Rare Metals

, Volume 37, Issue 4, pp 351–359 | Cite as

Optimization of thermoelectric properties of n-type Bi2(Te,Se)3 with optimizing ball milling time

  • Ji-Hee Son
  • Min-Wook Oh
  • Bong-Seo Kim
  • Su-Dong Park


The thermoelectric properties at elevated temperature were investigated for n-type Bi2(Te,Se)3 which is obtained from ball milling processed powder with various milling times. Electrical properties such as electrical resistivity and Seebeck coefficient are clearly dependent on milling time, in which the carrier concentration is attributed to the change of the electrical properties. The concentrations of the defects are also varied with the ball milling time, which is the origin of the carrier concentration variation. Even though finer grain sizes are obtained after the long ball milling time, the temperature dependence of the thermal conductivity is not solely understood with the grain size, whereas the electrical contribution to the thermal conductivity should be also considered. The highest figure of merit value of ZT = 0.83 is achieved at 373 K for the optimized samples, in which ball milling time is 10 h. The obtained ZT value is 48% improvement over that of the 0.5-h sample at 373 K.


Thermoelectric properties Ball milling Bi2Te3 Seebeck coefficient Grain size Thermal conductivity 

1 Introduction

A thermoelectric conversion technology has attracted attention due to power generation ability from recovering waste heat [1, 2]. By using the waste heat from automobiles and the industrial plants, the thermoelectric technology can increase efficiency of global energy consumption. The energy conversion efficiency of thermoelectric technology is determined and quantified by the dimensionless figure of merit (ZT) of the thermoelectric materials which constitute thermoelectric modules, where ZT is defined by ZT = S2T/ρκ, where S is the Seebeck coefficient, ρ is the electrical resistivity, κ is the thermal conductivity, and T is the absolute temperature [1]. The higher value of ZT gives the large energy conversion efficiency.

Bismuth telluride-based compounds are widely used in thermoelectric devices due to their excellent thermoelectric properties at room temperature region [3, 4, 5, 6, 7, 8, 9, 10, 11]. Poudel et al. [12] obtained nanocrystalline BiSbTe bulk materials by hot pressing nanopowders ball-milled from ingots. Nanocrystalline bulk alloys have excellent thermoelectric performance due to the reduction of the thermal conductivity. The detailed process of the ball milling for the high-ZT Bi–Te-based compounds is unrevealed. The optimization of ball milling process may be one of the key process parameters to achieve the high-ZT thermoelectric Bi–Te-based compounds. The ball milling process involves many parameters such as milling time, ball-to-material weight ratio, grinding ball size, milling speed. Kanatzia et al. [13] observed that the milling time is the most significant factor for the crystallite size, while ball-to-material weight ratio is not important. Our group previously reported that the thermoelectric properties and the microstructure of p-type (Bi,Sb)2Te3 were largely dependent on the ball milling time so that the optimization of the milling time is required to achieve the best performance [14]. For n-type Bi–Te-related compounds, Lin and Liao [15] reported the effect of ball milling time on the thermoelectric properties, where the properties were measured only at room temperature. Therefore, the investigation of temperature-dependent thermoelectric properties with respect to ball milling time will attract more attention. Kuo et al. [16] reported the temperature-dependent thermoelectric properties of Bi2Te3, where Bi2Te3 powder was fabricated with attrition milling and the variation of attrition milling time was a control parameter. Because the thermoelectric properties are varied with the type of milling condition, the report by Kuo et al. [16] cannot be used in comparing it with the previous Son’s report [14] on the p-type material.

In this study, the effect of ball milling time on the microstructures and thermoelectric properties of the n-type Bi2(Te,Se)3 compounds was investigated. The powder was obtained with planetary ball miller. The thermoelectric properties were investigated within the temperature range between 298 and 573 K. The investigated properties were understood with the change of the microstructures and carrier concentration. The variation of the properties with respect to the ball milling time was compared with that of p-type (Bi,Sb)2Te3 previously studied.

