Composition dependent charge transport and temperature dependent density of state effective mass interpreted by temperature normalized pisarenko plot in bi2−xsbxte3 compounds

Composition dependent charge transport and temperature dependent density of state effective mass interpreted by temperature normalized Pisarenko plot in Bi2−xSbxTe3 compounds Composition dependent cha[.]

Composition-dependent charge transport and temperature-dependent density

of state effective mass interpreted by temperature-normalized Pisarenko plot in Bi2-xSbxTe3 compounds

Tae-Ho An, Young Soo Lim, Mi Jin Park, Jang-Yeul Tak, Soonil Lee, Hyung Koun Cho, Jun-Young Cho, Chan Park, , and Won-Seon Seo,

Citation: APL Mater. 4, 104812 (2016); doi: 10.1063/1.4961106

View online: http://dx.doi.org/10.1063/1.4961106

View Table of Contents: http://aip.scitation.org/toc/apm/4/10

Published by the American Institute of Physics

Composition-dependent charge transport

and temperature-dependent density of state effective

mass interpreted by temperature-normalized Pisarenko plot

in Bi2−xSbxTe3 compounds

Tae-Ho An,1,2Young Soo Lim,3, aMi Jin Park,1Jang-Yeul Tak,1,4Soonil Lee,1

Hyung Koun Cho,4Jun-Young Cho,2Chan Park,2, aand Won-Seon Seo1, a

1Energy and Environmental Materials Division, Korea Institute of Ceramic Engineering

and Technology, Jinju 52851, South Korea

2Department of Materials Science and Engineering, Seoul National University,

Seoul 08826, South Korea

3Department of Materials System Engineering, Pukyong National University,

Busan 48547, South Korea

4School of Advanced Materials Science and Engineering, Sungkyunkwan University,

Suwon 16419, South Korea

(Received 16 May 2016; accepted 1 August 2016; published online 15 August 2016)

Composition-dependent charge transport and temperature-dependent density of state

effective mass-dependent Seebeck coefficient were investigated in Bi2−xSbxTe3

(x = 1.56-1.68) compounds The compounds were prepared by the spark plasma sintering of high-energy ball-milled powder High-temperature Hall measurements revealed that the charge transport in the compounds was governed dominantly by phonon scattering and influenced additionally by alloy scattering depending on the amount of Sb Contrary effects of Sb content on the Seebeck coefficient were dis-cussed in terms of carrier concentration and density of state effective mass, and it was elucidated by temperature-normalized Pisarenko plot for the first time C 2016 Au-thor(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4961106]

Recently, thermoelectric energy conversion has been explosively investigated for its applica-tions to power generation using waste heat and electronic cooling devices The efficiency of the thermoelectric energy conversion is dictated by the performance of thermoelectric material, and it

is determined by dimensionless figure of merit ZT = S2σT/κ, where S, σ, T, and κ are the See-beck coefficient, the electrical conductivity, the absolute temperature, and the thermal conductivity, respectively.1 3Among numerous thermoelectric materials, Bi2Te3and its alloyed compounds have been mostly commercialized due to their low thermal conductivities, high Seebeck coefficients, and high electrical conductivities near room temperature.4For the enhancement of ZT in Bi2Te3-based compounds, many approaches mostly based on nanostructuring have been attempted successfully to reduce the thermal conductivity.5 14

However, for the further enhancement of ZT in Bi2–xSbxTe3compounds, optimizing the power factor (PF= S2σ) in the nanostructured compounds is also critical and it can be carried out by the control of the Sb content in the compounds Although there have been numerous reports on the effects of Sb on the thermoelectric properties of Bi2–xSbxTe3compounds,15–19detailed studies

on the charge transport mechanism which governing the electrical conductivity, and on the density

of state (DOS) effective mass which influencing on the Seebeck coefficient can be hardly found especially at relatively high temperatures Because these properties are strongly correlated to each

a Authors to whom correspondence should be addressed Electronic addresses: yslim@pknu.ac.kr; pchan@snu.ac.kr; and wsseo@kicet.re.kr

2166-532X/2016/4(10)/104812/7 4, 104812-1 © Author(s) 2016.

