, H. Ahmed, D. C. Peacock, D. A. Ritchie, J. E. F. Frost and G. A. C. Jones, Microelectron. Eng., 1990, 11, 15–18.
121. S. F. Svensson, A. I. Persson, E. A. Hoffmann, N. Nakpathomkun, H. A. Nilsson, H. Q. Xu, L. Samuelson and H. Linke, New J. Phys., 2012, 14, 033041.
122. E. A. Hoffmann, H. A. Nilsson, L. Samuelson and H. Linke, Physics of Semiconductors: 30th International Conference on the Physics of Semiconductors, 2011, vol. 1399, pp. 397–398.
123. J. Guo, X. Wang and T. Wang, J. Appl. Phys., 2007, 101, 063537.
124. J. Moon, K. Weaver, B. Feng, H. G. Chae, S. Kumar, J. B. Baek and G. P. Peterson, Rev. Sci. Instrum., 2012, 83, 016103.
125. J. Q. Guo, X. W. Wang, D. B. Geohegan and G. Eres, Funct. Mater. Lett., 2008, 1, 71–76.
126. N. K. Mahanta and A. R. Abramson, Rev. Sci. Instrum., 2012, 83, 054904.
127. H. D. Wang, J. H. Liu, X. Zhang, R. F. Zhang and F. Wei, J. Nanosci. Nanotechnol., 2015, 15, 2939–2943.
128. M. C. Wingert, Z. C. Chen, E. Dechaumphai, J. Moon, J. H. Kim, J. Xiang and R. Chen, Nano Lett., 2011, 11, 5507–5513.
129. P. Kim, L. Shi, A. Majumdar and P. McEuen, Phys. Rev. Lett., 2001, 87, 215502.
130. J. Yang, Y. Yang, S. W. Waltermire, T. Gutu, A. A. Zinn, T. T. Xu, Y. Chen and D. Li, Small, 2011, 7, 2334–2340.
131. M. T. Pettes and L. Shi, Adv. Funct. Mater., 2009, 19, 3918–3925.
132. H. Tang, X. Wang, Y. Xiong, Y. Zhao, Y. Zhang, Y. Zhang, J. Yang and D. Xu, Nanoscale, 2015, 7, 6683–6690.
133. C. Yu, L. Shi, Z. Yao, D. Li and A. Majumdar, Nano Lett., 2005, 5, 1842–1846.
134. S. Y. Lee, G. S. Kim, J. Lim, S. Han, B. W. Li, J. T. L. Thong, Y. G. Yoon and S. K. Lee, Acta Mater., 2014, 64, 62–71.
135. G. Yuan, R. Mitdank, A. Mogilatenko and S. F. Fischer, J. Phys. Chem. C, 2012, 116, 13767–13773.
136. A. L. Moore and L. Shi, Meas. Sci. Technol., 2011, 22, 015103.
137. L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 12727–12731.
138. L. Shi, Nanoscale Microscale Thermophys. Eng., 2012, 16, 79–116.
139. M. S. Dresselhaus, G. Chen, M. Y. Tang, R. G. Yang, H. Lee, D. Z. Wang, Z. F. Ren, J. P. Fleurial and P. Gogna, Adv. Mater., 2007, 19, 1043–1053.
140. M. C. Wingert, Z. C. Chen, S. Kwon, J. Xiang and R. Chen, Rev. Sci. Instrum., 2012, 83, 024901.
141. M. C. Wingert, J. Moon, Z. Chen, J. Xiang and R. K. Chen, Proceedings of the Asme International Mechanical Engineering Congress and Exposition, 2012, vol. 11, pp. 385–391.
142. K. Davami, A. Weathers, N. Kheirabi, B. Mortazavi, M. T. Pettes, L. Shi, J. S. Lee and M. Meyyappan, J. Appl. Phys., 2013, 114, 134314.
143. M. Shaygan, N. Kheirabi, K. Davami, B. Mortazavi, J. S. Lee, G. Cuniberti and M. Meyyappan, Mater. Lett., 2014, 135, 87–91.
