Enhanced thermoelectric performance in three-dimensional superlattice of topological insulator thin films
© Fan et al.; licensee Springer. 2012
Received: 29 June 2012
Accepted: 24 September 2012
Published: 16 October 2012
We show that certain three-dimensional (3D) superlattice nanostructure based on Bi2Te3 topological insulator thin films has better thermoelectric performance than two-dimensional (2D) thin films. The 3D superlattice shows a predicted peak value of ZT of approximately 6 for gapped surface states at room temperature and retains a high figure of merit ZT of approximately 2.5 for gapless surface states. In contrast, 2D thin films with gapless surface states show no advantage over bulk Bi2Te3. The enhancement of the thermoelectric performance originates from a combination of the reduction of lattice thermal conductivity by phonon-interface scattering, the high mobility of the topologically protected surface states, the enhancement of Seebeck coefficient, and the reduction of electron thermal conductivity by energy filtering. Our study shows that the nanostructure design of topological insulators provides a possible new way of ZT enhancement.
is usually baffled by the competition of the Seebeck coefficient S, the electrical conductivity σ, the electron thermal conductivity κe and the lattice thermal conductivity κl. Recent discoveries that some of the best thermoelectric materials such as Bi2Te3 are also strong 3D topological insulators [3–5], and experimental studies of the mechanical exfoliation and growth of quintuple layers (QL, 1 QL ≈ 0.748 nm) of Bi2Te3[6, 7] attract much interest [8–11] in the thermoelectric properties of thin films of Bi2Te3 with one or a few QL.
High ZT values of Bi2Te3 thin films depend crucially on the opening of a subgap at the surface, which disappears quickly with the increasing of the film thickness, as suggested both theoretically [12–14] and experimentally [15, 16]. Relatively accurate density functional theory calculations [16, 17] show that the (indirect) surface gap of Bi2Te3 vanishes as soon as the thickness of the thin film increases to 3QL. Despite the high mobility  of the surface electrons, the gapless surface states would lead to poor thermoelectric performance due to low Seebeck coefficient and high electron thermal conductivity. However, by creating suitable nanostructures, extra energy-dependent electron scattering mechanisms can be introduced, which could increase the Seebeck coefficient [19, 20] and reduce the electron thermal conductivity. The consideration of nanostructures of thin films is also motivated by the fact that a single layer of thin film is not of much practical use for thermoelectric applications, and stacks of thin films have much lower lattice thermal conductivity compared with the bulk .
The 3D superlattice structure proposed here can be regarded as bulk Bi2Te3 which is nanoporous and resembles nanoporous Si  and nanoporous Ge , both of which show significant enhancement of the figure of merit due to orders of magnitude reduction in the lattice thermal conductivity. The difference is that the electronic transports for nanoporous Bi2Te3 and Si/Ge are dominated by surface and bulk carriers, respectively.
A comparison with nanoporous Si  and Ge  is helpful. While the values of lattice thermal conductivities for bulk Bi2Te3, Ge and Si range from a few watts per meter Kelvin to several hundred watts per meter Kelvin, the values for the corresponding nanoporous materials are all reduced to below 1 W/(m K). This fact is another indication of the dominance of phonon-interface scattering over the phonon-phonon scattering.
For the 3D superlattice structure, the square of velocity along the transport direction takes the same form as in Equation 10, and the effective 3D density of states is that of Equation 11 as scaled by a/(a + c). Since the quantum well states lie much above, we can safely disregard them and consider the surface states only. We also only consider the conduction band with E > 0.
This method of calculating the total electron relaxation time has been recently applied to the study of thermoelectric properties of nanocomposites [32, 33]. We assume 2Δ b = 0.15 eV for bulk Bi2Te3 according to the experimental value . The surface gap is chosen to be 2Δ f = 0.3, 0.06, and 0 eV for thin films with thickness 1QL, 2QL, and 3QL, respectively, as suggested by first-principle calculations . The effective mass m* entering Equation 13 stands for that of bulk Bi2Te3, which has a highly anisotropic effective mass tensor, with the in-plane components 0.021 m0 and 0.081 m0 and the out-of-plane component 0.32 m0 (m0 is the mass of a free electron) . For simplicity, we take m* to be 0.1 m0 in our calculations. The exact value of m* is not very crucial for our discussions, since it only affects the optimal value of b.
Results and discussion
To get an intuition of the necessity of violating the Wiedemann-Franz law for superior thermoelectric performance, suppose that the lattice thermal conductivity is reduced to zero, and the Seebeck coefficient is 200 μ VK−1, then if the Wiedemann-Franz law were strictly valid, we would have achieved a relatively low figure of merit ZT = S 2 /L0 ≈ 1.6 regardless how large the electrical conductivity would be. Thus, as we approach the lower limit of lattice thermal conductivity, it is imperative to find a way to change the shape of the transport distribution function [29, 30] either by altering the electronic structures  or by introducing energy-dependent electron scattering mechanisms.
Finally, we add some view points on the approach that we used in this work. For the study of thermoelectric transport of a nanostructured material, there are two complementary ways of viewing the system. One is to take the system as a whole, in which case the nanostructures do alter the electronic structure of the system, but it is difficult to calculate the band structure of such large system directly by first principles method due to large number of atoms presented in nanostructures. Another way is to view the system as some bulk material with nanostructures that do not affect the electronic structure of the bulk material significantly, but introduce some extra scatterings for the charge carriers. We have chosen the second approach in our study. This approach has been widely used in the community of thermoelectrics. For example, in the study of nanocomposites with grain boundaries [32, 33], one usually assumes that the electronic structure inside the grain boundary is the same as that of the corresponding bulk material. The grain boundary does not affect significantly the energy-band structure and only serves as a scattering interface. The only difference between our model and the nanocomposite models [32, 33] is that our bulk material is quasi-two-dimensional instead of three-dimensional, and the grain boundaries are replaced by the strips in our proposed structure. So long as the average distance between the strips is large compared with the size of the strips (which is the case for the optimized structures), this view point is valid and there is no significant deficiency in our model.
In summary, we demonstrated that certain nanostructures of topological insulators have the potential of overcoming the obstacle of competition of the individual thermoelectric transport coefficients to achieve high thermoelectric figure of merit. High electron mobility of the topologically protected surface states together with the holy structure of the 3D superlattice ensures a large B factor , and the energy filtering effect introduced by the inhomogeneous superlattice structure promotes the Seebeck coefficient and the ratio of electrical conductivity to the electron thermal conductivity. The optimal temperature of performance for the 3D superlattice with optimized geometric parameters is around or below room temperature, making it very appealing for thermoelectric power generation and refrigeration applications around and below room temperature, respectively. In addition, a similar structure has appeared in a thin film transistor array, with an insulating substrate and a stripe-shaped semiconductor layer for a plurality of transistors , which demonstrates the experimental feasibility of our proposed 3D superlattice structure. The detailed information of geometric and electronic properties of the fabricated superlattice can be characterized by integrated electron scattering and X-ray scattering techniques [40, 41].
This work is supported by the Minjiang Scholar Distinguished Professorship Program through Xiamen University of China, Specialized Research Fund for the Doctoral Program of Higher Education (grant numbers 20090121120028 and 20100121120026), Program for New Century Excellent Talents in University (NCET) (grant number NCET-09-0680) and the National Science Foundation of China (grant number U1232110).
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