TY - JOUR
AU - Li, Jiangyu
AB - Abstract In the last two decades, a nanostructuring paradigm has been successfully applied in a wide range of thermoelectric materials, resulting in significant reduction in thermal conductivity and superior thermoelectric performance. These advances, however, have been accomplished without directly investigating the local thermoelectric properties, even though local electric current can be mapped with high spatial resolution. In fact, there still lacks an effective method that links the macroscopic thermoelectric performance to the local microstructures and properties. Here, we show that local thermal conductivity can be mapped quantitatively with good accuracy, nanometer resolution and one-to-one correspondence to the microstructure using a three-phase skutterudite as a model system. Scanning thermal microscopy combined with finite element simulations demonstrate close correlation between sample conductivity and probe resistance, enabling us to distinguish thermal conductivities spanning orders of magnitude, yet resolving thermal variation across a phase interface with small contrast. The technique thus provides a powerful tool to correlate local thermal conductivities, microstructures and macroscopic properties for nanostructured materials in general and nanostructured thermoelectrics in particular. thermal conductivity, scanning thermal microscopy, thermoelectric materials, nanoscale heat transfer, thermal imaging INTRODUCTION Solid-state thermoelectric conversion is promising for recovering tremendous waste heat produced by human society and for enabling more effective thermal management. However, the high thermoelectric conversion efficiency, governed by the dimensionless figure of merit ZT, requires simultaneously high electrical conductivity and Seebeck coefficient, yet low thermal conductivity, which are rather difficult to obtain in a single-phase material [1–5]. One of the primary mechanisms for improving thermoelectric performance in a material is to reduce lattice thermal conductivity through scattering of phonons by structural heterogeneity such as defects, interfaces and impurities. In the last two decades, the nanostructuring paradigm has been successfully applied to a wide range of thermoelectric materials, resulting in significant reduction in thermal conductivity and superior thermoelectric performance [6–12]. For example, nanocrystalline (Bi,Sb)2Te3 with maximum ZT values of 1.4–1.6 were reported [7,13–15] and the improvement was largely attributed to the low lattice thermal conductivity resulting from intensified phonon scattering by nanostructures and defects [16]. In addition, by combining all-scale hierarchical architectural microstructures, including atomic defects, endotaxial nanoprecipitates and mesoscale grains [17], a wide range of heat-carrying phonons can be strongly scattered [9], resulting in record high ZTs in PbTe [17]. Similar reduction in thermal conductivity has also been reported in many nanocomposites, such as systems consisting of half-Heusler/full-Heusler and InxCeyCo4Sb12/InSb [18]. These advances in thermoelectric materials highlight the importance of nanostructuring in enhancing thermoelectric properties, yet, quite surprisingly, such improvements have been largely accomplished with no direct investigation of the local thermoelectric properties in nanostructured materials, even though local electric current can be mapped with high spatial resolution. Indeed, there still lacks an effective method that directly links the macroscopic thermoelectric performance to the local microstructures and properties. While the microstructural heterogeneity can be mapped with atomic resolution in terms of chemical and phase compositions, it reveals little about local transport behavior. Traditionally, the thermoelectric properties are only measured at the macroscopic scale, averaged over various microstructural features, and it is rather difficult to know exactly and directly which material constituent contributes to what in the local thermal transport processes. Therefore, high spatial resolution is critically needed in the thermal analysis of nanostructured materials in general, and nanostructured thermoelectrics in particular. In the last decade, time domain thermoreflectance (TDTR) has emerged as a powerful tool for thermal transport property measurements [19,20], though its spatial resolution is limited to hundreds of nanometers [21–24], making the detailed mapping of thermal transport properties in nanostructured materials challenging. Various scanning thermal microscopy (SThM) techniques have been developed based on temperature-sensitive phenomena in the sample, promising potentially higher spatial resolutions [25–36], though they have rarely provided even a qualitative thermal mapping that correlates with the microstructures in a heterogeneous material, and strong crosstalk between thermal imaging and surface topography is often observed. Such direct correlation, especially in a quantitative manner, is highly desirable for understanding as well as further designing and optimization of high-performance thermoelectric materials, which we seek to accomplish via tightly coupled SThM experiments and finite element simulations utilizing a resistive heating thermal probe. In this work, we show that local thermal conductivity can be mapped quantitatively with good accuracy, nanometer resolution and one-to-one correspondence to the microstructure, using filled skutterudite as a model system. Yb-filled CoSb3, with its maximum ZT up to 1.5, is one of the most promising thermoelectric materials for applications in the intermediate temperature range, since guest filling in the structural nanovoids acts to control the carrier concentration, while significantly suppressing the propagation of heat-carrying phonons [37–39]. However, impurity phases such as YbSb2, Yb2O3 and CoSb2 are commonly observed due to the filling fraction limit of approximately 0.3 