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Thermoelectric properties of phosphorene at the nanoscale

Published online by Cambridge University Press:  23 September 2016

Hangbo Zhou ,
Yongqing Cai ,
Gang Zhang  and
Yong-Wei Zhang
Hangbo Zhou
Affiliation:
Institute of High Performance Computing, A*STAR, Singapore 138632
Yongqing Cai
Affiliation:
Institute of High Performance Computing, A*STAR, Singapore 138632
Gang Zhang*
Affiliation:
Institute of High Performance Computing, A*STAR, Singapore 138632
Yong-Wei Zhang
Affiliation:
Institute of High Performance Computing, A*STAR, Singapore 138632
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

Phosphorene is a new-emerging two-dimensional material with many fascinating electronic and thermal properties. Using nonequilibrium Green's function technique, we investigate the thermoelectric transport properties of phosphorene in the ballistic transport regime. We find that while the electronic conductance and thermal conductance of phosphorene are highly anisotropic, the Seebeck coefficient is isotropic. The maximum predicted thermopower reaches 2500 μV/K. We also find that the Wiedemann–Franz law is valid only when the chemical potential is inside valence band or conduction band. When the chemical potential is near the valence band maximum or conduction band minimum; however, the Wiedemann–Franz law becomes invalid, and interestingly, the figure of merit ZT reaches its maximum value. We also find that figure of merit ZT increases with the increase of temperature, and ZT in the armchair direction is much higher than that in the zigzag direction. By analyzing the various effects on ZT, we discuss the possible routines to enhance figure of merit ZT.

Keywords

Thermoelectricitynanoscalethermal conductivity
Type
Invited Paper
Information
Journal of Materials Research , Volume 31 , Issue 20 , 28 October 2016 , pp. 3179 - 3186
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Copyright
Copyright © Materials Research Society 2016 

