# A Brief Review on the Recent Experimental Advances in Thermal Rectification at the Nanoscale
## 2 Experimental Study
### Thermal Rectification in Vanadium Dioxide Beams  
As early as 2009, [PERSON] et al. has experimentally demonstrated an oxide thermal rectifier in bulks, consisting of two cobalt oxides with different thermal conductivities depending strongly on temperature [43]. Here, [PERSON] and [PERSON] et al. experimentally realized an oxide thermal rectifier in vanadium dioxide microbeam with different physical mechanism, which can be switched between two states by controlling the temperature [44]. Up to 28% thermal rectification is observed in the rectifier state, while the thermal rectification effect disappears in the resistor state (<1%). Previous work has shown that thermal rectification occurs in a single metal-insulator interface composed of CuO-Cu. Polycrystalline VO\({}_{2}\) has been shown to undergo metal-insulator transition at the transition temperature of around 340 K and there exists a mixed metal-insulator interface in the VO\({}_{2}\) beam below 340 K [45]. The thermal rectification experiment was designed based on the unique metal-insulator transition property of VO\({}_{2}\). In this work, the VO\({}_{2}\) beams were synthesized by a modified vapor transport method and a tapered sample was selected for experiment, as shown in Figure 8B. The biaxial thermal conductivity was measured by using a typical micro-thermal bridge method. Several SiNx beams were used to support the suspended sample and two platinum coil electrodes were used as a heater and a resistance thermometer, respectively. A focused ion beam was used to deposit platinum/carbon composite symmetrically at both ends of the sample to enhance electrical and thermal contact. The biaxial thermal conductivity measurement can be easily done by changing the electrical heating power of each platinum electrode. Figure 7: **(A)** SEM images of Sample 4 (before and after nanoparticle deposition by EBID) and sample #5 with a tapered width. **(B)** The comparison between measured thermal conductivities in different heat flux directions as a function of temperature. Reprinted with permission from Springer Nature Publishing Group. The results of temperature reference and heat flow shown in the Figure 9 were measured at 300 K (below a transition temperature of around 340 K). As the temperature difference increases, the heat flow increases linearly. In the slope between heat flow and temperature difference, characterization of the thermal conductivity is different. The thermal conductivity when heat flows from the narrow side to the wide side is significantly smaller than that in the opposite direction, which represents 28% \(\pm\) 1.4% thermal rectification. However, at 385K when the VO\({}_{2}\) beam is completely metallized, the experimental results show no thermal rectification and the bidirectional thermal conductivity was higher than the value at low temperatures. The thermal conductivity is smaller when heat flows from the narrow side to the wide side, where the effect of the asymmetric geometry on the mean free path of phonons due to its tapered shape needs to be considered. However, it has been estimated that the size of the cross section of the VO\({}_{2}\) beam is approximately 1000 times larger than the mean free path of phonons, thus the thermal rectification effect caused by the asymmetric geometry dominated by the boundary scattering effect is unlikely. On the other hand, the thermal resistance at the metal-insulator interface is caused by both phonon-electron scattering and phonon-phonon coupling. Furthermore, [PERSON] et al. found that electronic thermal conductivity in metallic vanadium dioxide is anomalously low, which violated the Wiedemann-Franz law [46]. The phonon-electron scattering dominates the interface thermal resistance  
Figure 8: (**A**) Optical microscope image of a VO\({}_{2}\) beam suspended between two pads for thermal conductance measurement. (**B**) SEM image of an asymmetric VO\({}_{2}\) beam. Reprinted with permission from ACS Publications.