2 Experimental

The ball milling process was identical with that of p-type (Bi,Sb)2Te3 [14]. A planetary ball miller (PM-100, Retsch, Germany) was used to crush the commercial n-type ingot (KRYOTHERM, Russia). Stainless-steel jars and balls were used in the milling, and the rotation rate was 300 r·min−1. The balls with diameter of 9.5 mm were mixed with ingots in the weight ratio of 15:1. Spark plasma sintering (SPS) method (Dr. Sinter, SPS Systex, Japan) was employed to consolidate the obtained powder. The sintering with 50 MPa pressure was carried out under Ar atmosphere for 10 min at 693 K in SPS. The rectangular samples (3 mm × 3 mm × 10 mm) cut from the densified samples were used in measuring the Seebeck coefficient and the electrical resistivity under He atmosphere using a commercialized apparatus (ZEM-3, ULVAC-RIKO, Japan). A coin-shaped sample (diameter of 12.7 mm, thickness of 2 mm) was used to measure the thermal diffusivity. The thermoelectric properties were measured from 300 to 573 K. A planar rectangular piece (4 mm × 10 mm × 1 mm) was used for the Hall measurement using a commercialized equipment (Physical Properties Measurement System, Quantum Design, USA)

The phase of the samples was determined by X-ray diffractometer (XRD, X’pert PRO, PANalytical) at room temperature with Cu Kα radiation (λ = 0.15406 nm), from which the lattice parameters of all samples were obtained with Rietveld analysis implemented in the HighScore Plus program (PANalytical). Scanning electron microscope (SEM, S-4800, Hitachi) was used to investigate the fractured surfaces of the samples. Inductively coupled plasma optical emission spectrometer (ICP-OES, Optima 5300 DV, PerkinElmer Inc.) was used to analyze the composition of the samples. The starting materials show the composition of about Bi1.94Sb0.01Te2.76Se0.29. In this research, the composition of the samples was denoted as Bi2(Te,Se)3.

3 Results and discussion

Figure 1 shows XRD patterns of the consolidated Bi2(Te,Se)3 specimens fabricated by SPS. XRD patterns agree with the standard powder diffraction of the Bi2Te3-related compounds with the crystal structure of \(R\bar{3}m\), and no other decomposed or precipitated phases are found. The average grain size of the samples was calculated by using the obtained patterns and Williamson–Hall equation as shown below [17]
$$\frac{\beta \cos \theta }{\lambda } = \frac{1}{d} + 4\varepsilon \frac{\sin \theta }{\lambda }$$
where β is the integral breadth of the diffraction peak, λ is the wavelength of X-ray, d is the average grain size, θ is the Bragg diffraction angle, and ε is the microscopic strain.
Fig. 1

XRD patterns of bulk n-type Bi2(Te,Se)3 samples consolidated by SPS

Figure 2 shows the estimated grain size of the samples as a function of ball milling time. The grain size decreases as the milling time increases up to 10 h. However, the trend of the grain size variation shows much difference in the samples after 24 h. The grain size increases in the sample after 24 h and then decreases again with milling time increasing. These differences in the sample after the larger milling time seem to be due to the mechanism of the high-energy ball milling in which the repetitions of fracturing and welding of particles are performed [14]. The fracturing will mainly occur in the samples with relatively small milling time. However, the excessive mechanical energy with larger milling time will introduce the welding of particles, resulting in the growth of the particles [14]. Thus, the increase in the grain sizes or relatively small reduction in the grain size is observed with the larger milling time. It is also noteworthy that the estimated sub-grain sizes from XRD patterns are much smaller than those of the p-type (Bi,Sb)2Te3, where the milling process is identical in both studies [14]. The origin of the difference in the size at this stage could not be confirmed, whereas large difference in composition for the n-type and the p-type may be one of the origins.
Fig. 2

Estimated grain size of n-type Bi2(Te,Se)3 samples obtained with Williamson–Hall equation (Williamson–Hall plots for samples being presented in supplementary file)

SEM images of the fractured surface of the samples after 0.5-, 5.0-, 10.0-, and 48.0-h ball milling are shown in Fig. 3. It can be concluded that the grain size is relatively large in the samples with small milling time, which is in accordance with the conclusions from XRD pattern analysis. The direct comparison of the grain sizes between the values estimated by XRD and SEM is not rational, because the values from XRD analysis represent the grain sizes of the sub-grains and are generally smaller than those of the microscopy such as SEM and TEM [18]. Even though it is hard to give quantitative conclusions, both XRD and SEM analyses give identical and qualitative conclusions that the grain size decreases with the milling time. The grain sizes estimated from SEM for the n-type are also smaller than those for the p-type [14].
Fig. 3

