Crystal growth and flat-band effects on thermoelectric properties of Fe₂TiAl-based full-Heusler thin films Open Access

There is a strong demand for the recovery of wasted heat at room temperature (RT) because over two-thirds of wasted heat is known to exist below 300 °C. Although thermoelectric (TE) conversion is a promising solution to this problem, only a few TE materials such as Bi₂Te₃ and related compounds exhibit good performance (ZT > 1) at room temperature.^1–3 Here, ZT is a dimensionless figure of merit given by S²T/ρ(κ_e + κ_l), where S is the Seebeck coefficient, ρ is the resistivity, T is the temperature, κ_e is the electrical thermal conductivity, and κ_l is the lattice thermal conductivity. Fe-based full-Heusler (FH) alloys are promising candidates for such room-temperature applications because of the low cost, abundance, and non-toxicity of their constituent elements. For example, Fe₂VAl-based FH alloys show a large power factor (PF) defined by S²/ρ compared to well-known TE materials such as Bi₂Te₃.^4,5 Although several FH alloys such as Fe₂TiSn_1−xSi_x have been predicted to show high TE performance owing to the electronic flat band with a large density of states (DOS) in the Γ–X region,^6,7 not many FH alloys are known to be chemically stable, except for Fe₂VAl and Fe₂TiSn.^8,9 Recently, thin-film techniques have been shown to be effective for stabilizing meta-stable phases, as clarified in the case of Fe₂TiSi films grown on MgAlO₄ substrates with simultaneous annealing.^10,11 As various compositions are required to realize high-performance TE materials, rapid processing such as post-annealing is strongly desired.

In this study, the growth conditions of Fe-based FH alloys in the post-annealing process were investigated. Furthermore, the importance of lattice matching with the substrate and the initial amorphous state was clarified in the growth of FH phase. In the case of Fe₂TiAl-based FH alloys, almost epitaxially grown FH phases were obtained and the valence electron concentration (VEC) was modulated by adding chips of other elements on the sputtering target to improve the TE properties. Not only the VEC and Fe amount but also the bandgap strongly affected the PF; consequently, a large S of 99 µV/K and a ZT of 0.12 were obtained in the case of in Fe_2.01Ti_0.56V_0.67Al_0.76 as a p-type TE material.

The samples were prepared as follows: FH thin films were deposited on MgO (001) substrates by magnetron sputtering under a base pressure of 10⁻⁶ Pa at room temperature (RT). The sputtering targets used were Fe₂TiSn, Fe₂NbAl, Fe₂TiAl, Fe₂VAl, Fe₂TiSi, and Fe₂VSi, which have been investigated as potential TE materials.^{4–9,11–15} To vary the composition of the thin films, various square chips of V, Cr, Mn, Fe, and Co (side, 10 mm) were placed on circular FH alloy targets (diameter, 120 mm). The samples are abbreviated as “target + chip(n).” Here, “target” refers to the material of the used target, “chip” refers to the material placed on the target, and “n” denotes the number of chips placed on the target. The samples were then annealed at a temperature of 800 °C under a base pressure of 10⁻⁶ Pa for 1 h. The thickness of the deposited thin films was 200 nm in the as-deposited state, and it was reduced to around 180 nm by the post-annealing process.

