Anisotropic Analysis of Nanocrystalline Bismuth Telluride Thin Films Treated by Homogeneous Electron Beam Irradiation

Abstract

The in-plane and cross-plane transport properties of nanocrystalline bismuth telluride (Bi₂Te₃) thin films were evaluated to analyze their anisotropic behavior. Bi₂Te₃ thin films were prepared via radio frequency (RF) magnetron sputtering, followed by a subsequent treatment of thermal annealing and homogeneous electron beam (EB) irradiation at various EB doses. The crystallographic properties of the thin films were determined by X-ray diffraction (XRD) analysis. It was determined that the crystal orientation (Lotgering factor; F value) of Bi₂Te₃ thin films can be controlled by homogeneous EB irradiation treatments, without resulting in crystal growth. The electrical conductivity and Seebeck coefficient were measured in the in-plane direction of the films, and the thermal conductivity was measured in the cross-plane direction using the 3ω method. The anisotropic analysis was performed by combining the F value of the thin films with a simple model based on the transport properties of the basal and lateral planes of single- and poly-crystal Bi₂Te₃. The electrical and thermal conductivities of the in-plane and cross-plane directions of the EB-irradiated thin films clearly differed; however, there was no significant difference between the Seebeck coefficient values of the two planes. Finally, we determined that the figure of merit, ZT, was enhanced by the homogeneous EB irradiation treatment, and the in-plane ZT value was 25% greater than that of the cross-plane direction.

1. Introduction

Thermoelectric materials can potentially be used in thermoelectric power generators because they directly convert thermal energy due to a temperature gradient, into electrical energy via the Seebeck effect. Recently, the range of applications of thermoelectric generators has increased because of developments in energy-harvesting technology. Typical examples include mobile and wireless electronics.^1–3) The thermoelectric energy conversion efficiency of such generators depends on the dimensionless figure of merit, (ZT). This is defined as ZT = σS²T/κ_total, where σ is the electrical conductivity, S is the Seebeck coefficient, T is the absolute temperature, and κ_total is the total thermal conductivity, which comprises the electronic thermal conductivity, κ_e, and the lattice thermal conductivity, κ_l. To improve thermoelectric performance, the power factor, σS², should be maximized and the lattice thermal conductivity should be minimized.

Among many types of thermoelectric materials, the bismuth telluride (Bi₂Te₃) compound is of great interest because it exhibits the highest ZT value near room temperature (RT) and its ZT values can potentially be improved by structural modification. The Bi₂Te₃ compound is one of the materials of the tetradymite family; it has a rhombohedral crystal structure (a = 0.438 nm and c = 3.049 nm) and a space group of $D_{3d}^{5}(R \bar{3} m)$.⁴⁾ The structure of the Bi₂Te₃ compound is commonly described as a hexagonal unit cell, in which each charge-neutralized layer consists of five covalently-bonded monatomic sheets. The thermoelectric performance of the Bi₂Te₃ compound is characterized by its remarkable anisotropic behavior due to the high c-axis to a-axis length ratio of its crystal structure.^5,6) The thermoelectric properties of the material in the direction parallel to the basal plane are superior to those in the direction perpendicular to the plane (lateral plane).

Thin-film technology can potentially be used to improve the ZT values of modified structures, such as stacked layer-,^7–9) nanocrystalline-,^10–12) nano-porous-,^13,14) and phase-separating films.^15,16) However, it is difficult to accurately estimate the ZT values of anisotropic thin-film materials, such as the Bi₂Te₃ compound. This is because the electrical conductivity and Seebeck coefficient are usually measured in the in-plane direction whereas thermal conductivity is usually measured in the cross-plane direction, except for the freestanding films.^17,18) Therefore, it is important to analyze the anisotropic thermoelectric properties of Bi₂Te₃ thin films to estimate their in-plane and cross-plane ZT values.

In this study, we prepared n-type Bi₂Te₃ thin films via radio frequency (RF) magnetron sputtering. To modify the crystal orientation of the thin films whilst generally maintaining the crystallite size, we performed thermal annealing. This was followed by a homogeneous electron beam (EB) irradiation treatment, which is known not to significantly enlarge the crystallite size.^19,20) X-ray diffraction (XRD) patterns were used to determine the crystal orientation (Lotgering factor, F value) and crystallite size of the thin films, as well as the strain induced within them. We measured the in-plane electrical conductivity and Seebeck coefficient at RT. The cross-plane thermal conductivity was measured at RT using the 3ω method. Finally, we estimated the in-plane and cross-plane ZT values using the measured thermoelectric property values combined with a simple model to account for the crystal orientation.

