Detailed Theoretical Investigation and Comparison of the Thermal Conductivities of n- and p-type Bi 2 Te 3 Based Alloys
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Detailed Theoretical Investigation and Comparison of the Thermal Conductivities of n- and p-type Bi2 Te3 Based Alloys
¨ Ceyda Yelgel, Gyaneshwar P. Srivastava O. School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, United Kingdom
ABSTRACT In this work we present a detailed theoretical investigation of the thermal conductivities of n-type 0.1 wt.% CuBr doped 85% Bi2 Te3 - 15% Bi2 Se3 and p-type 3 wt% Te doped 20% Bi2 Te3 - %80 Sb2 Te3 single crystals. The thermal conductivity contributions arising from carriers, electron-hole pairs and phonons are computed rigorously in the temperature range 300 K 6 T 6 500 K. In agreement with available experimental measurements we theoretically find that the lowest total thermal conductivity is 3.15 W K−1 m−1 at 380 K for the n-type alloy and 1.145 W K−1 m−1 at 400 K for the p-type alloy. Stronger mass-defect scattering is found to be responsible for the lower thermal conductivity of the p-type alloy throughout the temperature range of the study. INTRODUCTION Thermoelectric devices are capable of converting temperature differences into electric voltage and vice versa. The maximum efficiency of a thermoelectric material is determined by its dimensionless figure of merit (ZT ): ZT =
S 2σ T, κc + κbp + κph
(1)
where T is the absolute temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κc , κbp , κph , are the carrier, electron-hole pair (bipolar) and phonon contributions of the thermal conductivity, respectively. One of the traditional ways to improve ZT is making alloys of single crystals. By this method significant reduction can be gained for the phonon thermal conductivity and larger values of ZT attained [1, 2]. Among various thermoelectric materials, Bi2 Te3 based alloys are chracterised with reasonably large ZT values near room temperature and further enhancement can be attempted by using diverse methods [3, 4, 5, 6]. In this present study we report a detailed theoretical investigation of the thermal conductivities of n-type 0.1 wt.% CuBr doped 85% Bi2 Te3 - 15% Bi2 Se3 and p-type 3 wt% Te doped 20% Bi2 Te3 - %80 Sb2 Te3 single crystals. Our theoretical thermal conductivity results are compared with the experimental values previously obtained by Hyun et al. [7] and Li et al. [8]. Various contributions of the conductivity are analysed to provide an explanation
for the difference in the results for the n-type and p-type alloys. Moreover, the frequency dependence of phonon thermal conductivity is studied for the p-type alloy and compared to n-type alloy reported in our former work [9]. THEORY The total thermal conductivity in semiconductors is expressed as κtotal = κc + κbp + κph where the contributions are from carriers (electrons or holes, κc ), electron-hole pairs (bipolar, κbp ) and phonons (κph ). Carrier Thermal Conductivity: The carrier thermal conductivity is determined by the Wiedemann-Franz law as [1, 2] κc = σLT =
k 2 B
e
σT L0 ,
(2)
where kB is the Boltzmann constant, L is the Lorenz number L0 is described i
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