in YbxCo4Sb12, low formation energy of Yb oxide and complexity in the Yb-Co-Sb phase diagram, and these impurity phases could exert significant influence on thermoelectric properties [40]. It thus provides us with an ideal model system to study its local thermal and electric conductivities. RESULTS Three-phase microstructure The sample with a stoichiometry of Yb0.7Co4Sb12 was prepared by a conventional induction melting-vacuum melting-quenching-annealing-sintering method, resulting in a three-phase microstructure as shown in Fig. 1. A back-scattered electron (BSE) image of the sample clearly reveals three phases as marked (Fig. 1a), with impurity phases 2 and 3 embedded in the matrix phase 1. It is anticipated that the excessively added Yb reacts with Sb to form the YbSb2 phase, and the resultant Sb-deficiency leads to the formation of CoSb2. Such scenarios are indeed confirmed by the elemental mappings of Yb, Co, Sb and O (Fig. 1b–e) as well as elemental ratios in each phases determined from the energy-dispersive X-ray spectroscopy (EDS) (Fig. 1f and Supplementary Fig. 1, available as Supplementary Data at NSR online), suggesting that the matrix phase 1 is filled skutterudite Yb0.3Co4Sb12, while the impurity phases 2 and 3 are CoSb2 and surface-oxidized YbSb2, respectively. This analysis of phase composition is also confirmed by X-ray diffraction shown in Supplementary Fig. 2 (available as Supplementary Data at NSR online). Figure 1. Open in new tabDownload slide Composition analyses of three-phase microstructure in a Yb0.7Co4Sb12; (a) a typical BSE image, wherein the three phases are labeled as 1, 2 and 3; (b)–(e) corresponding elemental mappings of Yb, Co, Sb and O for the area shown in (a); (f) a typical EDS spectrum of phase 1, and elemental ratios of three different phases labeled in (a). Figure 1. Open in new tabDownload slide Composition analyses of three-phase microstructure in a Yb0.7Co4Sb12; (a) a typical BSE image, wherein the three phases are labeled as 1, 2 and 3; (b)–(e) corresponding elemental mappings of Yb, Co, Sb and O for the area shown in (a); (f) a typical EDS spectrum of phase 1, and elemental ratios of three different phases labeled in (a). Scanning thermal microscopy The microstructural analysis in Fig. 1 is powerful in mapping local chemical composition and phase structure of a material, yet it reveals nothing about the local thermoelectric properties. Traditionally, such properties are measured at the macroscopic scale, and their local variations, if any, can only be deduced indirectly from the macroscopic measurement or from computational analyses. If one can correlate local thermal properties directly with the microstructural features, then the effect of structural heterogeneity on the macroscopic thermoelectric conversion can be better understood and optimized. We seek to accomplish this via a scanning thermal probe [29,41,42], as shown in Fig. 2a. It has a micro-fabricated solid-state resistive heater at the end of the cantilever [31,43–46], which forms one branch of the Wheatstone bridge circuit that allows precise measurement of its electrical resistance. When the probe scan phases with lower (Fig. 2b) and higher (Fig. 2c) thermal conductivities, it will have lower and higher temperature drops, respectively, resulting in different probe resistances that can be measured accurately from the imbalanced Wheatstone bridge voltage. This enables us to image local thermal response quantitatively. Indeed, as shown in Fig. 2d, there is a linear relationship between probe resistance and temperature around the SThM operation temperature, calibrated by passively probing a hot-plate stage with well-defined temperatures: \begin{equation} R(T) = {R_0}({1 + \alpha ({T - {T_0}})}),\end{equation} (1) where R0 is the resistance of the thermal probe at room-temperature reference T0 = 293.15 K and α is the temperature coefficient of resistance (TCR) measured to be 0.8/K between 350 and 450 K (Fig. 2d)—the temperature range relevant to our subsequent experiments. As such, the thermal probe functions not only as a heater, but also as a local temperature sensor via the resistance measurement, making it possible to measure the local thermal properties of the sample quantitatively [25,47]. Figure 2. Open in new tabDownload slide The schematics of SThM setup; (a) resistive heating thermal probe in a balanced Wheatstone bridge circuit (VA − VB = 0) before touching the sample; the thermal probe scans phases with (b) lower and (c) higher thermal conductivities, resulting in different probe temperatures that can be measured via imbalanced Wheatstone bridge for imaging; (d) linear correlation between temperature and resistance of the thermal probe calibrated by a hot plate with known temperatures. Figure 2. Open in new tabDownload slide The schematics of SThM setup; (a) resistive heating thermal probe in a balanced Wheatstone bridge circuit (VA − VB = 0) before touching the sample; the thermal probe scans phases with (b) lower and (c) higher thermal conductivities, resulting in different probe temperatures that can be measured via imbalanced Wheatstone bridge for imaging; (d) linear correlation between temperature and resistance of the thermal probe calibrated by a hot plate with known temperatures. In order to precisely measure the change in resistance induced by heat transfer to areas with different thermal conductivities, the Wheatstone bridge is balanced by adjusting the variable resistor before contacting the sample, and the bridge voltage is amplified with a 10× gain using a differential amplifier for enhanced sensitivity. After it touches the sample, heat transfers from the probe to the sample, resulting in drops in its temperature and resistance, and thus a voltage drop between nodes A and B of the Wheatstone bridge. Lower sample thermal conductivity has lower heat loss and thus a lower drop in resistance, corresponding to lower bridge voltage difference (Fig. 2b). Hence higher voltage difference