Thermoelectric 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 DARPA-TI meeting, August 15, 2012

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., Bi 2 Te 3 ). 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, (2010). ZT ~ 7 F. Zahid and R. Lake, Appl. Phys. Lett. 97, (2010). The work presented here reproduces and expands these results. 2

Figure-of-merit IeIe IQIQ T1T1 T2T2 ΔT = T 1 – T 2 ΔV = V 1 – V 2 V1V1 V2V2 G : Electrical conductance S: Seebeck coefficient k e : Electronic thermal conductance k l : Lattice thermal conductance Material properties Thermoelectric figure-of-merit : (open circuit, zero electrical current) 3

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

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

6 kxkx kyky E(k) Number of conducting channels How do we calculate the # of conducting channels (modes)? Let’s consider a simple example: 2D film with parabolic E k. E kxkx M(E,k y ) 012 E kyky 1 00 Transport E M(E)M(E)

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

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

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

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

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

Power factor 12 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 :

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

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 Bi 2 Se 3, Sb 2 Te 3 and MoS 2. 14