Two-Dimensional Tellurene as Excellent Thermoelectric Material

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Cite This: ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX

Two-Dimensional Tellurene as Excellent Thermoelectric Material Sitansh Sharma, Nirpendra Singh, and Udo Schwingenschlögl* Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia ABSTRACT: We study the thermoelectric properties of two-dimensional tellurene by firstprinciples calculations and semiclassical Boltzmann transport theory. The HSE06 hybrid functional results in a moderate direct band gap of 1.48 eV at the Γ point. A high room temperature Seebeck coefficient (Sxx = 0.38 mV/K, Syy = 0.36 mV/K) is combined with anisotropic lattice thermal conductivity (κlxx = 0.43 W/m K, κlyy = 1.29 W/m K). Phonon band structures demonstrate a key role of optical phonons in the record low thermal conductivity that leads to excellent thermoelectric performance of tellurene. At room temperature and moderate hole doping of 1.2 × 10−11 cm−2, for example, a figure of merit of ZTxx = 0.8 is achieved.

KEYWORDS: thermoelectrics, 2D material, tellurene, first-principles calculation, Boltzmann theory exploring n- and p-doped tellurene by means of first-principles calculations in combination with Boltzmann transport theory.

I. INTRODUCTION Due to increasing energy consumption and shortage of fossil resources, harvesting of waste heat becomes more and more important. To this purpose, thermoelectric technology provides an effective route to convert waste heat into electricity.1−4 The thermoelectric performance of a material is given by the dimensionless figure of merit, ZT = S2σT/(κe + κl), where S is the Seebeck coefficient, σ is the electrical conductivity, and κe and κl are the electronic and lattice contributions to the thermal conductivity. Because two-dimensional materials often show better performance than bulk materials,5−10 many of them nowadays are being explored for thermoelectric applications,11−15 in particular, monoelemental borophene,16 graphene,17 silicene,18 germanene,19 arsenene,20 stanene,21 and antimonene.20 Bulk tellurium is known for its low thermal conductivity (1.6 W/(m K)) and nested band structure due to that the material achieves ZT ∼ 0.2 at 673 K, which can be enhanced to ZT ∼ 1.0 by suitable doping.22−25 In addition, many other thermoelectric materials contain tellurium, such as PbTe,26 Bi2Te3,27 Sb2Te3,28,29 GeTe,30,31 and SnTe.32 It has been demonstrated that ultrathin flakes of tellurium can be realized by exfoliation,33 and very recently two-dimensional tellurium, so-called tellurene, has been grown expitaxially on graphene/6H-SiC(0001)34 and on pyrolytic graphite35 using molecular beam epitaxy. The material’s electronic structure subsequently has been studied by first-principles calculations in refs 36 and 37, and ref 38 has discussed a field effect transistor based on high-quality tellurene (synthesized in a substrate-free solution process) that is stable in air with high in-plane carrier mobility. On the other hand, for now no experimental or theoretical investigation of the thermoelectric properties of tellurene has been reported in the literature. We will fill this gap in the present work by © XXXX American Chemical Society

II. THEORETICAL APPROACH First-principles calculations are performed using density functional theory as implemented in the Vienna ab initio simulation package (VASP).39 The exchange−correlation potential is treated in the generalized gradient approximation (Perdew−Burke−Ernzerhof flavor), and the cutoff energy of the plane-wave basis is set to 500 eV. The crystal structure is relaxed with a total energy convergence criterion of 10−6 eV and a force convergence criterion of 0.001 eV/Å, considering long-range van der Waals interactions by means of the DFT-D3 method40 and using for Brillouin zone integration the Monkhorst−Pack scheme with 9 × 9 × 1 k-mesh. The tetrahedron method with 16 × 16 × 1 k-mesh is used to calculate the density of states at the Heyd−Scuseria−Ernzerhof (HSE06) level of theory,41 taking into account the spin−orbit interaction.39 Semiclassical Boltzmann transport theory within the constant relaxation time approximation and the rigid band approach are employed to determine the electronic transport coefficients (S, σ, and κe) by the BoltzTraP code.42 This approach earlier has been used successfully to model the thermoelectric properties of various twodimensional materials.11,43−45 The Fourier interpolation of the Kohn− Sham eigenvalues (HSE06 level of theory) is conducted on a dense 21 × 21 × 1 k-mesh. Moreover, κl is obtained by self-consistent solution of the Boltzmann transport equation for phonons using the ShengBTE code,46 with the second and third order force constants as input. Employing a 4 × 5 × 1 supercell with 3 × 3 × 1 k-mesh, the second order force constants are determined by the Phonopy code47 and interactions up to seventh nearest neighbors are considered to obtain the third order force constants by the VASP and Phonopy codes. Integrations are carried out on a 90 × 90 × 1 q-mesh. The fact that the Received: January 9, 2018 Accepted: April 10, 2018

A

DOI: 10.1021/acsaem.8b00032 ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX

Article

ACS Applied Energy Materials values of κl show differences below 2% as compared to a 70 × 70 × 1 q-mesh indicates that our results are well converged. A volume correction is employed based on a layer thickness of 5.93 Å.