2. Experimental Setup

N-type Bi₂Te₃ thin films were fabricated on SiO₂/Silicon (dimensions: 20 mm × 30 mm × 0.6 mm) substrates via an RF magnetron sputtering method (Tokuda, CFS-8EP). The detailed experimental procedure for the sputtering method is described in our previous report.²¹⁾ The target consisted of high-purity (99.9%) Bi (30 at%)-Te (70 at%) and had a diameter of 127 mm (Kojundo Chemical Laboratory Co., Ltd). The substrate-to-target distance was maintained as 140 mm. Prior to the film deposition, the chamber was evacuated to a pressure of 2.5 × 10⁻⁴ Pa, and the substrate temperature was maintained at 200℃. The sputtering was performed in argon gas (99.995%) at a pressure of 1.0 Pa, using an RF power of 200 W. To deposit a film with a uniform thickness, the substrate holder was rotated at 20 rpm. The thickness of the resulting films was approximately 0.8 μm.

To improve the crystallinity and thermoelectric properties of the Bi₂Te₃ thin films, we performed thermal annealing using an electric furnace. The furnace was filled with an argon (95%) and hydrogen (5%) mixture at atmospheric pressure. The gas flow rate was maintained at 1.0 SLM throughout the annealing process. The temperature was increased to 300°C at a rate of 4 K/min and the samples were annealed at this temperature for 1 h. Following thermal annealing, the samples were cooled to RT naturally in the furnace.

The Bi₂Te₃ thin films were subjected to homogenous irradiation with an electron-curtain accelerator (Type CB175/15/180L, Iwasaki Electric Group Co., Ltd.) at RT.^22–24) In the vacuum, a tungsten filament was used to generate an EB with a voltage of 0.17 MeV and an irradiation dose of 0.43 or 0.86 MGy. The maximum rise in temperature was evaluated to be 25 K at these EB irradiation doses.²⁰⁾ The samples were placed in a vacuum chamber, which had a diameter of 24 cm, and were irradiated with the EB through a titanium window. To prevent oxidation, the samples were held in a nitrogen atmosphere with a residual oxygen concentration of less than 0.04%, at 0.1 MPa. The flow rate of the nitrogen gas was 90 SLM.

The surface morphology of the Bi₂Te₃ thin films was investigated using scanning electron microscopy (SEM; JSM-6301F, JEOL). The atomic composition was estimated by energy-dispersive X-ray spectroscopy using the SEM equipment. The crystallographic properties of the thin films were evaluated by XRD (Mini Flex II, Rigaku) using the Cu-K_α line (λ = 0.154 nm).

The in-plane electrical conductivity, σ, of the Bi₂Te₃ thin films was measured at RT using the four-point probe method (RT-70V, Napson) with an accuracy of ±5%. The in-plane Seebeck coefficient, S, of the thin films was also measured at RT with an accuracy of ±7%. To measure the Seebeck coefficient, both ends of the thin film were connected to a heat sink and heater, respectively. The Seebeck coefficient was determined as the ratio of the potential difference along the film to the temperature difference across it. The in-plane power factor, σS², was calculated using the measured electrical conductivity and Seebeck coefficient values.

The cross-plane thermal conductivity of the Bi₂Te₃ thin films was determined at RT using the 3ω method with an accuracy of ±10%. Details of the thermal conductivity measurement and the sample fabrication process for the 3ω method have been described in a previous report.²⁵⁾ To summarize, a SiO₂ film (thickness: 500 nm) was deposited on a Bi₂Te₃ thin film via RF magnetron sputtering. A thin aluminum wire was deposited on the sample via EB evaporation, using shadow masks. The thin aluminum wire had a width of 20 μm and the length of the heater section was 2 mm. We also fabricated reference samples that did not incorporate the Bi₂Te₃ thin film but were otherwise identical to the primary samples. The reference samples were used to subtract the thermal properties of the insulation layer. In our previous study, we confirmed that it was possible to disregard the thermal contact resistance values to estimate the thermal conductivity values of the thin films.²⁶⁾