indicates a higher sample thermal conductivity (Fig. 2c), making it possible to image local thermal conductivity variation based on the bridge voltage. With a marker made near the area of the BSE image (Supplementary Fig. 3, available as Supplementary Data at NSR online), we were able to locate the same area in our SThM studies. The topography mapping in Fig. 3a obtained from the contact mode reveals relatively flat surface without any correlation with the microstructure shown in BSE image of Fig. 1. However, simultaneously to the topography scan, the mapping of Wheatstone bridge voltage difference in Fig. 3b clearly reveals three different contrasts that correlate well with the BSE microstructure, repeated here in Fig. 3c for a direct comparison. Due to the drop in the probe temperature, and thus the resistance, the Wheatstone bridge voltage drops to negative. The matrix phase 1 has the smallest voltage drop, while the impurity phase 2 has the largest. Such contrast is induced by the difference in thermal conductivity, not from the topography variation, as evident by the line scan comparison in Fig. 3d. When a phase interface is crossed, sharp change in voltage difference is observed, while topography is relatively flat. On the other hand, within an individual phase, voltage difference is roughly constant, while topography variation is observed. The voltage difference mapped thus reflects the variation in thermal conductivity with no crosstalk to topography, wherein the matrix phase has the lowest thermal conductivity, while the impurity phase 2 has the highest. Thus, this is a direct characterization of local thermal conductivity that illustrates the role of impurity phases in thermal transport. Higher-resolution scans of two boxes marked in Fig. 3b are shown in Fig. 3e and f, demonstrating even higher sensitivity and spatial resolution. It is worth noting that, although YbSb2 (phase 3) is supposed to have the highest thermal conductivity, it appears that the significant surface oxidation reduces its thermal conductivity, resulting in intermediate voltage drops as mapped. Figure 3. Open in new tabDownload slide SThM mapping of Yb0.7Co4Sb12; (a) topography; (b) distribution of Wheatstone bridge voltage with 10× amplification; (c) BSE image; (d) comparison of line scans in topography and voltage mappings; (e) and (f) higher-resolution voltage mapping in smaller areas. Figure 3. Open in new tabDownload slide SThM mapping of Yb0.7Co4Sb12; (a) topography; (b) distribution of Wheatstone bridge voltage with 10× amplification; (c) BSE image; (d) comparison of line scans in topography and voltage mappings; (e) and (f) higher-resolution voltage mapping in smaller areas. Finite element simulation In order to interpret and analyse the SThM data quantitatively, a finite element model (FEM) implemented in the COMSOL Multiphysics package was developed to study heat transfer among the thermal probe, the sample and surrounding air, as shown in Supplementary Fig. 4 (available as Supplementary Data atNSR online). Two dominant physical processes were considered: one is Joule heating in the resistive heater of thermal probe, and the other is heat conduction in the thermal probe, sample and surrounding air. The quasi-steady problem was solved using a stationary solver based on the conduction equation \begin{equation} {-}\nabla \cdot \left( {\kappa \nabla T} \right) = \ Q,\end{equation} (2) where κ is the thermal properties of each domain listed in Supplementary Table 1 (available as Supplementary Data at NSR online) and Q is the heat source, set to be zero in all domains except in the resistive heater part of the thermal probe under an input voltage V0, \begin{equation}Q\ = \frac{{V_0^2}}{{R\left( T \right)}}\ .\end{equation} (3) It is important to recognize that the temperatures of the thermal probe and its resistance are intimately coupled, resulting in a nonlinear governing equation to solve. In the simulations, the initial value of temperature is set as T0 = 293.15 K for all domains, and the external boundaries of air-box and the sample (far from the thermal probe) are set to have ambient temperature T = T0 as well. Across interfaces between different domains, temperature and heat flux density are assumed to be continuous, except on the tip-sample contact wherein a thermal contact resistance of 1.0 × 108 K/W was defined, which was measured using similar type of SThM probe as in a previous study [48]. The presence of the contact resistance results in significant temperature drop at the tip-sample junction but rather small temperature increase in the resistive heater that is more relevant for the measurement (Supplementary Fig. 5, available as Supplementary Data at NSR online). More importantly, the temperature of the resistive heater is sensitive to the change in thermal conductivity of the sample, but insensitive to the contact resistance (Supplementary Fig. 6, available as Supplementary Data at NSR online), as the total heat loss due to the contact resistance is less than 1 μW while the total heat conductance through tip-sample junction is in the order of 100 μW. We also point out that the radiative and convective heat losses, as shown in Supplementary Figs 7 and 8 (available as Supplementary Data at NSR online), are negligible in comparison to the heat conduction, and thus are not considered. More detailed analysis can be found in the Supplementary Data available at NSR online. We first examine the thermal probe in air, far away from the sample. Under an input voltage of 3.5 V, the temperature distribution is shown in Fig. 4a and b, indicating a substantial temperature rise in the thermal probe up to 683 K. The resistance of the probe is expected to rise with the increased input voltage in a nonlinear manner, caused by the higher temperature induced by the heating voltage. This is confirmed in Fig. 4c, wherein good agreement between the experimental measurement and FEM simulation is observed, giving us confidence that