144. F. Zhou, A. Persson, L. Samuelson, H. Linke and L. Shi, Appl. Phys. Lett., 2011, 99, 063110.
145. J. Zhu, K. Hippalgaonkar, S. Shen, K. Wang, Y. Abate, S. Lee, J. Wu, X. Yin, A. Majumdar and X. Zhang, Nano Lett., 2014, 14, 4867–4872.
146. J. Zhou, C. Jin, J. H. Seol, X. Li and L. Shi, Appl. Phys. Lett., 2005, 87, 133109.
147. H. Kim, Y. H. Park, I. Kim, J. Kim, H. J. Choi and W. Kim, Appl. Phys. A: Mater. Sci. Process., 2011, 104, 23–28.
148. S. C. Andrews, M. A. Fardy, M. C. Moore, S. Aloni, M. Zhang, V. Radmilovic and P. Yang, Chem. Sci., 2011, 2, 706–714.
149. K. Hippalgaonkar, B. Huang, R. Chen, K. Sawyer, P. Ercius and A. Majumdar, Nano Lett., 2010, 10, 4341–4348.
150. Z. Guan, T. Gutu, J. K. Yang, Y. Yang, A. A. Zinn, D. Y. Li and T. T. Xu, J. Mater. Chem., 2012, 22, 9853–9860.
151. C. L. Hsin, M. Wingert, C. W. Huang, H. Guo, T. J. Shih, J. Suh, K. Wang, J. Wu, W. W. Wu and R. Chen, Nanoscale, 2013, 5, 4669–4672.
152. A. L. Moore, M. T. Pettes, F. Zhou and L. Shi, J. Appl. Phys., 2009, 106, 034310.
153. J. Kim, S. Lee, Y. M. Brovman, P. Kim and W. Lee, Nanoscale, 2015, 7, 5053–5059.
154. H. S. Shin, S. G. Jeon, J. Yu, Y. S. Kim, H. M. Park and J. Y. Song, Nanoscale, 2014, 6, 6158–6165.
155. J. E. Sale, M. Bemark, G. T. Williams, C. J. Jolly, M. R. Ehrenstein, C. Rada, C. Milstein and M. S. Neuberger, Philos. Trans. R. Soc. London, Ser. B, 2001, 356, 21–28.
156. J. W. Roh, S. Y. Jang, J. Kang, S. Lee, J. S. Noh, J. Park and W. Lee, J. Korean Inst. Met. Mater., 2010, 48, 175–179.
157. A. Mavrokefalos, M. T. Pettes, S. Saha, Z. Feng and S. Li, Thermoelectrics, 2006. ICT ’06. 25th International Conference on, 2006, pp. 234–237.
158. O. Bourgeois, T. Fournier and J. Chaussy, J. Appl. Phys., 2007, 101, 016104.
159. S. W. Finefrock, Y. Wang, J. B. Ferguson, J. V. Ward, H. Fang, J. E. Pfluger, D. S. Dudis, X. Ruan and Y. Wu, Nano Lett., 2013, 13, 5006–5012.
160. S. Y. Lee, M. R. Lee, N. W. Park, G. S. Kim, H. J. Choi, T. Y. Choi and S. K. Lee, Nanotechnology, 2013, 24, 495202.
161. K. M. Lee, T. Y. Choi, S. K. Lee and D. Poulikakos, Nanotechnology, 2010, 21, 125301.
162. S. Vollebregt, S. Banerjee, A. N. Chiaramonti, F. D. Tichelaar, K. Beenakker and R. Ishihara, J. Appl. Phys., 2014, 116, 023514.