3. Results and Discussion

3.1 Structural properties of Bi₂Te₃ thin films

Figure 1 shows the surface morphology of the Bi₂Te₃ thin films, captured by SEM. The untreated film had a very similar structure to the film that was treated with an EB irradiation dose of 0.43 MGy. The stoichiometric atomic composition (Bi:Te = 40:60) of the films was determined by EDX, as shown in Figs. 1(a) and 1(b). These films exhibited a relatively rough surface, and consisted of a large quantity of granular-like grains with diameters of less than 100 nm. Moreover, in Fig. 1(c), the film that was treated with an EB irradiation dose of 0.83 MGy had a very similar average grain size to that of the untreated film and the film that was treated with an irradiation dose of 0.43 MGy. The atomic composition of the film that was treated with an EB irradiation dose of 0.83 MGy slightly deviated from the stoichiometric composition.

Fig. 1

Surface morphologies of the Bi₂Te₃ thin films, imaged using SEM. The atomic composition is determined by EDX. Photographs (a), (b), and (c) represent the untreated film, and those treated with EB irradiation doses of 0.43 and 0.86 MGy, respectively.

The XRD patterns of the Bi₂Te₃ thin films obtained after the various EB irradiation treatments are shown in Fig. 2. In all the samples, the peaks in the patterns correspond to the reflections of the rhombohedral phase of Bi₂Te₃ (JCPDS 15-0863). The strongest crystal peak was (0 1 5), and c-axis-oriented peaks (0 0 l) were also observed for all the samples. The XRD peak intensities were enhanced as the EB irradiation dose was increased, indicating that the films were well crystallized.

Fig. 2

X-ray diffraction patterns of Bi₂Te₃ thin films treated with various EB irradiation doses.

To further investigate the crystallographic properties of the Bi₂Te₃ thin films, we estimated the values for the crystal orientation, average crystallite size, and strain, as shown in Fig. 3. The crystal orientation of the Bi₂Te₃ thin films as a function of the EB irradiation dose is shown in Fig. 3(a). The degree of c-axis orientation was evaluated using the Lotgering factor, F, which is calculated using eq. (1):²⁷⁾   

\[F = \frac{P-P_0}{1-P_0},\](1)

where P₀ = ∑I₀(0 0 l)/∑I₀(h k l) and P = ∑I(0 0 l)/∑I(h k l). I₀ and I are the intensities of the peaks in the XRD patterns provided in the JCPDS file (15-0863) and those that were experimentally obtained, respectively. An F value of zero indicates that the crystals exhibit non-orientation and isotropic transport properties; whereas an F value of 1.0 indicates that the crystals are completely oriented in the c-axis direction and exhibit the highest degree of anisotropy. In our experiment, the F value of the untreated thin film was 0.21. As the EB irradiation dose increased, the F value increased linearly, attaining a value of 0.28 at an EB irradiation dose of 0.86 MGy. Therefore, we can conclude that the crystal orientation of such thin films can be controlled by homogeneous EB irradiation treatments.

Fig. 3

(a) Crystal orientation (Lotgering factor, F), (b) average crystallite size, and (c) strain generated in the a-axis and c-axis directions of the Bi₂Te₃ thin films as a function of the EB irradiation dose, measured using X-ray diffraction peaks.

The average crystallite size of the thin films is shown in Fig. 3(b). The average crystallite size was estimated from the full-width at half-maximum of the (0 1 5) XRD peaks using Scherrer's equation. The average crystallite size of all of the samples was approximately 23 nm, indicating that the crystals had hardly grown even though the crystallinity and crystal orientation had been altered by the homogeneous EB irradiation treatment.

