Thermal transport properties of monolayer phosphorene: a mini-review of theoretical studies
Guangzhao QIN, Ming HU
Thermal transport properties of monolayer phosphorene: a mini-review of theoretical studies
Phosphorene, a two-dimensional (2D) elemental semiconductor with a high carrier mobility and intrinsic direct band gap, possesses fascinating chemical and physical properties distinctively different from other 2D materials. Its rapidly growing applications in nano-/opto-electronics and thermoelectrics call for fundamental understanding of the thermal transport properties. Considering the fact that there have been so many studies on the thermal transport in phosphorene, it is on emerging demand to have a review on the progress of previous studies and give an outlook on future work. In this mini-review, the unique thermal transport properties of phosphorene induced by the hinge-like structure are examined. There exists a huge deviation in the reported thermal conductivity of phosphorene in literature. Besides, the mechanism underlying the deviation is discussed by reviewing the effect of different functionals and cutoff distance in calculating the thermal transport properties of phosphorene. It is found that the van der Waals (vdW) interactions play a key role in the formation of resonant bonding, which leads to long-ranged interactions. Taking into account of the vdW interactions and including the long-ranged interactions caused by the resonant bonding with large cutoff distance are important for getting the accurate and converged thermal conductivity of phosphorene. Moreover, a fundamental insight into the thermal transport is provided based on the review of resonant bonding in phosphorene. This mini-review summarizes the progress of the thermal transport in phosphorene and gives an outlook on future horizons, which would benefit the design of phosphorene based nano-electronics.
thermal transport / phosphorene / resonant bonding
[1] |
Balandin A A, Nika D L. Phononics in low-dimensional materials. Materials Today, 2012, 15(6): 266–275
CrossRef
Google scholar
|
[2] |
Zhang Y, Wang H, Luo Z, Tan H T, Li B, Sun S, Li Z, Zong Y, Xu Z J, Yang Y, Khor K A, Yan Q. An air-stable densely packed phosphorene-graphene composite toward advanced lithium storage properties. Advanced Energy Materials, 2016, 6(12): 1600453
CrossRef
Google scholar
|
[3] |
Wan F, Wu X L, Guo J Z, Li J Y, Zhang J P, Niu L, Wang R S. Nanoeffects promote the electrochemical properties of organic Na2C8H4O4 as anode material for sodium-ion batteries. Nano Energy, 2015, 13: 450–457
CrossRef
Google scholar
|
[4] |
Liu D H, Lü H Y, Wu X L, Wang J, Yan X, Zhang J P, Geng H B, Zhang Y, Yan Q Y. A new strategy for developing superior electrode materials for advanced batteries: using a positive cycling trend to compensate the negative one to achieve ultralong cycling stability. Nanoscale Horiz, 2016, 1(6): 496–501
CrossRef
Google scholar
|
[5] |
Liu H, Neal A T, Zhu Z, Luo Z, Xu X, Tománek D, Ye P D. Phosphorene: an unexplored 2D semiconductor with a high hole mobility. ACS Nano, 2014, 8(4): 4033–4041
CrossRef
Pubmed
Google scholar
|
[6] |
Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H, Feng D, Chen X H, Zhang Y. Black phosphorus field-effect transistors. Nature Nanotechnology, 2014, 9(5): 372–377
CrossRef
Pubmed
Google scholar
|
[7] |
Xia F, Wang H, Jia Y. Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nature Communications, 2014, 5: 4458
CrossRef
Pubmed
Google scholar
|
[8] |
Tran V, Soklaski R, Liang Y, Yang L. Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Physical Review B: Condensed Matter and Materials Physics, 2014, 89(23): 235319
CrossRef
Google scholar
|
[9] |
Churchill H O H, Jarillo-Herrero P. Two-dimensional crystals: phosphorus joins the family. Nature Nanotechnology, 2014, 9(5): 330–331
CrossRef
Pubmed
Google scholar
|
[10] |
Koenig S P, Doganov R A, Schmidt H, Castro Neto A H, Ozyilmaz B. Electric field effect in ultrathin black phosphorus. Applied Physics Letters, 2014, 104(10): 103106
CrossRef
Google scholar
|
[11] |