SEM images of fractured surface of n-type Bi2(Te,Se)3 samples obtained from ball-milled powders for milling time of a 0.5 h, b 5 h, c 10 h, and d 48 h

The temperature dependence of the electrical resistivity and the Seebeck coefficient of the samples is shown in Figs. 4 and 5. The electrical resistivity increases with the temperature in the whole temperature range, which is a behavior of the highly degenerated semiconductor. The electrical resistivity increases as the milling time increases up to 10.0 h, whereas the values of the 24.0- and 48.0-h samples are smaller than that of the 10.0-h samples. The absolute values of the Seebeck coefficient are also maximized in the 10.0-h samples, and then the values are decreased in the 24.0- and 48.0-h samples. The milling time dependence of the grain size also shows the change of the variation after 10 h. In the fabrication process, this milling time seems to be the critical turning point of the properties. The electrical resistivity is related to the carrier concentration and the mobility. The smaller grain sizes will decrease the mobility due to the grain boundary scattering. Thus, the larger electrical resistivity in 10.0-, 24.0-, and 48.0-h samples may be due to the smaller grain sizes, which will be justified below. However, in order to confirm the origin of the change of the electrical resistivity, the carrier concentration should be also investigated. Moreover, the Seebeck coefficient is also largely dependent on the carrier concentration. Thus, the carrier concentration was estimated with the Hall coefficient measurement.
Fig. 4

Temperature dependence of electrical resistivity of Bi2(Te,Se)3 samples with different milling time

Fig. 5

Temperature dependence of Seebeck coefficient of Bi2(Te,Se)3 samples with different milling time

The estimated carrier concentration at 298 K is shown in Fig. 6 as a function of the milling time. The value of the carrier concentration (n) is related to the Hall coefficient (RH) by following equation:
$$R_{\text{H}} = \frac{{A_{\text{H}} }}{nq}$$
where q is a charge of the carrier and AH is a constant which depends on the scattering mechanism, the mobility (μ) ratio between electrons and holes, etc. [3, 14]. For the degenerated semiconductor, AH is generally replaced by unity and unity for AH was also used to estimate carrier concentration from the Hall coefficient measurement. The values of the carrier concentration decrease with the milling time and reach the minimum at 10.0 h and then increase again. The ratio of the carrier concentration between 0.5- and 10.0-h samples is about 2.3. The mobility was also estimated with the equation, \(1 /\rho = \sum\nolimits_{i} {q_{i} } \mu_{i} n_{i}\), where the major carrier was only considered. The difference of the mobility between samples is rather small compared with the carrier concentration, as shown in Table 1. The values of mobility are 88.0, 81.0, 81.4, 74.3, and 62.2 cm2·V−1·s−1 for 0.5-, 2.0-, 10.0-, 24.0-, and 48.0-h samples, respectively. The ratio of the electrical conductivity (σ = \(1 /\rho = \sum\nolimits_{i} {q_{i} } \mu_{i} n_{i}\)) between both samples is about 1.7. Thus, the variation of the electrical resistivity with the milling time is mainly attributed to the change of the carrier concentration. The Seebeck coefficient for the degenerated semiconductor is largely dependent on the carrier concentration and the density of states effective mass of the carrier (m*) by following equation
$$S = \frac{{8\uppi^{2} k_{\text{B}}^{2} T}}{{3qh^{2} }}m^{*} \left( {\frac{\uppi }{3n}} \right)^{2/3}$$
where kB is the Boltzmann’s constant and h is the Plank’s constant [1, 19]. It is noteworthy that the variation of the carrier concentration with milling time is in accordance with that of the Seebeck coefficient. Thus, it is concluded that the variation of the Seebeck coefficient with milling time is due to the change of the carrier concentration.
Fig. 6

Carrier concentration of Bi2(Te,Se)3 samples with different milling time at room temperature

Table 1

Measured values of carrier concentration, mobility, density, and relative density at room temperature (theoretical density of Bi2Te3 7.80 g·cm−3 being used in estimation of relative density)