The strain values for the thin films are shown in Fig. 3(c). In the a-axis direction, for example, the strain can be determined as follows: strain (a-axis) = (a − a₀)/a₀ × 100%, where “a” is the a-axis lattice constant of our samples, and “a₀” is that provided by the standard data (JCPDS 15-0863) for Bi₂Te₃. The strain induced in the a-axis direction of the untreated film was 0.09%. On one occasion, the strain decreased at an EB irradiation dose of 0.43 MGy, and subsequently increased as the EB irradiation dose was increased to 0.86 MGy. All the thin films exhibited positive strain values in the a-axis direction, indicating that tensile strains were generated in the a-axis direction of the thin films. Moreover, no strain was generated in c-axis direction of the untreated film. The strain decreased and then reached a value of −0.13% at an EB irradiation dose of 0.43 MGy, indicating that a compressive strain had been induced in the film. The strain increased as the EB irradiation dose was further increased to 0.86 MGy; the strain had still a negative value, but its magnitude had increased. Therefore, compressive strain was induced in the c-axis direction of the film as a result of the EB irradiation treatment. Finally, we compared the magnitude of the strain in the a-axis direction with that in the c-axis direction. In the untreated film, the magnitude of the positive strain in the a-axis direction was greater than the magnitude of the negative strain in the c-axis direction; therefore, we can conclude that the film was in a state of tensile strain. In contrast, in the case of the film that was irradiated with a dose of 0.43 MGy, the magnitude of the positive strain in the a-axis direction was lower than the magnitude of the negative strain in the c-axis direction; therefore, the film was in a state of compressive strain. In the case of the film that was irradiated with an EB irradiation dose of 0.86 MGy, the magnitude of the positive strain in the a-axis direction was almost equal to the magnitude of the negative strain in the c-axis direction, indicating that no strain had generated in the film.

3.2 Anisotropic analysis of Bi₂Te₃ thin films

To estimate the in-plane and cross-plane transport properties of the Bi₂Te₃ thin films, we used a simple model based on the transport properties of the basal plane (perpendicular to the c-axis) and lateral plane (parallel to the c-axis) of single- and poly-crystal Bi₂Te₃,^5,28–31) as presented in Table 1. At an F value of zero, the transport property values of the basal and lateral planes are expected to converge, so the normalized value of the averaged property values is equal to 1.0, as shown in Fig. 4. At an F value of 1.0, the transport property values in the in-plane direction are expected to be at their highest. At the same time, those in the cross-plane direction are expected to be at their lowest. Therefore, the normalized property values in the in-plane direction were estimated by dividing the basal plane property values by the average values. As a result, the normalized values in the in-plane direction of the electrical conductivity, Seebeck coefficient, and lattice thermal conductivity were determined as 1.35, 1.00, and 1.19, respectively. On the other hand, the normalized property values in the cross-plane direction were estimated by dividing the lateral plane property values by the average values. As a result, the normalized values in the cross-plane direction of the electrical conductivity, Seebeck coefficient, and lattice thermal conductivity were determined as 0.29, 0.97, and 0.65, respectively. In this model, we assumed that the normalized transport properties linearly depend on the F value by interpolating the properties of poly-crystal Bi₂Te₃. Here, it is noted that the transport properties are influenced by the crystallite size of the film.^32–34) However, we did not consider the effect of the crystallite size because the thin films in this study had very similar crystallite sizes. Finally, we also assumed that the degree of anisotropy was not dependent on the crystallite size.

Table 1 Transport properties of basal and lateral planes of single- and poly-crystal Bi₂Te₃. The average values are estimated using the properties of both planes. The normalized values are calculated using the values of the basal plane as well as the average values.

	Single-crystal Bi2Te3				Poly-crystal Bi2Te331)
	F	σ [104 S/m]	S [μV/K]	κl [W/(m·K)]	F	σ [104 S/m]	S [μV/K]	κl [W/(m·K)]
Basal plane : A (perpendicular to c-axis)	1.0	8.135) 10.029) 6.6030)	−227.85) −24029)	1.528) 1.4729)	0.50 0.56	8.55 1.09	−198 −194	0.87 0.80
Lateral plane : B (parallel to c-axis)	1.0	2.245) 1.8529) 1.5030)	−206.75) −24029)	0.728) 0.8629)	0.50 0.56	4.80 4.35	−194 −191	0.65 0.66
Average : C (2A + B)/3	0.0	6.175) 7.2829) 4.9030)	−220.85) −24029)	1.228) 1.2729)	0.0 0.0	7.30 8.70	−197 −193	0.80 0.75
A/C (normalized)		1.325) 1.3729) 1.3530)	1.035) 1.0029)	1.2528) 1.1629)		1.17 1.25	1.01 1.01	1.08 1.07
B/C (normalized)		0.365) 0.2529) 0.3130)	0.945) 1.0029)	0.5828) 0.6829)		0.66 0.50	0.98 0.99	0.81 0.88

Fig. 4

Normalized electrical conductivity, Seebeck coefficient, and lattice thermal conductivity of Bi₂Te₃ thin films as a function of the F value, calculated using a simple model based on the transport properties of the basal and lateral planes of single- and poly-crystal Bi₂Te₃.

