# Electrical, Thermal, and Thermoelectric Transport Properties of Co-Doped *n*-type Cu_{0.008}Bi_{2}Te_{2.6}Se_{0.4} Polycrystalline Alloys

## Article information

## Abstract

Bi_{2}Te_{3}-based alloys have been extensively studied as thermoelectric materials near room temperature. In this study, the electrical, thermal, and thermoelectric transport properties of a series of Co-doped *n*;-type Cu_{0.008}Bi_{2}Te_{2.6}Se_{0.4} polycrystalline alloys (Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4}, *x*; = 0, 0.03, 0.06, 0.09 and 0.12) are investigated. The electrical conductivity of the Cu_{0.008}Bi_{1.97}Co_{0.03}Te_{2.6}Se_{0.4} (*x*; = 0.03) sample was significantly enhanced, by 34%, to 1199 S/cm compared to 793 S/cm of the pristine Cu_{0.008}Bi_{2}Te_{2.6}Se_{0.4} (*x*; = 0) sample at 300 K, and gradually decreased to 906 S/cm for *x*; = 0.12 upon further doping. Power factors of the Co-doped samples decreased compared to the 3.26 mW/mK<sup>2</sup> of the pristine Cu_{0.008}Bi_{2}Te_{2.6}Se_{0.4} sample at 300 K. Meanwhile, the power factor of the Cu_{0.008}Bi_{1.97}Co_{0.03}Te_{2.6}Se_{0.4} (*x*; = 0.03) sample became higher at 520 K. The lattice thermal conductivities of the Co-doped samples decreased due to additional point defect phonon scattering by the Co dopant. Consequently, the * zT*; for the Cu

_{0.008}Bi

_{1.97}Co

_{0.03}Te

_{2.6}Se

_{0.4}alloy at 520 K was 0.83, which is approximately 15% larger than that of pristine Cu

_{0.008}Bi

_{2}Te

_{2.6}Se

_{0.4}, while the

*; of the Cu doped samples at 300 K was smaller than that of the pristine Cu*

*zT*_{0.008}Bi

_{2}Te

_{2.6}Se

_{0.4}sample. Electrical transport properties of the Co-doped Cu

_{0.008}Bi

_{2−x}Co

_{x}Te

_{2.6}Se

_{0.4}samples were analyzed by experimental phenomenological parameters, including the density-of-state, effective mass, weighted mobility, and quality factor.

**Keywords:**thermoelectric; Bi

_{2}Te

_{3}; doping

## 1. INTRODUCTION

Bi 2 Te 3 -based alloys have been extensively studied as thermoelectric materials at room temperature. These materials are semiconductors with a narrow band gap (~ 0.13 eV) [1,2]. They have excellent electrical transport properties with a high carrier concentration (~ 10^{19} cm^{−3}) and exhibit a relatively low thermal conductivity due to layered structures with a weak Van der Waals bonding between layers [3-5], resulting in a good thermoelectric figure of merit (*zT*) at room temperature [6,7]. Thermoelectric performance is evaluated by the dimensionless Figure of merit, *zT* = S^{2}σT/*κ _{tot}* , where

*S, σ, T*, and

*κ*are Seebeck coefficient, electrical conductivity, absolute temperature, and total thermal conductivity (

_{tot}*κ*=

_{tot}*κ*+

_{ele}*κ*, where

_{latt}*κ*and

_{ele}*κ*are electron and lattice thermal conductivities, respectively), respectively. At elevated temperatures Bi

_{latt}_{2}Te

_{3}-based alloys also induce an intrinsic excitation of electron-hole pairs, resulting in a decrease in S and an increase in

*κ*. Therefore, Bi

_{tot}_{2}Te

_{3}-based alloys exhibit rapidly degrading thermoelectric performance above 500 K [8-10], which limits the application of Bi

_{2}Te

_{3}alloys to low temperatures, of 450 K or less.