Milling time/h

Carrier concentration/cm−3


Measured density/(g·cm−3)

Relative density/%




































In order to check the effect of the effective mass, the Seebeck coefficient at 298 K is plotted in Fig. 7 as a function of the carrier concentration (a so-called Pisarenko plot). The values of the effective mass are only varied from 1.1m0 to 1.3m0, where m0 is the rest mass of an electron. Thus, the carrier concentration is largely varied with the milling time and mainly affects the electrical resistivity and the Seebeck coefficient. It may be stressed that the effect of the grain boundary on the electrical resistivity would exist as mentioned before, but the variation of the electrical resistivity with the milling time is mainly attributed to the change of the carrier concentration.
Fig. 7

Plot of Seebeck coefficient versus carrier concentration for Bi2(Te,Se)3 samples with different milling time (each solid line representing calculated Seebeck coefficient with Eq. (3) as effective mass increased by 0.1 m0; inset showing carrier concentration of samples with different milling time at room temperature, from which milling time for each point in the main plot can be easily assigned)

The change of the carrier concentration is confirmed in results and discussion of the electrical properties. Therefore, the origin of the variation of the carrier concentration should be investigated. It is known that the carrier concentration of the n-type Bi2Te3 is determined with the antisite defects [20, 21, 22]. It is also reported that the high-energy mechanical ball milling can change the concentration of the antisite defects [23]. Thus, the change of the concentration of the antisite defects was investigated. The investigation of the lattice parameters can be a probe to examine the antisite defects [21]. The lattice parameters obtained from XRD patterns are shown in Fig. 8 as a function of the milling time. The lattice parameters of c-axis of the unit cell increase with milling time, reach the peak at the 10.0-h samples, and then decrease, while the values of the a-axis are almost sustained. For the n-type Bi2Te3, the TeBi antisite defect where the Te atom occupies the Bi site acts as the n-type doping via following equation.
Fig. 8

Lattice parameters of Bi2(Te,Se)3 samples with different milling time

$${\text{Te}}_{\text{Te}} {\text{ + V}}_{\text{Bi}}^{{{\prime \prime \prime }}} +3{\text{h}}^{{\circ}} \to {\text{V}}_{\text{Te}}^{{{\circ\circ}}} + {\text{Te}}_{\text{Bi}}^{{\circ }} + 3{\text{e}}^{{\prime }}$$

If TeBi is formed in the lattices, the lattice parameters will decrease, because the atomic radii of Bi and Te are 1.6 and 1.4, respectively [24]. On the other hand, the lattice parameters will increase if the concentration of TeBi ([TeBi]) decreases. Thus, the increased lattice parameters of the c-axis may be attributed to the reduction of [TeBi], resulting in the reduction of electrons concentration. Actually, the variation of the lattice parameters with milling time shows good agreement with the results of the carrier concentration. The origin of the reduction of [TeBi] may be attributed to the vaporization of Te. The thermal energy induced by the mechanical bombardment between balls may promote the vaporization of Te and increase the concentration of the Te vacancy ([VTe]). The increased [VTe] for the reaction tends to occur in the way from the right side to the left in the equation, resulting in the reduction of [TeBi].

As well as the major n-type antisite defects, the minor p-type antisite defects can be considered. The BiTe antisite defects are a major p-type antisite defects [22]. The reaction equation of BiTe is as follows
$${\text{Bi}}_{\text{Bi}} + {\text{V}}_{\text{Te}}^{{{\circ\circ }}} + 2{\text{e}}^{{\prime }} \to {\text{V}}_{\text{Bi}}^{{{\prime \prime \prime }}} {\text{ + Bi}}_{\text{Ti}}^{{\prime }} + 4{\text{h}}^{{\circ }}$$

If the concentration of BiTe ([BiTe]) increases, the lattice parameters will increase due to the larger atomic radius of Bi and the concentration of holes also increases, meaning the reduction of the electrons concentration. Moreover, [BiTe] will increase as [VTe] increases. The increment in [BiTe] will also introduce the reduction of [TeBi]. Therefore, the increment in [BiTe] can explain properly all observed properties, as done with the reduction of [TeBi]. Conclusively, it can be insisted that the reduction of the electron concentration is attributed to the change of the antisite defects concentration: reduction of [TeBi] or increment in [BiTe].