163. H.-F. Lee, B. A. Samuel and M. A. Haque, J. Therm. Anal. Calorim., 2009, 99, 495–500.
164. C. Dames and G. Chen, Rev. Sci. Instrum., 2005, 76, 124902.
165. J. Hou, X. Wang, P. Vellelacheruvu, J. Guo, C. Liu and H.-M. Cheng, J. Appl. Phys., 2006, 100, 124314.
166. O. M. Corbino, Phys. Z., 1910, 11, 413–417.
167. D. G. Cahill, Rev. Sci. Instrum., 1990, 61, 802.
168. D. G. Cahill and R. O. Pohl, Phys. Rev. B: Condens. Matter Mater. Phys., 1987, 35, 4067–4073.
169. S. M. Lee and S. I. Kwun, Rev. Sci. Instrum., 1994, 65, 966–970.
170. I. K. Moon, Y. H. Jeong and S. I. Kwun, Rev. Sci. Instrum., 1996, 67, 29–35.
171. L. R. Holland and R. C. Smith, J. Appl. Phys., 1966, 37, 4528–4536.
172. J. H. Kim, A. Feldman and D. Novotny, J. Appl. Phys., 1999, 86, 3959–3963.
173. C. E. Raudzis, F. Schatz and D. Wharam, J. Appl. Phys., 2003, 93, 6050–6055.
174. G. D. Li, D. Liang, R. L. J. Qiu and X. P. A. Gao, Appl. Phys. Lett., 2013, 102, 043104.
175. H. Wang and M. Sen, Int. J. Heat Mass Transfer, 2009, 52, 2102–2109.
176. H. C. Chang, C. H. Chen and Y. K. Kuo, Nanoscale, 2013, 5, 7017–7025.
177. D. Yang, C. Lu, H. Yin and I. P. Herman, Nanoscale, 2013, 5, 7290–7296.
178. J. Lu, R. Guo, W. Dai and B. Huang, Nanoscale, 2015, 7, 7331–7339.
179. S. T. Huxtable, A. R. Abramson, C. L. Tien, A. Majumdar, C. LaBounty, X. Fan, G. H. Zeng, J. E. Bowers, A. Shakouri and E. T. Croke, Appl. Phys. Lett., 2002, 80, 1737–1739.
180. C. Zhen, J. Yang and Y. Chen, IEEE International Conference on Nano/micro Engineered and Molecular Systems, 2006, pp. 283–286.
181. T. Y. Choi, M. H. Maneshian, B. Kang, W. S. Chang, C. S. Han and D. Poulikakos, Nanotechnology, 2009, 20, 315706.
182. F. Chen, J. Shulman, Y. Xue, C. W. Chu and G. S. Nolas, Rev. Sci. Instrum., 2004, 75, 4578–4584.
183. Y. Hasegawa, M. Murata, F. Tsunemi, Y. Saito, K. Shirota, T. Komine, C. Dames and J. E. Garay, J. Electron. Mater., 2013, 42, 2048–2055.
184. J. Xie, A. Frachioni, D. S. Williams and B. E. White Jr, Appl. Phys. Lett., 2013, 102, 193101.
185. B. Hamdou, A. Beckstedt, J. Kimling, A. Dorn, L. Akinsinde, S. Bassler, E. Pippel and K. Nielsch, Nanotechnology, 2014, 25, 365401.
186. L. Li, C. Jin, S. Xu, J. Yang, H. Du and G. Li, Nanotechnology, 2014, 25, 415704.
187. S. Dhara, H. S. Solanki, A. R. Pawan, V. Singh, S. Sengupta, B. A. Chalke, A. Dhar, M. Gokhale, A. Bhattacharya and M. M. Deshmukh, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 84, 121307.
188. T. C. Hsiung, C. Y. Mou, T. K. Lee and Y. Y. Chen, Nanoscale, 2015, 7, 518–523.
189. T. Y. Choi, D. Poulikakos, J. Tharian and U. Sennhauser, Appl. Phys. Lett., 2005, 87, 013108.
190. T. Y. Choi, D. Poulikakos, J. Tharian and U. Sennhauser, Nano Lett., 2006, 6, 1589–1593.
191. C. Xing, C. Jensen, T. Munro, B. White, H. Ban and M. Chirtoc, Appl. Therm. Eng., 2014, 73, 317–324.
192. B. Feng, Z. X. Li, X. Zhang and G. P. Peterson, J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.--Process., Meas., Phenom., 2009, 27, 2280–2285.
193. C. Xing, C. Jensen, T. Munro, B. White, H. Ban and M. Chirtoc, Appl. Therm. Eng., 2014, 71, 589–595.
194. P. C. Lee, H. C. Chen, C. M. Tseng, W. C. Lai, C. H. Lee, C. S. Chang and Y. Y. Chen, Chin. J. Phys., 2013, 51, 854–861.