Pristine Bi_{2}Te_{3} is an n-type semiconductor and is typically doped with Se into the Te-site to improve its thermoelectric performance. However, Bi_{2}Te_{3} compositions exhibit unstable carrier transport properties because of self-defects, the formation of anti-site defects, and Te-site vacancies [11]. The unstable carrier transport properties of n-type Bi_{2}Te_{3−x}Se_{x} can be stabilized by adding Cu [12-15].

Defect engineering, such as doping, addition, and solidsolution, are the most used strategies for reducing *κ _{latt}* by promoting point defect phonon scattering [16-19]. Doping strategies have been widely applied to enhance the thermoelectric transport properties of thermoelectric materials, particularly the n-type Bi

_{2}Te

_{3}-based alloys [19-22]. Lee et al. reported that using I-doping to improve the carrier transport properties of Cu

_{0.008}Bi

_{2}Te

_{2.7}Se

_{0.3}enhanced

*zT*to 0.86 at 400 K [21]. A higher

*zT*of 1.07 at 423 K was observed in CuI-doped Bi

_{2}Te

_{2.7}Se

_{0.3}processed by hot–deformation [22]. Similarly, Co doping was used to enhance the electrical transport properties of pristine Bi

_{2}Te

_{3}and ptype Bi

_{0.5}Sb

_{1.5}Te

_{3}[23,24].

However, Co-doping to Bi_{2}Te_{3−x}Se_{x}, a representative type of n-type Bi_{2}Te_{3} based alloy, has not yet been reported. Therefore, in this study, the electrical, thermal, and thermoelectric transport properties of Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4} (*x* = 0, 0.03, 0.06, 0.09 and 0.12) polycrystalline bulk alloys were investigated. The electrical transport properties of a Codoped Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4} composition were analyzed by experimental phenomenological parameters, including the density-of-state effective mass (*m _{d}**), weighted mobility (

*μ*), and quality factor (

_{w}*B*).

## 2. EXPERIMENTAL

Polycrystalline Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4} (*x* = 0, 0.03, 0.06, 0.09 and 0.12) samples were prepared via the solid-state reaction method. Stoichiometric ratios of high purity Bi (99.999%, 5N Plus), Te (99.999 %, 5N Plus), and Co (99.99%, Sigma Aldrich) were sealed in a quartz tube under a pressure of 10^{−5} Torr to prevent oxidation or other reactions with air. The raw materials placed in the sealed quartz ampoules were synthesized at 1323 K for 12 h (heating rate of 3 K/min), and then slowly cooled in a box furnace. The synthesized ingots were pulverized for 5 min via high energy ball milling (SPEX 8000D, SPEX) in an Ar atmosphere. The powders placed in the graphite molds were sintered using spark plasma sintering (SPS-1030, Sumitomo Coal Mining Co., Ltd.) under 10^{−6} Torr at 707 K for 5 min (heating rate = 100 K/min) under 70 MPa. The sintered bulk samples had relative densities of more than ~ 99%.

X-Ray diffraction (XRD, D8 Discover, Bruker) analysis was performed to analyze the crystal structure of the samples. The polycrystalline powder samples were excited with 0.154 nm wavelength Cu–Kα radiation. For the σ and S measurements, the sintered samples were processed into rectangular shapes with dimensions of 2 mm × 2 mm × 8 mm. The processed specimens were analyzed using ZEM-3 (Advanced-Riko) in the temperature range 300–520 K in a He atmosphere, and the power factor was calculated using the measured σ and S. The Hall carrier concentrations (*n _{H}*) and Hall carrier mobilities (

*μ*) were measured using a Hall measurement system (HMS5300, Ecopia) under a magnetic field of 0.548 T; the Hall measurements were performed using the van der Pauw configuration. The laser flash method (LFA457, Netzsch) was performed to obtain the thermal diffusivity (α) required to calculate