The film structure was characterized by cross-sectional transmission electron microscopy (TEM) (Hitachi, H-9000UHR), cross-sectional high-angle annular dark-field scanning TEM (HAADF-STEM) (Hitachi, HD-2700), and electron diffractometry. The crystal structure of the films was characterized on the basis of out-of-plane x-ray diffraction (XRD) measurements (Rigaku, RINT1400) with a Cu Kα radiation source. The diffraction patterns were collected via ω–2θ scanning in the 2θ range of 25°–70°. The film composition of the entire film was determined via inductively coupled plasma-atomic emission spectroscopy (ICP-AES), and the local film composition was evaluated via energy dispersive x-ray spectroscopy (EDX). The in-plane S and ρ at temperatures above RT were measured using two- and four-probe methods, respectively (ADVANCE RIKO, ZEM-3). Careful configurations were adopted to evaluate intrinsic S of thin films because shunts of electric and thermal flow to the substrates prevent evaluations of the intrinsic S in the case of substrates with low resistivity such as Si substrates (see supplementary material 1). The in-plane S and ρ at temperatures below RT were measured using the two-probe method and the van der Pauw method, respectively (TOYO Technica, ResiTest8300). The out-of-plane κ at RT was evaluated using the picosecond thermo-reflectance method (PicoTherm), which has been reported in a previous study,¹⁶ and Mo(105) was applied on the top of the film as a reflective coating. The Hall measurements were obtained under a maximum magnetic field of 0.56 T using the van der Pauw method (TOYO Technica, ResiTest8300). The electronic structures of the FH alloys were determined after optimizing the lattice constants by first-principles calculations using OPENMX code based on density-functional theory (DFT) under the generalized gradient approximation (GGA).^17–19 

Figure 1(a) shows the out-of-plane XRD patterns of a ω–2θ scan of the Fe-based FH alloy thin films in the as-deposited state. Here, the vertical axis representing the intensity is shown in the logarithmic scale. All the films except for Fe₂VAl show no specific diffraction peak other than the peaks from the MgO substrates with the (001) orientation, indicating amorphous films. In the case of Fe₂VAl, which is known to be a stable ternary material, the diffraction peak was observed at 2θ of ∼64.5°, indicating the existence of body-centered-cubic (BCC) Fe along the (002) direction or disordered Fe₂VAl along the (004) direction. Figure 1(b) shows the out-of-plane XRD patterns of a ω–2θ scan of the Fe-based FH alloy thin films annealed at 800 °C. For all the films, strong (00L) diffraction peaks were observed in addition to those from the MgO substrates, indicating that the FH alloy phases grew almost epitaxially along the (001) orientation in the majority of the films, as observed in previous studies.^20–22 Note that the adopted fabrication method, i.e., crystallization from amorphous states with MgO seed layers, facilitated the crystallization of not only stable FH alloys such as Fe₂TiSn, Fe₂TiAl, and Fe₂VSi but also unstable FH alloys such as Fe₂NbAl and Fe₂TiSi, which have not been obtained in bulk. However, the diffraction peak of an impurity phase was observed at 2θ of ∼41° in the case of Fe₂NbAl possibly because of the instability of Fe₂V_1−xNb_xAl bulk, as reported previously.¹³ The (022) diffraction peak was also observed in the case of Fe₂VAl, while such a peak was not observed in the case of other Fe-based FH alloys. As Fe₂VAl is known as a fairly stable ternary material, these results suggest that stable phases could be easily formed by post-annealing without the seed effects from the MgO substrates and that initial crystallization would prevent the epitaxial growth of the FH phases. In fact, a recent study on Co₂(Mn, Fe)Ge showed that the initial amorphous states are important for the growth of FH phases from seed layers.^23,24

Hereafter, we focus on Fe₂TiAl because this material has a small lattice mismatch without any impurity phase, as clarified in Fig. 1(b) (see also supplementary material 2 and 3). The cross-sectional TEM image of Fe₂TiAl is shown in Fig. 2(a). Large grains with a size of ∼100 nm were observed. The local compositions were evaluated via EDX point analysis, and all the points shown in Fig. 2(a), denoted as 1–6, were clarified to have nearly the same composition, suggesting homogeneously grown films. The local composition measured via EDX (Fe_2.24Ti_0.78Al_0.98) was comparable to the film composition measured via ICP-AES (Fe_2.18Ti_0.73Al_1.09). Figure 2(b) shows a cross-sectional DF-STEM image of region b in Fig. 2(a). In the vicinity of the interface between the Fe₂TiAl film and the MgO substrate, both lattices seem to connect smoothly, suggesting an epitaxial growth from the substrate. Figure 2(c) shows an image of the inverse fast Fourier transformation in region c, where the grain boundary exists. There is a small contrast between the grains, suggesting a small stress, whereas the lattice seems to be distributed nearly homogeneously. Figures 2(d)–2(f) show electron diffraction patterns of points 4, 5, and 6, respectively. The difference in the crystal orientation both between the grains and between the Fe₂TiAl film and the MgO substrate was less than 1%. These results suggest that the Fe₂TiAl film fabricated by the post-annealing process was an epitaxially grown single phase with homogeneous elemental compositions.

