Characterization of Bipolar Transport in Hf(Te_1−xSe_x)₂ Thermoelectric Alloys

Abstract

Control of bipolar conduction is essential to improve the high-temperature thermoelectric performance of materials for power generation applications. Recently, Hf(Te_1−xSe_x)₂ alloys have gained much attention due to their potential use in thermoelectric power generation. Increasing the Se alloying content significantly increases the band gap while decreasing its carrier concentration. These two factors affect bipolar conduction substantially. In addition, the weighted mobility ratio is estimated from the experimental electronic transport properties of Hf(Te_1−xSe_x)₂ alloys (x = 0.0, 0.025, 0.25, 0.5, 1.0) by using the Two-Band model. From the bipolar thermal conductivity also calculated using the Two-Band model, we find that it peaks near x = 0.5. The initial bipolar conductivity increase of x < 0.5 is mostly due to the decrease in the weighted mobility ratio and carrier concentration with increasing x. For x > 0.5, the drop in the bipolar conductivity can be understood with significant band gap enlargement.

1. Introduction

Thermoelectric technology can be used to harvest electricity from waste heat. Because the burning of no fossil fuels is required to produce electricity, the demand for thermoelectric technology is growing fast. The process of generating electricity using the thermoelectric device is also simple. When one side of the thermoelectric device (p- and n-type thermoelectric elements connected in series) is attached to the waste heat source, the induced temperature gradient across the device makes holes (in the p-type element) and electrons (in the n-type element) move away from the heat source while generating electricity [1,2,3,4,5]. The conversion (from heat to electricity) efficiency of the thermoelectric device is largely determined by the thermoelectric performance of the materials used in the device. Most importantly, how much electric voltage is induced within the thermoelectric material due to the applied temperature gradient is defined as the Seebeck coefficient (S). To achieve high conversion efficiency in the thermoelectric device, thermoelectric materials with high S is desired. However, the thermoelectric performance of a material is better represented by a Figure-of-merit zT than the S alone. The zT is defined as Equation (1) [6].

$$zT=\frac{S^2\sigma T}{{\kappa }_e+{\kappa }_l}$$

(1)

The σ, κ_e, κ_l, and T are the electrical conductivity, thermal conductivity by charged carriers, lattice thermal conductivity, and temperature (unit of K), respectively. According to Equation (1), the S and σ (electronic properties) need to be improved while suppressing κ_e and κ_l (thermal properties) to enhance zT. The thermoelectric parameters in Equation (1) are interconnected with one another, except κ_l. If the σ is increased by increasing the Hall carrier concentration (n_H), the S will decrease but κ_e will increase. For this reason, the zT is always optimized at a narrow range of n_H. To avoid any complication, many researchers have focused on reducing κ_l or the engineering band structure to overcome the strong S–σ trade-off relation [7,8,9,10,11,12,13]. The strong S–σ trade-off relation observed in thermoelectric materials is mainly due to the density-of-states effective mass (m_d*) of the material. At a fixed carrier concentration, increasing m_d* increases the S while decreasing the σ. However, more specifically, the S is related to the m_d*, but the σ is related to the single band mass (m_b) and not to the m_d* directly. Of course, the m_d* is a product of m_b and the number of valley degeneracy to the power of 2/3 (N_V ^2/3). If we can increase the S without decreasing σ, the strong S–σ trade-off relationship can be overcome. It can be achieved if the increase in S is due to N_V increase and not the m_b increase. The improvement of S via the N_V increase can be achieved by converging adjacent bands, and in this case, σ will remain intact.

As one of the approaches to bypass the S–σ trade-off relationship, semiconducting transition metal dichalcogenides (TMDs) have been studied extensively because of their novel electronic and thermal properties [14,15,16,17,18,19,20]. According to Yumnam et al., HfX₂ (X = S, Se) compounds exhibit high theoretical S and σ at the same time, stemming from the interaction between the light and heavy bands. In addition, they show significantly low theoretical κ_l (< 2 W m⁻¹ K⁻¹) due to the low phonon group velocity [21]. Recently, Bang et al. have reported experimental electronic transport properties of bulk Hf(Te_1−xSe_x)₂ alloys (x = 0.0–1.0). A high-power factor (PF = S²σ) of 0.24 mW m⁻¹ K⁻¹ is obtained for HfTe₂ at 600 K [22]. They also provide how band parameters such as the m_d*, non-degenerate mobility (μ₀), and weighted mobility (μ_W) change as the Se alloying content increases from 0.0 (HfTe₂) to 1.0 (HfSe₂) using the Single Parabolic Band (SPB) model [23]. Based on the SPB model, increasing the Se alloying content sharply decreases m_d*, μ₀, and μ_W. Bang et al. also report that the band gap estimated by using the Goldsmid–Sharp equation increases significantly with the increasing Se alloying content [24,25]. However, the effect of the band gap increase was not taken into consideration when estimating the electronic band parameters.

