Reduced Bipolar Conduction in Bandgap-Engineered n-Type Cu_0.008Bi₂(Te,Se)₃ by Sulfur Doping

Abstract

Significant bipolar conduction of the carriers in Bi₂Te₃-based alloys occurs at high temperatures due to their narrow bandgaps. Therefore, at high temperatures, their Seebeck coefficients decrease, the bipolar thermal conductivities rapidly increase, and the thermoelectric figure of merit, zT, rapidly decreases. In this study, band modification of n-type Cu_0.008Bi₂(Te,Se)₃ alloys by sulfur (S) doping, which could widen the bandgap, is investigated regarding carrier transport properties and bipolar thermal conductivity. The increase in bandgap by S doping is demonstrated by the Goldsmid–Sharp estimation. The bipolar conduction reduction is shown in the carrier transport characteristics and thermal conductivity. In addition, S doping induces an additional point-defect scattering of phonons, which decreases the lattice thermal conductivity. Thus, the total thermal conductivity of the S-doped sample is reduced. Despite the reduced power factor due to the unfavorable change in the conduction band, zT at high temperatures is increased by S doping with simultaneous reductions in bipolar and lattice thermal conductivity.

1. Introduction

BiTe-based alloys are thermoelectric materials widely used for room-temperature applications such as solid-state cooling. However, the broader use of BiTe-based alloys is limited by their low thermoelectric conversion performance [1,2]. The thermoelectric performance has often been evaluated by the dimensionless figure of merit—thermoelectric figure of merit (zT) = σS²T/κ_tot, where σ is the electrical conductivity, S is the Seebeck coefficient, κ_tot is the total thermal conductivity, and T is the absolute temperature. The maximum zT of Bi₂(Te,Se)₃ n-type alloys is below one, while different studies on (Bi,Sb)₂Te₃ p-type alloys have demonstrated values higher than one. Recently, the zT of polycrystalline Bi₂(Te,Se)₃ n-type alloys has been improved by doping with the Cu element [3], but it is still lower than the p-type alloys. Considering the fact that the efficiency of a thermoelectric module is closely related to the average material zT between p- and n-type thermoelectric materials, the zT of p- and n-type alloys needs to be high and similar.

Many efforts have been made to increase the zT of both p- and n-type alloys. For (Bi,Sb)₂Te₃ p-type alloys, substituting cation sites with Pb, Ag, and Cu elements has been effective in shifting the maximum zT to temperatures greater than 400 K [4]. The formation of 0-dimensional point defects (from substitutional doping) intensifies point-defect phonon scattering and suppresses lattice thermal conductivity. Point defects can also enhance the power factor (=S²σ) of the alloys by changing their band structures. A similar approach has also been adopted in Bi₂(Te,Se)₃ n-type alloys by substituting the cation site with different elements. Unfortunately, the observed improvement in the power factor was negligible. This is due to a significant decrease in the S (compared to an increase in σ) resulting from the increased carrier concentration from the doping. For the substitutional doping strategy to be successful in n-type alloys, additional band engineering, which improves the S by making the density-of-states effective mass (m^*) greater near the Fermi level and/or opening up the bandgap (bipolar conduction suppression), is also required. The bipolar conduction of carriers in BiTe-based alloys with narrow bandgaps (E_g, 0.1–0.2 eV) becomes significant at higher temperatures [5,6,7], which leads to detrimental influences on the thermoelectric properties. The S rapidly decreases, while the bipolar thermal conductivity, κ_bp, rapidly increases at temperatures higher than 300 K. Therefore, the zT rapidly decreases at higher temperatures. The proper band modification with E_g widening is beneficial owing to the reduction in detrimental influence, including the rapid S decrease and the κ_bp increase. In p-type (Bi,Sb)₂Te₃, the E_g widening by In doping increases the zT by reducing κ_bp, while simultaneously reducing the lattice thermal conductivity, κ_latt, owing to the additional point defects originated from the doping [8].