_{H}*κ*(

_{tot}*κ*= α ×

_{tot}*ρ*×

_{s}*C*, where

_{p}*ρ*and

_{s}*C*are the sample density and heat capacity, respectively). The

_{p}*ρ*value is the theoretical density of Bi

_{s}_{2}Te

_{2.6}Se

_{0.4}––assuming a linear increase in the Bi

_{2}Te

_{3}(7.834 g/cm

^{3})−Bi

_{2}Se

_{3}(7.664 g/cm

^{3}) system. The

*C*value of Bi

_{p}_{2}Te

_{3}was determined from the empirical formulas of 108.06 + 5.53 × 10

^{−2}T J/mol·K and

*C*of Bi

_{p}_{2}Se

_{3}= 118.61 + 1.92 ×10

^{−2}T J/mol·K [25]. The

*zT*value was evaluated using the calculated power factor and

*κ*.

_{tot}## 3. RESULTS AND DISCUSSION

The XRD patterns for the Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4} powder samples indicated a single rhombohedral Bi_{2}Te_{3} phase without any additional phases (Figure 1(a)). The lattice parameters, *a* and *c* were calculated using the (015) and (1010) diffraction peaks (Figure 1(b)). The calculated lattice parameters gradually decreased with an increase in x values; a decreased from 4.365 to 4.348 Å and c decreased from 30.390 to 30.323 Å. This is because Co is substituted and doped at the Bi–site, that is, a Co-cation (~ 88.5 pm) with a relatively small ionic radius replaced the Bi^{+3} (117 pm).

Figures 2(a) and 2(b) show σ and *S* as a function of temperature, respectively, for the polycrystalline bulk samples along the direction perpendicular to the sintering pressure. The σ values of the Co-doped samples were higher than those of the undoped sample at all temperature ranges, and all samples exhibited intrinsic metal behavior. As shown in the inset of Figure 2(a), the σ values for *x* = 0, 0.03, 0.06, 0.09, and 0.12 were 793, 1199, 1028, 960, and 906 S/cm, respectively, at 300 K. Remarkably, the σ values systemically decreased with increases in doping level, after abruptly increasing at *x* = 0.03. The *S* values were similar even with the increase in temperature with a decrease in the doped samples, owing to the trade-off relationship between σ and S. Therefore, the *S* values showed the opposite trend compared to σ. The *S* values for *x* = 0, 0.03, 0.06, 0.09, and 0.12 were −202, −152, −154, −163, and −168 μV/K (inset of Figure 2(b)), respectively, at 300 K.

Figures 2(c) and 2(d) present the calculated power factor and weighted mobility *μ _{w}* as a function of temperature for the Cu

_{0.008}Bi

_{2−x}Co

_{x}Te

_{2.6}Se

_{0.4}samples. As shown in Figure 2(c), the power factor for the samples decreased with the increase in temperature. The power factor of the doped samples decreased in the temperature range of 300–400 K compared to the undoped sample. However, after 450 K, the

*x*= 0.03 and 0.06 samples showed a reverse trend; the power factor of the

*x*= 0.03 sample increased by approximately 10% compared to the undoped sample at 520 K. The power factor values of the

*x*= 0, 0.03, and 0.06 samples were 1.83, 1.99, and 1.92 mW/mK

^{2}at 520 K, respectively. The maximum power factor was 3.26 mW/mK 2 for the

*x*= 0 sample at 300 K. The

*μ*value was obtained from a simple analytical form that approximates the exact Drude–Sommerfeld free-electron model given in Equation (1) for |

_{w}*S*| > 20 μV/K [26].

where *k, m _{e}, e*, and

*h*are the Boltzmann constant, mass of the electron, elementary charge, and Planck’s constant, respectively. The

*μ*parameter infers the maximum reachable power factor when

_{w}*n*is optimized. The

_{H}*μ*value of each sample was evaluated using the measured σ and

_{w}*S*parameters; the

*μ*values showed a similar trend as the power factor. The maximum

_{w}*μ*value was 373 cm

_{w}^{2}/Vs for the

*x*= 0 sample at 300 K.