Here, the effect of the band gap change in the electronic transport properties of bulk Hf(Te_1−xSe_x)₂ alloys (x = 0.0, 0.025, 0.25, 0.5, and 1.0) is investigated using the Two-Band (TB) model. Experimental n_H-dependent S and Hall mobility (μ_H) are used to estimate m_d,i*, μ_0,i, and μ_W,i (i = maj for majority carrier band and min for minority carrier band) for one valence band and one conduction band that contribute to electronic transport. From the individual band parameter for each band, the ratio of majority carrier-weighted mobility to minority carrier-weighted mobility, A, and bipolar thermal conductivity (κ_b) are also characterized. The calculated κ_b at 300 K peaks when x = 0.5, and this is an interplay among A, the Goldsmid–Sharp band gap (E_g,G-S), and n_H that are known to affect the κ_b, but change differently with increasing x.

2. Materials and Methods

The ingots of Hf(Te_1−xSe_x)₂ (x = 0, 0.025, 0.25, 0.5, and 1) were first prepared using melting stoichiometrically weighed Hf (99.6%), Te (99.999%), and Se (99.999%) powders within vacuum quartz tubes at 950 °C for 60 h. The ingots were transferred to a glove box and pulverized in the glove box into powders using a mortar and pestle. The powders were then sintered using a spark plasma sintering at 580 °C for 10 min under 50 MPa in a vacuum. The Hall carrier concentration and Hall mobility of the sintered samples were obtained from the Hall coefficient measured via the Van der Pauw method using a commercial Hall measurement system (AHT-55T5 from Ecopia, Anyang, South Korea) under a magnetic field of 0.5 T. For the samples with low Hall mobility, a very thin sample (~ 500 μm) is fabricated to minimize measurement errors.

The m_d,i* and μ_0,i (i = maj, min) are fitted to the experimental n_H-dependent S and σ, respectively, using the TB model. According to the TB model, the S_i, σ_i, and Hall coefficient (R_H,i) (i = maj, min) are defined as below.

$$S_{maj}=\frac{k_B}{e}\left(\frac{2F_1\left(\eta \right)}{F_0\left(\eta \right)}-\eta \right)$$

(2)

$$S_{min}=\frac{k_B}{e}\left(\frac{2F_1\left(-\eta -{\epsilon }_g\right)}{F_0\left(-\eta -{\epsilon }_g\right)}+\eta +{\epsilon }_g\right)$$

(3)

$$S=\frac{S_{maj}{\sigma }_{maj}+S_{min}{\sigma }_{min}}{{\sigma }_{maj}+{\sigma }_{min}}$$

(4)

$${\sigma }_{maj}=\left(\frac{e^3{h}^5}{48\sqrt{2}{\pi }^5}\right)\frac{{\mu }_{0,maj}}{{\left(m_{d,maj}^{*}{k}_{B}T\right)}^{3/2}}{F}_0\left(\eta \right)$$

(5)

$${\sigma }_{min}=\left(\frac{e^3{h}^5}{48\sqrt{2}{\pi }^5}\right)\frac{{\mu }_{0,min}}{{\left(m_{d,min}^{*}{k}_{B}T\right)}^{3/2}}{F}_0\left(-\eta -{\epsilon }_g\right)$$

(6)

$$\sigma ={\sigma }_{maj}+{\sigma }_{min}$$

(7)

$$\frac{1}{R_{H,maj}}=\frac{16\pi e}{3}{\left(\frac{2m_{d,maj}^{*}{k}_{B}T}{h^2}\right)}^{3/2}\frac{{\left(F_0\left(\eta \right)\right)}^2}{F_{-1/2}\left(\eta \right)}$$