3.3 Electrical transport properties of Bi₂Te₃ thin films

Figure 5 shows the in-plane and cross-plane electrical transport property values (electrical conductivity, Seebeck coefficient, power factor) of the Bi₂Te₃ thin films as a function of the EB irradiation dose. In Fig. 5(a), the electrical conductivity was measured in the in-plane direction. The cross-plane electrical conductivity was calculated by dividing the in-plane electrical conductivity by the normalized electrical conductivity corresponding to the F value of the thin film, as depicted in Fig. 4. For example, in the case of the untreated film, the measured in-plane electrical conductivity was 1.79 × 10⁴ S/m, and the F value was 0.21. The corresponding normalized electrical conductivities in the in-plane direction and cross-plane direction were 1.08 and 0.83, respectively. Therefore, the cross-plane electrical conductivity of the untreated film was calculated to be 1.38 × 10⁴ S/m. As the homogeneous EB irradiation treatment was performed, the electrical conductivity of both planes drastically decreased. This may be because the carrier concentration decreased by the EB irradiation treatment. When the EB irradiation dose was 0.43 MGy, the in-plane and cross-plane electrical conductivities were 0.8 × 10⁴ and 0.6 × 10⁴ S/m, respectively. For both planes, as the EB irradiation dose was further increased to 0.86 MGy, the electrical conductivity values did not significantly change.

Fig. 5

(a) Electrical conductivity, (b) Seebeck coefficient, and (c) power factor of the Bi₂Te₃ thin films as a function of the EB irradiation dose. The in-plane properties are represented by measured values, and the cross-plane properties are represented by calculated values.

In Fig. 5(b), the Seebeck coefficient was measured in the in-plane direction. The cross-plane Seebeck coefficient was calculated using the same procedure as that used to calculate the electrical conductivity. The in-plane and cross-plane Seebeck coefficient values were almost identical for each EB irradiation dose. This is because the Seebeck coefficient is slightly anisotropic.⁵⁾ For both planes of the untreated film, the Seebeck coefficient was determined to be approximately −45 μV/K. The Seebeck coefficients of both planes significantly improved as a result of the EB irradiation treatment, and reached a value of approximately −150 μV/K at an EB irradiation dose of 0.43 MGy. This enhancement of the Seebeck coefficient can be well explained by the Mahan-Sofo theory.³⁵⁾ This theory points out that the enhancement of Seebeck coefficient is caused by the increase in the slope of the density of states (DOS) near the Fermi level. The DOS near the Fermi level is expected to increase by inducing the compressive strain for shrinking the distance between atoms in the unit cells, as presented in Fig. 3(c). As the EB irradiation dose was further increased to 0.86 MGy, the absolute value of the Seebeck coefficient slightly decreased. Based on the results obtained on the electrical conductivity and Seebeck coefficient of the thin films, we can conclude that the carrier concentration of the thin films decreased as a result of the EB irradiation treatment. It is known that the carrier concentration depends on the doping density and defect density.^36–38) In this case, the defect density affects the carrier concentration because low crystallinity materials have a large quantity of defects at their grain boundaries, and the defects provide unpaired electrons as carriers. When the thin films were treated with homogeneous EB irradiation, the number of defects at the grain boundaries decreased, leading to a reduction in the carrier concentration.

The power factor was estimated by the electrical conductivity and Seebeck coefficient, as shown in Fig. 5(c). The differences between the in-plane and cross-plane power factors were attributed to the differences in the electrical conductivity values because the Seebeck coefficient is slightly isotropic. The in-plane and cross-plane power factors of the untreated films were less than 40 μW/(m·K²). The maximum power factor value was 194 μW/(m·K²), which was achieved in the in-plane direction of the thin film that received an EB irradiation treatment of 0.43 MGy. This is because the increase in the absolute value of the Seebeck coefficient resulting from the EB irradiation treatment, contributed to, rather than decreased, the electrical conductivity of the film. Finally, there were differences between the power factor values obtained for the in-plane and cross-plane directions of the thin films. In particular, in the case of the film that was treated with an EB irradiation treatment of 0.43 MGy, the in-plane power factor was 38% higher than the cross-plane power factor. Therefore, we can conclude that it is possible to estimate the anisotropic electrical transport property values of Bi₂Te₃ thin films.