Next, we investigated the thermoelectric properties of the element-added Fe₂TiAl-based films. To improve the thermoelectric performance, the carrier concentration should be reduced because, in general, the metallic states are known to have small S. The composition of the film was varied by adding other element chips, as explained in the experimental section (see also supplementary material 4). Figures 3(a) and 3(b) show S and ρ, respectively, of Fe₂TiAl + TM(n) films (TM ≡ V, Fe, Cr, Mn, and Co) as a function of VEC. Here, S and ρ of the Fe₂TiAl-based bulks (Fe_2−xCo_xTiAl) are also plotted in the figures.¹⁴ Our Fe₂TiAl-based thin films showed relatively large S compared to the Fe₂TiAl-based bulks although the annealing temperature of 800 °C is lower than the FH bulks. If the initial state of the film has metastable states such as amorphous or nanocrystals same as our cases, a high free energy for crystallization or crystal growth enables the chemical ordering at relatively low temperatures as discussed in the literature.²³ In addition, most of our films have the Fe amount larger than the stoichiometric value of 2.0, which is known to increase p-type S larger owing to the created anti-sites.⁵ If we consider the dependence of S on VEC in further detail, we find that most of the films show nearly the same trend whereby S increases gradually and becomes ∼40 µV/K at a VEC of ∼6.0 when the VEC is decreased. These observations suggest that the fabricated films were successfully carrier-doped by adding other elements on the Fe₂TiAl target. Both S and ρ of the films varied depending on VEC; however, the change was small compared to those of the bulks, which rapidly changed at a VEC of ∼6.0, originating from the carrier-type change as clarified in previous studies on semiconducting FH bulks.^4,5 The observed weak dependence of the films on the VEC may be because the addition of elements as chips in this study caused not only a change in the VEC but also a reduction in the Fe amount. Doped thermoelectric FH alloys such as Fe₂V_1−aX_aAl and Fe₂VAl_1−bY_b show a change in S mainly depending on the VEC owing to the change in both the carrier concentration and the carrier type in a rigid band model, consequently showing a universal curve of S depending on not kinds of substituents but only VEC.^4,25 On the other hand, the decrease in Fe is known to affect the amount of anti-sites and consequently shift the universal curve of S depending on VEC to the lower VEC side.^5,26,27 When the chip is added on the Fe₂TiAl target with the valence electron count different from the VEC of thin films without the addition, the added chip causes not only a change in the VEC but also a reduction in the Fe amount, simultaneously causing a shift of the universal curve to the lower VEC side. Our films are considered to show weaker dependence on the VEC than the bulks owing to the above-mentioned reasons.

Most of the Fe₂TiAl-based films, except for those with V-additions and Fe₂TiAl-based bulks, shown in Fig. 3(a) have small S and ρ less than 50 µV/K and 7 μΩ m, respectively, even at a VEC of ∼6.0. This suppression may be due to the strong bipolar effects of a flat band in the conduction band. Figures 4(a) and 4(b) show the band structure around the Fermi level of Fe₂TiAl and Fe₂VAl, respectively. Both band structures have several characteristic bands: a parabolic band in the conduction band at the X-point (“para-1”) originating from the Ti and V e_g orbitals, a flat band in the conduction band in the Γ–X direction (“flat”) originating from the Fe e_g orbitals, and a parabolic band in the valence band at the Γ-point (“para-2”) originating from the Fe t_2g orbitals. The flat band is known to have a larger density of states than the parabolic bands and strong effects on the thermoelectric properties, as clarified in previous reports.^6,7,28 As shown in Fig. 4(a), in the case of Fe₂TiAl, the flat band is located at the bottom of the conduction band, and the energy difference between the conduction band and the valence band is only 0.18 eV. As shown in Fig. 4(c), a sharp rise in the density of state (DOS) originating from the flat band (“flat”) is observed at the bottom of the conduction band when the composition is stoichiometric, while a rather small DOS originating from the parabolic band (“para-2”) exists at the top of the valence band. As the energy gap of Fe₂TiAl is small, bipolar conduction affects S as follows:

where σ_p, σ_n, S_p, and S_n are the conductivities and Seebeck coefficients for p-type and n-type carriers, respectively. The flat band is known to show a large S_n and thus prevents p-type S from taking large values when the majority carriers are not electrons but holes. In other words, the large DOS of the minority carriers (electrons) makes it difficult to shift the chemical potential η when the temperature increases, thereby increasing the thermoelectromotive force at a constant temperature difference because η is known to maintain the carrier concentration and is affected by bands with a large DOS. Therefore, it is important to increase the p-type S to move the flat band away from the valence band (“para2”). In fact, only small S_p less than 50 µV/K was observed in previous reports on Fe₂TiSn, which also has a flat band at the bottom of the conduction band, and the energy gap is small (0.07 eV).⁶ 

It is worth noting that the V-doped films, namely, Fe₂TiAl + V(n) and Fe₂TiAl + V(6) + Fe(n), showed a larger S than the other films, which reached a maximum of 99 µV/K in the case of Fe₂TiAl + V(6) + Fe(3), as shown in Fig. 3(a). We suspect that the enhancement of S in the case of the Fe_2.01Ti_0.56V_0.67Al_0.76 film originated from the modifications of the band structures induced by the substitution of Ti by V. In the case of Fe₂TiAl, the flat band with a large DOS is located at the bottom of the conduction band, and it strongly affects the thermoelectric properties as discussed above. Meanwhile, the parabolic band (“para1”) is located at the bottom of the conduction band and the flat band (“flat”) exists in the high-energy state in the case of Fe₂VAl, as shown in Fig. 4(b). From these results, by substituting Ti of Fe₂TiAl by V, the flat band can be moved to a higher energy, and the parabolic band can be moved to a lower energy. In fact, as shown in Fig. 4(c), the bottom of the conduction band of Fe₁₆Ti₄V₄Al₈ has a small DOS owing to the parabolic band (“para1”), whereas that of Fe₁₆Ti₆V₂Al₈ has a large DOS owing to the flat band (“flat”). The calculated energy difference between the flat band (“flat”) and the parabolic band in the valence band (“para2”) monotonically increases with the V amount in the case of Fe₁₆Ti_8−xV_xAl₈, as shown in Fig. 4(d). Meanwhile, the calculated energy difference between the valence and conduction bands is nearly the same for Fe₁₆Ti₈Al₈ and Fe₁₆Ti₄V₄Al₈.

To clarify the origin of the enhancement of S experimentally, we focus on the temperature dependence of the thermoelectric properties. Figures 5(a) and 5(b) show S and ρ, respectively, of Fe₂TiAl + V(6) + Fe(3) and Fe₂TiAl + Cr(4) films with those of the Fe₂TiAl film as a function of temperature. The compositions of Fe₂TiAl + V(6) + Fe(3) and Fe₂TiAl + Cr(4) are Fe_2.01Ti_0.56V_0.67Al_0.76 and Fe_1.99Ti_0.66Cr_0.45Al_0.90, respectively. These films have nearly the same Fe amount (2.01 and 1.99) and nearly the same VEC (5.96 and 5.99), while the former showed S and ρ values around twice as high as those of the latter in the entire temperature range. As the third element (in this case, Al) is known to have a small effect on the band structures around the Fermi level,²⁹ the VEC can be controlled by adjusting the third element within the scheme of the rigid band model. A possible reason for the observed enhancement is the smaller carrier concentration in the Fe_2.01Ti_0.56V_0.67Al_0.76 film because both S and ρ are inversely proportional to the carrier concentration. The measured carrier concentration of the Fe_2.01Ti_0.56V_0.67Al_0.76 film might be lower because of the slight difference in the Fe amount and VEC. However, the lower carrier concentration may not be the main origin because not only other films such as Fe₂TiAl + Cr(n) and Fe₂TiAl + Mn(n) but also Fe₂Ti_1−xCr_xAl and Fe_2−yCo_yTiAl bulks showed small S of at most 50 µV/K even when the VEC was ∼6.0.¹⁴ 

