Reduced temperature-dependent thermal conductivity of magnetite thin films by controlling film thickness
© Park et al.; licensee Springer. 2014
Received: 15 January 2014
Accepted: 19 February 2014
Published: 26 February 2014
We report on the out-of-plane thermal conductivities of epitaxial Fe3O4 thin films with thicknesses of 100, 300, and 400 nm, prepared using pulsed laser deposition (PLD) on SiO2/Si substrates. The four-point probe three-omega (3-ω) method was used for thermal conductivity measurements of the Fe3O4 thin films in the temperature range of 20 to 300 K. By measuring the temperature-dependent thermal characteristics of the Fe3O4 thin films, we realized that their thermal conductivities significantly decreased with decreasing grain size and thickness of the films. The out-of-plane thermal conductivities of the Fe3O4 films were found to be in the range of 0.52 to 3.51 W/m · K at 300 K. For 100-nm film, we found that the thermal conductivity was as low as approximately 0.52 W/m · K, which was 1.7 to 11.5 order of magnitude lower than the thermal conductivity of bulk material at 300 K. Furthermore, we calculated the temperature dependence of the thermal conductivity of these Fe3O4 films using a simple theoretical Callaway model for comparison with the experimental data. We found that the Callaway model predictions agree reasonably with the experimental data. We then noticed that the thin film-based oxide materials could be efficient thermoelectric materials to achieve high performance in thermoelectric devices.
KeywordsIron oxide (Fe3O4) Thermal conductivity 2D thin films 3-ω technique Callaway model In-plane and out-of-plane
In recent decades, there has been a great interest in the application of thermoelectric (TE) effects in alternative clean energy sources [1–6]. For the evaluation of the thermoelectric performances of TE devices, their efficiencies can usually be quantified by a dimensionless figure of merit (ZT), S2σT/κ or a power factor S2σ, where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature. High-performance thermoelectric materials with high ZT values should have a large Seebeck coefficient, high electrical conductivity, and low thermal conductivity [2, 7, 8]. To obtain an efficiently comparable to a household refrigerator, a ZT value at least 3 is desired for more widespread applications . Recently, several researchers have alternatively studied two-dimensional (2D) thin films [9, 10] to overcome the limitations of 1D nanostructured materials whose thermal properties are highly dependent on their dimensionality and morphology [3, 11–13]. In 2010, Tang et al. reported that the thermal conductivity of holey Si thin film consistently reduces by around 2 orders of magnitude with a reduction in the pitch of the hexagonal holey pattern down to approximately 55 nm with approximately 35% porosity . Similarly, Yu et al. reported that a Si nanomesh structure exhibits a substantially lower thermal conductivity than an equivalently prepared array of Si nanowires . Hence, we believe that the 2D materials (i.e., thin film formation) could be highly promising candidates as TE materials for scalable and practical TE device applications.
Magnetite (Fe3O4) is a well-known half-metallic material, whose electronic density of states is 100% spin polarized at the Fermi level [14, 15]. These properties allow Fe3O4 to be a promising candidate for spintronic devices . However, the thermal property of this metal compound has not been widely studied. In 1962, Slack extensively studied and analyzed the thermal conductivity of a single crystal of paramagnetic bulk Fe3O4 materials at temperatures of 3 to 300 K . He found that the thermal conductivity of Fe3O4 falls sharply with increasing temperature at the approximately 121 ± 2 K transition and reported a notable effect of vacancy and impurities on Fe3O4, particularly below 30 K. The thermal conductivity of pure Fe3O4 was as low as approximately 6 W/m · K at 300 K, owing to phonon scattering by local disorder in the materials, thus implying that pure Fe3O4 is a promising TE material. To the best of our knowledge, there have been no studies on the thermal properties of Fe3O4 thin films.
In this work, we present the out-of-plane thermal conductivities of epitaxial Fe3O4 thin films with thicknesses of 100 to 400 nm having different grain sizes and surface roughness. The films were grown at a deposition temperature of 300°C using pulsed laser deposition (PLD). We successfully demonstrated the temperature-dependent thermal conductivities of epitaxial Fe3O4 thin films via four-point probe 3-ω method in the temperature range of 20 to 300 K. The measured out-of-plane thermal conductivities of the Fe3O4 thin films (0.52 to 3.51 W/m · K) at 300 K are considerably reduced compared to those of the bulk materials (approximately 6 W/m · K)  because of strongly enhanced phonon-boundary scattering, as expected in the Callaway model . Furthermore, we clearly realized that the thermal conductivity increased with an increase in film thickness and grain size, which agreed well with the theoretical predictions of the Callaway model.
