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T hermoelectric properties of ultra-thin Bi 2 Te 3 films

DARPA-TI meeting, August 15, 2012. T hermoelectric properties of ultra-thin Bi 2 Te 3 films. Jesse Maassen and Mark Lundstrom. Network for Computational Nanotechnology, Electrical and Computer Engineering, Purdue University, West Lafayette, IN USA. Motivation.

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T hermoelectric properties of ultra-thin Bi 2 Te 3 films

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  1. DARPA-TI meeting, August 15, 2012 Thermoelectric properties of ultra-thin Bi2Te3 films Jesse Maassen and Mark Lundstrom Network for Computational Nanotechnology, Electrical and Computer Engineering, Purdue University, West Lafayette, IN USA

  2. Motivation • In recent years, much research has focused energy-related science and technology, in particular thermoelectrics. • Some of the best known thermoelectric materials happen to be topological insulators (e.g., Bi2Te3). • Work has appeared showing that TI surface states in ultra-thin films (<10 nm) can lead to enhanced thermoelectric properties. ZT ~ 2 P. Ghaemi, R.S.K. Mong and J. Moore, Phys. Rev. Lett. 105, 166603 (2010). ZT ~ 7 F. Zahid and R. Lake, Appl. Phys. Lett. 97, 212102 (2010). The work presented here reproduces and expands these results.

  3. Figure-of-merit G : Electrical conductance S : Seebeck coefficient ke: Electronic thermal conductance kl: Lattice thermal conductance Thermoelectric figure-of-merit : (open circuit, zero electrical current) Material properties (open circuit, zero electrical current) ΔT = T1 – T2 T2 T1 Ie IQ V1 V2 ΔV = V1 – V2

  4. Thermoelectric transport coefficients Differential conductivity/conductance is the central quantity for thermoelectric calculations. Conductivity Seebeck Electronic thermal conductivity (zero field) Electronic thermal conductivity (zero current)

  5. Conductance / conductivity in the Landauer picture Scattering T = 1 (ballistic) T = λ/ L (diffusive) Band structure CONDUCTANCE CONDUCTIVITY Conductance (conductivity) is better suited to describe ballistic (diffusive) transport.

  6. Number of conducting channels • How do we calculate the # of conducting channels (modes)? • Let’s consider a simple example: 2D film with parabolic Ek. M(E,ky) Transport E(k) E M(E,ky) kx 0 1 2 kx ky 1 E M(E) 0 0 ky E

  7. Ultra-thin Bi2Te3 films Te1 : A site Bi c-axis : B site Te2 Bi : C site Te1 1 quintuple layer 6 QL Experimental bulk lattice parameters are assumed: 5 QL ab-axis = 4.38 Å c-axis = 30.49 Å 4 QL 3 QL 2 QL 1 QL 0.74 nm 1.76 nm 2.77 nm 3.79 nm 4.81 nm 5.82 nm

  8. Band structure • Band gap exists only for 1QL and 2QL. • For QL>2, surface state close the gap. Computed using density functional theory (DFT), with the VASP simulation package.

  9. Distribution of modes • Modes corresponds to the number of quantum conducting channels. • 1QL, 2QL, 3QL are different, but QL>4 are very similar. • Sharp increase in modes at the valence edge only with 1QL. • Analytical model by Moore [PRL 105, 166603 (2010)], only well describes the conduction band. • Scaling factor disprepancy with the result of Zahid & Lake [APL 97, 212102 (2010)].

  10. Why sharp increase with 1QL? Answer comes from analyzing the k-resolved modes.

  11. Seebeck coefficient • Large positive Seebeck with 1 QL. • Seebeck decreases with increasing film thickness. • Max. Seebeck with 1 QL, the result of a larger band gap. ΔEbulk ΔE1QL

  12. Power factor • 1 QL : maximum PF is 6-7x larger than others. • Large PF results from enhanced conduction near the VB edge. • Demonstration of TE enhancement through band structure. Numerator of ZT :

  13. Figure-of-merit • 1 QL : potential ZT 4x larger than bulk. • QL > 2 leads to low ZT, due to small (or zero) band gap.

  14. Conclusions / future work • Electronic enhancement of ZT with 1 QL, due to the shape of the VB. • Strict constraint on thickness, enhancement only predicted for 1 QL. • Future work: • Impact of scattering on TE parameters. • Predict lattice thermal conductivity (phonon transport). • Study thin films of Bi2Se3, Sb2Te3 and MoS2.

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