the simulation does capture the physical processes in SThM experiments accurately. We then in our simulation bring the thermal probe into contact with a sample having a thermal conductivity of κ = 5W/(m.K), and the increased heat conduction through probe-sample junction results in a drop in the probe temperature, and thus a drop in its resistance. Analysis on the overall heat flux and temperature distributions suggests that only a few percentage of the generated heat passes to the sample through the contact via heat conduction. Nevertheless, due to the small contact area of the probe-sample junction, the heat flux density is substantial, and the resulting temperature drop in the thermal probe is significant, at around 190 K. These are evident in the distributions of heat flux density and temperature in the probe-sample junction shown in Fig. 4d and e. Note the significant temperature drop observed at the contact, yet the problem can be treated as quasi-static, and thus the temperature drop does not significantly influence the temperature of the resistive heater, as compared in Supplementary Fig. 5 (available as Supplementary Data at NSR online). Further zoom-in on the sample in Fig. 4f and g shows that the radius of the sample thermal volume affected by the probe is less than 100 nm, within which around 90% of the temperature variation in the sample occurs. This confirms the nanoscale resolution of our SThM technique. Figure 4. Open in new tabDownload slide FEM simulation of the SThM experiment; (a)–(c) when the probe is held in air: (a) 3D and (b) cross-sectional temperature distribution of thermal probe under 3.5 V; (c) measured probe resistance as a function of DC drive voltage in comparison with simulation; (d)–(g) when the probe is in contact with a homogeneous sample having κ = 5W/(m.K), and the contact resistance is taken to be 1.0 × 108 K/W; cross-sectional distribution of (d) heat flux density and (e) temperature on the tip-sample junction; and overlaid contour on the distribution of (f) heat flux distribution and (g) temperature in the sample underneath the probe. Figure 4. Open in new tabDownload slide FEM simulation of the SThM experiment; (a)–(c) when the probe is held in air: (a) 3D and (b) cross-sectional temperature distribution of thermal probe under 3.5 V; (c) measured probe resistance as a function of DC drive voltage in comparison with simulation; (d)–(g) when the probe is in contact with a homogeneous sample having κ = 5W/(m.K), and the contact resistance is taken to be 1.0 × 108 K/W; cross-sectional distribution of (d) heat flux density and (e) temperature on the tip-sample junction; and overlaid contour on the distribution of (f) heat flux distribution and (g) temperature in the sample underneath the probe. Quantitative mappings of local properties Are we capable of experimentally distinguishing materials with different thermal conductivities then? To answer this question, both FEM simulations and SThM experiments were carried out on a dozen or so samples with nominal thermal conductivities ranging from 0.66 to 80.8 W/mK, spanning two orders of magnitude, as listed in Supplementary Table 2 (available as Supplementary Data at NSR online). Under a constant 3.5-V input to the thermal probe, the drop in the resistances when the probe contacts the samples was predicted by FEM simulations and measured by SThM experiments, as shown in Fig. 5a. The point-wise experiments were repeated five times on each calibration sample in different areas, and the mean and standard deviations were obtained with the SThM contact force kept constant throughout all the experiments. In the simulation, a constant contact resistance of 1.0 × 108 K/W is assumed, as explained earlier, and the results suggest that the thermal contact resistance is only significant for samples with higher thermal conductivity, consistent with what we observed in Supplementary Fig. 6 (available as Supplementary Data at NSR online). The good agreement between simulations and experiments observed in Fig. 5a suggests that the thermal conductivity of the sample and the resistance drop can be quantitatively correlated. Indeed, for the three-phase microstructure mapped in Fig. 3, the distribution of resistance change, shown here in Fig. 5b, can be directly converted into a mapping of thermal conductivity shown in Fig. 5c based on this correlation. The resulting thermal conductivities in the three phases are summarized in Table 1, and good agreements with nominal values reported in literature are observed [39,49,50], validating quantitative SThM mapping. Of particular interests is the variation in thermal response at an interface between two phases, for which we investigated an interface marked by the dashed line in the box in Fig. 3f, passing from phase 3 to phase 1. The variation of expected resistance change when the probe scans across the interface is simulated by FEM and compared with experiments, and again good agreement is observed, as shown in Fig. 5d, with quantitative difference much less than 1%. FEM simulations were carried out under nominal thermal conductivity distributions with a sharp interface, as indicated by the blue line in Fig. 5d, while the transition length of thermal response variation is in the order of 100 nm for both experiment and simulation. Note that we have not considered the interfacial resistance in our analysis. Figure 5. Open in new tabDownload slide Quantitative mapping of thermal conductivities; (a) changes in the probe resistance induced by samples with different thermal conductivities; and mappings of (b) resistance change and (c) corresponding thermal conductivities in Yb0.7Co4Sb12; (d) line scan of resistance change across an interface between phase 1 and phase 3. Figure 5. Open in new tabDownload slide Quantitative mapping of thermal conductivities; (a) changes in the probe resistance induced by samples with different thermal conductivities; and mappings of (b) resistance change and (c) corresponding