The increment in electrons concentration for larger milling time (24.0 and 48.0 h) may be due to the unintentional doping of Fe. Because the steel jar and balls were used in the milling process, the samples may be contaminated by Fe [14]. The amount of Fe was analyzed by ICP. The amounts of Fe in 0.5-, 5.0-, 10.0-, 24.0-, and 48.0-h samples are 0.028 wt%, 0.102 wt%, 0.214 wt%, 0.440 wt%, and 0.587 wt%. It is known that Fe doping in the n-type Bi2Te3 increases the electron concentration, whereas Fe doping in p-type is unclear [25, 26]. Therefore, the unintentional Fe doping will increase the electrons concentration. It seems that the increment in electrons concentration by Fe overcomes the reduction of that by vaporization Te in the larger milling time, whereas the reduction of n is still larger in the smaller milling time.

The power factor (S2/ρ) of the samples is shown in Fig. 9 as a function of the temperature. The value for 10.0-h sample is the largest at low temperature (2.40 × 10−3 W·m−1·K−2 at 323 K), which is mainly due to the largest Seebeck coefficient among the samples. It is well known that the power factor is maximized at the specific carrier concentration [27, 28, 29]. Thus, it can be concluded that the carrier concentration is optimized in the 10.0-h sample.
Fig. 9

Temperature dependence of power factor of Bi2(Te,Se)3 samples with different milling time

Figure 10 shows temperature dependence of the thermal conductivity of the samples as a function of the milling time. The values for the samples with smaller milling time (0.5–5.0 h) show relatively large values at room temperature compared with the samples with larger milling time. However, as the temperature increases, the behavior is varied and quite different from that of the samples with low temperature, especially the behavior of the sample after 10.0 h is peculiar. In order to understand these, the thermal conductivity is divided into electrical thermal conductivity (κe) and phonon thermal conductivity (κp), because the total thermal conductivity (κ) is a sum of κe and κp (κ = κe + κp). κe can be estimated with Wiedemann–Franz equation, κe = qLT, in which L is the Lorenz number whose value is dependent on the Fermi energy, the scattering mechanism, etc. [30]. Particularly, the estimation of κe should be more carefully considered, because the value of L is largely dependent on the Fermi energy and the scattering mechanism as shown in Eq. (6)
$$L = \left( {\frac{{k_{\text{B}} }}{\text{e}}} \right)^{2} \frac{{(1 + \lambda )(3 + \lambda )F_{\lambda } (\eta ) - (2 + \lambda )^{2} F_{(1 + \lambda )} (\eta )^{2} }}{{(1 + \lambda )^{2} F_{\lambda } (\eta )^{2} }}$$
where λ is the scattering factor in which acoustic phonon scattering and ionized impurity scattering corresponds to λ = 0 and λ = 2, respectively, η is the reduced Fermi energy and \(F_{\lambda } (\eta ) = \int_{0}^{\infty } {\xi^{\lambda} } f_{0} (\eta ){\text{d}}\xi\), where f0 is the Fermi distribution and ξ is the reduced energy of carriers. In order to determine the value of L, the value of η should be estimated. The estimation of η can be done by fitting the Seebeck coefficient with following Eq. (7) [30].
Fig. 10

Temperature dependence of thermal conductivity of Bi2(Te,Se)3 samples with different milling time

$$S = \frac{{k_{\text{B}} }}{q}\left[ {\frac{{(2 + \lambda )F_{(1 + \lambda )} }}{{(1 + \lambda )F_{\lambda } }} - \eta } \right]$$
Because the considered temperature is much higher than the Debye temperature, it is assumed that the acoustic phonon scattering is a dominant scattering mechanism and the value of λ = 0 is used in the estimation of L and η. The difference between Eq. (3) and Eq. 7 is that the latter is derived with Fermi–Dirac statistic in the Boltzmann transport equation, whereas the former is with the Boltzmann statistic for the highly degenerated scheme. The single carrier is assumed to fit the measured Seebeck coefficient with Eq. (7), as assumed in the calculation of the carrier concentration. The obtained L of the samples is shown in Fig. 11 as a function of the temperature. The sample after 0.5 h shows the largest value of L at room temperature, whereas the sample after 10.0 h shows the smallest value. In the degenerated semiconductor scheme, a small value of the Fermi energy in Eq. (6) gives a small value of L. It is notable that the value of L is determined by the Fermi energy which also determines the carrier concentration. Therefore, the estimated L exhibits the similar milling time dependence compared with that of the carrier concentration.
Fig. 11