Qin G, Qin Z, Yue S Y, Yan Q B, Hu M. External electric field driving the ultra-low thermal conductivity of silicene. Nanoscale, 2017, 9(21): 7227–7234
CrossRef
Pubmed
Google scholar
|
[12] |
Rodin A S, Carvalho A, Castro Neto A H. Strain-induced gap modification in black phosphorus. Physical Review Letters, 2014, 112(17): 176801
CrossRef
Pubmed
Google scholar
|
[13] |
Qiao J, Kong X, Hu Z X, Yang F, Ji W. High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nature Communications, 2014, 5: 4475
CrossRef
Pubmed
Google scholar
|
[14] |
Zhu Z, Tománek D. Semiconducting layered blue phosphorus: a computational study. Physical Review Letters, 2014, 112(17): 176802
CrossRef
Pubmed
Google scholar
|
[15] |
Jiang J W, Park H S. Negative Poisson’s ratio in single-layer black phosphorus. Nature Communications, 2014, 5: 4727
CrossRef
Pubmed
Google scholar
|
[16] |
Wei Q, Peng X H. Superior mechanical flexibility of phosphorene and few-layer black phosphorus. Applied Physics Letters, 2014, 104(25): 251915
CrossRef
Google scholar
|
[17] |
Qin G, Yan Q B, Qin Z, Yue S Y, Cui H J, Zheng Q R, Su G. Corrigendum: hinge-like structure induced unusual properties of black phosphorus and new strategies to improve the thermoelectric performance. Scientific Reports, 2016, 6(1): 21233
CrossRef
Pubmed
Google scholar
|
[18] |
Low T, Engel M, Steiner M, Avouris P. Origin of photoresponse in black phosphorus phototransistors. Physical Review B: Condensed Matter and Materials Physics, 2014, 90(8): 081408
CrossRef
Google scholar
|
[19] |
Lv H Y, Lu W J, Shao D F, Sun Y P. Enhanced thermoelectric performance of phosphorene by strain-induced band convergence. Physical Review B: Condensed Matter and Materials Physics, 2014, 90(8): 085433
CrossRef
Google scholar
|
[20] |
Akinwande D, Petrone N, Hone J. Two-dimensional flexible nanoelectronics. Nature Communications, 2014, 5: 5678
CrossRef
Pubmed
Google scholar
|
[21] |
Fei R, Faghaninia A, Soklaski R, Yan J A, Lo C, Yang L. Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Letters, 2014, 14(11): 6393–6399
CrossRef
Pubmed
Google scholar
|
[22] |
Zhu J, Park H, Chen J, Gu X, Zhang H, Karthikeyan S, Wendel N, Campbell S A, Dawber M, Du X, Li M, Wang J, Yang R, Wang X. Revealing the origins of 3D anisotropic thermal conductivities of black phosphorus. Advanced Electronic Materials, 2016, 2(5):1600040
CrossRef
Google scholar
|
[23] |
Luo Z, Maassen J, Deng Y, Du Y, Garrelts R P, Lundstrom M S, Ye P D, Xu X. Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus. Nature Communications, 2015, 6: 8572
CrossRef
Pubmed
Google scholar
|
[24] |
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, Wu J. Anisotropic in-plane thermal conductivity of black phosphorus nanoribbons at temperatures higher than 100 K. Nature Communications, 2015, 6: 8573
CrossRef
Pubmed
Google scholar
|
[25] |
Jang H, Wood J D, Ryder C R, Hersam M C, Cahill D G. Anisotropic thermal conductivity of exfoliated black phosphorus. Advanced Materials, 2015, 27(48): 8017–8022
CrossRef
Pubmed
Google scholar
|
[26] |
Liu T H, Chang C C. Anisotropic thermal transport in phosphorene: effects of crystal orientation. Nanoscale, 2015, 7(24): 10648–10654
CrossRef
Pubmed
Google scholar
|
[27] |
Hong Y, Zhang J, Huang X, Zeng X C. Thermal conductivity of a two-dimensional phosphorene sheet: a comparative study with graphene. Nanoscale, 2015, 7(44): 18716–18724
CrossRef
Pubmed
Google scholar
|
[28] |
Xu W, Zhu L, Cai Y, Zhang G, Li B. Direction dependent thermal conductivity of monolayer phosphorene: Parameterization of Stillinger-Weber potential and molecular dynamics study. Journal of Applied Physics, 2015, 117(21): 214308
CrossRef
Google scholar
|
[29] |
Zhang Y Y, Pei Q X, Jiang J W, Wei N, Zhang Y W. Thermal conductivities of single- and multi-layer phosphorene: a molecular dynamics study. Nanoscale, 2016, 8(1): 483–491
CrossRef
Pubmed
Google scholar
|
[30] |
Zhu L, Zhang G, Li B. Coexistence of size-dependent and size-independent thermal conductivities in phosphorene. Physical Review B: Condensed Matter and Materials Physics, 2014, 90(21): 214302