Results and discussion
where d2 is the corresponding film thickness. For the Fe3O4 films, we estimated that the values of A and B in Equation 4 were numerically optimized as approximately 8.46 × 10-43 S3 and approximately 7.89 × 10-18 S/K, respectively, from the fitting to the bulk material values . According to the Callaway model in Equations 3 and 4, the first term represents the boundary scattering; the second term A ω4 represents the scattering by point impurities or isotopes, and the third term represents the Umklapp process. Theoretical fits of the temperature dependence of the out-of-plane thermal conductivities of the Fe3O4 films from 20 to 300 K of Equations 2 and 4, which were obtained using the commercial application Mathematica (http://www.wolfram.com), are compared with the experimental results in Figure 5a,b. From the numerical calculation of the temperature dependence of thermal conductivity, it was noted that the κ values indisputably decreased when the grain size was reduced, indicating that the effect of the nano-grained thin films on the thermal conductivity is essentially due to the relaxation time model based on phonon-boundary scattering. As shown in Figure 5a,b, the theoretical modeling based on the Callaway model agrees well quantitatively with the experimental data even though there is a difference in the κ values between the theoretical and experimental results for the 100-nm Fe3O4 film. The measured thermal conductivity results in the 100-nm films were approximately five times lower than the Callaway model prediction. This deviation can be explained by two arguments. First, the deviation in the thermal conductivity for the 100-nm thick film could be explained by the boundary effect, i.e., surface boundary scattering of the thinner films, in which the surface boundary scattering is more dominant compared to that of bulk and bulk-like thicker films, providing more phonon-boundary effect in thermal conductivity. However, in our theoretical model, no size and surface boundary scattering effects were considered. Thus, the measured temperature dependence of the thermal conductivity (0.52 W/m · K at 300 K) was relatively lower than the results expected from the theoretical calculation (1.9 to 2.4 W/m · K at 300 K), as shown in Figure 5b [2, 34, 35]. Previously, Li et al. also reported a similar observation for the thermal conductivity of Bi2Se3 nanoribbon . Second, to numerically calculate the thermal conductivity using the Callaway model, we used the fitting parameters of A and B in the relaxation rate from the bulk materials. Thus, the theoretical calculation could be closer to the bulk material values. To clearly understand this inconsistency between the theoretical and experimental results, especially in nanoscale thin films (100-nm thin film in our case), the size and surface boundary effects in the Callaway model should be studied in detail for 1D and 2D nanostructures.
In summary, we first present the thermal conductivity of epitaxial Fe3O4 thin films with thicknesses of 100 to 400 nm prepared on SiO2/Si (100) substrates using PLD. By measuring the temperature-dependent thermal characteristics of three Fe3O4 thin films using the effective four-point probe 3-ω method, we found that the thermal conductivities of the films are greatly reduced when compared with those of the corresponding bulk materials and that the thermal conductivity decreases with decreasing film thickness from 400 to 100 nm. Both theoretical and experimental results indicate that the Umklapp peaks of the thermal conductivity of Fe3O4 films move toward higher temperatures with decreasing film thickness, owing to the phonon-boundary scattering. The thermal conductivity was found to be in the range of 0.52 to 3.51 W/m · K at 300 K, which was 1.7 to 11.5 orders of magnitude lower than that of bulk materials at 300 K. We found that the modified Callaway theoretical model including the film thickness effect agreed well with the results obtained using the 3-ω method. Furthermore, we indirectly measured the in-plane thermal conductivity by re-analyzing the Callaway model using the measured out-of-plane thermal conductivity. We then suggested that the thin film-based oxide materials could be promising candidates as thermoelectric materials to achieve high-performance TE devices.
This study was supported by the Priority Research Centers Program and by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2013R1A12012685, NRF-2013R1A4A1069528). This study was also supported by a grant from the Global Excellent Technology Innovation R&D Program funded by the Ministry of Knowledge Economy, Republic of Korea (10038702-2010-01).
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