Nanostructure design for high performance thermoelectric materials based on anomalous Nernst effect using metal/semiconductor multilayer

Thermoelectric (TE) conversion, which generates electricity from wasted heat, has drawn considerable attention as one of the energy harvesting technologies. In addition to a representative Seebeck effect-based TE conversion, the conversion based on anomalous Nernst effect (ANE) has recently drawn much attention. ^1–7) According to the recent report, ¹⁾ TE conversion efficiency based on ANE can be higher than that based on Seebeck effect in the case of the same dimensionless figure-of-merit. However, the dimensionless figure-of-merit for ANE (ZT_ANE) is quite small (∼0.001) ^1,8–10) compared with that for Seebeck effect in general.

For increasing ZT_ANE, described as Q_ANE ²(μ₀ M)² σ _yy T/κ, most of the research groups have enthusiastically worked on increasing anomalous term of transverse Seebeck coefficient (S_ANE = Q_ANE μ₀ M), where Q_ANE is anomalous Nernst coefficient, μ₀ is vacuum permeability, M is magnetization, κ is thermal conductivity, σ_yy is electrical conductivity and T is absolute temperature. Nakatsuji et al. experimentally found that the increase of the S_ANE is likely attributed to Berry curvature near Fermi level. ^6,8,11) Other groups have observed that S_ANE was increased by the ferromagnetic metal/paramagnetic metal interface effect such as magnetic proximity effect and spin–orbit interaction or by nano-sized granular structures, etc., ^12–17) the detail of which mechanism remains unclear. Although various methodologies for high S_ANE have been suggested, nobody has paid attention to κ reduction for increasing ZT_ANE because it is difficult to reduce κ in metal with inherently-high κ.

We have developed the TE semiconductor materials based on Seebeck effect, which have low κ by nanostructuring approach: ^18–28) ∼0.78 Wm⁻¹ K⁻¹ for connected Si nanodots, ∼3 Wm⁻¹ K⁻¹ for Si/Si_1−x Ge_x superlattice, etc. This κ reduction is yielded by the introduction of nanostructured interfaces working as phonon scattering centers into the semiconductor where the main heat carrier is phonon. If the aforementioned κ reduction, caused by the semiconductor nanostructured interfaces, could also be applicable to metal with ANE, and there could be the interface effect for S_ANE enhancement in metal/semiconductor system, ZT_ANE value would be greatly increased.

In this study, we propose a ferromagnetic metal/semiconductor multilayer, where a ferromagnetic metal/semiconductor multilayer interface prevents heat carrier transport (κ reduction), and is expected to increase S_ANE additionally (Fig. 1). For this demonstration of the nanostructure design, we focus on Co with relatively-high Curie temperature as a ferromagnetic metal and Si as a representative ubiquitous semiconductor. The amorphous Co/Si multilayer films (MLF) exhibit an extremely-low κ of ∼1.5 Wm⁻¹ K⁻¹ thanks to both the interface phonon scattering and the contribution of amorphous Si with inherently-low κ. A remarkable fact is that the κ is reduced even in ferromagnetic metal/semiconductor multilayer, which is beneficial for developing ANE-based TE materials with high ZT_ANE. Furthermore, we also observe the 2.4 times S_ANE enhancement by the introduction of metal/semiconductor interface. This study opens a renewed avenue for the development of TE generation based on ANE.

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The samples were fabricated by electron beam deposition using high purity Si (99.999%) and Co (99.9%) sources as follows. Undoped Si(001) substrates were cleaned by a standard wet chemical process and hydrogen-terminated Si surfaces were prepared by HF solution. The cleaned Si substrates with a size of 6 × 7 × 0.3 mm³ were introduced into vacuum chamber at a base pressure of ∼1 × 10⁻⁴ Pa. The amorphous Co/Si MLFs were grown on the Si substrates at room temperature (RT) by alternately depositing Co and Si, where each layer thickness was 20 nm; namely periodicity was 40 nm and MLF thickness (L) was 40 nm × (periodic number). For reference, we also formed amorphous Co films with a thickness of 20 nm on the Si substrates (CF) at RT.