The crystal structure of Bi₂S₃ (orthorhombic phase) is different from those of Bi₂Se₃ and Bi₂Te₃ (rhombohedral phase, thus also from that of Bi₂(Te,Se)₃). However, a small amount of S doping in a Bi₂(Te,Se)₃ n-type alloy would maintain its original crystal structure and would modify its electronic structure [9]. Typically, the E_g values of the series of tellurides, selenides, and sulfides with identical cations increase with the size of the anion [10,11,12]. Therefore, the E_g widening can be anticipated in S-doped Bi₂(Te,Se)₃ alloys. In this study, we investigated S-doped Bi₂(Te,Se)₃ alloys to evaluate the effects of S doping on the E_g and thermoelectric properties, while the Cu-doped Bi₂(Te,Se)₃ alloys were utilized due to their stability and higher zT than Bi₂(Te,Se)₃ alloys. A typical problem with Bi₂(Te,Se)₃ n-type alloys is the lack of reproducibility of the thermoelectric properties, since Te vacancies are easily formed during synthesis [13]. Cu intercalation between the quintuple layer of Bi–Te material is known to suppress the formation of Te vacancies and improve reproducibility [14,15]. The thermoelectric properties of a series of S-doped Cu_0.008Bi₂Te_2.8Se_0.2 (n-type Cu_0.008Bi₂Te_2.8−xSe_0.2S_x, x = 0, 0.05, 0.15, and 0.30) samples were analyzed to verify the influence of S doping and E_g widening.

2. Materials and Methods

Bi (5N Plus, 99.999%), Te (5N Plus, 99.999%), Se (5N Plus, 99.999%), S (Sigma Aldrich, 99.999%), and Cu (Sigma Aldrich, 99.99%) were used as raw materials in the fabrication of the samples. Samples with compositions of Cu_0.008Bi₂Te_2.8−xSe_0.2S_x (x = 0, 0.05, 0.15, and 0.30) were synthesized by a solid-state reaction in a vacuum-sealed quartz tube (diameter: 15 mm) under 10⁻⁵ Torr. The synthesized ingots were ball milled using a SPEX mill for 10 min. The sieved powders (below 45 μm) were spark plasma sintered at 723 K and 50 MPa for 2 min.

The crystallographic phases of the samples were determined by X-ray diffraction (XRD) with Cu K_α1 (λ = 1.54059 Å) radiation. The carrier concentrations were measured by Hall measurements in a magnetic field of 0.5 T (AHT-55T5, Ecopia, Toronto, ON, Canada) in the direction perpendicular to the pressing direction. The S and σ values in a temperature range of 320–520 K were measured using a thermoelectric property measurement system (ZEM-3) in a He atmosphere in the same direction. The κ_tot values were calculated using the sample densities (ρ_s), heat capacities (C_p), and thermal diffusivities (λ) (κ = ρ_sC_pλ). The temperature dependence of λ was measured using the laser flash method (LFA 457, Netzsch, Selb, Germany) in the same direction, so that the zT could be properly calculated.

3. Results and Discussion

Figure 1a shows the XRD patterns of the investigated series of Cu_0.008Bi₂Te_2.8−xSe_0.2S_x, where x = 0, 0.05, 0.15, and 0.30. The samples with x = 0, 0.05, and 0.15 exhibited single phases (Bi₂Te_2.7Se_0.3, JCPDS 00-050-0954) without impurities, while the highly doped sample with x = 0.3 exhibited a phase separation with Bi₂Te₂S (JCPDS 00-042-1447). The calculated lattice parameters a and c (Figure 1b) simultaneously decreased with the S doping, as the S ion is considerably smaller than Te and Se. The systematic changes in a and c to x = 0.15 imply that substitutional doping was successfully achieved. However, the observed phase separation with inconsistent changes in lattice parameters shows that the solid solution might be unstable near x = 0.3. Measurement of the thermoelectric transport properties was not carried out for x = 0.3 (with a different phase).

Figure 2a,b shows the σ and S values of the S-doped Cu_0.008Bi₂Te_2.8−xSe_0.2S_x (x = 0, 0.05, and 0.15) as functions of the temperature. The σ of the undoped sample was approximately 940 S/cm at 300 K, which slightly increased to 1020 S/cm for x = 0.05, and then decreased to 920 S/cm at x = 0.15. As shown in Figure 2b, the magnitude of the S at 300 K significantly decreased from 183 to ~160 μV/K by the doping. However, the undoped sample exhibited a decrease in the S at higher temperatures around 400 K, while the magnitudes of the S of the S-doped samples increased at temperatures higher than 440 K. At temperatures higher than 480 K, the magnitudes of the S of the S-doped samples were higher than those of the undoped sample. Thus, the power factor (S²σ) at 300 K (inset of Figure 2b) decreased with doping at all measurement temperatures.

