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Mechanically-Exfoliated Stacks of Thin Films of Bismuth Telluride Topological Insulators with Enhanced Thermoelectric Performance

We report on"graphene-like"mechanical exfoliation of single-crystal Bi2Te3 films and thermoelectric characterization of the stacks of such films. Thermal conductivity of the resulting"pseudo-superlattices"was measured by the"hot disk"and"laser flash"techniques. The room-temperature in-plane (cross-plane) thermal conductivity of the stacks decreases by a factor of ~2.4 (3.5) as compared to bulk. The thermal conductivity reduction with preserved electrical properties leads to strong increase in the thermoelectric figure of merit. It is suggested that the film thinning to few-quintuples and tuning of the Fermi level can help in achieving the topological-insulator surface transport regime with an extraordinary thermoelectric efficiency.

for ZT enhancement in Bi 2 Te 3 thin films. It was discovered that Bi 2 Te 3 family of materials are topological insulators (TIs) [5]. TIs are materials with a bulk insulating gap and conducting surface states that are topologically protected against scattering by the time-reversal symmetry [5][6]. It was shown theoretically that ZT can be strongly enhanced in Bi 2 Te 3 thin-film TIs provided that the Fermi level is tuned to ensure the surface transport regime and the films are thin enough to open a gap in the "Dirac cone" dispersion on the surface [7].
We previously demonstrated that a "graphene-like" procedure can be used to mechanically exfoliate the ultra-thin films of Bi 2 Te 3 with the thickness down to a single quintuple [8]. The quintuples (thickness W~ 1 nm) are structural units in Bi 2 Te 3 crystal separated from each other by the van der Waals gaps. The mechanically exfoliated few-quintuple films have a number of benefits compared to grown thin films. They are perfectly crystalline and have an essentially infinite potential barrier for electrons and holes. The latter is a drastic difference from Bi 2 Te 3based superlattices grown by molecular beam epitaxy or other techniques. The ultimately high potential barriers together with a few-quintuple thickness and possibility of electrical back-gating can ensure the strong quantum confinement for electrons and E F fine-tuning. In this letter we report on the thermoelectric properties of stacks of mechanically exfoliated Bi 2 Te 3 films focusing on a possibility of ZT enhancement via reduction of the thermal conductivity. The thermoelectric applications require a sufficient quantity of material, i.e. "bulk", i.e. the single quintuples would hardly be practical. For this reason, we studied the stacks of the exfoliated films, which were put on top of each other and subjected to thermal treatment.
The details of the "graphene-like" process for exfoliating Bi 2 Te 3 films were reported by us elsewhere [8]. The resulting stacks were composed of the individual films with different thicknesses (from a few nm to m). The stacks were intentionally made rather thick (up to ~0.5 mm). The material crystallinity and quality were verified with micro-Raman spectroscopy.   [9]. It is interesting to note an additional peak, identified as A 1u , which appears as a result of the crystal symmetry breaking in thin films with the thickness below the light penetration depth [10]. It is not present in the bulk Bi 2 Te 3 crystals. The intensity of A 1u peak and the intensity ratio I(A 1g 2 )/I(E g 2 ) can be used for nanometrology of few-quintuple films [10]. The shown spectra correspond to the film with the thickness W~50 nm. The thickness was crosschecked with the atomic force microscopy. The inset shows a scanning electron microscopy (SEM) image (Philips XL-30 FEG) of two overlapping exfoliated Bi 2 Te 3 films.
The "graphene-like" exfoliated films were transferred to a substrate and mechanically put on top of each other. The stacks were annealed at ~250 0 C to reduce the air gaps between the layers and improve structural stability. Figure 2 shows the cross-sectional SEM image of a stacked sample.
One can see that the films of different thicknesses are assembled into a non-periodic "pseudosuperlattice" (also referred to as compositionally modulated structures or "random superlattices"). The non-periodic "superlattices" may have certain benefits for thermoelectric applications owing to flexibility for tuning the phonon transport [11]. The films elemental     [14] marked by the stars. The monotonic K decrease with T is characteristic for semiconductor materials where thermal transport is limited by the crystal inharmonicity. The data for the bulk cross-plane K are also consistent. The good agreement for bulk attests for accuracy of our measurements. One can see in Figure 3 that there is a strong decrease in the in-plane thermal conductivity of the "pseudosuperlattices" as compared to the bulk. The in-plane K for the stacked Bi 2 Te 3 superlattices is ~0.7 W/mK, which is a reduction by a factor of ~2.4 from the bulk value of ~1.7 W/mK. The RT cross-plane K of the stacked films is ~0.14 W/mK, which is a significant drop, by a factor of 3.5, V. Goyal, D. Teweldebrhan and A.A. Balandin, UC Riverside, submitted to Applied Physics Letters, 2010 6 from the bulk cross-plane value of ~0.5 W/mK. The "pseudo-superlattice" K is only weakly dependent on temperature. This is expected for the thermal transport limited the phononboundary scattering [3,4,15]. The cross-plane K reduction is much stronger possibly owing to the large thermal boundary resistance between the exfoliated films. The thermal conduction in our samples was mostly by the acoustic phonons as estimated from the Wiedemann-Franz law.
Another observation is that K values obtained for the stacks with different thicknesses are nearly the same. It means that the thermal conductivity was limited by the phonon scattering at the interfaces between the individual Bi 2 Te 3 layers rather than by the scattering on the outside boundaries of the samples. The overall decrease of K in our stacks is exceptional. It is on the higher end or exceeds that reported for Bi 2 Te 3 nanoparticles [15], alloy films [16] and highlytextured materials [17]. The cross-plane K in our "pseudo-superlattices" approaches the theoretical minimum value predicted for the disordered crystals [18]. which is close to the optimum for the thermoelectric applications. The strong decrease in the thermal conductivity with preserved electrical properties translates to ~140-250% increase in ZT at RT. It is important to emphasize that the estimated increase is achieved entirely via reduction in the thermal conductivity. The Fermi level in the "pseudo-superlattices" was not optimized.
The carrier transport in the films was likely of the mixed volume and surface nature. The further increase in crystal quality, thinning of the films and gating (for achieving the pure surface transport) is expected to result in additional strong ZT increase predicted theoretically [7].
In conclusions, we studied thermoelectric properties of "pseudo-superlattices" prepared by staking of the "graphene-like" mechanically exfoliated of single-crystal Bi 2 Te 3 films. We showed that ZT in such structures can be substantially increased via reduction of the in-plane and cross-plane thermal conductivity. It is an important observation, since Bi 2 Te 3 were shown to be topological insulators. Eventually, it may become possible to achieve the pure surface transport regime through the Dirac surface states, topologically protected against scattering, and achieve the theoretically predicted strong enhancement of ZT over a wide temperature range.