† Corresponding author. E-mail:
Project supported by the Key-Area Research and Development Program of Guangdong Province, China (Grant No. 2020B010190004), the National Natural Science Foundation of China (Grant Nos. 11674245, 11775158, 11890703, and 11935010), and the Open Fund of Zhejiang Provincial Key Laboratory of Quantum Technology and Device, China (Grant No. 20190301), and the Shanghai Committee of Science and Technology in China (Grant Nos. 17142202100, 17ZR1447900, and 17ZR1432600).
Unveiling the thermal transport properties of various one-dimensional (1D) or quasi-1D materials like nanowires, nanotubes, and nanorods is of great importance both theoretically and experimentally. The dimension or size dependence of thermal conductivity is crucial in understanding the phonon–phonon interaction in the low-dimensional systems. In this paper, we experimentally investigate the size-dependent thermal conductivity of individual single crystalline α-Fe2O3 nanowires collaborating the suspended thermal bridge method and the focused electron-beam self-heating technique, with the sample diameter (d) ranging from 180 nm to 661 nm and length (L) changing from 4.84 μm to 20.73 μm. An empirical relationship for diameter-/length-dependent thermal conductivity is obtained, which shows an approximately linear dependence on the aspect ratio (L/(1 + Cd)) at T = 300 K, where C is a fitting parameter. This is related to the boundary scattering and diameter effect of α-Fe2O3 nanowires although rigorous calculations are needed to confirm the result.
On Mars, the existence of hematite (α-Fe2O3) was confirmed by the Curiosity Rover, which is partly responsible for the red tone, and its analysis provides valuable clues to the history of liquid water in the planet’s environment.[1] Here on Earth, iron is one of the most abundant elements while iron oxides are ubiquitous in nature, among which hematite is the most common morphology due to its high thermodynamic stability.[2] Iron oxides are inexpensive, environment-friendly, and corrosion-resistant materials that have various novel applications in many aspects, e.g., catalysts/photocatalysts,[3–5] gas sensing,[6,7] drug delivery,[8] gene therapy,[9] photoelectrochemical water splitting,[10] and energy storage.[11] Hence, scientists including biologists, chemists, physicists, geologists, and engineers have all displayed the liveliest interests in iron oxides.
In recent years, various one-dimensional (1D) or quasi-1D materials like nanowires, nanotubes, and nanorods have attracted wide interests, due to the exotic dimensional/size dependent properties which are different from their bulk counterparts and have potential applications in miniaturized electronic and energy conversion devices.[12–21] As the peculiar properties and applications of α-Fe2O3 are closely related to the dimension, shape, and surface morphology, amount of researches were focused on relevant investigations, e.g., synthesis and characterization of α-Fe2O3 nanoparticles, nanorod, and nanowires by controlling the experimental conditions and parameters in various methods.[22–27] In particular, synthesis[22] of α-Fe2O3 nanowires has attracted much attention and some of the intrinsic physical properties including electrical,[23] optical,[24] and magnetic[25–27] properties were investigated. However, one of the most basic and important properties of α-Fe2O3 nanowires, the thermal conductivity, is still missing as far as we know.
Here, we synthesized α-Fe2O3 nanowire arrays vertically on the surface of the substrate by oxidation of pure iron. We demonstrated the size-dependent thermal conductivity of individual single crystalline α-Fe2O3 nanowires with the thermal bridge method and focused electron beam self-heating technique.
Synthesis A high purity of iron foil, ultrasonically cleaned with ethanol, was used to synthesize the nanowires both as reagent and substrate. The foil with some metal catalyst carried by the quartz boat was placed in the quartz tube reactor, which was heated to 800 °C in the Ar gas environment with the flow rate of 500 standard cubic centimeter per minute (sccm). An oxygen flow with the rate of 30 sccm was introduced for reaction for 0.5–1 h. With Ar gas keeping flowing, the tube was cooled down to room temperature.