The other possible reason is that the flat band in the conduction band strongly affects the thermoelectric properties, as theoretically suggested above. The bandgap could be estimated from the temperature dependence of S shown in Fig. 5(a) by using the Goldsmid–Sharp formulation,³⁰ 

where S_max is the maximum S and T_max is the temperature for S_max. The estimated value of 0.07 eV for the Fe_2.01Ti_0.56V_0.67Al_0.76 film is much greater than that of 0.04 eV for the Fe_2.18Ti_0.73Al_1.09 films; nevertheless, 50% Ti substitution by V does not change the energy difference between the valence and conduction bands significantly, as discussed above. Previous studies have reported a similar phenomenon in which n-type ZrNiSn with a weighted mobility ratio (A) of 5 has a larger S than p-type ZrNiSn with a weighted mobility ratio of 1/5.^31,32 The weighted mobility ratio is defined as

where μ is the mobility and m_maj and m_min are the effective masses for majority and minority carriers, respectively. As clarified by the calculations, Ti substitutions by V cause both a reduction in m and an increase in μ in n-type conductions owing to the change in the dominant band from the flat band (“flat”) to the parabolic band (“para1”), while the valence band does not change significantly(“para2”). These results suggest that V-additions caused an increase in A and a simultaneous increase in S. The effect of the impurity bands resulting from the off-stoichiometry of Fe was not considered in the above-mentioned discussion.

Finally, we comment on the ZT of our fabricated Fe₂TiAl-based films. The thermal conductivity κ was evaluated using the thermoreflectance method at room temperature. The κ of the Fe_2.18Ti_0.73Al_1.09 film was 7.2 W/K m and the lattice thermal conductivity κ_lat was estimated to be 2.7 W/K m using the Wiedemann–Franz law. The κ_lat was small compared to the Fe₂TiAl-based bulks;¹⁴ nevertheless, the film was almost epitaxially grown on the MgO substrates. The reduction may be attributed to both alloy scattering and boundary scattering owing to the off-stoichiometry and the small thickness compared to the phonon mean free path, respectively, as observed previously in the case of other FH films.^11,20–22 Consequently, the ZT of the Fe_2.18Ti_0.73Al_1.09 and Fe_2.01Ti_0.56V_0.67Al_0.76 films was 0.067 and 0.12, respectively. Note that no element with large mass such as W and Ta was used in our study, and a further increase in ZT could be expected by combining heavy-element doping with flat-band engineering.

In conclusion, we synthesized Fe-based FH thin films on MgO substrates by a post-annealing process. The films grew nearly epitaxially when the initial state was amorphous and the lattice mismatch was small. The TE properties of Fe₂TiAl-based films were investigated by modulating the composition of the films, and the p-type S was found to increase only when V was added. It was clarified that the flat band of Fe₂TiAl moves away from the valence band by substitutions of Ti by V, and consequently, the p-type S increases because of the increase in the weighted mobility ratio. As a result, almost the maximum of p-type ZT in FH alloys was realized even without heavy element doping owing to both large S and small κ. Our results strongly suggest that not only parabolic-band engineering, such as realizing degenerate states, but also flat-band engineering is important for realizing materials with high ZT.

See the supplementary material for methods of measuring the Seebeck coefficient of the thin films, detailed analysis of crystal structures by XRD, and electric transport properties.

The data that support the findings of this study are available within the article and its supplementary material.