195. M. Fujii, X. Zhang and K. Takahashi, Phys. Status Solidi B, 2006, 243, 3385–3389.
196. X. Zhang, S. Fujiwara and M. Fujii, Int. J. Thermophys., 2000, 21, 965–980.
197. J. L. Wang, M. Gu, X. Zhang and Y. Song, J. Phys. D: Appl. Phys., 2009, 42, 105502.
198. M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe and T. Shimizu, Phys. Rev. Lett., 2005, 95, 065502.
199. Y. Ito, K. Takahashi, M. Fujii and X. Zhang, Heat Transfer-Asian Research, 2009, 38, 297–312.
200. C. T. Harris, J. A. Martinez, E. A. Shaner, J. Y. Huang, B. S. Swartzentruber, J. P. Sullivan and G. Chen, Nanotechnology, 2011, 22, 275308.
201. X. Zhang and J. L. Wang, Proceedings of the Asme 9th International Conference on Nanochannels, Microchannels and Minichannels, 2011, vol. 2, pp. 707–712.
202. J. Wang and X. Zhang, Jpn. J. Appl. Phys., 2011, 50, 11RC01.
203. C. Dames, S. Chen, C. T. Harris, J. Y. Huang, Z. F. Ren, M. S. Dresselhaus and G. Chen, Rev. Sci. Instrum., 2007, 78, 104903.
204. M. F. P. Bifano, J. Park, P. B. Kaul, A. K. Roy and V. Prakash, J. Appl. Phys., 2012, 111, 054321.
205. A.-T. Chien, P. V. Gulgunje, H. G. Chae, A. S. Joshi, J. Moon, B. Feng, G. P. Peterson and S. Kumar, Polymer, 2013, 54, 6210–6217.
206. J. B. Hou, X. W. Wang and J. Q. Guo, J. Phys. D: Appl. Phys., 2006, 39, 3362–3370.
207. J. B. Hou, X. W. Wang and L. J. Zhang, Appl. Phys. Lett., 2006, 89, 152504.
208. B. Feng, W. G. Ma, Z. X. Li and X. Zhang, Rev. Sci. Instrum., 2009, 80, 064901.
209. J. Q. Guo, X. W. Wang, D. B. Geohegan, G. Eres and C. Vincent, J. Appl. Phys., 2008, 103, 113505.
210. J. W. Tan, Y. Cheng, D. S. G. Yap, F. Gong, S. T. Nguyen and H. M. Duong, Chem. Phys. Lett., 2013, 555, 239–246.
211. J. Guo, X. Wang, L. Zhang and T. Wang, Appl. Phys. A: Mater. Sci. Process., 2007, 89, 153–156.
212. X. Feng, X. Wang, X. Chen and Y. Yue, Acta Mater., 2011, 59, 1934–1944.
213. X. Feng and X. Wang, Thin Solid Films, 2011, 519, 5700–5705.
214. X. Huang, J. Wang, G. Eres and X. Wang, Carbon, 2011, 49, 1680–1691.
215. G. Liu, H. Lin, X. Tang, K. Bergler and X. Wang, J. Visualized Exp., 2014, 83, e51144.
216. F. Gong, Y. Cheng, J. W. Tan, S. G. D. Yap, S. T. Nguyen and H. M. Duong, Int. J. Therm. Sci., 2014, 77, 165–171.
217. C. Xing, T. Munro, C. Jensen and H. Ban, Meas. Sci. Technol., 2013, 24, 105603.
218. T. Wang, X. Wang, J. Guo, Z. Luo and K. Cen, Appl. Phys. A: Mater. Sci. Process., 2007, 87, 599–605.
219. Y. A. Yue, G. Eres, X. W. Wang and L. Y. Guo, Appl. Phys. A: Mater. Sci. Process., 2009, 97, 19–23.
220. Q. Li, C. Liu, X. Wang and S. Fan, Nanotechnology, 2009, 20, 145702.
221. H. Scheel, S. Reich, A. C. Ferrari, M. Cantoro, A. Colli and C. Thomsen, Appl. Phys. Lett., 2006, 88, 233114.
222. P. Puech, A. Anwar, E. Flahaut, D. Dunstan, A. Bassil and W. Bacsa, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 085418.