3.4 Thermal transport properties of Bi₂Te₃ thin films

Figure 6 shows the in-plane and cross-plane thermal transport property values (total-, electronic-, and lattice thermal conductivity) of the Bi₂Te₃ thin films as a function of the EB irradiation dose. The total cross-plane thermal conductivity (κ_total) was measured using the 3ω method. The electronic thermal conductivities (κ_e) of both planes were estimated based on their electrical conductivity and the Wiedemann-Franz law, with the Lorenz number L_n = 2.44 × 10⁻⁸ WΩ/K². The cross-plane lattice thermal conductivity (κ_l) was calculated by subtracting the cross-plane κ_e value from the cross-plane κ_total value. To evaluate the in-plane κ_l value, we employed anisotropic analysis, as shown in Fig. 4. For example, for the untreated film, the estimated cross-plane κ_l value was 0.36 W/(m·K), and the F value was 0.21. The corresponding normalized lattice thermal conductivities in the in-plane and cross-plane direction were 1.03 and 0.94, respectively. Therefore, the in-plane κ_l value of the untreated film was calculated to be 0.39 W/(m·K). As a result, the in-plane κ_total was calculated by the addition of the in-plane κ_e and κ_l values. For both planes, the κ_total and κ_l values exhibited a similar trend when plotted as a function of the EB irradiation dose because all the samples had low κ_e values. Therefore, the κ_l value is a key parameter for determining the thermal conductivity of the thin films. The κ_l value of both planes increased following an EB irradiation dose of 0.43 MGy. This could possibly be attributed to the strains induced in the thin films. In our previous study, we determined that the κ_l value increased as compressive strains were generated in the thin films.³⁹⁾ In this study, the film that was treated with an EB irradiation dose of 0.43 MGy, was in a state of compressive strain, so it exhibited a relatively high κ_l value.

Fig. 6

Total-, electronic-, and lattice thermal conductivity of the Bi₂Te₃ thin films as a function of the EB irradiation dose. These thermal conductivities are estimated by combining the experimentally measured results with the calculated results.

3.5 Dimensionless figure of merit (ZT) of Bi₂Te₃ thin films

Figure 7 shows the ZT values of the in-plane and cross-plane directions of the Bi₂Te₃ thin films as a function of the EB irradiation dose. As the EB irradiation dose was increased, the ZT of both planes increased. The highest ZT values of 0.07 and 0.06, corresponding to the in-plane and cross-plane directions, respectively, were achieved by the film that was treated with an EB irradiation dose of 0.86 MGy because it had relatively low thermal conductivity. There was an 25% difference between the ZT values of the in-plane and cross-plane directions, whereas there was a 38% difference in the respective power factors. Therefore, we determined that the ZT value was less anisotropic than the power factor. Finally, even though the films in this study exhibited low ZT values compared with those of established Bi₂Te₃-based alloy thin films,⁴⁾ we developed a method for the anisotropic analysis of Bi₂Te₃-based alloys, and this method can be applied to other anisotropic materials.

Fig. 7

Dimensionless figure of merit, ZT, of the Bi₂Te₃ thin films as a function of the EB irradiation dose. The ZT values were estimated by combining the experimentally measured results with the calculated results.

4. Conclusions

To perform anisotropic analysis on n-type nanocrystalline Bi₂Te₃ thin films, the in-plane and cross-plane transport property values were estimated. The thin films were prepared via RF magnetron sputtering, followed by a subsequent treatment of thermal annealing and homogeneous EB irradiation at various EB doses. We evaluated the structural properties of the thin films via SEM observation and XRD analysis. It was determined that the crystal orientation (Lotgering factor; F value) of the thin films could be controlled by homogeneous EB irradiation treatments, in which significant growth of the crystal grains does not occur. The anisotropic analysis was performed to estimate the in-plane and cross-plane transport property values of Bi₂Te₃ thin films using a simple model based on the transport properties of the basal (perpendicular to c-axis) and lateral planes (parallel to c-axis) of single- and poly-crystal Bi₂Te₃. For this analysis, it was possible to estimate the in-plane transport property values from those of the cross-plane, and vice versa. There was a clear difference between the in-plane and cross-plane electrical conductivities of the samples; however, the Seebeck coefficients of the two planes did not significantly differ. As a result, we observed differences between the power factor values of the in-plane and cross-plane directions. In particular, for the film that was treated with an EB irradiation dose of 0.43 MGy, the in-plane power factor was 38% greater than that of its cross-plane direction. We estimated the thermal conductivity of both planes by categorizing it into three constituents, namely κ_total, κ_e, and κ_l. It was determined that κ_l predominantly governs the thermal conductivity of the thin films. As the EB irradiation dose was increased to 0.43 MGy, there was an increase in the κ_l value of both planes owing to the compressive strain induced in the film. The highest ZT values were achieved by the film that was treated with an EB irradiation dose of 0.86 MGy because it exhibited relatively low thermal conductivity. The ZT was less anisotropic than the power factor. Even though the ZT values of the films in this study were low compared with those of established Bi₂Te₃-based alloy thin films, we developed a method for the anisotropic analysis of Bi₂Te₃ based alloys. Furthermore, this method can be applied to other anisotropic materials.