According to the Goldsmid–Sharp equation [16], the E_g can be estimated as E_g = 2e|S_max|T_max, where T_max is the temperature at which the Seebeck coefficient has the maximum value. For the S-doped sample, the E_g estimated by using the Goldsmid–Sharp equation was increased to 0.159 eV, compared to that of the undoped sample (0.152 eV) (Figure 3a). Figure 3b shows the S as a function of the carrier concentration, n, at 300 K. The effective mass (m_d^*) was calculated using

$$S = \frac{8{\pi }^2 k_B{}^2}{3e{h}^2}{\left(\frac{\pi }{3n}\right)}^{2/3}{m}^{*}T$$

(1)

where k_B, e, h, and n denote the Boltzmann constant, elementary charge, Planck constant, and hole carrier concentration, respectively. The gray dashed lines correspond to m^* = 1.0, 1.1, and 1.2 m₀, plotted using Equation (1). The m^* increased from 1.07 to 1.24 with the S doping to x = 0.15. This suggests that the conduction-band electronic structure of the n-type Cu_0.008Bi₂Te_2.8Se_0.2 was modified by the S doping, along with possible bandgap modification. In other words, with increased S doping, the curvature of the conduction band was relaxed (the band became heavier), and its energy level was also increased relative to that of the valence band maximum.

The carrier concentrations (n) and Hall mobilities (μ_H) estimated using the Hall measurement results are shown in Figure 3c,d. The n values at 300 K were 2.8, 4.2, and 4.7 × 10¹⁹ cm⁻³ at x = 0, 0.05, and 0.15, respectively; they increased with the S doping. As the n is inversely proportional to the S according to Equation (1), the S with S doping observed in Figure 2b was lower than that without S doping, especially at temperatures lower than 450 K. However, at temperatures higher than 450 K, the S of the S-doped samples was higher than that of the pristine sample (without S doping). The overall S (when the majority carriers are electrons) measured in Figure 2b was in fact a conductivity-weighted average of the S from the conduction band (S_CB) and the valence band (S_VB), as presented in Equation (2) below (σ_CB and σ_VB are the electrical conductivities from the conduction band and the valence band, respectively):

$$\left|S\right| = \frac{{\sigma }_{CB}\left|S_{CB}\right|-{\sigma }_{VB}\left|S_{VB}\right|}{{\sigma }_{CB} + {\sigma }_{VB}}.$$

(2)

For n-type materials, the carrier concentration of the holes present was much smaller than that of the electrons. As a result, the S_VB was much higher than the S_CB (based on Equation (1)), but as the σ_VB was negligible when compared to the σ_CB for the same reason, the contribution of the S_VB to the overall S was minimal at low temperatures. However, with increased temperature, the σ_VB was significantly improved owing to the broadening of the Fermi distribution. This was the reason behind the S rollover (due to bipolar contribution) observed in all the samples in Figure 2b. In addition, Figure 2b shows that the degrees of rollover for the S-doped samples were not as drastic as those measured for the pristine sample (without S doping). An enlarged bandgap with increased S doping (Figure 3a) is commonly known for suppressing the bipolar contribution to the overall S and to bipolar thermal conductivity. Therefore, the higher S of the S-doped samples in reference to that of the pristine sample originated from the enlarged bandgap. Notably, μ_H at 300 K was significantly decreased to 121 at x = 0.15, compared to that of the undoped sample (208 cm²V⁻¹s⁻¹). Therefore, the power factor was decreased (inset of Figure 2b), even with the m* increase, which would imply that the conduction band was modified favorably for the S. The decrease should be related to both an increase in n and to possible impurity scattering by the S doping. The sudden increase in the electrical conductivity of x = 0.05 (S doping) and its drop at higher S doping (x = 0.15) can both be explained by an interplay between the decreasing μ_H and increasing n.

To investigate the bipolar conductions of the samples, the characteristics of the hole carriers were deduced from the two-band model (conduction band (CB) and valence band (VB)) based on a single-parabolic-band model (Section S1 in Supplementary Materials) [17]. By using the measured σ, S, n, and μ_H values, the deformation potentials (E_def) and weighted mobilities (U) for the CB and VB were calculated (U_CB and U_VB, respectively) (see Section S1 in Supplementary Materials) to investigate the carrier transport of electrons and holes, separately. The E_def describes the carrier–phonon interaction, e.g., a band with a large E_def has low mobility. U, the product of the nondegenerate mobility (μ₀, as in Equation (1) as a function of E_def) and (m^*)^3/2 (U = μ₀(m^*)^3/2), elucidates the influence of the changes in the m^* and the E_def on the charge transport (Figure 4 and

Table 1. Band parameters estimated using the two-band model (see Section S1 in Supplementary Materials).