104812-2 An et al. APL Mater 4, 104812 (2016)

other, the simultaneous understanding of the effects of Sb content on the charge transport and also

on the DOS effective mass in detail is of great significance

In this work, we report the composition-dependent charge transport and temperature-dependent DOS effective mass in Bi2−xSbxTe3compounds Although the charge transport in the compound was governed generally by the well-known hole-phonon scattering regardless of the Sb content, the

effect of Sb on the additional alloy scattering was elucidated by high-temperature Hall measure-ment The change in the DOS effective mass depending on both the Sb content and the temperature was interpreted by temperature-normalized Pisarenko plot for the first time, and the contrary effects

of the Sb incorporation on the Seebeck coefficient were discussed

Bi2−xSbxTe3 (x= 1.56-1.68) compounds were synthesized by a vacuum melting method Bi (99.999%, 5 N Plus), Sb (99.999%, 5 N Plus), and Te (99.999%, 5 N Plus) were used as starting materials Mixtures of starting materials in evacuated silica tubes were melted at 1273 K for 6 h, annealed at 973 K for 3 h, and quenched in water to obtain a homogeneous Bi2−xSbxTe3phase The annealed ingots were pulverized by Spex-mill (Spex Certiprep, 8000M mixer/mill) for 50 min in an

Ar ambient, and then consolidated by using spark plasma sintering (Well Tech, WT 4000A) under

an uniaxial pressure of 60 MPa at 753 K for 3 min Phase analyses were performed by using an X-ray diffractometer (XRD, New D8 Advance, Bruker) Microstructural characterizations were also carried out by using a scanning electron microscope (SEM, JSM-6700, JEOL) Electrical conductiv-ities and Seebeck coefficients were measured by using a four-point probe method (TPMS, ZEM-3, ULVAC-RIKO), and temperature-dependent carrier concentrations and mobility were characterized

by using a high-temperature Hall measurement system (ResiTest 8300, Toyo Corporation) Both the TPMS and high-temperature Hall measurements were carried out along the perpendicular direction

to the pressing axis for the sintering process

Fig 1(a) shows XRD patterns of the Bi2−xSbxTe3 (x = 1.56-1.68) compounds prepared by spark plasma sintering The XRD patterns showed that the compounds consisted of a single phase

of Bi2−xSbxTe3(PDF #49-1713) without any secondary phase The relative intensities of (006) to (015) peak in the XRD patterns were ∼0.13 in all Bi2−xSbxTe3 compounds, and they were not strongly dependent on the amount of Sb in the compounds Figs 1(b)-1(e) show the fractured surfaces of the Bi2−xSbxTe3 compounds Randomly oriented grains with shape anisotropy were observed clearly in all compounds, and structural difference between them could be hardly observed

in the micrographs With these XRD and SEM results, it was found that the Sb content does not considerably influence the microstructure of the Bi2−xSbxTe3compounds in this experimental range Therefore, the following thermoelectric properties of the compounds, which are critically

affected by the microstructure, can be directly compared without further consideration on the additional effects of the microstructure

Fig 2(a) shows temperature-dependent hole concentrations of the Bi2−xSbxTe3 compounds The Hall measurements were carried out within the temperature range from room temperature (RT) to 450 K, and detailed results at RT are summarized in Table I The increase in the hole concentration with increasing Sb content was observed obviously, resulting from the generation of antisite defects (Sb′Te).20 – 23Due to the small difference in the electronegativity between Bi (2.02) and Te (2.1), antisite defect of Bi′Tecan be easily produced in Bi2Te3 compound In Bi2−xSbxTe3 compounds, the formation energy of antisite defects can be reduced further by the decrease in the difference of the electronegativity between Sb (2.05) and Te atoms, leading to the increase

in the hole concentration via the formation of Sb′Teantisite defects It is noteworthy that the hole concentrations in the compounds with a relatively high Sb content (x ≥ 1.64) were not significantly influenced by temperature, demonstrating that they are degenerately doped with the antisite defects However, the compounds with low Sb content exhibited slightly increasing hole concentration with increasing temperature, and this tendency could be more clearly observed in the Bi0.44Sb1.56Te3

compound with the lowest Sb content In a degenerately doped p-type semiconductor where its Fermi level is located below the valence band maxima (VBM), the carrier concentration is indepen-dent of temperature up to extrinsic-intrinsic transition temperature.24 Therefore, this result shows that all the Bi2−xSbxTe3compounds in this experiment are heavily doped extrinsic semiconductors, and that the large amount of hole originates from the extrinsic antisite defects facilitated by the Sb incorporation

FIG 1 (a) X-ray diffraction patterns and ((b)-(e)) SEM micrographs of the Bi 2−x Sb x Te 3 compounds (x = 1.56-1.68).