Acknowledgments

This work was partially supported by the Japan Science and Technology Agency (JST). The authors wish to thank H. Hagino at Fujikura Ltd., as well as Y. Miyamoto, K. Kusagaya, N. Hatsuta, and K. Yamauchi at Tokai University for providing experimental support.

REFERENCES

• 1)  J.A. Paradiso and T. Starner: Pervasive Comput. 4 (2005) 18–27. 10.1109/MPRV.2005.9
• 2)  N.S. Hudak and G.G. Amatucci: J. Appl. Phys. 103 (2008) 101301. 10.1063/1.2918987
• 3)  Z. Wang, A. Chen, R. Winslow, D. Madan, R.C. Juang, M. Nill, J.W. Evans and P.K. Wright: J. Micromech. Microeng. 22 (2012) 094001. 10.1088/0960-1317/22/9/094001
• 4)  D. M. Rowe: CRC Handbook of Thermoelectrics, (CRC, Boca Raton, 1995) Sec.19, pp. 211–237.
• 5)  H. Kaibe, Y. Tanaka, M. Sakata and I. Nishida: J. Phys. Chem. Solids 50 (1989) 945–950. 10.1016/0022-3697(89)90045-0
• 6)  P.J. Taylor, J.R. Maddux, W.A. Jesser and F.D. Rosi: J. Appl. Phys. 85 (1999) 7807–7813. 10.1063/1.370589
• 7)  R. Venkatasubramanian, E. Siivola, T. Colpitts and B. O'Quinn: Nature 413 (2001) 597–602. 10.1038/35098012
• 8)  N. Peranio, O. Eibl and J. Nurnus: J. Appl. Phys. 100 (2006) 114306. 10.1063/1.2375016
• 9)  K. Matsuoka, M. Okuhata and M. Takashiri: J. Alloy. Compd. 649 (2015) 721–725. 10.1016/j.jallcom.2015.07.166
• 10)  H. Obara, S. Higomo, M. Ohta, A. Yamamoto, K. Ueno and T. Iida: Jpn. J. Appl. Phys. 48 (2009) 085506. 10.1143/JJAP.48.085506
• 11)  Y. Zhao, J.S. Dyck, B.M. Hernandez and C. Burda: J. Phys. Chem. C 114 (2010) 11607–11613. 10.1021/jp102816x
• 12)  M. Takashiri, S. Tanaka and K. Miyazaki: J. Electron. Mater. 43 (2014) 1881–1889. 10.1007/s11664-013-2896-1
• 13)  M. Kashiwagi, S. Hirata, K. Harada, Y. Zheng, K. Miyazaki, M. Yahiro and C. Adachi: Appl. Phys. Lett. 98 (2011) 023114. 10.1063/1.3543852
• 14)  M. Takashiri, S. Tanaka, H. Hagino and K. Miyazaki: J. Appl. Phys. 112 (2012) 084315. 10.1063/1.4759326
• 15)  K. Agarwal and B.R. Mehta: J. Appl. Phys. 116 (2014) 083518. 10.1063/1.4894145
• 16)  M. Takashiri, K. Kurita, H. Hagino, S. Tanaka and K. Miyazaki: J. Appl. Phys. 118 (2015) 065301. 10.1063/1.4928311
• 17)  D. Song and G. Chen: Appl. Phys. Lett. 84 (2004) 687–689. 10.1063/1.1642753
• 18)  K. Nishimura, H. Wang, T. Fukunaga, K. Kurata and H. Takamatsu: Int. J. Heat Mass Transfer 95 (2016) 727–734. 10.1016/j.ijheatmasstransfer.2015.12.047
• 19)  M. Takashiri, K. Imai, M. Uyama, H. Hagino, S. Tanaka, K. Miyazaki and Y. Nishi: J. Alloy. Compd. 612 (2014) 98–102. 10.1016/j.jallcom.2014.05.146