thermal conductivities in Yb0.7Co4Sb12; (d) line scan of resistance change across an interface between phase 1 and phase 3. Table 1. Comparison of thermal conductivities measured from SThM experiment and reported in the literature at 300 K. κ [W/(m.K)] . Yb0.3Co4Sb12a . CoSb2b . YbSb2 . Yb2O3c . Phase 1 2 3 3 Measured 4.63 11.71 – 9.52 Reported 3.2 11.8 15.0 – Remarks Polycrystal Single-crystal Polycrystal Surface-oxidized κ [W/(m.K)] . Yb0.3Co4Sb12a . CoSb2b . YbSb2 . Yb2O3c . Phase 1 2 3 3 Measured 4.63 11.71 – 9.52 Reported 3.2 11.8 15.0 – Remarks Polycrystal Single-crystal Polycrystal Surface-oxidized aRef. [39]; bRef. [49]; cRef. [50]. Open in new tab Table 1. Comparison of thermal conductivities measured from SThM experiment and reported in the literature at 300 K. κ [W/(m.K)] . Yb0.3Co4Sb12a . CoSb2b . YbSb2 . Yb2O3c . Phase 1 2 3 3 Measured 4.63 11.71 – 9.52 Reported 3.2 11.8 15.0 – Remarks Polycrystal Single-crystal Polycrystal Surface-oxidized κ [W/(m.K)] . Yb0.3Co4Sb12a . CoSb2b . YbSb2 . Yb2O3c . Phase 1 2 3 3 Measured 4.63 11.71 – 9.52 Reported 3.2 11.8 15.0 – Remarks Polycrystal Single-crystal Polycrystal Surface-oxidized aRef. [39]; bRef. [49]; cRef. [50]. Open in new tab We also examined the electrical conductivity of the sample in the same area using a conductive AFM (cAFM), as shown in Fig. 6, where good correlation between current mapping and phase distribution is again evident. The current mapping in Fig. 6b suggests that the electrical conductivity in the matrix phase 1 and secondary phase 2 is relatively high, while that of phase 3 is relatively low due to the surface oxidation that we discussed earlier. As shown in Supplementary Table 3 (available as Supplementary Data at NSR online), phases 1 and 2 have comparable electrical conductivities of 2.3 × 105 S/m and 3.0 × 105 S/m, respectively, consistently with the slight contrast in Fig. 6b. For phase 3, the oxidation of YbSb2 introduces an insulating layer on the surface, resulting in very low electrical conductivity. The I-V curves measured in each phase shown in Fig. 6c also confirm this observation. Obviously, these impurity phases with higher thermal conductivity but lower electrical conductivity exert detrimental influence on the thermoelectric properties of skutterudites, and thus are not desirable. Indeed, the thermoelectric properties measured at the macroscopic scale, as shown in Supplementary Fig. 9 (available as Supplementary Data at NSR online), confirmed this analysis that its figure of merit ZT is not optimal due to these impurity phases. As such, in order to exert significant scattering on phonons while negligible influence on electrons, it is critical to control precisely the stoichiometry and phase composition, as well as the size and morphology of impurity phases in filled skutterudites. In fact, this is important for nanostructured thermoelectrics in general. Figure 6. Open in new tabDownload slide Mapping of local electric conductivity; (a) BSE image; (b) mapping of current; (c) IV curves measured in three phases using cAFM. Figure 6. Open in new tabDownload slide Mapping of local electric conductivity; (a) BSE image; (b) mapping of current; (c) IV curves measured in three phases using cAFM. DISCUSSIONS It is rather remarkable that small contrasts in local thermal conductivity can be accurately mapped with nanoscale resolution via SThM as demonstrated. To help us understand this better, we compare the FEM-simulated heat-transfer processes involving three representative phases: matrix skutterudite Yb0.3Co4Sb12 (phase 1), impurity phase CoSb2 (phase 2) and surface-oxidized phase Yb2O3 (phase 3), using as the input their nominal thermal conductivities of 4.5, 11 and 9.5 W/(m.K), respectively. The relevant thermal transport parameters computed are summarized in Table 2. It is interesting to note that, although less than 2% of the total heat generated transfers through the tip-sample junction for each of the phases considered, the process, i.e. the change in heat transfer, is still dominated by the conductivity of the sample, and thus the heat flux at the tip-sample junction changes significantly for samples with different thermal conductivities, resulting in different temperatures of the contact and thus different probe temperatures and resistance that can be precisely measured using a Wheatstone bridge. This confirms the feasibility of the proposed technique and validates the experimental data. Further improvement can be achieved by carrying out SThM in a vacuum [51], which would enhance the sensitivity and resolution, though our study shows that it is not absolutely necessary. Table 2. Numerical heat-transfer properties at the contact of thermal probe with different phases of the sample. κ . Source . Contact heat conduction/ . Contact heat flux . Flux air to . Contact temp. . Probe temp. . ΔR . [W/(m.K)] . [mW] . source [%] . [GW/m2] . sample [kW/m2] . [K] . [K] . [Ω] . 4.5 9.968 0.9805 –4.861 –22.352 442.74 525.64 88.81 11 9.994 1.208 –6.105 –22.069 410.58 521.44 92.38 9.5 9.990 1.229 –6.004 –22.127 416.33 522.12 91.72 κ . Source . Contact heat conduction/ . Contact heat flux . Flux air to . Contact temp. . Probe temp. . ΔR . [W/(m.K)] . [mW] . source [%] . [GW/m2] . sample [kW/m2] . [K] . [K] . [Ω] . 4.5 9.968 0.9805 –4.861 –22.352 442.74 525.64 88.81 11 9.994 1.208 –6.105 –22.069 410.58 521.44 92.38 9.5 9.990 1.229 –6.004 –22.127 416.33 522.12 91.72 Open in new tab Table 2. Numerical heat-transfer properties at the contact of thermal probe with different phases of the sample. κ . Source . Contact heat conduction/ . Contact heat flux . Flux air to . Contact temp. . Probe temp. . ΔR . [W/(m.K)] . [mW] . source [%] . [GW/m2] . sample [kW/m2] . [K] . [K] . [Ω] . 4.5 9.968 0.9805 –4.861 –22.352 442.74 525.64 88.81 11 9.994 1.208 –6.105 –22.069 410.58 521.44 92.38 9.5 9.990 1.229 –6.004 –22.127 416.33 522.12 91.72 κ . Source . Contact heat conduction/ . Contact heat flux . Flux air to . Contact temp. . Probe temp. . ΔR . [W/(m.K)] . [mW] . source [%] . [GW/m2] . sample [kW/m2] . [K] . [K] . [Ω] . 