(8)

$$\frac{1}{R_{H,min}}=\frac{16\pi e}{3}{\left(\frac{2m_{d,min}^{*}{k}_{B}T}{h^2}\right)}^{3/2}\frac{{\left(F_0\left(-\eta -{\epsilon }_g\right)\right)}^2}{F_{-1/2}\left(-\eta -{\epsilon }_g\right)}$$

(9)

$$R_H=\frac{R_{H,maj}{\sigma }_{maj}^2+R_{H,min}{\sigma }_{min}^2}{{\left({\sigma }_{maj}+{\sigma }_{min}\right)}^2}$$

(10)

$$n_H=\frac{1}{R_{H}e}$$

(11)

The k_B, e, η, h, ε_g, and F_j are the Boltzmann constant, electric charge, fermi level, Planck constant, band gap divided by k_BT, and Fermi integral of order j (Equation (12)).

$$F_j\left(\eta \right)=\underset{0}{\overset{\infty }{{\displaystyle \int }}}\frac{{\epsilon }^j}{1+\exp (\epsilon -\eta )}d\epsilon$$

(12)

The calculated S (Equation (4)) as a function of n_H (Equation (11)) is fitted to the measurement to obtain m_d,i* (i = maj, min). The calculated σ (Equation (7)) as a function of n_H (Equation (11)) is fitted to the measurement to obtain μ_0,i (i = maj, min). The ε_g for Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) are adopted from Bang et al. and they are listed in the

Table 1. The ε_g for Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) at 300 K [22].

x in Hf(Te1−xSex)2	εg (Band gap/kBT)
0.0	2.06
0.025	2.19
0.25	3.12
0.5	5.92
1.0	20.00

below [22]. In a Single Parabolic Band (SPB) model, where we assume there is only one band participating in the electronic transport properties, we only have to fit one band parameter, which is the m_d* to the experimental n_H-dependent S. However, in the TB model, the total S is an electrical conductivity-weighted average between S_maj and S_min (Equation (4)). In other words, when there are two bands participating in transport, even when we want to describe the experimental n_H-dependent S, both m_d,i* (i = maj, min) and μ_0,i (i = maj, min) need to be fitted simultaneously while changing the ε_g for different x. Therefore, instead of fitting m_d* from the n_H-dependent S and μ₀ from the n_H-dependent σ, consecutively, all four unknown band parameters m_d,i* (i = maj, min) and μ_0,i (i = maj, min) were fitted to n_H-dependent S and σ concurrently. Plus, to minimize the complexity of the TB modeling, once the m_d,imin* and μ_0,min were fitted in x with the lowest ε_g (where the contribution from the minority carrier band is maximum), they were kept constant for the TB model calculation of the samples with different x. This is because the impact of the minority carrier band on the electronic transport properties decreases with an increasing ε_g.

The μ_W,i is characterized from the estimated m_d,i* and μ_0,i (i = maj, min) via Equation (13) (m₀ is the electron rest mass).

$${\mu }_{W,i}={\mu }_{0,i}{\left(\frac{m_{d,i}^{*}}{m_0}\right)}^{3/2}$$

(13)

The weighted mobility ratio a is computed using Equation (14).

$$A=\frac{{\mu }_{W,maj}}{{\mu }_{W,min}}$$

(14)

3. Results and Discussion

3.1. Estimation of the m_d,i* (i = VB, CB) Via the TB Model

Figure 1a presents the experimental S in terms of n_H at 300 K adopted from Bang et al. (in symbols) [22]. The magnitude of S drastically increases with the increasing Se alloying content (x). While S of the samples with x ≤ 0.25 is smaller than 30 μV K⁻¹, the S of x = 0.5 and x = 1.0 amount to 220 and 730 μV K⁻¹, respectively. On the contrary, measured n_H significantly decrease with increasing x. For example, the n_H of x = 0.0, which is 7.7 × 10²⁰ cm⁻³, sharply decreases to 3.0 × 10¹⁶ cm⁻³ when x = 1.0. If we assume that there is only one electronic band contributing to the electronic transport properties of the sample, the S increase with x would be explained by the fermi level (η) decrease with the increasing Se alloying content (x) (Equation (2)). The n_H depends both on η and m_d* (Equations (8) and (11)). Again, with a single band contributing to electronic transport, the n_H decrease with x can be explained with η and m_d*. Both η and m_d* are directly proportional to the n_H. Because we already know that the η decreases with x, the measured n_H decrease with x suggests that the m_d* can be decreased or increased with x. Here, the effect of m_d* increase in n_H should be smaller than the effect of η decrease in n_H.