Figure 3(a) shows *n _{H}* as a function of x for the Cu

_{0.008}Bi

_{2−x}Co

_{x}Te

_{2.6}Se

_{0.4}samples along the direction perpendicular to the sintering pressure. The

*n*values showed a trend similar to the σ values;

_{H}*n*increased approximately twice for the

_{H}*x*= 0.03 (6.66 × 10

^{19}cm

^{−3}) sample compared to the

*x*= 0 (3.54 × 10

^{19}cm

^{−3}) sample at 300 K and then decreased linearly with increases in x. The

*μ*values for the Co-doped samples decreased because μ H is inversely proportional to

_{H}*n*; however, unlike

_{H}*n*, the

_{H}*μ*values were constant after

_{H}*x*= 0.06 (Figure 3(b)). The

*μ*values for the

_{H}*x*= 0, 0.03, 0.06, 0.09, and 0.12 samples are 139 108, 105, 106, and 109 cm

^{2}/Vs at 300 K, respectively.

The magnitude of the density of states is directly related to the density-of-state effective mass *m _{d}** and the electrical transport behavior was interpreted in terms of changes in the electron structure by calculating

*m*. Equation (2), which was optimized to a single parabolic band model, is used to plot

_{d}**m*for the samples (Figure 3(c)) [27].

_{d}*The *m _{d}** value of the

*x*= 0.03 (1.55

*m*) sample was larger than that of the

_{0}*x*= 0 (1.529

*m*) sample at 300 K because

_{0}*m*is proportional to both |

_{d}**S*| and

*n*. This indicates that the decrease in |

_{H}*S*| for the

*x*= 0.03 sample is less than the increase in

*n*at 300 K. The inset of Figure 3(c) shows a plot of log

_{H}_{10}(

*n*) as a function of |

_{H}*S*| for the samples. The

*m*becomes generally lower with the Co doping.

_{d}*Figure 4(a) shows *κ _{tot}* as a function of temperature for the Cu

_{0.008}Bi

_{2−x}Co

_{x}Te

_{2.6}Se

_{0.4}samples along the direction perpendicular to the sintering pressure. The

*κ*values of the

_{tot}*x*= 0.03, 0.06, 0.09, and 0.12 samples at 300–450 K increased with the increase in

*κ*(inset of Figure 4(a)). The

_{ele}*κ*values were calculated using

_{ele}*κ*= LσT (where L is the Lorenz number [28]) and the increase in

_{ele}*κ*significantly affected the increase in σ of the Co-doped samples. Therefore, the values of

_{tot}*κ*for the

_{tot}*x*= 0, 0.03, 0.06, 0.09, and 0.12 samples at 300 K were 1.08, 1.22, 1.18, 1.16, and 1.16 W/mK, respectively, In contrast, the

*κ*values of the

_{tot}*x*= 0.03, 0.06, and 0.12 samples at 520 K decreased to 1.24, 1.29, and 1.31 W/mK, respectively, from that of the

*x*= 0 (1.31 W/mK at 520 K) sample. Interestingly, the κ latt reached its lowest value at

*x*= 0.03, and increased for the higher doping samples. The physical reason behind the unusual observation for

*κ*may be the complex defect structures produced by the Co doping, which requires further study.

_{latt}Figure 5(a) illustrates the *zT* of the Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4} polycrystalline bulk samples. The thermoelectric performance of the Co-doped samples significantly decreased in contrast to the undoped sample at 300 K. The maximum *zT* value of the undoped sample at 300 K was 1.0. However, the *zT* of the undoped sample decreased above 360 K, while those of the *x* = 0.03 and 0.06 samples marginally increased above 450 K. Therefore, the *zT* values of *x* = 0.03 and 0.06 were enhanced more than the *x* = 0 sample at 480 and 520 K. The *zT* values of the *x* = 0.03, and 0.06 samples were 0.91, and 0.84 at 480 K and 0.83, and 0.77 at 520 K, respectively. Further, the *zT* values of the *x* = 0.03 and 0.06 samples were enhanced to approximately 8% and 3% at 480 K and to approximately 15% and 7% at 520 K, compared with the *x* = 0 (0.82 and 0.72 at 480 and 520 K, respectively), respectively.

