Thermoelectric Characteristics of A Single-Crystalline Topological Insulator Bi₂Se₃ Nanowire

Abstract

The discovery of topological insulators (TIs) has motivated detailed studies on their physical properties, especially on their novel surface states via strong spin–orbit interactions. However, surface-state-related thermoelectric properties are rarely reported, likely because of the involvement of their bulk-dominating contribution. In this work, we report thermoelectric studies on a TI bismuth selenide (Bi₂Se₃) nanowire (NW) that exhibit a larger surface/volume ratio. Uniform single-crystalline TI Bi₂Se₃ NWs were successfully synthesized using a stress-induced growth method. To achieve the study of the thermoelectric properties of a nanowire (NW), including electrical conductivity (σ), Seebeck coefficient (S), and thermal conductivity (κ), a special platform for simultaneously performing all measurements on a single wire was designed. The properties of σ, S, and κ of a 200 nm NW that was well precharacterized using transmission electron microscope (TEM) measurements were determined using the four-probe method, the two-probe EMF across ∇T measurement, and the 3ω technique, respectively. The integrated TE properties represented by the figure of merit ZT (S²σT/κ) were found to be in good agreement with a theoretical study of Bi₂Se₃ NW.

1. Introduction

The study of nanoengineered thermoelectric materials used for converting waste heat into electricity has become a compelling research topic [1,2,3,4,5]. The thermoelectric (TE) generator and the TE sensor are devices that can harvest renewable energy for power generation and thermal sensing, respectively [6,7,8,9,10,11]. The efficiency of TE materials is determined by the dimensionless figure of merit ZT, which is defined as S²σT/(κ_e + κ_l), where S is the TE power or Seebeck coefficient, σ represents the electrical conductivity, κ_e is the electronic thermal conductivity, and κ_l is the lattice thermal conductivity. The quantity S²σ is defined as the power factor (PF). The Weidmann–Franz law restricts the ratio σ/κ in a bulk TE compound. Furthermore, a sharply peaked density of states (DOS) favors a large S, while the density of states in bulk materials is a smoothly variable function. As dimensionality is reduced from three to one, the electronic DOS at the energy-band edges is significantly increased, increasing the TE PF (S²σ) and yielding an improved ZT [12,13]. Then, according to Dresselhaus et al., 1D nanowires can boost thermoelectric performance [13,14]. A Bi nanowire would also have a reduced κ due to phonon scattering off the sidewalls, which helps increase ZT, based on a previous study [13,15].

Slack et al. reported that semiconductors exhibiting narrow band gaps and high mobility carriers are optimal TE materials [16]. Bi₂Se₃ is a V–VI topological-insulator material that exhibits a narrow band gap of approximately 0.3 eV and crystallizes in a rhombohedral structure belonging to the tetradymite space group $D_{3d}^5$ (R-3m) [17,18,19]. This material demonstrates potential for application in optical recording systems [20], photo-electrochemical devices [21], and TE devices [17,18]. In recent years, bismuth chalcogenides have attracted substantial research interest because of their superior TE properties of high ZT at room temperature [22]. Diverse synthesis techniques have been developed to synthesize various nanostructures of Bi₂Se₃, such as microwave heating [23,24], a single-source precursor method [25,26,27], solvothermal method [28,29,30], the metal–organic chemical vapor deposition method [31,32], and mechanical exfoliation [33,34,35], whereas the commonly used synthesis method for producing Bi₂Se₃ bulk single-crystalline material is based on the Bridgman technique [36,37,38,39,40,41]. However, only a few studies have been reported on growing Bi₂Se₃ NWs and characterizing their TE properties.

2. Materials and Methods

We previously synthesized PbTe NWs from a PbTe thin film (TF) on a SiO₂/Si substrate using a stress-induced method [42,43] based on a mechanism in which mismatched thermal expansion between a substrate and deposited film drove the mass flow along grain boundaries at thermal annealing temperatures. This innovative NW-growth method (which does not involve conventional templates, catalysts, or starting materials) enables us to control growth conditions for growing different diameters, shapes, and aspect ratios of single-crystalline NWs [44,45], thus enabling exploration of any possible novel TE property of Bi₂Se₃ NWs.