However, when we take the minority carrier band into consideration as well to describe the experimental S in terms of n_H, we must consider how μ_0,i (i = maj, min) and ε_g change with x to estimate m_d,i* (i = maj, min) (Equations (2)–(4) and (8)–(11)). According to Table 1, the band gap increases significantly with x. In other words, the effect of the minority carrier band (conduction band in the case of Hf(Te_1−xSe_x)₂) in electronic transport decreases with x. The lines in Figure 1a are the TB model calculation results. From the fact that the lines in Figure 1a coincide with the experimental data in symbols, we can conclude that the fitted band parameters capture important features of the electronic bands in Hf(Te_1−xSe_x)₂. The reason that the TB model calculation results (in lines) are only available for n_H > 10¹⁸ cm⁻³ for x < 1.0 is that for n_H < 10¹⁸ cm⁻³, the TB model results in a change in the type of material change due to the narrow band gap (x < 1.0).

Figure 1b shows the m_d,VB* (= m_d,maj*) and m_d,CB* (= m_d,min* in the inset) of Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) estimated by using the TB model at 300 K. To avoid any complexity, the m_d,CB* of Hf(Te_1−xSe_x)₂ was kept constant for all x (1.5 m₀). According to the TB model, the m_d,VB* first decreases with x and increases again after x = 0.25. For example, while the m_d,VB* at x = 0.0 and 1.0 are the same (0.9 m₀), that at x = 0.25 is the lowest (0.23 m₀). The gray solid line is also provided for the guide-to-the-eye. The Se alloying makes the m_d,VB* lighter until x = 0.25 and for x greater than 0.25, and the same Se alloying increases the m_d,VB*. The increase in m_d,VB* for x ≥ 0.25 may have increased the corresponding n_H. However, the observed decrease in n_H with increasing x must be the η decrease that outweighs the m_d,VB* increase for x ≥ 0.25.

3.2. Estimation of the μ_0,i (i = VB, CB) Via the TB Model

Figure 2a shows the experimental μ_H in terms of n_H at 300 K adopted from Bang et al. (in symbols) [22]. The μ_H is substantially suppressed with increasing x. The μ_H of approximately ~13 cm² V⁻¹ s⁻¹ for x = 0.0 and 0.025 is decreased down to 0.15 cm² V⁻¹ s⁻¹ when x = 1.0. Because only the x = 0.0 and 0.025 samples have n_H that are higher than 5 × 10²⁰ cm⁻³ (other samples with x ≥ 0.25 have n_H those are lower than 5 × 10¹⁹ cm⁻³), only the x = 0.0 and 0.025 samples have σ that are higher than 1200 S cm⁻¹ (σ = e μ_H n_H). The σ of the samples with x ≥ 0.25 are lower than 100 S cm⁻¹ at 300 K [22]. In order to evaluate the characteristics of the electronic bands contributing to the electronic transport, we need to convert the μ_H into μ₀. The μ_H is a function of μ₀ and η, so depending on η, the trend observed in μ_H may not reflect the trend in the band parameter, μ₀, which represents the carrier mobility without any defects. By fitting m_d,i* and μ_0,i (i = maj, min) with different ε_g (Table 1) to the experimental μ_H in terms of n_H by using the TB model, the lines in Figure 2a that accurately describe the experimental data (in symbols) are obtained. From the reasonable agreements between the experiments and the TB model results, we demonstrate that the band parameter μ_0,i (i = maj, min) provided in Figure 2b describes the electronic bands well.