CrossRef
Google scholar
|
[31] |
Jain A, McGaughey A J H. Strongly anisotropic in-plane thermal transport in single-layer black phosphorene. Scientific Reports, 2015, 5(1): 8501
CrossRef
Pubmed
Google scholar
|
[32] |
Qin G, Yan Q B, Qin Z, Yue S Y, Hu M, Su G. Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles. Physical Chemistry Chemical Physics: PCCP, 2015, 17(7): 4854–4858
CrossRef
Pubmed
Google scholar
|
[33] |
Lindsay L, Broido D A, Mingo N. Flexural phonons and thermal transport in multilayer graphene and graphite. Physical Review B: Condensed Matter and Materials Physics, 2011, 83(23): 235428
CrossRef
Google scholar
|
[34] |
Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K. The electronic properties of graphene. Reviews of Modern Physics, 2009, 81(1): 109–162
CrossRef
Google scholar
|
[35] |
Zhang X L, Xie H, Hu M, Bao H, Yue S Y, Qin G Z, Su G. Thermal conductivity of silicene calculated using an optimized Stillinger-Weber potential. Physical Review B: Condensed Matter and Materials Physics, 2014, 89(5): 054310
CrossRef
Google scholar
|
[36] |
Xie H, Hu M, Bao H. Thermal conductivity of silicene from first-principles. Applied Physics Letters, 2014, 104(13): 131906
CrossRef
Google scholar
|
[37] |
Fei R, Yang L. Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Letters, 2014, 14(5): 2884–2889
CrossRef
Pubmed
Google scholar
|
[38] |
Qin G, Zhang X L, Yue S Y, Qin Z, Wang H M, Han Y, Hu M. Resonant bonding driven giant phonon anharmonicity and low thermal conductivity of phosphorene. Physical Review B: Condensed Matter and Materials Physics, 2016, 94(16): 165445
CrossRef
Google scholar
|
[39] |
Qin G, Qin Z, Fang W Z, Zhang L C, Yue S Y, Yan Q B, Hu M, Su G. Diverse anisotropy of phonon transport in two-dimensional group IV-VI compounds: a comparative study. Nanoscale, 2016, 8(21): 11306–11319
CrossRef
Pubmed
Google scholar
|
[40] |
Zhang L C, Qin G, Fang W Z, Cui H J, Zheng Q R, Yan Q B, Su G. Tinselenidene: a two-dimensional auxetic material with ultralow lattice thermal conductivity and ultrahigh hole mobility. Scientific Reports, 2016, 6: 19830
|
[41] |
Ong Z Y, Cai Y, Zhang G, Zhang Y W. Strong thermal transport anisotropy and strain modulation in single-layer phosphorene. Journal of Physical Chemistry C, 2014, 118(43): 25272–25277
CrossRef
Google scholar
|
[42] |
Smith B, Vermeersch B, Carrete J, Ou E, Kim J, Mingo N, Akinwande D, Shi L. Temperature and thickness dependences of the anisotropic in-plane thermal conductivity of black phosphorus. Advanced Materials, 2017, 29(5): 1603756
CrossRef
Pubmed
Google scholar
|
[43] |
Thomas J A, Turney J E, Iutzi R M, Amon C H, McGaughey A J H. Predicting phonon dispersion relations and lifetimes from the spectral energy density. Physical Review B: Condensed Matter and Materials Physics, 2010, 81(8): 081411
CrossRef
Google scholar
|
[44] |
Larkin J, Turney J, Massicotte A, Amon C, Mc-Gaughey A. Comparison and evaluation of spectral energy methods for predicting phonon properties. Journal of Computational and Theoretical Nanoscience, 2014, 11(1): 249–256
CrossRef
Google scholar
|
[45] |
Zhang X, Bao H, Hu M. Bilateral substrate effect on the thermal conductivity of two-dimensional silicon. Nanoscale, 2015, 7(14): 6014–6022
CrossRef
Pubmed
Google scholar
|
[46] |
Sun B, Gu X, Zeng Q, Huang X, Yan Y, Liu Z, Yang R, Koh Y K. Temperature dependence of anisotropic thermal-conductivity tensor of bulk black phosphorus. Advanced Materials, 2017, 29(3): 1603297
CrossRef
Pubmed
Google scholar
|
[47] |
Li W, Carrete J, Mingo N. Thermal conductivity and phonon linewidths of monolayer MoS2 from first principles. Applied Physics Letters, 2013, 103(25): 253103
CrossRef
Google scholar
|
[48] |
Li W, Mingo N, Lindsay L, Broido D A, Stewart D A, Katcho N A. Thermal conductivity of diamond nanowires from first principles. Physical Review B: Condensed Matter and Materials Physics, 2012, 85(19): 195436
CrossRef
Google scholar
|
[49] |
Broido D A, Malorny M, Birner G, Mingo N, Stewart D A. Intrinsic lattice thermal conductivity of semiconductors from first principles. Applied Physics Letters, 2007, 91(23): 231922