The starting Bi₂Se₃ crystalline ingot was synthesized from Bi and Se source materials using the Bridgman method. Bi (99.999%, −200 mesh, Alfa Aesar, Lancashire, UK) and Se (99.999%, −200 mesh, Alfa Aesar, Lancashire, UK) powders were first mixed at a 2:3 ratio and then melted at 800 °C for 4 h in a vacuumed quartz tube at a pressure less than 5 × 10⁻⁶ torr. The molten compound was slowly cooled in the furnace to room temperature. Subsequently, a pellet specimen cut from the compound served as the target for pulsed laser deposition (PLD). Single-crystal SiO₂/Si (100) wafers (E-light Tech. Inc. Taipei, Taiwan; SiO₂ thickness = 1µm; diameter = 100 ± 0.5 mm) with double-side polishing were cut into 1.5 × 1.5 cm² squares for substrates. All substrates were cleaned using acetone, isopropyl alcohol, and deionized water in an ultrasonic bath for 10 min before being dried with an N₂ stream. The Bi₂Se₃ films were fabricated using an ArF excimer laser (Lambda Physik LPXPro 210, Santa Clara, California, USA) and deposited onto substrates in a vacuum system with a base pressure of 5.0 × 10⁻⁷ torr. The Bi₂Se₃ TFs were grown at a deposition rate of 0.3 Å/s, and the excimer laser was applied at 140 mJ (frequency = 10 Hz) for 15 min at room temperature. The substrate was rotated at approximately 10 rpm, and the film thickness was 30 nm. The films were sealed in a vacuumed quartz tube at less than 5 × 10⁻⁶ torr for annealing at 450 °C for 5 d, followed by cooling the furnace to room temperature. During the annealing process, Bi₂Se₃ NWs grew from the film via the different thermal expansion coefficients of the Bi₂Se₃ film (19 × 10⁻⁶/°C) [46] and the SiO₂/Si substrate (0.5 × 10⁻⁶/°C)/(2.4 × 10⁻⁶/°C) [42,43,44,45].

3. Results and Discussion

3.1. Characterization of Materials

Field emission scanning electron microscopy (Hitachi Co., S-4800, Tokyo, Japan) images of the Bi₂Se₃ NWs (Figure 1a) showed that the NWs exhibited diameters ranging from 50 to 500 nm and lengths up to 100 µm. Straight and uniform Bi₂Se₃ NWs of high aspect ratio grew on the substrate after annealing. A tungsten needle (d = 100 nm) and a binocular optical microscope were used to extract a single-crystal NW from the Bi₂Se₃ film; the NW was then suspended on a Si₃N₄ microchip by using electrodes (Figure 1b) and employed in structural analyses and thermoelectricity measurements. A transmission electron microscope (TEM; JEOL JEM-2100 at 200 kV, Tokyo, Japan) was used to examine the crystalline structure of the Bi₂Se₃ NW (Figure 1c,d).

The electrical resistivity ρ and Seebeck coefficient S of the Bi₂Se₃ bulk were measured simultaneously using commercial equipment (ZEM-3, ULVAC-RIKO, Chigasaki, Kanagawa, Japan) in a He atmosphere from 300 to 540 K. The thermal conductivity κ of the Bi₂Se₃ bulk was calculated using the equation κ = D.C_p.d, where D is the thermal diffusivity, C_p is the specific heat, and d is the density of the sample. The thermal diffusivity D was examined via a laser-flash apparatus (NETZSCH, LFA 457, Selb, Germany), and the density d was obtained using the Archimedes method (presented in Figure S1, electronic supporting information (ESI)). The Seebeck coefficient S and the electrical resistivity ρ of an NW were measured using a conventional steady-state method in an Oxford cryostat. The NW thermal conductivity was measured using the 3ω method.

The TEM image (TEM; JEOL JEM-2100 at 200 kV, Tokyo, Japan) in Figure 1c reveals that the ordered hexagonal structure exhibiting lattice fringes of 0.21 nm gaps between the [11,12,13,14,15,16,17,18,19,20] planes were consistent with those of other lattice spacing measurements of Bi₂Se₃ NWs [47]. A corresponding selected area electron diffraction (SAED) pattern (Figure 1d) reveals that the Bi₂Se₃ NWs were high-quality single crystals that exhibited growth along the [11,12,13,14,15,16,17,18,19,20] direction. The chemical composition of the Bi₂Se₃ NW was examined using energy dispersive X-ray spectroscopy (EDS, JEOL, Tokyo, Japan); the EDS mapping shown in the inset of Figure 1e indicates the uniform spatial distribution of Bi and Se elements throughout the NW.