III. RESULTS AND DISCUSSION Tellurene has three Te atoms in the unit cell, as shown in Figure 1. The optimized lattice constants are a = 5.69 Å and b =

Figure 1. Top and side views of the two-dimensional crystal structure.

4.22 Å. There exist two kinds of Te−Te bonds with lengths of 2.77 and 3.03 Å. The band structure and density of states shown in Figure 2 reflect a semiconducting nature with direct

Figure 3. Seebeck coefficient, electrical conductivity, and electronic contribution to the thermal conductivity in the x- and y-directions.

for S in the x-direction and for σ and κe in the y-direction (anisotropic electronic transport). At sufficiently high ρ, |S| increases for growing temperature. Both σ and κe turn out to be higher for p-doping than for n-doping in both directions, reflecting the differences in the carrier effective masses mentioned above. Turning to Figure 4, the phonon band structure demonstrates stability of the crystal structure and significant l anisotropy is observed between κxx and κyyl . At room temperature we obtain κlxx = 0.43 W/(m K) and κlyy = 1.29 W/(m K). Because κl depends on the phonon group velocity (∂ω/∂q), its anisotropy is explained by comparison of the phonon dispersions along the Γ−X and Γ−Y directions. Importantly, the obtained values of κl at room temperature are

Figure 2. Electronic band structure and density of states. The energy zero is set to the valence band maximum.

band gap of 1.48 eV at the Γ point. The dispersion is stronger at the valence band maximum than at the conduction band minimum, implying that the hole effective mass is lower than the electron effective mass. Comparison of the Γ−X and Γ−Y high-symmetry directions demonstrates anisotropic electronic transport, as expected from the crystal structure of the material. Results for S, σ, and κe are given in Figure 3 as functions of the electron and hole concentrations (ρ) at 300, 500, and 700 K, separately for the x- and y-directions. Higher values are found B

DOI: 10.1021/acsaem.8b00032 ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX

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ACS Applied Energy Materials

Figure 4. Phonon band structure, lattice thermal conductivity, scattering rate, and cumulative lattice thermal conductivity.

Figure 5. Figure of merit along the x- and y-directions.

the lowest among the monoelemental two-dimensional materials (graphene, 2200 W/(m K);17 silicene, 9.4 W/(m K);18 germanene, 2.4 W/(m K);48 arsenene, 62 W/(m K);20 stanene, 11.6 W/(m K);21 antimonene, 25 W/(m K)20). This property is explained by the close proximity of the lowfrequency optical phonons to the acoustic phonons. As a result, the probability of the three-phonon scattering processes acoustic + acoustic → optical and acoustic + optical → optical is high; compare the high scattering rates for the acoustic phonons in Figure 4. Accordingly, Figure 4 shows that the optical phonons are responsible for a large part of κl in both directions (65% of κlxx and 45% of κlyy at room temperature), because the acoustic phonons transport very little heat. A similar, though less pronounced, behavior previously has been observed for twodimensional dumbbell silicene49 and monolayer C3N.50 Using the carrier mobilities and effective masses given in ref 36, electron (hole) relaxation times of τxx = 2.4 × 10−14 s (43.9 × 10−14 s) and τyy = 1.1 × 10−14 s (2.8 × 10−14 s) are calculated in order to determine the figure of merit; see the results in Figure 5. We observe at all temperatures that ZTxx is higher than ZTyy, as κlxx is lower than κlyy. At room temperature and the optimal electron (hole) doping, maximal values of ZTxx = 0.60 (0.80) and ZTyy = 0.46 (0.38) are obtained. Moreover, consideration of the cumulative lattice thermal conductivity, κlc, shows that ZT can be enhanced by nanostructuring; see Figure 4. For example, reduction of the phonon mean free path below 4.6 nm (3.2 nm) reduces κlxx (κlyy) to less than half.

of acoustic into optical phonons. As a consequence, a promising figure of merit of 0.80 is observed at a p-doping of 1.2 × 1011 cm−2, for example.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +966(0) 54470080. ORCID

Nirpendra Singh: 0000-0001-8043-0403 Udo Schwingenschlögl: 0000-0003-4179-7231 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). For computer time, this research used the resources of the Supercomputing Laboratory at KAUST.

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REFERENCES

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IV. CONCLUSION In conclusion, the thermoelectric response of two-dimensional tellurene has been studied by combining first-principles calculations with semiclassical Boltzmann transport theory. The calculated electronic and phonon band structures reveal strong directional anisotropy of the material’s transport properties. Tellurene turns out to have the lowest lattice thermal conductivity among all monoelemental materials. This exceptional behavior can be attributed to very strong scattering C

DOI: 10.1021/acsaem.8b00032 ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acsaem.8b00032 ACS Appl. Energy Mater. XXXX, XXX, XXX−XXX