Morphology characterization The morphology and crystal structure of the as-grown nanowires were characterized by scanning electron microscopy (FEI SEM Nova 450), transmission electron microscopy (TEM JEOL JEM-2100 F), x-ray diffraction (XRD D8), and Raman spectroscopy (HR800). Figure
Suspended sample preparation The suspended microdevices applied for thermal measurements were fabricated with the similar standard lithography, metal deposition/lift-off technique, deep RIE, and wet etching process as shown in the reference.[28–32] The as-prepared null devices were annealed at 250 °C in H2/Ar atmosphere for 2–3 hours, with which the possible residues on the surface of the devices were cleaned. Since the grass-like grown nanowires rooted to the substrate (Fig.
Thermal conductivity measurements Two approaches, the thermal bridge method[30–32,35] and the focused electron-beam self-heating technique,[36–38] were utilized to measure the thermal conductance and derive the thermal contact resistance of the samples, both based on the prepatterned suspended device. For the thermal bridge method, one membrane of the device acts as a heater, which is heated by a DC current, and the other acts as a sensor. The thermal conductance of the supporting Pt/SiNx beams and the sample can be written as
The focused electron-beam self-heating method was used to measure the intrinsic thermal resistance Ri. The total thermal resistance R was measured by the thermal bridge method. The thermal contact resistance Rc could be obtained by subtracting the intrinsic thermal resistance from the total thermal resistance, i.e., Rc = R – Ri.
In order to figure out the influence of the EBID process on the thermal contact resistance, the effect of contacts and the EBID process on the measured total thermal resistance and thermal contact resistance is discussed first. The lengths and diameters of the individual nanowires were measured with SEM after the EBID process. Dimensions of the measured samples are given in Table
Figure
As shown in Table
Here we propose a phenomenological theoretical model to describe the length and diameter dependences of the thermal conductivities of nanowires. For a nanowire, the scattering of phonons usually comes from four parts: boundary scattering, defect/isotopic effect, nonlinear effect, and diameter effect. Here we ignore the defect/isotopic effect since it does not change with the sample size. We also ignore the roughness effect assuming that the surface of the nanowire is smooth enough. The nonlinear effect can be neglected as the phonon mean free path is comparable to the sample length for small nonlinearity close to the ballistic regime. The diameter effect is specific for the nanowires whose diameters are much less than the phonon mean free path. If the diameters are small comparing to the phonon mean free path, the nanowires can be treated as quasi-1D materials. The volume of unit cell will increase as the diameter increases. The larger unit cell will bring more optical phonon branches which will introduce more scattering channels for the acoustic phonons which is responsible for the heat conduction. In another word, the increase of the nanowire diameters will reduce the thermal conductivity if the diameters are much smaller than the phonon mean free path.
Therefore, we can model the phonon scattering rate assuming the Matthiesen’s rule as follows:
If we notice that the thermal conductivity κ is proportional to the phonon mean path l, we can arrive at
We measured the thermal conductivity of individual single crystalline α-Fe2O3 nanowires with thermal bridge method and focused electron-beam self-heating technique based on prepatterned suspended device in the temperature range from 20 K to 300 K. EBID process obviously improved the contact condition and the thermal contact resistances were reduced to about 20% or less of the total thermal resistance. Thermal conductivity was not only L but d dependent simultaneously and diverged anomalously with the aspect ratio as κ ∝ L/(1 + Cd) in the measured samples with diameter (d) ranging from 180 nm to 661 nm and length (L) changing from 4.84 μm to 20.73 μm. Rigorous calculations and more experiments are needed to further prove whether this divergence is universal in α-Fe2O3 nanowires.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] | |
[35] | |
[36] | |
[37] | |
[38] | |
[39] | |
[40] | |
[41] | |
[42] | |
[43] | |
[44] | |
[45] | |
[46] | |
[47] | |
[48] | |
[49] | |
[50] | |
[51] |