4.5 9.968 0.9805 –4.861 –22.352 442.74 525.64 88.81 11 9.994 1.208 –6.105 –22.069 410.58 521.44 92.38 9.5 9.990 1.229 –6.004 –22.127 416.33 522.12 91.72 Open in new tab It is also important to examine the transient behavior of heat transfer during SThM scanning, which is shown in Supplementary Fig. 10 (available as Supplementary Data at NSR online) obtained from FEM simulations. It takes less than 1.2 mSec for the probe temperature to reach its steady-state value, and this is much less than the pixel time of SThM (3.1 mSec for 0.5-Hz line scan), ensuring a quasi-steady-state condition during the SThM scanning. This also imposes an upper limit on scanning rate at 1.3 Hz per line. Finally, we note that the spatial resolution of this technique can be further improved using a dynamic approach. Under a quasi-steady-state condition, the affected thermal volume in the sample is substantial, with a radius on the order of 100 nm. This has been confirmed by the temperature distribution in the sample underneath of the probe (Fig. 4g), as well as the line scan of resistance change across an interface (Fig. 5d). If a dynamic probing is adopted instead, wherein the heating voltage of the probe is frequency-modulated and the corresponding harmonic response is probed, much higher spatial resolution in the order of 10 nm is expected. This will provide us with a powerful tool to study the effect of structural heterogeneity such as defects, interfaces and impurities on thermoelectric materials, which can be used to guide the design and optimization of thermoelectric materials with enhanced performance, especially when the thermoelectric coefficient can also be mapped in addition to thermal conductivity and electric current. CONCLUSION In this work, local thermal conductivities of a three-phase filled skutterudite were mapped quantitatively with good accuracy, nanometer resolution and one-to-one correspondence with microstructure. Quantitative mapping was accomplished via a SThM using a resistive heating thermal probe complemented by FEM simulations, enabling us to distinguish thermal conductivities spanning two orders of magnitude, yet resolving thermal variation across a phase interface with small thermal conductivity contrast. The technique developed thus provides a powerful tool to correlate local thermal conductivities, microstructures and macroscopic properties for nanostructured materials in general and thermoelectric materials in particular, which can be used to guide the design and optimization of thermoelectric materials with enhanced performance. METHODS Sample preparation The sample with a stoichiometry of Yb0.7Co4Sb12 was prepared by a conventional induction melting-vacuum melting-quenching-annealing-sintering method. High-purity Co powders (99.995%, Alfa Aesar), Sb shots (99.9999%, Alfa Aesar) and Yb chunks (99.95%, Alfa Aesar) were used as the starting materials. Co powders were first purified and melted into small shots with sizes of 1–5 mm by arc melting (SA-200, MRF Inc., USA), then loaded into a BN crucible together with Sb shots for induction melting (at 2000°C for 30 s under an Ar atmosphere, EQ-SP-25VIM, MTI Corporation, USA). The obtained ingot was subsequently crushed and loaded into a carbon-coated quartz tube with appropriate amounts of Yb and Sb in an argon-filled glove-box (Lab Star, Mbraun, Germany) and vacuum-sealed (10−3 torr). Subsequently, the tube with raw materials was placed into a box furnace, heated to 1000°C in 5 h, soaked for 24 h and then rapidly quenched in ice water. The obtained ingot was ultrasonically cleaned and vacuum-sealed in a quartz tube, then annealed in a box furnace at 750°C for 168 h. After annealing, the ingot was crushed, hand-grounded into fine powders and sintered into a bulk material using the spark plasma sintering (SPS-211Lx, Dr. Sinter, Japan) at 680°C and 50 MPa for 5 min. Structure and property characterization The phase composition was determined by the powder X-ray diffraction (XRD, Bruker D8 Focus X-ray diffraction, Germany) using the Cu Kα radiation (λ = 1.5406 Å). The BSE images were obtained in a TM3000 electron microscope (Hitachi, Japan). The chemical composition and elemental mapping were determined by a field emission scanning electron microscope equipped with EDS (FESEM/EDS, FEI Sirion, Japan). The electrical conductivity and Seebeck coefficient were simultaneously measured via commercial equipment (ZEM-3, Ulvac Riko, Inc., Japan) under a low-pressure helium atmosphere. Thermal conductivity was calculated from the product of the measured thermal diffusivity, specific heat and density. Thermal diffusivity was measured by a laser flash method (Netzsch LFA-457, Germany) and specific heat was measured by a differential scanning calorimetry method (DSC) using sapphire as the reference (Netzsch 404F1, Germany). The measurement temperature ranges from 300 K to 850 K. Scanning thermal microscopy The SThM was performed using an Asylum Research MFP-3D atomic force microscope (AFM) using a thermal probe with a spring constant of 0.2–0.5 N/m (AN2-300, Anasys Instruments) in contact mode with contact force around 110 nN and a scan rate of 0.5 Hz per line. The thermal probe is similar to any silicon AFM probe in geometry with an integrated heater at the end. A small region (7.5 μm ×  15 μm) close to the cantilever tip with light phosphorus doping acts as a solid-state heater. The heater region connects through two heavily doped branches acting as the electrical leads. The electrical resistivity of the probe varies between 600 Ω and 2 kΩ for different probes and different drive voltages. Conductive AFM The variations of electrical conductivity of the sample were characterized using ORCA, a conductive AFM (cAFM) module developed by Asylum Research. All measurements and images were obtained using AFM contact mode with a metallic Pt/lr-coated probe having a force constant of 2.8 N/m (PPP-EFM, Nanosensors). Two different modes were used: imaging mode to map the variation of electrical conductivity, and spectroscopic mode to measure the I-V characteristics at points of interest. In the imaging mode, 2-V DC bias was applied to the sample substrate and the necessary current for virtually keeping the tip ground was used to image the electrical conductivity. In the spectroscopic mode under the stationary probe, a sweeping DC bias (–0.6 V to 0.6 V) was applied to the sample while measuring the current that kept the conductive tip ground. SUPPLEMENTARY DATA Supplementary data are available at NSR online. FUNDING We acknowledge National Key Research and Development Program of China (2016YFA0201001), the National Natural Science Foundation of China (11627801 and11472236) and the US National Science Foundation (CBET-1435968). This material is based in part upon work supported by the State of Washington through the University of Washington Clean Energy Institute. REFERENCES 1. Snyder GJ , Toberer ES. Complex thermoelectric materials . Nat Mater 2008 ; 7 : 105 – 14 . Google Scholar Crossref Search ADS PubMed WorldCat 2. Venkatasubramanian R , Siivola E, Colpitts Tet al. Thin-film thermoelectric devices with high room-temperature figures of merit . Nature 2001 ; 413 : 597 – 602 . Google Scholar Crossref Search ADS PubMed WorldCat 3. Tritt TM , Subramanian MA. Thermoelectric materials, phenomena, and applications: a bird's eye view . MRS Bull 2006 ; 31 : 188 – 94 . Google Scholar Crossref Search ADS WorldCat 4. Zebarjadi M , Esfarjani K, Dresselhaus MSet al. Perspectives on thermoelectrics: from fundamentals to device applications . Energ Environ Sci 2012 ; 5 : 5147 – 62 . Google Scholar Crossref Search ADS WorldCat 5. Zhao LD , Dravid VP, Kanatzidis MG. The panoscopic approach to high performance thermoelectrics . Energ Environ Sci 2014 ; 7 : 251 – 68 . Google Scholar Crossref Search ADS WorldCat 6. Dresselhaus MS , Chen G, Tang MYet al. New directions for low-dimensional thermoelectric materials . Adv Mater 2007 ; 19 : 1043 – 53 . Google Scholar Crossref Search ADS WorldCat 7. Poudel B , Hao Q, Ma Yet al. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys . Science 2008 ; 320 : 634 – 8 . Google Scholar Crossref Search ADS PubMed WorldCat 8. Minnich AJ , Dresselhaus MS, Ren ZFet al. Bulk nanostructured thermoelectric materials: current research and future prospects . Energ Environ Sci 2009 ; 2 : 466 – 79 . Google Scholar Crossref Search ADS WorldCat 9. Vineis CJ , Shakouri A, Majumdar Aet al. Nanostructured thermoelectrics: big efficiency gains from small features . Adv Mater 2010 ; 22 : 3970 – 80 . Google Scholar Crossref Search ADS PubMed WorldCat 10. Joshi G , Lee H, Lan Yet al. Enhanced thermoelectric figure-of-merit in nanostructured p-type silicon germanium bulk alloys . Nano Lett 2008 ; 8 : 4670 – 4 . Google Scholar Crossref Search ADS PubMed WorldCat 11. Pei YZ , Heinz NA, LaLonde Aet al. Combination of large nanostructures and complex band structure for high performance thermoelectric lead telluride . Energ Environ Sci 2011 ; 4 : 3640 – 5 . Google Scholar Crossref Search ADS WorldCat 12. Vaqueiro P , Powell AV. Recent developments in nanostructured materials for high-performance thermoelectrics . J Mater Chem 2010 ; 20 : 9577 – 84 . Google Scholar Crossref Search ADS WorldCat 13. Xie W , He J, Kang HJet al. Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites . Nano Lett 2010 ; 10 : 3283 – 9 . Google Scholar Crossref Search ADS PubMed WorldCat 14. Cao YQ , Zhao XB, Zhu TJet al. Syntheses and thermoelectric properties of Bi2Te3/Sb2Te3 bulk nanocomposites with laminated nanostructure . Appl Phys Lett 2008 ; 92 : 3106 . Google Scholar OpenURL Placeholder Text WorldCat 15. Guin SN , Chatterjee A, Negi DSet al. High thermoelectric performance in tellurium free p-type AgSbSe2 . Energ Environ Sci 2013 ; 6 : 2603 – 8 . Google Scholar Crossref Search ADS WorldCat 16. Poudeu PFP , D’Angelo J, Kong Het al. Nanostructures versus solid solutions: low lattice thermal conductivity and enhanced thermoelectric figure of merit in Pb9.6Sb0.2Te10–xSex bulk materials . J Am Chem Soc 2006 ; 128 : 14347 – 55 . Google Scholar Crossref Search ADS PubMed WorldCat 17. Biswas K , He J, Blum IDet al. High-performance bulk thermoelectrics with all-scale hierarchical architectures . Nature 2012 ; 489 : 414 – 8 . Google Scholar Crossref Search ADS PubMed WorldCat 18. Li H , Tang XF, Zhang QJet al. High performance InxCeyCo4Sb12 thermoelectric materials with in situ forming nanostructured InSb phase . Appl Phys Lett 2009 ; 94 : 102114 . Google Scholar Crossref Search ADS WorldCat 19. Paddock CA , Eesley GL. Transient thermoreflectance from thin metal-films . J Appl Phys 1986 ; 60 : 285 – 90 . Google Scholar Crossref Search ADS WorldCat 20. Cahill DG , Goodson KE, Majumdar A. Thermometry and thermal transport in micro/nanoscale solid-state devices and structures . J Heat Trans-T ASME 2002 ; 124 : 223 – 41 . Google Scholar Crossref Search ADS WorldCat 21. Christofferson J , Shakouri A. Thermoreflectance based thermal microscope . Rev Sci Instrum 2005 ; 76 : 24903 . Google Scholar Crossref Search ADS WorldCat 22. Huxtable S , Cahill DG, Fauconnier Vet al. Thermal conductivity imaging at micrometre-scale resolution for combinatorial studies of materials . Nat Mater 2004 ; 3 : 298 – 301 . Google Scholar Crossref Search ADS PubMed WorldCat 23. Cahill DG. Analysis of heat flow in layered structures for time-domain thermoreflectance . Rev Sci Instrum 2004 ; 75 : 5119 – 22 . Google Scholar Crossref Search ADS WorldCat 24. Hatori K , Taketoshi N, Baba Tet al. Thermoreflectance technique to measure thermal effusivity distribution with high spatial resolution . Rev Sci Instrum 2005 ; 76 : 114901 . Google Scholar Crossref Search ADS WorldCat 25. Nonnenmacher M , Wickramasinghe HK. Scanning probe microscopy of thermal-conductivity and subsurface properties . Appl Phys Lett 1992 ; 61 : 168 – 70 . Google Scholar Crossref Search ADS WorldCat 26. Majumdar A , Carrejo JP, Lai J. Thermal imaging using the atomic force microscope . Appl Phys Lett 1993 ; 62 : 2501 – 3 . Google Scholar Crossref Search ADS WorldCat 27. Luo K , Shi Z, Varesi Jet al. Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy . J Vac Sci Technol B 1997 ; 15 : 349 – 60 . Google Scholar Crossref Search ADS WorldCat 28. Mills G , Zhou H, Midha Aet al. Scanning thermal microscopy using batch fabricated thermocouple probes . Appl Phys Lett 1998 ; 72 : 2900 – 2 . Google Scholar Crossref Search ADS WorldCat 29. Majumdar A. Scanning thermal microscopy . Annu Rev Mater Sci 1999 ; 29 : 505 – 85 . Google Scholar Crossref Search ADS WorldCat 30. Fiege GBM , Altes A, Heiderhoff Bet al. Quantitative thermal conductivity measurements with nanometre resolution . J Phys D-Appl Phys 1999 ; 32 : L13 – 7 . Google Scholar Crossref Search ADS WorldCat 31. King WP , Kenny TW, Goodson KEet al. Design of atomic force microscope cantilevers for combined thermomechanical writing and thermal reading in array operation . J Microelectromech Syst 2002 ; 11 : 765 – 74 . Google Scholar Crossref Search ADS WorldCat 32. Lyeo HK , Khajetoorians AA, Shi Let al. Profiling the thermoelectric power of semiconductor junctions with nanometer resolution . Science 2004 ; 303 : 816 – 8 . Google Scholar Crossref Search ADS PubMed WorldCat 33. Kim K , Jeong W, Lee Wet al. Ultra-high vacuum scanning thermal microscopy for nanometer resolution quantitative thermometry . ACS Nano 2012 ; 6 : 4248 – 57 . Google Scholar Crossref Search ADS PubMed WorldCat 34. Rojo MM , Martin J, Grauby Set al. Decrease in thermal conductivity in polymeric P3HT nanowires by size-reduction induced by crystal orientation: new approaches towards thermal transport engineering of organic materials . Nanoscale 2014 ; 6 : 7858 – 65 . Google Scholar Crossref Search ADS PubMed WorldCat 35. Pumarol ME , Rosamond MC, Tovee Pet al. Direct nanoscale imaging of ballistic and diffusive thermal transport in graphene nanostructures . Nano Lett 2012 ; 12 : 2906 – 11 . Google Scholar Crossref Search ADS PubMed WorldCat 36. Grauby S , Puyoo E, Rampnoux JMet al. Si and SiGe nanowires: fabrication process and thermal conductivity measurement by 3ω-scanning thermal microscopy . J Phys Chem C 2013 ; 117 : 9025 – 34 . Google Scholar Crossref Search ADS WorldCat 37. Zhao XY , Shi X, Chen LDet al. Synthesis of YbyCo4Sb12/Yb2O3 composites and their thermoelectric properties . Appl Phys Lett 2006 ; 89 : 92121 . Google Scholar Crossref Search ADS WorldCat 38. Dahal T , Jie Q, Joshi Get al. Thermoelectric property enhancement in Yb-doped n-type skutterudites YbxCo4Sb12 . Acta Mater 2014 ; 75 : 316 – 21 . Google Scholar Crossref Search ADS WorldCat 39. Wang SY , Salvador JR, Yang Jet al. High-performance n-type YbxCo4Sb12: from partially filled skutterudites towards composite thermoelectrics . NPG Asia Mater 2016 ; 8 : e285 . Google Scholar Crossref Search ADS WorldCat 40. Tang Y , Chen S-W, Snyder GJ. Temperature dependent solubility of Yb in Yb–CoSb3 skutterudite and its effect on preparation, optimization and lifetime of thermoelectrics . J Materiomics 2015 ; 1 : 75 – 84 . Google Scholar Crossref Search ADS WorldCat 41. Williams CC , Wickramasinghe HK. Scanning thermal profiler . Appl Phys Lett 1986 ; 49 : 1587 – 9 . Google Scholar Crossref Search ADS WorldCat 42. Zhao KY , Zeng HR, Xu KQet al. Scanning thermoelectric microscopy of local thermoelectric behaviors in (Bi,Sb)(2)Te-3 films . Physica B-Condensed Matter 2015 ; 457 : 156 – 9 . Google Scholar Crossref Search ADS WorldCat 43. King WP , Kenny TW, Goodson KEet al. Atomic force microscope cantilevers for combined thermomechanical data writing and reading . Appl Phys Lett 2001 ; 78 : 1300 – 2 . Google Scholar Crossref Search ADS WorldCat 44. Chui BW , Stowe TD, Kenny TWet al. Low-stiffness silicon cantilevers for thermal writing and piezoresistive readback with the atomic force microscope . Appl Phys Lett 1996 ; 69 : 2767 – 9 . Google Scholar Crossref Search ADS WorldCat 45. Vettiger P , Cross G, Despont Met al. The ‘millipede’-nanotechnology entering data storage . IEEE T Nanotechnol 2002 ; 1 : 39 – 55 . Google Scholar Crossref Search ADS WorldCat 46. Eshghinejad A , Esfahani EN, Wang PQet al. Scanning thermo-ionic microscopy for probing local electrochemistry at the nanoscale . J Appl Phys 2016 ; 119 : 205110 . Google Scholar Crossref Search ADS WorldCat 47. Lefevre S , Volz S, Saulnier JBet al. Thermal conductivity calibration for hot wire based dc scanning thermal microscopy . Rev Sci Instrum 2003 ; 74 : 2418 – 23 . Google Scholar Crossref Search ADS WorldCat 48. King WP , Bhatia BS, Felts JRet al. Heated atomic force microscope cantilevers and their applications . Ann Rev Heat Transfer 2013 ; 12 : 287 – 326 . Google Scholar Crossref Search ADS WorldCat 49. Caillat T. Preparation and thermoelectric properties of IrxCo1−xSb2 alloys . J Phys Chem Solids 1996 ; 57 : 1351 – 8 . Google Scholar Crossref Search ADS WorldCat 50. Lal HB , Gaur K. Electrical-conduction in non-metallic rare-earth solids . J Mater Sci 1988 ; 23 : 919 – 23 . Google Scholar Crossref Search ADS WorldCat 51. Lee J , Wright TL, Abel MRet al. Thermal conduction from microcantilever heaters in partial vacuum . J Appl Phys 2007 ; 101 : 014906 . Google Scholar Crossref Search ADS WorldCat Author notes Equally contributed to this work. © The Author(s) 2017. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is properly cited. for commercial re-use, please contact journals.permissions@oup.com © The Author(s) 2017. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
TI - Quantitative nanoscale mapping of three-phase thermal conductivities in filled skutterudites via scanning thermal microscopy
JF - National Science Review
DO - 10.1093/nsr/nwx074
DA - 2018-01-01
UR - https://www.deepdyve.com/lp/oxford-university-press/quantitative-nanoscale-mapping-of-three-phase-thermal-conductivities-1s2Pph9m01
SP - 59
EP - 69
VL - 5
IS - 1
DP - DeepDyve
ER -