• 20)  M. Takashiri, K. Imai, M. Uyama, H. Hagino, S. Tanaka, K. Miyazaki and Y. Nishi: J. Appl. Phys. 115 (2014) 214311. 10.1063/1.4881676
• 21)  K. Kusagaya, H. Hagino, S. Tanaka, K. Miyazaki and M. Takashiri: J. Electron. Mater. 44 (2015) 1632–1636. 10.1007/s11664-014-3496-4
• 22)  Y. Nishi, S. Takagi, K. Yasuda and K. Itoh: J. Appl. Phys. 70 (1991) 367–371. 10.1063/1.350282
• 23)  Y. Nishi, T. Toriyama, K. Oguri, A. Tonegawa and K. Takayama: J. Mater. Res. 16 (2001) 1632–1635. 10.1557/JMR.2001.0226
• 24)  Y. Nishi, H. Sato, K. Iwata and K. Iwata: J. Mater. Res. 24 (2009) 3503–3509. 10.1557/jmr.2009.0429
• 25)  M. Takashiri, S. Tanaka, K. Miyazaki and H. Tsukamoto: J. Alloy. Compd. 490 (2010) L44–L47. 10.1016/j.jallcom.2009.10.117
• 26)  S. Kudo, H. Hagino, S. Tanaka, K. Miyazaki and M. Takashiri: J. Electron. Mater. 44 (2015) 2021–2025. 10.1007/s11664-015-3646-3
• 27)  F.K. Lotgering: J. Inorg. Nucl. Chem. 9 (1959) 113–123. 10.1016/0022-1902(59)80070-1
• 28)  G. S. Nolas, J. Sharp and H. J. Goldsmid, Thermoelectrics (Springer, Berlin, 2001) Chap. 5.1, pp. 111–131.
• 29)  A. Jacquot, N. Farag, M. Jaegle, M. Bobeth, J. Schmidt, D. Ebling and H. Böttner: J. Electron. Mater. 39 (2010) 1861–1868. 10.1007/s11664-009-1059-x
• 30)  H.J. Goldsmid: J. Appl. Phys. 32 (1961) 2198–2202. 10.1063/1.1777042
• 31)  T. Kajihara, K. Fukuda, Y. Sato and M. Kikuchi, Proc. 17th Int. Conf. on Thermoelectrics (1998) pp. 129–133.
• 32)  M. Takashiri, K. Miyazaki, S. Tanaka, J. Kurosaki, D. Nagai and H. Tsukamoto: J. Appl. Phys. 104 (2008) 084302. 10.1063/1.2990774
• 33)  C. Liao, Y. Wang and H. Chu: J. Appl. Phys. 104 (2008) 104312. 10.1063/1.3026728
• 34)  Z. Wang, J. Alaniz, W. Jang, J.E. Garay and C. Dames: Nano Lett. 11 (2011) 2206–2213. 10.1021/nl1045395
• 35)  G.D. Mahan and J.O. Sofo: Proc. Natl. Acad. Sci. USA 93 (1996) 7436–7439. 10.1073/pnas.93.15.7436
• 36)  A. Giani, A. Boulouz and F. Pascal-Delannoy: J. Mater. Sci. Lett. 18 (1999) 541–543. 10.1023/A:1006670327086
• 37)  M. Takashiri, K. Miyazaki and H. Tsukamoto: Thin Solid Films 516 (2008) 6336–6343. 10.1016/j.tsf.2007.12.130
• 38)  R. Rostek, V. Sklyarenko and P. Woias: J. Mater. Res. 26 (2011) 1785–1790. 10.1557/jmr.2011.141
• 39)  M. Takashiri, S. Tanaka, H. Hagino and K. Miyazaki: Int. J. Heat Mass Transfer 76 (2014) 376–384. 10.1016/j.ijheatmasstransfer.2014.04.048