Temperature dependence of Lorentz number of Bi2(Te,Se)3 samples

The temperature dependence of the lattice thermal conductivity obtained using the estimated L is shown in Fig. 12. It is well known that κp decreases as temperature increases when phonon scattering is dominant. However, the positive temperature coefficient of κp (dκp/dT) is observed at high temperature for all samples. This positive coefficient of κp at high temperature is believed to be due to the bipolar transport [14]. When the bipolar transport occurs, the estimation of L is not simple and the sophisticate consideration of transport properties of each carrier is needed [31]. The same positive coefficient at high temperature was also reported in the p-type Bi0.5Sb1.5Te3 compounds [14]. The value of κp is generally smaller in the smaller grain sizes compared with that in the larger grains. This kind of the behavior is well reported in the p-type Bi0.5Sb1.5Te3 [8, 12, 14]. However, in this research, the smallest κp is observed at elevated temperatures in the sample after 0.5 h which has the largest grains. The value of κp for 10.0-h sample is much larger than those of the others at high temperature, whereas the sub-grain size is much smaller than that of the 0.5-h sample. The variation of κp at high temperature is almost the same with the variation of the carrier concentration. Because the mean free path of phonons decreases with the temperature, the largest κp after 10.0-h milling time is due to the smallest defects concentration which can be a source of atomic scale scattering of phonons. The irregular change of κp at room temperature may be due to the ambiguity in evaluating κp because of the bipolar transport. The lower total thermal conductivity for 10.0-, 24.0-, and 48.0-h samples is due to the smaller κe, originated from the larger resistivity.
Fig. 12

Temperature dependence of lattice thermal conductivity of Bi2(Te,Se)3 samples obtained using estimated Lorenz number

Figure 13 shows the temperature dependence of ZT of all the samples. The highest value of ZT = 0.83 is achieved for the 10.0-h samples, which is about 48% enhancement over that of 0.5-h sample at 373 K. The Seebeck coefficient and the reduced thermal conductivity contribute to the enhanced ZT. It is clearly seen that the value of ZT is much dependent on milling time. The change of ZT in the p-type samples after the varied milling time is only about 10%. Thus, the fabrication process optimization is much more crucial for the n-type Bi2(Te,Se)3 compounds than for the p-type Bi0.5Sb1.5Te3 compounds.
Fig. 13

Temperature dependence of ZT of Bi2(Te,Se)3 samples with different milling time

4 Conclusion

The thermoelectric properties and the microstructure of Bi2(Te,Se)3 were investigated as a function of the ball milling times. The reduction of the grain size with the ball milling times was clearly demonstrated via microscopy images and the estimation from XRD patterns. As well as the change in the grain size, the thermoelectric properties were also investigated after various ball milling times. The electrical resistivity and the Seebeck coefficient are clearly changed with the milling time, and there was optimum milling time to maximize the power factor. The change of the electrical properties is attributed to the variation of the carrier concentration. The thermal conductivity is largely affected by the electrical properties, rather than by the grain sizes, which is different from that of the p-type Bi0.5Sb1.5Te3 compounds. The maximum ZT of 0.83 at 373 K is achieved in 10-h samples, and the obtained ZT value for 10 h has a 48% improvement over the ZT value of the 0.5-h sample at 373 K.



This research was supported by the research fund of Hanbat National University in 2015.

Supplementary material

12598_2018_1028_MOESM1_ESM.docx (107 kb)
Supplementary material 1 (DOCX 107 kb)


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Copyright information

© The Nonferrous Metals Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Thermoelectric Conversion Research CenterKorea Electrotechnology Research InstituteChangwonKorea
  2. 2.Department of Materials Science and EngineeringHanbat National UniversityDaejeonKorea

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