The cross-sectional sample structures were observed using scanning electron microscopy (SEM) with a 10 keV electron beam. The amorphous phase was confirmed by X-ray diffraction (XRD) with Cu Kα line (wavelength: 0.15418 nm). The out-of-plane κ values of the MLF (κ_MLF) were measured by 2ω method ^{18–20,23,25)} (TCN-2ω, Advance Riko Inc.) which is a κ measurement technique based on the thermoreflectance method with periodic heating. The 2ω method was performed at RT under vacuum (∼1 Pa) using a laser with a wavelength of 635 nm and the heating electric current with the frequency from 1 to 5 kHz, where Mo films (100 nm) as transducer and SiO₂ films (18 nm) for insulating were deposited on the sample surfaces by RF sputtering. The in-plane σ _yy and Seebeck coefficient (S_SE) values were measured at RT using van der Pauw method and ZEM-3 (ADVANCE-RIKO Inc.), respectively. The transverse Seebeck coefficient (S _yx ) was obtained from the V_NE/d∇T in perpendicular magnetized (PM) configuration, where V_NE is transverse TE voltage and d is measurement distance. ²⁾ The V_NE was measured at RT using physical property measurement system (PPMS). The V_NE is usually measured using PM or in-plane magnetized (IM) configurations [Fig. 2(a)], where the directions of T gradient, magnetic field (H), and the V_NE are perpendicular to each other. In IM configuration of multilayers, it is well-known that spin Seebeck effect appears in addition to ANE, making it difficult to understand the physics of S_ANE enhancement. On the other hand, in PM configuration, we can measure the V_NE coming from only ANE because spin Seebeck effect does not appear. ²⁹⁾ In this study, to discuss S_ANE enhancement easily, we used PM configuration shown in Fig. 2(a), where the V_NE along the y direction was measured when applying T gradient along the x direction and H along the z direction. The Hall resistivity (ρ _yx ) in the in-plane direction was measured by Hall effect measurement. We also measured M curves of samples with magnetic property measurement system (MPMS3).

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Figures 2(b) and 2(c) show cross-sectional SEM images of CF and MLF with periodic number of 2, respectively. It was confirmed that the total thicknesses of MLF and CF samples were ∼80 and ∼20 nm, respectively, and each layer thickness of MLF was ∼20 nm. In addition, as denoted by the arrows in Figs. 2(b) and 2(c), the interfaces between film and substrate were sharply formed. The XRD proved that these samples were amorphous (not shown). Thus, it was found that samples were formed as amorphous films.

Mo films for transducer and SiO₂ layers for insulating were deposited on the MLFs for 2ω method. Total thermal resistance (R_total) of SiO₂/MLF was acquired as shown in Fig. 3(a). In thermal circuit model, R_total is described as L/κ_MLF + R_SiO2 + ITR_Mo/SiO2 + ITR_SiO2/MLF + ITR_MLF/sub, where R_SiO2, ITR_Mo/SiO2, ITR_SiO2/MLF, and ITR_MLF/sub, are thermal resistance of SiO₂ layer and interfacial thermal resistances at the Mo/SiO₂, SiO₂/MLF, and MLF/substrate interfaces. The linear dependence in Fig. 3(a) validated thermal circuit model in the present MLFs with 40 nm periodicity. Using the slope of L dependence of R_total in Fig. 3(a), κ_MLF was acquired to be ∼1.5 Wm⁻¹ K⁻¹. Figure 3(b) summarizes the experimental κ_MLF (MLF exp.), the reported κ value of bulk Co ³⁰⁾ (BC), the calculated κ value of CF (κ_Co) and the calculated κ_MLF (MLF cal.) at RT. Therein, the out-of-plane κ_Co was calculated to be 47 Wm⁻¹ K⁻¹ from Wiedemann–Franz law (L₀ Tσ _yy ), where in-plane σ _yy of CF was measured to be 6.4 × 10⁻⁴ Ω⁻¹ cm⁻¹ and L₀ is Lorenz number, by assuming that there is no anisotropic electrical conductivity in the amorphous CF. The calculated κ_MLF was estimated (2.9–4.9 Wm⁻¹ K⁻¹) using a series thermal resistance model described as L/κ_MLF = L/2κ_Co + L/2κ_Si, where κ_Si is the κ value of Si film (1.5–2.6 Wm⁻¹ K⁻¹). ^31–34) In the calculated κ_MLF, the interfacial thermal resistance at the Co/Si interface (ITR_Co/Si) is not included. The experimental κ_MLF was ∼31 times smaller than that of κ_Co, which is mainly attributed to the contribution of amorphous Si layer with smaller κ. Note that the experimental κ_MLF was smaller than the calculated one without ITR_Co/Si. This experimental fact indicates that Co/Si interface plays some role for κ reduction.