Figure 5(b) shows the *n _{H}*-dependent

*zT*calculated via the single parabolic band model and experimental

*zT*at 300 K;

*n*-dependent experimental

_{H}*zT*(denoted using symbols) and calculated

*zT*(denoted using a line), which indicates the theoretically achievable

*zT*at 300 K. The

*zT*values of all the Co-doped samples were lower than the achievable

*zT*(line in Figure 5(b)), which would infer the band structure was unfavorably changed by the doping. Because the

*n*value of the

_{H}*x*= 0.03 sample was the highest, it is plotted at the rightmost side (

*n*of 6.7 ×10

_{H}^{19}cm

^{−3}) in the graph (solid red). As the doping content increases, the symbols shift toward the left, which indicates a decrease in

*n*. However, the peak value of the calculated

_{H}*zT*was observed when

*n*was 2.2 × 1019 cm

_{H}^{−3}. Therefore,

*n*optimization of the samples is required. Based on the calculation, shown in Fig 5(b),

_{H}*zT*can be increased to 0.94 at 300 K when

*n*is optimized (decreased) to ~ 2.2 × 1019 cm

_{H}^{−3}. Dopants to decrease the mother compound Cu0.008Bi

_{2}Te

_{2.6}Se

_{0.4}could be introduced to enhance

*zT*at 300 K.

Figure 5(c) shows the dimensionless thermoelectric quality factor B, which was evaluated using Equation (3) [26]:

Based on previous studies, *B* is proportional to the maximum *zT* value that can be achieved for an optimized *n _{H}* [29, 30]. Therefore, the general trend of B is similar to that of

*zT*; however, in this study, the x=0.03 sample has a maximum B value (0.49) at 440 K. In particular, the B values for all doped samples above 480 K were less than that of the undoped sample. The B values of the

*x*= 0, 0.03, 0.06, 0.09, and 0.12 samples were 0.29, 0.45, 0.37, 0.30, and 0.32, respectively, at 520 K. This indicates that in the Co-doped samples at 520 K,

*zT*can be increased to a greater extent, when

*n*is optimized.

_{H}## 4. CONCLUSIONS

In summary, the thermoelectric properties of Co-doped Bi_{2}Te_{2.6}Se_{0.4}, Cu_{0.008}Bi_{2−x}Co_{x}Te_{2.6}Se_{0.4} (*x* = 0, 0.03, 0.06, 0.09, and 0.12) polycrystalline samples were investigated. The electrical conductivity generally increased for the Co-doped samples and the *S* values decreased. The measured power factor of the Co-doped samples was lower than 3.26 mW/mK^{2} for the pristine Cu0.008Bi_{2}Te_{2.6}Se_{0.4} sample at 300 K. However, the power factor of the Cu_{0.008}Bi_{1.97}Co_{0.03}Te_{2.6}Se_{0.4} (*x* = 0.03) sample became higher at 520 K. A decrease in lattice thermal conductivity was observed for the Co-doped samples due to additional point defect phonon scattering. Consequently, a maximum *zT* of 1.0 was observed for the *x* = 0 sample at 300 K; however, above 440 K, the *zT* values of the *x* = 0.03 and 0.06 samples were approximately 15% and 7% larger than that of the *x* = 0 sample, at 520 K, respectively. Furthermore, a maximum quality factor of 0.49 was observed for the *x* = 0.03 sample at 440 K, which would infer that the highest *zT* can be obtained with the *x* = 0.03 sample at 440 K by optimizing carrier concentration.

## Notes

There is no conflict of interest.

## Acknowledgements

This study was supported by the National Research Foundation of Korea (NRF-2019R1C1C1005254 and NRF2022R1F1A1063054).