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References

REFERENCES

Goldsmid, H.J.: Introduction to Thermoelectricity (Springer, Berlin, Heidelberg, 2009).Google Scholar
Rowe, D.M.: CRC Handbook of Thermoelectrics (CRC Press, Boca Raton, 1995).Google Scholar
DiSalvo, F.J.: Thermoelectric cooling, and power generation. Science 285(5428), 703 (1999).Google Scholar
Ashcroft, N.W. and Mermin, N.D.: Solid State Physics (Holt, Rinehart and Winston, California, 1976).Google Scholar
Dubi, Y. and Di Ventra, M.: Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions. Rev. Mod. Phys. 83(1), 131–155 (2011).Google Scholar
Bhimanapati, G.R., Lin, Z., Meunier, V., Jung, Y., Cha, J., Das, S., Xiao, D., Son, Y., Strano, M.S., Cooper, V.R., Liang, L., Louie, S.G., Ringe, E., Zhou, W., Kim, S.S., Naik, R.R., Sumpter, B.G., Terrones, H., Xia, F., Wang, Y., Zhu, J., Akinwande, D., Alem, N., Schuller, J.A., Schaak, R.E., Terrones, M., and Robinson, J.A.: Recent advances in two-dimensional materials beyond graphene. ACS Nano 9(12), 11509 (2015).Google Scholar
Butler, S.Z., Hollen, S.M., Cao, L., Cui, Y., Gupta, J.A., Gutiérrez, H.R., Heinz, T.F., Hong, S.S., Huang, J., Ismach, A.F., Johnston-Halperin, E., Kuno, M., Plashnitsa, V.V., Robinson, R.D., Ruoff, R.S., Salahuddin, S., Shan, J., Shi, L., Spencer, M.G., Terrones, M., Windl, W., and Goldberger, J.E.: Progress, challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano 7(4), 2898 (2013).CrossRefGoogle ScholarPubMed
Zhang, G. and Zhang, Y-W.: Strain effects on thermoelectric properties of two-dimensional materials. Mech. Mater. 91, 382 (2015).Google Scholar
Bonaccorso, F., Colombo, L., Yu, G., Stoller, M., Tozzini, V., Ferrari, A.C., Ruoff, R.S., and Pellegrini, V.: Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage. Science 347(6217), 1246501 (2015).Google Scholar
Fei, R., Faghaninia, A., Soklaski, R., Yan, J-A., Lo, C., and Yang, L.: Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Lett. 14(11), 6393 (2014).Google Scholar
Gunst, T., Markussen, T., Jauho, A-P., and Brandbyge, M.: Thermoelectric properties of finite graphene antidot lattices. Phys. Rev. B: Condens. Matter Mater. Phys. 84, 155449 (2011).Google Scholar
Lv, H.Y., Lu, W.J., Shao, D.F., and Sun, Y.P.: Enhanced thermoelectric performance of phosphorene by strain-induced band convergence. Phys. Rev. B: Condens. Matter Mater. Phys. 90, 085433 (2014).Google Scholar
Qin, G., Yan, Q-B., Qin, Z., Yue, S-Y., Cui, H-J., Zheng, Q-R., and Su, G.: Hinge-like structure induced unusual properties of black phosphorus and new strategies to improve the thermoelectric performance. Sci. Rep. 4, 6946 (2014).CrossRefGoogle ScholarPubMed
Sevinçli, H., Sevik, C., Çaın, T., and Cuniberti, G.: A bottom-up route to enhance thermoelectric figures of merit in graphene nanoribbons. Sci. Rep. 3, 1355 (2013).CrossRefGoogle ScholarPubMed
Zhang, J., Liu, H.J., Cheng, L., Wei, J., Liang, J.H., Fan, D.D., Shi, J., Tang, X.F., and Zhang, Q.J.: Phosphorene nanoribbon as a promising candidate for thermoelectric applications. Sci. Rep. 4, 6452 (2014).CrossRefGoogle ScholarPubMed
Li, L., Yu, Y., Ye, G., Ge, Q., Ou, X., Wu, H., Feng, D., Chen, X., and Zhang, Y.: Black phosphorus field-effect transistors. Nat. Nanotechnol. 9, 372 (2014).Google Scholar
Cai, Y., Zhang, G., and Zhang, Y-W.: Layer-dependent band alignment, and work function of few-layer phosphorene. Sci. Rep. 4, 6677 (2014).CrossRefGoogle ScholarPubMed
Hong, Y., Zhang, J., Huang, X., and Zeng, X.C.: Thermal conductivity of a two-dimensional phosphorene sheet: A comparative study with graphene. Nanoscale 7(44), 18716 (2015).Google Scholar
Jain, A. and McGaughey, A.J.H.: Strongly anisotropic in-plane thermal transport in single-layer black phosphorene. Sci. Rep. 5, 8501 (2015).Google Scholar
Lee, S., Yang, F., Suh, J., Yang, S., Lee, Y., Li, G., Sung Choe, H., Suslu, A., Chen, Y., Ko, C., Park, J., Liu, K., Li, J., Hippalgaonkar, K., Urban, J.J., Tongay, S., and Wu, J.: Anisotropic in-plane thermal conductivity of black phosphorus nanoribbons at temperatures higher than 100 K. Nat. Commun. 6, 8573 (2015).CrossRefGoogle Scholar
Liu, T-H. and Chang, C-C.: Anisotropic thermal transport in phosphorene: Effects of crystal orientation. Nanoscale 7(24), 10648–10654 (2015).Google Scholar
Ong, Z-Y., Cai, Y., Zhang, G., and Zhang, Y-W.: Strong thermal transport anisotropy and strain modulation in single-layer phosphorene. J. Phys. Chem. C 118(43), 25272 (2014).Google Scholar
Xu, W., Zhu, L., Cai, Y., Zhang, G., and Li, B.: Direction dependent thermal conductivity of monolayer phosphorene: Parameterization of Stillinger-Weber potential and molecular dynamics study. J. Appl. Phys. 117(21), 214308 (2015).Google Scholar
Zhu, L., Zhang, G., and Li, B.: Coexistence of size-dependent and size-independent thermal conductivities in phosphorene. Phys. Rev. B: Condens. Matter Mater. Phys. 90(21), 214302 (2014).Google Scholar
Jiang, J-W. and Park, H.S.: Analytic study of strain engineering of the electronic bandgap in single-layer black phosphorus. Phys. Rev. B: Condens. Matter Mater. Phys. 91, 235118 (2015).Google Scholar
Lew Yan Voon, L.C., Lopez-Bezanilla, A., Wang, J., Zhang, Y., and Willatzen, M.: Effective Hamiltonians for phosphorene and silicene. New J. Phys. 17(2), 025004 (2015).CrossRefGoogle Scholar
Zhou, X.Y., Zhang, R., Sun, J.P., Zou, Y.L., Zhang, D., Lou, W.K., Cheng, F., Zhou, G.H., Zhai, F., and Chang, K.: Landau levels and magneto-transport property of monolayer phosphorene. Sci. Rep. 5, 12295 (2015).CrossRefGoogle ScholarPubMed
Rudenko, A.N. and Katsnelson, M.I.: Quasiparticle band structure and tight-binding model for single- and bilayer black phosphorus. Phys. Rev. B: Condens. Matter Mater. Phys. 89, 201408 (2014).Google Scholar
Wang, J-S., Agarwalla, B.K., Li, H., and Thingna, J.: Nonequilibrium Green's function method for quantum thermal transport. Front. Phys. 9(6), 673 (2013).Google Scholar
Zhang, W., Fisher, T.S., and Mingo, N.: Simulation of interfacial phonon transport in Si–Ge heterostructures using an atomistic Green's function method. J. Heat Transfer 129(4), 483 (2007).Google Scholar
Wang, J-S., Wang, J., and Lü, J.T.: Quantum thermal transport in nanostructures. Eur. Phys. J. B 62(4), 381 (2008).Google Scholar
Paolo, G., Stefano, B., Nicola, B., Matteo, C., Roberto, C., Carlo, C., Davide, C., Guido, L.C., Matteo, C., Ismaila, D., Andrea Dal, C., Stefano de, G., Stefano, F., Guido, F., Ralph, G., Uwe, G., Christos, G., Anton, K., Michele, L., Layla, M-S., Nicola, M., Francesco, M., Riccardo, M., Stefano, P., Alfredo, P., Lorenzo, P., Carlo, S., Sandro, S., Gabriele, S., Ari, P.S., Alexander, S., Paolo, U., and Renata, M.W.: Quantum ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21(39), 395502 (2009).Google Scholar
Zhou, H., Cai, Y., Zhang, G., and Zhang, Y-W.: Quantum thermal transport in stanene. Phys. Rev. B: Condens. Matter Mater. Phys. 94, 045423 (2016).Google Scholar
Liao, B., Zhou, J., Qiu, B., Dresselhaus, M.S., and Chen, G.: Ab initio study of electron-phonon interaction in phosphorene. Phys. Rev. B: Condens. Matter Mater. Phys. 91, 235419 (2015).Google Scholar
Zhang, G. and Zhang, Y-W.: Thermal conductivity of silicon nanowires: From fundamentals to phononic engineering. Phys. Status. Sollidi RRL 7, 754 (2013).Google Scholar