223. J. Yang, S. Waltermire, Y. Chen, A. A. Zinn, T. T. Xu and D. Li, Appl. Phys. Lett., 2010, 96, 023109.
224. J. Liu, H. Wang, W. Ma, X. Zhang and Y. Song, Rev. Sci. Instrum., 2013, 84, 044901.
225. Y. Yue, X. Huang and X. Wang, Phys. Lett. A, 2010, 374, 4144–4151.
226. M. Soini, I. Zardo, E. Uccelli, S. Funk, G. Koblmüller, A. Fontcuberta i Morral and G. Abstreiter, Appl. Phys. Lett., 2010, 97, 263107.
227. Z. L. Wang, X. J. Chen, Q. Yan and J. Zhang, EPL, 2012, 100, 14002.
228. G. S. Doerk, C. Carraro and R. Maboudian, ACS Nano, 2010, 4, 4908–4914.
229. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao and C. N. Lau, Nano Lett., 2008, 8, 902–907.
230. W. Cai, A. L. Moore, Y. Zhu, X. Li, S. Chen, L. Shi and R. S. Ruoff, Nano Lett., 2010, 10, 1645–1651.
231. I. K. Hsu, R. Kumar, A. Bushmaker, S. B. Cronin, M. T. Pettes, L. Shi, T. Brintlinger, M. S. Fuhrer and J. Cumings, Appl. Phys. Lett., 2008, 92, 063119.
232. H. D. Wang, J. H. Liu, X. Zhang and Y. Song, Int. J. Heat Mass Transfer, 2014, 70, 40–45.
233. Q. Y. Li and X. Zhang, Thermochim. Acta, 2014, 581, 26–31.
234. H. Yan, N. K. Mahanta, L. J. Majerus, A. R. Abramson and M. Cakmak, Polym. Eng. Sci., 2014, 54, 977–983.
235. L. J. Majerus, Application of the Thermal Flash Technique for Characterizing High Thermal Diffusivity Micro and Nanostructures, Case Western Reserve University, 2009.
236. N. K. Mahanta, A. R. Abramson and J. Y. Howe, J. Appl. Phys., 2013, 114, 163528.
237. N. K. Mahanta and A. R. Abramson, Proceedings of the ASME/JSME 2011 8th Thermal Engineering Joint Conference, 2011, vol. 3, pp. 181–187.
238. Y. Zhang, J. Christofferson, A. Shakouri, D. Y. Li, A. Majumdar, Y. Y. Wu, R. Fan and P. D. Yang, IEEE Trans. Nanotechnol., 2006, 5, 67–74.
239. J. Christofferson, D. Vashaee, A. Shakouri and P. Melese, Metrology-based Control for Micro-Manufacturing, 2001.
240. D. Y. Li, Y. Y. Wu, P. Kim, L. Shi, P. D. Yang and A. Majumdar, Appl. Phys. Lett., 2003, 83, 2934–2936.
241. E. Puyoo, S. Grauby, J. M. Rampnoux, E. Rouviere and S. Dilhaire, J. Appl. Phys., 2011, 109, 024302.
242. S. P. Lefèvre and S. Volz, Rev. Sci. Instrum., 2005, 76, 033701.
243. L. Shi, S. Plyasunov, A. Bachtold, P. L. McEuen and A. Majumdar, Appl. Phys. Lett., 2000, 77, 4295.
244. M. Muñoz Rojo, S. Grauby, J. M. Rampnoux, O. Caballero-Calero, M. Martin-Gonzalez and S. Dilhaire, J. Appl. Phys., 2013, 113, 054308.
245. S. Grauby, E. Puyoo, J. M. Rampnoux, E. Rouviere and S. Dilhaire, J. Phys. Chem. C, 2013, 117, 9025–9034.
246. A. Saci, J. L. Battaglia, A. Kusiak, R. Fallica and M. Longo, Appl. Phys. Lett., 2014, 104, 263103.
247. M. M. Rojo, J. Martin, S. Grauby, T. Borca-Tasciuc, S. Dilhaire and M. Martin-Gonzalez, Nanoscale, 2014, 6, 7858–7865.

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