Figure 2b shows the μ_0,VB (=μ_0,maj) and μ_0,CB (=μ_0,min in the inset) of Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) estimated by using the TB model at 300 K. Again, to minimize any complications, the μ_0,CB is kept constant for all different x (0.84 cm² V⁻¹ s⁻¹). Overall, the μ_0,VB decreases with increasing x. At first, the μ_0,VB rapidly decreases with x, but for x > 0.25, the rate of the μ_0,VB decrease decreases. The guide-to-the-eye is provided in the gray solid line. This suggests that increasing the Se alloying content deteriorates the mobility of the holes. The physical reason behind the μ_0,VB reduction can be found by looking at how the carrier–phonon interaction changes with Se alloying. The μ₀ of any band is related to the m_d* and deformation potential (E_def), as in Equation (15). The ħ and C_l in Equation (15) are the h/2π and the elastic constant, respectively.

$${\mu }_0=\left(\frac{2\sqrt{2\pi }}{3}\right)\frac{e{\hslash }^4}{{\left(k_{B}T\right)}^{3/2}}\frac{C_l}{m_d^{*}{}^{5/2}{E}_{def}^2}$$

(15)

As shown in Equation (15), the μ₀ is inversely proportional to E_def². The E_def quantifies how strong the scattering of charged carriers is due to lattice vibrations (phonons). If the E_def is high, this means that the charged carriers are more often scattered by phonons hindering the electronic transport properties. The E_def,VB (the E_def of the valence band) for different x are obtained from m_d,VB* (Figure 1b) and μ_0,VB (Figure 2b), and are provided in

Table 2. The m_d,VB*, μ_0,VB, and E_def,VB for Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) at 300 K.

x in Hf(Te1−xSex)2	md,VB* (m0)	μ0,VB (cm2 V−1 s−1)	Edef,VB (eV)
0.0	0.9	48.39	0.051
0.025	0.59	54.78	0.081
0.25	0.23	20.45	0.43
0.5	0.65	6.19	0.21
1.0	0.9	0.17	0.86

. The general trend observed in E_def,VB is that the carrier–phonon interaction becomes stronger as x increases. However, it is to be noted that there is a local minimum in E_def,VB at x = 0.5.

3.3. Estimation of the μ_W,i (i = VB, CB) Via the TB Model

Figure 3a shows the experimental power factor (= S²σ, PF) in terms of n_H at 300 K adopted from Bang et al. (in symbols) [22]. The experimental PF decreases significantly with increasing x, except when x = 0.5. When x = 0.5 (PF = 0.025 mW m⁻¹ K²), the corresponding PF is approximately four times greater than that measured when x = 0.25 (PF = 0.006 mW m⁻¹ K²). However, when x = 1.0, its PF decreases to lower than 0.001 mW m⁻¹ K². According to Figure 1a, the S of x = 1.0 (S = 730 μV K⁻¹) is much higher than those of other x. However, the μ_H of x = 1.0 is the lowest mostly due to high E_def (Table 2). The PF is a product between S² and σ (= e μ_H n_H). The large PF discrepancy between x = 0.0 and 1.0 is mostly due to the significant difference in n_H (incorporated in σ). While the n_H of x = 0.0 is in the order of 10²¹ cm⁻³, that for x = 1.0 is only in the order of 10¹⁶ cm⁻³. The factor of 10⁵ difference cannot be offset, even with a large difference in the S. Based on the m_d,i* and μ_0,i (i = VB, CB) estimated using the TB model (Figure 1b and Figure 2b), the PF in terms of n_H are estimated for different x (Figure 3a in lines). Regardless of the x, the theoretical maximum PF are predicted near 10¹⁹ cm⁻³, and the predicted maximum PF decreases significantly with increasing x. The theoretical maximum PF for x = 0.0 is as high as 0.37 mW m⁻¹K². Since the experimental PF for x = 0.0 is only 0.076 mW m⁻¹ K², when the n_H is tuned from 7.7 × 10²⁰ to 2.8 × 10²⁰ cm⁻³, an improvement of approximately 4.5 times in the PF is expected.

When there is only one band contributing to electronic transport, the theoretical maximum PF is directly proportional to the μ_W of the band. When there are two bands (valence and conduction bands) contributing, the theoretical maximum PF is related to the interplay between the μ_W,maj and μ_W,min. Out of the two band parameter, μ_W,maj would be more important when determining the theoretical maximum PF. Figure 3b shows the μ_W,VB and μ_W,CB (inset) of Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) at 300 K. Because we assume that the m_d,CB* and μ_0,CB are invariant with x, corresponding μ_W,CB (Equation (13)) in terms of x (Figure 3b inset) is also independent to x. Generally, the calculated μ_W,VB decreases with increasing x. The values of μ_W,VB are approximately proportional to the theoretical maximum PF in Figure 3a. The values of μ_W,VB are not directly proportional to the theoretical maximum PF as the μ_W,CB values also contribute when determining the theoretical maximum PF. The contribution from μ_W,CB becomes larger for small x as the ε_g reduces for decreasing x (Table 1).