Figure 2 shows a SEM image of a Bi₂Se₃ NW (d = 200 nm) suspended on a Si₃N₄ microchip between 10 nm Ni/50 nm Au electrodes and a Pt/C electrical contact deposited by a focus ion beam (FIB). The sample used in this study showed nearly an ohmic contact. Subsequently, the microchip was used to determine the values of electrical resistivity ρ and S via four-point measurements.

3.2. Characterization of Thermoelectric Properties

Figure 3a shows the temperature dependence of the electrical resistance at 290–320 K for a 200 nm Bi₂Se₃ NW that exhibited weak metallic conductivities. The σ of the NW at near room temperature was 1.50767 × 10⁵ S m⁻¹ (Figure 3b), which was approximately 55% lower than that of the Bi₂Se₃ bulk single-crystal (2.7550 × 10⁵ S m⁻¹) [41] (

Table 1. The transport properties of Bi₂Se₃ nanowire and bulk at room temperature.

Sample *	S [µV K−1]	Σ [S m−1]	PF [10−5 W m−1K−2]	κ W m−1K−1	ZT	Ref.
Bi2Se3	−53	38678	10.70	0.78	0.04	[26]
Bi2Se3	−115	212	2.80	0.75	0.01	[28]
Bi2Se2.83	−60	25000	9	0.55	0.05	[29]
Bi2Se3 Nanowire SC (φ = 200 nm)	−51	150767	39.32	2.05	0.06	Our Work
Bi2Se3 Bulk SC	−62.10	259998	100	1.55	0.19	Our Work
Bi2Se3 Bulk SC	−190	47619	172	2.96	0.17	[39]
Bi2Se3 Bulk SC	−59	275500	95.90	3.1	0.09	[41]

* SC = single-crystalline.

). Furthermore, the surface scattering of charge carriers typically yields a reduced σ value [48]. However, the σ values of the Bi₂Se₃ NW at room temperature was higher than those reported in previous studies on the Bi₂Se₃ bulk [23,24,25,26,28,29,32], and even higher than that of the Bi₂Se₃ single-crystal made by Hor et al. [39], probably the result of the increased contribution of conduction surfaces up to 73% of the total electrical conduction upon decreasing the NW dimension via the high surface-to-volume ratio s/v ~ 2 nm⁻¹ of the nanowires. A previous report [19] of electrical transport experiments on Bi₂Te₃ and Bi₂Se₂Te nanowires in the range of 200–300 nm in diameter revealed that the two-dimensional TI surface channels contribute up to 30–70% of the total electrical conduction at surface-to-volume ratios of s/v = 2−5 × 10⁻² nm⁻¹.

The S values with the negative sign obtained for the Bi₂Se₃ NW (Figure 3c) show that the Bi₂Se₃ NW is an n-type semiconductor, because electrons have much higher mobility than holes and dominate the transport [49,50]. This is reasonable because undoped Bi₂Se₃ is strongly n-type [51]. Furthermore, the room temperature S values for the n-type Bi₂Se₃ NW was −51 μVK⁻¹ for the 200 nm NW, the value was comparable to those typically reported by Greenaway and Harbeke for this material (i.e., in the −55 to −73 μVK⁻¹ range) [52], indicating that the Fermi level lay well inside the conduction band. The magnitude of the S smoothly increased as the temperature increased. This behavior was consistent with that expected of a metallically doped material. The magnitude of S for the NW tends to be zero when the temperature is decreased because S represents the entropy per electric charge and must decrease to zero at 0 K [15]. Figure 3d indicates the temperature dependence of the PF of Bi₂Se₃ NW, indicating that the PF increased as temperature increased; this can be attributed to the increase in the S with the temperature of the Bi₂Se₃ NW. The PF value of the 200 nm Bi₂Se₃ NW at room temperature was 39.32 × 10⁻⁵ Wm⁻¹K⁻², which was higher than the PF of the Bi₂Se₃ bulk nanostructures [21,22,23,24,26,27,31]. The enhanced PF value is likely a result of enhanced electronic transport of the NW.