Fig 2(b) represents temperature-dependent Seebeck coefficients of the Bi2−xSbxTe3 com-pounds Seebeck coefficients decreased with increasing Sb content in the Bi2−xSbxTe3compounds, and it resulted from the increase of the hole concentration by the Sb incorporation as discussed above In an extrinsic degenerate semiconductor, Seebeck coefficients can be described by Pis-arenko relation in Eq (1),25

S=8π

2k2BT 3qh2 m∗d( π

where kB is the Boltzmann constant, q is the carrier charge, h is the Plank constant, m∗d is the DOS effective mass, and p is the hole concentration Therefore, the Seebeck coefficient is not only affected by the carrier concentration, but also influenced by the DOS effective mass in the compound

To elucidate the complex effects of Sb on the DOS effective mass and related Seebeck coeffi-cient in the Bi2−xSbxTe3compounds, we adopted temperature-normalized Pisarenko plot (S/T vs p) as shown in Fig.2(c) In this figure, dashed lines indicate the relation between the temperature-normalized Seebeck coefficient and hole concentration at a constant DOS effective mass deter-mined by Eq (1), and me is the mass of electron (9.11 × 10−31 kg) The DOS effective mass in the compound increases significantly with increasing Sb content At the lowest temperature of T1 (∼306 K), the effective masses in the Bi2−xSbxTe3 compounds were 0.691, 0.811, 0.902, and 0.923 me when x= 1.56, 1.60, 1.64, and 1.68, respectively Therefore, the effects of Sb alloying

on the Seebeck coefficient should be considered from two different viewpoints The increase in the

104812-4 An et al. APL Mater 4, 104812 (2016)

FIG 2 Temperature-dependent (a) hole concentrations and (b) Seebeck coe fficients (T1: ∼306 K, T6: ∼420 K) of the

Bi 2−x Sb x Te 3 compounds (c) S/T is plotted as a function of hole concentration with estimated DOS e ffective mass obtained

by Pisarenko relation (dashed line: m ∗

d /m e = 0.6, 0.7, 0.8, and 0.9), and (d) temperature-dependent DOS effective mass of the compounds.

hole concentration via the formation of antisite defect weakens the Seebeck coefficient as discussed above, while the increase in the DOS effective mass can make a positive impact upon it These contrary effects of Sb are especially important to the optimization of power factor (PF = S2σ)

in the Bi2−xSbxTe3 compounds because each parameter in PF is critically dependent on both the carrier concentration and the DOS effective mass It is noteworthy that the DOS effective mass tends

to decrease monotonously with the increase in the temperature (see the arrows from T1 to T6) The estimated DOS effective masses are shown in Fig.2(d) This temperature-dependence of the DOS

effective mass leads to the weakened Seebeck coefficient at relatively high temperatures, and it is the reason why the Seebeck coefficients are not linearly increasing with the temperature even in the degenerately doped Bi2−xSbxTe3compounds (x= 1.64 and 1.68) whose hole concentrations are almost independent of temperature as shown in Fig.2(a)

In addition, detailed composition-dependent charge transport behavior in the Bi2−xSbxTe3 com-pounds was investigated Figs.3(a)and3(b)show temperature-dependent electrical conductivities and Hall mobilities of the Bi2−xSbxTe3compounds, respectively As the amount of Sb in the com-pounds increased, the electrical conductivity was significantly improved mostly due to the increase

in the hole concentration The effect of Sb content on the mobility was not clear in this figure,

TABLE I Charge transport properties of Bi 2−x Sb x Te 3 compounds at room temperature: electrical conductivity, Seebeck coefficient, hole concentra-tion, Hall mobility, and DOS effective mass obtained by Pisarenko relation

at room temperature.

x σ (S/cm) S (µV/K) P (10 19 /cm 3 ) µ (cm 2 /Vs) m ∗

d /m e

1.56 803.16 211.12 1.74 260.60 0.69 1.60 993.19 194.64 2.51 239.51 0.81 1.64 1092.52 187.78 3.10 242.35 0.90 1.68 1175.26 177.82 3.48 232.92 0.92

FIG 3 (a) Temperature-dependent electrical conductivities and (b) Hall mobilities of the Bi 2−x Sb x Te 3 compounds (c) Nor-malized mobilities as a function of T −3/2 and (d) temperature-dependent power factor of the compounds.

and it was differently observed at each temperature The electrical conductivities exhibited nega-tive temperature-dependence in all compounds, resulting from the well-known phonon scattering (µ ∝ T−3/2).19 , 26 – 28To clarify the scattering mechanism in detail, normalized mobilities were replot-ted as a function of T−3/2in Fig.3(c) The normalized mobilities exhibited linear relationship with