3.4. Estimation of the Bipolar Thermal Conductivity (κ_b) Via the TB Model

Figure 4a presents the theoretical weighted mobility ratio a computed using the μ_W,VB and μ_W,CB from Figure 3b. The A is defined as the ratio of μ_W,maj to μ_W,min (Equation (14)). Because Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) alloys are p-type, the A in Figure 4a is obtained by μ_W,VB divided by μ_W,CB. As we have kept the μ_W,CB constant for all x, the trend calculated in the A is almost identical to that observed in μ_W,VB. Similar to the μ_W,VB, the A rapidly decreases with increasing x. Except x = 0.0 and 0.025, the A of all x are smaller than 2.2. What A represents is how mobile majority carriers are with respect to the minority carriers. If A is much larger than one, it means that the majority carriers move much faster than minority carriers. In such a case, the bipolar contribution to electronic contribution weakens. Therefore, a much-suppressed bipolar conduction is expected when the A is large. According to Figure 4a, the samples with small x would experience much weaker bipolar conduction than those with large x. However, this only applies when other factors that affect the κ_b stay the same.

Figure 4b shows how the band gap estimated using the Goldsmid–Sharp equation (E_g,G-S) and the measured n_H change in terms of x. The band gap and n_H are also important factors that affect the κ_b. First of all, increasing the band gap will decrease the κ_b. Secondly, increasing n_H will also decrease the κ_b. In Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) alloys, increasing x will increase E_g,G-S but decrease the n_H at the same time. From Figure 4a,b, we now know that the increasing x will decrease A and n_H, but increase E_g,G-S. We have two factors (A and n_H) changing to increase the κ_b, and one factor (E_g,G-S) changing to suppress the κ_b with increasing x. The relative impact of each factor on κ_b is difficult to evaluate as those factors are strongly interdependent. Instead, the κ_b itself is estimated to see which factor affects bipolar conduction more strongly.

Figure 4c is the κ_b in terms of x estimated by using the TB model at 300 K. The κ_b is a function of S_i, σ_i (i = maj, min), and T (Equation (16)). The S_i and σ_i (i = maj, min) are defined as in Equations (2)–(3) and (5)–(6) [26,27,28,29,30,31,32,33].

$${\kappa }_b=\left[{\sigma }_{maj}{S}_{maj}^2+{\sigma }_{min}{S}_{min}^2-\frac{{\left({\sigma }_{maj}{S}_{maj}+{\sigma }_{min}{S}_{min}\right)}^2}{{\sigma }_{maj}+{\sigma }_{min}}\right]T$$

(16)

According to Figure 4c, the κ_b increases with x until x = 0.5, and for x > 0.5 it starts to decrease. For small x, the E_g,G-S is also narrow. In such a circumstance, decreases in A and n_H result in an increase in κ_b. However, once the E_g,G-S becomes wider than 0.15 eV (when x = 0.5), the effect of the band gap on bipolar conduction becomes much greater than those of A and n_H. Hence, despite the decrease in A and n_H, a reduction in κ_b is obtained with the band gap increase.

4. Conclusions

In summary, the electronic transport properties of p-type Hf(Te_1−xSe_x)₂ (x = 0.0, 0.025, 0.25, 0.5, and 1.0) alloys have been investigated in terms of electronic band parameters. Because the band gap of the Hf(Te_1−xSe_x)₂ alloys increases with increasing x, the Two-Band (TB) model (one valence band and one conduction band) has been adopted to take the band gap change into consideration. When we consider the majority carrier band (valence band in this case), its density-of-states effective mass first decreases but for x > 0.25, it increases again. The deformation potential increases with increasing x. Consequently, the weighted mobility and weighted mobility ratio of the valence band decrease with increasing x. The bipolar thermal conductivity is also estimated using the TB model. It peaks near x = 0.5 and decreases for x > 0.5. This trend observed in the bipolar thermal conductivity can be explained with the weighted mobility ratio, band gap, and carrier concentration change with increasing x. When the band gap is narrow (x < 0.5), the effects of the weighted mobility ratio and carrier concentration are strong, but when the band gap becomes wide (x > 0.5), the band gap becomes a more critical factor to bipolar conduction than the other two factors.