For semiclassical transport (metals or degenerate semiconductors) the carrier-density dependence of the thermopower is described by the Mott relation [53,54,55]:

$$S=\frac{8{\pi }^2{k}_B^{2}T}{3q{h}^2}{m}^{*}{\left(\frac{\pi }{3n}\right)}^{\frac{2}{3}}$$

(1)

where k_B is Boltzmann’s constant, q is the electron charge, h is Planck’s constant, T is the measurement temperature, m* is the effective mass of the carrier (m* = 0.14 m_o in Bi₂Se₃) [56] and m_o is the electron mass. This formula is valid for assessing metals or degenerate semiconductors that exhibit an n value in the range of 10¹⁸ to 10²⁰ cm⁻³ [57,58]. The value of n is in the range of 1.26–1.35 × 10¹⁹ cm⁻³ at 290–320 K for the 200 nm NW (Figure 4), indicating that the NW is a degenerate semiconductor. This value is close to that calculated by Boechko et al. for n-type single crystals of a Bi₂Se₃ single crystal (1–4 × 10¹⁹ cm⁻³) [59]. The value of n increased as the temperature increased, indicating the intrinsic condition [60], with the number of thermally generated carriers exceeding the number of donor carriers. The intrinsic carrier concentration in a material n_i is generally much smaller than the dopant carrier concentration at room temperature, but n_i (=n·p) has a very strong temperature dependence:

$$n_i\propto T^{1.5}{e}^{-\frac{E_{g0}}{2kT}}$$

(2)

where E_g0 is the energy band gap at T = 0 K [60].

Figure 4 also depicts the calculated T dependences of carrier mobility μ for the Bi₂Se₃ NW. The μ value is obtained using the following equation:

$$\mu =\frac{1}{\rho nq}= \frac{\sigma }{nq}$$

(3)

Our calculated values of μ at 290–320 K were 754–681 cm² V⁻¹ s⁻¹ for the 200 nm NW; these values were much smaller than those of the Bi₂Se₃ bulk (approximately 920–1060 cm² V⁻¹ s⁻¹) [41], but higher than those reported by Le et al. [60] for Bi₂Se₃ TFs (7.2 ± 0.2 to 98.4 ± 0.5 cm² V⁻¹ s⁻¹). The μ values decreased as temperature increased because of the phonon concentration increase that caused increased scattering. Thus, lattice scattering reduced the carrier mobility at higher temperature. The mobility of a semiconductor depends on the impurity concentrations (including donor and acceptor concentrations), defect concentration, temperature, and electron and hole concentrations.

The primary factor involved in determining μ in the semiconductor is the scattering mechanism through the relation ${\mu }_j\propto T^{\alpha }$ [61]. Conduction carriers are scattered by acoustic phonons ${\mu }_l$ when $\mathsf{\alpha }=-\frac{3}{2}$, whereas they are scattered by ionized impurities ${\mu }_i$ when $\mathsf{\alpha }=\frac{3}{2}$. The μ values of the 200 nm Bi₂Se₃ NW continually decreased as the T increased, indicating that phonon scattering was dominant throughout the whole temperature range.

The thermal conductivity of Bi₂Se₃ NW was measured by the self-heating 3ω method in the temperature range of 290–320 K. The 3ω signal can be expressed as [62,63]:

$$V_{3\omega }=\frac{4I_0^3{LRR}^{\prime }}{{\pi }^4\kappa S\sqrt{1 + {\left(2\omega \gamma \right)}^2}}$$

(4)

where I and ω are the amplitude and frequency of the alternating current applied on the nanowire, respectively; R and R′ are the resistance and derivative of resistance at the corresponding temperature, respectively; κ is the thermal conductivity; S is the NW cross-section area; and γ is the characteristic thermal time constant. Figure 5a shows the current dependence of V_3ω at 300 K, demonstrating an I₀ dependence in an intermediate current range; one can see that V_3ω(I₀) followed the I₀³ dependence well, in agreement with Equation (4). Figure 5b,c show the frequency dependencies of the amplitude and the phase angle of V_3ω at 300 K, respectively, compared with the predicted functional forms (the solid lines). The fitting parameters for Figure 5a,b are shown in Tables S1 and S2, respectively.

