A Detailed Theoretical Study of the Thermal Conductivity of Bi 2 (Te 0.85 Se 0.15 ) 3 Single Crystals
- PDF / 814,312 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 9 Downloads / 148 Views
A Detailed Theoretical Study of the Thermal Conductivity of Bi2(Te0.85Se0.15)3 Single Crystals ¨ Ceyda Yelgel, Gyaneshwar P. Srivastava O. School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
ABSTRACT We present a theoretical investigation of the thermal conductivity for n-type doped Bi2 (Te0.85 Se0.15 )3 single crystals by using the Debye model within the single-mode relaxationtime approximation. A detailed account of alloy, electron-phonon, phonon-phonon and electron-hole pair (bipolar) interactions are included. Different levels (0.1 and 0.05 wt.%) of n-doping from CuBr and SbI3 dopants were considered. The calculated conductivity, by combining lattice (κph ) and electronic bipolar (κbp ) contributions, successfully explains the experimental results obtained by Hyun et al. [J. Mat. Sci. 33 5595 (1998)]. The κph contribution was calculated using Srivastava’s scheme and the κbp contribution was obtained by employing Price’s theory. INTRODUCTION Thermoelectric (TE) devices convert temperature differences into electric voltage and vice versa. The efficiency of TE materials is expressed by the dimensionless figure of merit ZT = S 2 σT /κ, where T is the absolute temperature, S is the Seebeck coefficient, σ is the electrical conductivity, and κ = κel + κph + κbp is the total thermal conductivity with electronic (κel ), lattice (phonons) (κph ), and bipolar (electron-hole pairs) (κbp ) contributions [1, 2]. Reducing the thermal conductivity by making alloys of single crystals is found one way to significantly improve ZT . Among the single crystals with highest ZT values near room temperature are the Bi2 Te3 -Sb2 Te3 and Bi2 Te3 -Bi2 Se3 alloys [3, 4, 5, 6]. It is generally believed that it is the low thermal conductivity of these materials that results in high ZT values. The thermal conductivity (κ) of n-doped 85% Bi2 Te3 - 15%Bi2 Se3 single crystals has been measured over the temperature range 190 - 600 K by Hyun et al. [7] and a clear ‘dip’ is observed in the κ − T curve around room temperature, exhibiting almost a parabolic shape around the minimum. The purpose of this work is to present a detailed theoretical investigation of the thermal conductivity of Bi2 (Te0.85 Se0.15 )3 single crystals doped with CuBr and SbI3 (with 0.1 and 0.05 wt.% doping levels), and attempt to explain the experimental results obtained by Hyun et al. [7] . Moreover, for 0.1 wt.% CuBr doped alloy, the frequency as well as percentage contributions from different polarisations (transverse and longitudinal) towards the phonon thermal conductivity are presented.
THEORY In Bi2 (Te0.85 Se0.15 )3 narrow band-gap semiconductor the total thermal conductivity κ is contributed by donor electrons (κel ), lattice vibrations (κph ), and electron-hole pairs contribution (κbp ). Lattice thermal conductivity: Employing Debye’s isotropic continuum model, within the single-mode relaxation time scheme, we express κph in the form [8] κph
5 X Z 1 ~2 qD c4 dxx4 τ n ¯ (¯ n + 1), = 2 6π kB T 2 s s 0
(1)
where τ is the relaxation time for a
Data Loading...