T−3/2in all compounds, indicating that the mobility is dominantly governed by acoustic phonon scattering and/or nonpolar optical phonon scattering.28However, if the charge transport was dictated solely by the phonon scattering, the extrapolated mobility should be zero when 1/T is zero As shown in this figure, the extrapolated mobility did not converge on the origin point, and the offset from the origin point decreased with increasing Sb content as marked by an arrow This result implies strongly that an additional charge scattering mechanism is also working in the compounds

as well as the phonon scattering, and that the additional scattering can be weakened by the Sb incor-poration Although the increasing effective mass with increasing Sb content can retard the charge transport, this weakened additional scattering by the Sb incorporation can give beneficial effects on the charge transport Therefore, the effect of Sb content on the mobility could be elucidated by the temperature-dependence of mobility rather than the value of mobility itself

For the additional effects in the Bi2−xSbxTe3compounds, grain boundary scattering, ionized impurity scattering, and alloy scattering can be suggested.29 , 30Firstly, the effects of the grain bound-ary scattering on the charge transport can be disregarded in this experiment because the structural properties in the compounds were not significantly different to each other as shown in Fig.1 Our observation in Fig 3(c) cannot be explained by the ionized impurity scattering either Because the Sb incorporation increases the antisite defect with the hole concentration, the incorporation of

Sb should intensify the additional scattering by the ionized impurity Therefore, the effect of the ionized impurity scattering on the charge transport can be negligible in the experiment On the other hand, because the alloy scattering is due to the locally distorted band structure in the alloyed compounds, it can be alleviated in the Bi2−xSbxTe3compounds by the dominant occupation of Sb at Bi-sites.19 , 31 , 32Recently, Hu et al reported the enhancement of mobility by the incorporation of Sb

in Bi2−xSbxTe3compounds especially when x > 1.60, and they attributed the enhanced mobility to the weakened alloy scattering.19Although their Bi2−xSbxTe3compounds were prepared by hot press and hot deformation methods, their result is quite consistent to ours Therefore, it was manifested

104812-6 An et al. APL Mater 4, 104812 (2016)

that the charge transport in the Bi2−xSbxTe3compounds is dominantly governed by the hole-phonon scattering and partially influenced by the alloy scattering in this experimental condition Further-more, this alleviated additional alloy scattering with increasing x is the reason why the mobility values in Fig.3(b)were weakly dependent on the increasing effective mass with the Sb content in the Bi2−xSbxTe3compounds

When we simultaneously consider its metallic charge transport behaviour in Fig.3(a)and the temperature-dependent DOS effective mass in Fig 2(d), the maximum power factor should be achieved at the lowest temperature of T1 (∼306 K) as shown in Fig.3(d)and this behaviour can be one of the reasons why Bi2−xSbxTe3compound exhibits the best thermoelectric performance near room temperature

In summary, the effects of Sb content on the charge transport and DOS effective mass-related Seebeck coefficient in Bi2−xSbxTe3compounds were investigated The increase in the hole concen-tration with increasing Sb content led to the enhancement of the electrical conductivity The charge transport was dominantly governed by the phonon scattering in all compounds However, the charge transport was additionally affected by the alloy scattering and it could be alleviated by increasing

Sb content in the compounds Therefore, it was proven that the incorporation of Sb gives the positive effects on the charge transport properties not only by increasing the carrier concentration, but also by restraining the additional alloy scattering On the other hand, contrary effects of Sb incorporation on the Seebeck coefficient were observed Although the Seebeck coefficient decreased with increasing Sb content due to the drastic generation of hole carriers via the easy formation

of antisite defects, the degree of the reduction was limited due to the increase in the DOS e ffec-tive mass with increasing Sb content Furthermore, temperature-dependent DOS effective masses

in Bi2−xSbxTe compounds were estimated for the first time based on the temperature-normalized Pisarenko plot The temperature-normalized Pisarenko plot not only provides the relation between the carrier concentration and Seebeck coefficient in the compound, but also presents the dependence

of the DOS effective mass on temperature which critically affects the Seebeck coefficient It can

be generally applicable to other thermoelectric materials system, and it will be helpful for the comprehensive understanding of the temperature-dependent thermoelectric transport properties This research was supported by the Nano·Material Technology Development Program (No 2011-0030147) and also supported by the Mid-career Researcher Program (No 2015R1A2A2A01005929) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology, Republic of Korea

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