By fitting the data in Figure 5a to equation $V_{3\omega }=\frac{4I_0^3{LRR}^{\prime }}{{\pi }^4\kappa S}$ (ωγ→ 0), we obtained the thermal conductivity κ, and the thermal time constant γ was ~2 ms at 300 K, comparable to a simple theoretical calculation of κ based on the Callaway model for nanostructured Bi₂Se₃ made by Li et al. [64,65]. It is known that phonon-boundary scattering can suppress the thermal conductivity in nanowires [66,67]. However, the data on a Bi₂Se₃ NW with d = 200 nm from the experimental κ values (κ = 2.02 to 2.09 W m⁻¹ K⁻¹ at 290–320 K) as plotted in Figure 6a are in reasonable agreement with the Callaway model between the κ values of 300 nm (κ > 2 W m⁻¹ K⁻¹) and 100 nm (κ < 2 W m⁻¹ K⁻¹) [64]. The measured thermal conductivity, given by the κ value (κ is measured perpendicular to c plane) at T = 300 K of the NW (2.05 W m⁻¹ K⁻¹) was ~33% lower than those for Bi₂Se₃ bulk single-crystal (2.96 W m⁻¹ K⁻¹ or 3.1 W m⁻¹ K⁻¹ in Table 1) [39,41].

The electronic thermal conductivity κ_e values of the Bi₂Se₃ NWs here were calculated according to the Wiedemann–Franz law:

κ_e = LσT

(5)

where L is the Lorenz number (2.44 × 10⁻⁸ W Ω K⁻²). When subtracting the κ_e values from the measured thermal conductivity, one obtains the phonon (or lattice) part of the thermal conductivity as κ_{l =} κ-κ_e. The temperature-dependent data for κ_l thus obtained are shown in Figure 6a. The obtained for κ_l and κ_e at 300 K for NWs were 29% and 37% lower than that of the Bi₂Se₃ bulk single-crystal (κ_l = 1.33 W m⁻¹ K⁻¹ and κ_e = 1.77 W m⁻¹ K⁻¹) [41]. The thermal conductivity was dominated by the electronic contribution in the 290–320 K range, although Birkholz and Rosi both reported a value for κ_l of Bi₂Se₃ bulk of between 2.0 and 2.4 W m⁻¹ K⁻¹ [51]. It was shown that the large surface-to-volume ratio s/v of nanowires could enhance phonon surface scattering and decrease κ_l.

Additionally, for this nanowire, ZT calculated from the obtained S, σ, and κ was approximately 0.06 at 300 K (Figure 6b). However, the ZT values of this nanowire were still higher than those of Bi₂Se₃ bulk used to construct nanostructures at 290–320 K, as reported previously [26,28,29]. Table 1 shows a summary of the transport properties of single-crystalline Bi₂Se₃ NW, compared with those reported Bi₂Se₃ bulk at room temperature. Our S, σ, and κ results of Bi₂Se₃ NW d = 200 nm were in reasonable agreement with a theoretical study [19]. This agreement indicates the high-quality crystallinity of the Bi₂Se₃ NWs grown by the stress-induced method.

4. Conclusions

The stress-induced method was applied to grow single-crystalline Bi₂Se₃ nanowires (NWs) from a Bi₂Se₃ TF on a SiO₂/Si substrate, offering an alternative technique for Bi₂Se₃ NWs synthesis without a catalyst. This technique had not been previously applied to Bi₂Se₃ alloys. In this work, at room temperature, the Bi₂Se₃ nanowire (NW) (d = 200 nm) exhibited a PF of approximately 39.32 × 10⁻⁵ Wm⁻¹K⁻², which was higher than that reported for Bi₂Se₃ bulk nanostructures; this discrepancy was mainly attributed to the electron-transport contribution of this NW. The measured thermal conductivity κ value of a NW was 2.05 W m⁻¹ K⁻¹, which was 31−34% lower than those for a Bi₂Se₃ bulk single crystal [39,41] because of the electron-scattering contribution. The figure of merit ZT value of Bi₂Se₃ NW rose up to approximately 0.06 at room temperature, in agreement with a theoretical study of the thermoelectric properties on a topological insulator of Bi₂Se₃ NWs [19]. Our results indicated that NWs grown using the stress-induced method yield high-quality single crystals.