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Figure 4(a) shows S _yx –H curve in PM configuration. S _yx value includes normal and anomalous terms of transverse Seebeck coefficient. To remove the normal term of S _yx , here, the anomalous term of S _yx is experimentally obtained as (S _yx )_sat = (∣(S _yx )_sat ⁺ − (S _yx )_sat ⁻∣)/2, where (S _yx )_sat ⁺ and (S _yx )_sat ⁻ are the intercepts determined by extrapolating fitted line functions in positive and negative high H ranges (M saturation region) to zero field in S _yx –H graph, respectively. Figure 4(b) summarizes (S _yx )_sat values of the MLF with periodic number of 2 and the CF. Intriguingly, the MLF exhibited 2.4 times larger (S _yx )_sat than the CF. So far, the enhancement of (S _yx )_sat had been reported only in ferromagnetic metal/paramagnetic metal multilayers. ^12–14) This result demonstrated that (S _yx )_sat was enhanced even in ferromagnetic metal/semiconductor multilayer. It is considered that electrical current flows almost only in Co layers in MLF because of undoped Si layers with high resistivity. The σ _yy in CF (6.4 × 10⁴ Ω⁻¹ cm⁻¹) was twice larger than that (3.2 × 10⁴ Ω⁻¹ cm⁻¹) in MLF with the layer thickness ratio of Co (20 nm)/Si (20 nm) of ∼1, revealing that Co layers in MLF have almost the same σ _yy as the CF.

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Now, we consider the origin of (S _yx )_sat enhancement. First, we checked saturation magnetization (M_S) because (S _yx )_sat is basically proportional to the μ₀ M_S. The M–H curves of the MLF and the CF in PM configuration in Fig. 4(c) revealed that the both samples have almost the same M_S values, indicating that (S _yx )_sat enhancement does not come from M_S increase. Actually, Q_ANE, which is obtained as (S _yx )_sat divided by μ₀ M_S, exhibits the 2.6 times larger value in the MLF than that of the CF as shown in Fig. 4(d). Next, we consider the Hall effect contribution. The (S _yx )_sat is described as (S _yx )_sat = ρ _xx α _yx  + ρ _yx α _xx , where α _xx and α _yx are longitudinal and transverse TE conductivities, respectively, ³⁵⁾ and ρ _xx is longitudinal electrical resistivity. When the approximation that ρ _xx  ≫ ρ _yx and α _xx  = S_SE /ρ _xx works out, (S _yx )_sat is written as follows:

$$\begin{eqnarray}&&{\left({S}_{{yx}}\right)}_{{\rm{sat}}}\sim {\rho }_{{xx}}{\alpha }_{{yx}}-{\sigma }_{{yx}}{\rho }_{{xx}}{S}_{{\rm{SE}}},\end{eqnarray} \tag{ 1 }$$

where the σ _yx is the anomalous Hall conductivity. It is known that the second term of Eq. (1) comes from Hall effect of Seebeck effect-induced charge current. On the other hand, the first term of Eq. (1) is a direct generation of transverse charge current originating from α _yx . Therefore, there is a possible mechanism that the (S _yx )_sat enhancement comes from σ _yx ρ _xx S_SE increase owing to contribution of high S_SE of Si. However, as shown in Fig. 4(e), the enhancement of σ _yx ρ_xx S_SE value in the MLF was not observed, indicating that the (S _yx )_sat enhancement does not come from enhancement of the Hall effect due to high S_SE of Si. Furthermore, it is also difficult to explain the present enhancement effect by the effect of the spin–orbit interaction at the interface ¹⁶⁾ because of the light element Si. Next, as a mechanism for (S _yx )_sat enhancement, we consider the increase of Berry curvature at the metal/semiconductor interfaces. The increment of Berry curvature function [Ω(E)] with a variable of electron energy (E) increases the second term of Eq. (1) (S_SE < 0) because σ _yx is proportion to integrated Ω(E) in the range of E less than Fermi energy. ^36–39) However, as shown in Fig. 4(f), it was not confirmed that the σ _yx value [=−ρ _yx /(ρ _yx ² ₊ ρ _xx ²)], which were obtained from measurement values (ρ _yx and ρ _xx ), increases in the MLF. However, there is still a possibility that increment of Berry curvature Ω(E_F) at Fermi energy (E_F) increases α_yx because α _yx is proportional to Ω(E_F). The inset in Fig. 4(f) shows larger estimated α _yx in MLF, indicating that the increment mechanism of Ω(E_F) cannot be excluded. Although the increment of Ω(E_F) can explain (S _yx )_sat enhancement, there can also be other mechanisms: magnetic proximity effect mechanism at the ferromagnetic metal/semiconductor interface or other mechanisms. The similar magnetic proximity effect was observed in conformable multilayer systems with the ferromagnetic metal/paramagnetic metal interfaces. ^12–14) The study about the mechanism will be done in the future.

In summary, we demonstrated that κ was reduced even in amorphous ferromagnetic metal (Co)/semiconductor (Si) multilayer. Therein, the extremely-low κ_MLF of ∼1.5 Wm⁻¹ K⁻¹ was brought by both the interface phonon scattering and the contribution of amorphous Si with inherently-low κ. Furthermore, we also observed the (S _yx )_sat enhancement. These results give us a beneficial knowledge for developing ANE-based TE material with high ZT_ANE using metal/semiconductor interfaces.

Acknowledgments