Cu0.008Bi2Te2.8−xSe0.2Sx
Band Parameters		x = 0	x = 0.05	x = 0.15
Conduction Band	CB Edef (eV)	17.9	19.0	19.1
	CB m* (in m0)	1.07	1.14	1.24
	UCB (cm2/Vs)	302	254	230
	Electron concentration (1019 cm−3)	2.81	4.20	4.72
Valence Band	VB Edef (eV)	29.8	25.8	26.5
	VB m* (in m0)	1.00	1.00	1.00
	UVB (cm2/Vs)	117	157	148
	Hole concentration (1016 cm−3)	4.71	2.66	2.61
A (=$\frac{U_{CB}}{U_{VB}}$)		2.58	1.62	1.55
Bandgap (eV)		0.152	0.156	0.159

),

$${\mu }_0=\frac{e\pi {\hslash }^4{v}_l^{2}d}{\sqrt{2}{E}_{def}^2{m}^{*}{}^{5/2}{\left(kT\right)}^{3/2}}.$$

(3)

The U_CB decreased from 302 to 230 cm²V⁻¹s⁻¹, while the U_VB increased from 117 to 148 cm²V⁻¹s⁻¹ upon S doping. Therefore, the S doping was detrimental to the electron carrier transport through the reduction in electron mobility, U_CB. However, as shown in Figure 4c, the smaller weighted mobility ratio (A = U_CB/U_VB) of the S-doped sample suggests that the magnitude of the bipolar conduction can be reduced [7,16]. The electron and hole carrier concentrations are shown in Figure 4 and Table 1. The electron concentration increased, while the hole concentration decreased with the S doping, which also reduced the bipolar conduction.

Figure 5a shows the κ_tot values of the measured samples as functions of the temperature. Despite the increase in the σ of the sample with x = 0.05, its κ_tot was unchanged. The κ_tot of the sample with x = 0.15 was smaller than those of the other samples. To understand the change in the thermal transport behavior by S doping, we separated the electronic (electronic thermal conductivity, κ_ele), bipolar (κ_bp), and lattice contributions (κ_latt) from κ_tot. The electronic thermal conductivity, κ_ele, was estimated using the Wiedemann–Franz law. The calculations of κ_bp and κ_latt are described in Sections S1 and S2 in the Supplementary Materials, respectively. Figure 5b presents the κ_bp calculated using the two-band model based on the fitted parameters listed in Table S1 and shows the reduction in κ_bp with S doping. A reduction in κ_bp was expected considering the decrease in A and the increase in the electron concentration in Figure 4a. Thus, the κ_bp was reduced by the S doping, which induced the bandgap widening shown in Figure 3a. The experimental κ_latt (= κ − κ_ele − κ_bp) values are shown as symbols in Figure 5c, which are well matched with the calculated theoretical κ_latt (lines). The theoretical κ_latt calculation is presented in Section S2 in the Supplementary Materials [18]. The experimental and theoretical κ_latt values decreased with the doping, which implies an additional phonon scattering originated from the doped S. Owing to the effects of the mass and lattice constant differences between the two constituents of the alloy, a large additional contribution from phonon scattering was observed, owing to the large mass and ionic radius differences between S and Te/Se (atomic masses M_Te = 127.60 u, M_Se = 78.96 u, M_S = 32.06 u, ionic radii r_Te = 221 pm, r_Se = 198 pm, and r_S = 184 pm). Considering the rather large ΔM and Δa values, the additional phonon scattering was expected.

The temperature-dependent zT is shown in Figure 6. The temperature at which the zT had the maximum value was shifted to a higher temperature and high zT values of around 0.8 were retained. The lower zT values of the doped samples at lower temperatures originated from their low power factors (inset of Figure 2b) owing to the large suppression of carrier transport by the S doping. However, the zT of the sample with x = 0.15 above 400 K was higher than that of the undoped sample, mainly owing to the reductions in κ_bp and κ_latt, which originated from the S doping.

4. Conclusions

In this study, the band modification of n-type Cu_0.008Bi₂(Te,Se)₃ alloys by S doping, which could widen the bandgap, was investigated regarding the carrier transport properties and the bipolar thermal conductivity. The bandgap calculated using the Goldsmid–Sharp estimation increased with the S doping. The carrier transport characteristics and thermal conductivity showed the reduction in bipolar conduction. The carrier transport characteristics showed that the weighted mobility ratio was reduced, while the electron carrier concentration was increased. The bipolar thermal conductivity was reduced by the S doping. However, electron mobility was reduced as a detrimental effect of the S doping, which reduced the power factor. The S doping induced additional point-defect phonon scattering and decreased the lattice thermal conductivity. The zT values at high temperatures were increased by the S doping owing to the simultaneous reductions in bipolar and lattice thermal conductivities.