CrossRef
Google scholar
|
[50] |
Li W, Lindsay L, Broido D A, Stewart D A, Mingo N. Thermal conductivity of bulk and nanowire Mg2SixSn1-x alloys from first principles. Physical Review B: Condensed Matter and Materials Physics, 2012, 86(17): 174307
CrossRef
Google scholar
|
[51] |
Li W, Carrete J, Katcho N A, Mingo N. ShengBTE: a solver of the Boltzmann transport equation for phonons. Computer Physics Communications, 2014, 185(6): 1747–1758
CrossRef
Google scholar
|
[52] |
Carrete J, Li W, Mingo N, Wang S, Curtarolo S. Finding unprecedentedly low-thermal-conductivity half-heusler semiconductors via high-throughput materials modeling. Physical Review X, 2014, 4(1): 011019
CrossRef
Google scholar
|
[53] |
Jain A, McGaughey A J. Effect of exchange-correlation on first-principles-driven lattice thermal conductivity predictions of crystalline silicon. Computational Materials Science, 2015, 110: 115–120
CrossRef
Google scholar
|
[54] |
Lee S, Esfarjani K, Luo T, Zhou J, Tian Z, Chen G. Resonant bonding leads to low lattice thermal conductivity. Nature Communications, 2014, 5(4): 3525
Pubmed
|
[55] |
Hu Z X, Kong X, Qiao J, Normand B, Ji W. Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus. Nanoscale, 2016, 8(5): 2740–2750
CrossRef
Pubmed
Google scholar
|
[56] |
Kong B D, Paul S, Nardelli M B, Kim K W. First-principles analysis of lattice thermal conductivity in monolayer and bilayer graphene. Physical Review B: Condensed Matter, 2009, 80(3): 033406
CrossRef
Google scholar
|
[57] |
Cocemasov A I, Nika D L, Balandin A A. Phonons in twisted bilayer graphene. Physical Review B: Condensed Matter and Materials Physics, 2013, 88(3): 035428
CrossRef
Google scholar
|
[58] |
Li H, Ying H, Chen X, Nika D L, Cocemasov A I, Cai W, Balandin A A, Chen S. Thermal conductivity of twisted bilayer graphene. Nanoscale, 2014, 6(22): 13402–13408
CrossRef
Pubmed
Google scholar
|
[59] |
Zhang X, Gao Y, Chen Y, Hu M. Robustly engineering thermal conductivity of bilayer graphene by interlayer bonding. Scientific Reports, 2016, 6(1): 22011
CrossRef
Pubmed
Google scholar
|
[60] |
Qin G, Qin Z, Wang H, Hu M. Anomalously temperature-dependent thermal conductivity of monolayer GaN with large deviations from the traditional 1/T law. Physical Review B: Condensed Matter and Materials Physics, 2017, 95(19): 195416
CrossRef
Google scholar
|
[61] |
Balandin A A. Thermal properties of graphene and nanostructured carbon materials. Nature Materials, 2011, 10(8): 569–581
CrossRef
Pubmed
Google scholar
|
[62] |
Gu X, Yang R. First-principles prediction of phononic thermal conductivity of silicene: a comparison with graphene. Journal of Applied Physics, 2015, 117(2): 025102
CrossRef
Google scholar
|
[63] |
Xie H, Ouyang T, Germaneau É, Qin G, Hu M, Bao H. Large tunability of lattice thermal conductivity of monolayer silicene via mechanical strain. Physical Review B: Condensed Matter and Materials Physics, 2016, 93(7): 075404
CrossRef
Google scholar
|
[64] |
Bonini N, Garg J, Marzari N. Acoustic phonon lifetimes and thermal transport in free-standing and strained graphene. Nano Letters, 2012, 12(6): 2673–2678
CrossRef
Pubmed
Google scholar
|
[65] |
Kuang Y, Lindsay L, Shi S, Wang X, Huang B. Thermal conductivity of graphene mediated by strain and size. International Journal of Heat and Mass Transfer, 2016, 101(1): 772–778
CrossRef
Google scholar
|
[66] |
Kuang Y D, Lindsay L, Shi S Q, Zheng G P. Tensile strains give rise to strong size effects for thermal conductivities of silicene, germanene and stanene. Nanoscale, 2016, 8(6): 3760–3767
CrossRef
Pubmed
Google scholar
|
[67] |
Lucovsky G, White R M. Effects of resonance bonding on the properties of crystalline and amorphous semiconductors. Physical Review B: Condensed Matter and Materials Physics, 1973, 8(2): 660–667
CrossRef
Google scholar
|
[68] |
Shportko K, Kremers S, Woda M, Lencer D, Robertson J, Wuttig M. Resonant bonding in crystalline phase-change materials. Nature Materials, 2008, 7(8): 653–658
CrossRef
Pubmed
Google scholar
|
[69] |
Lencer D, Salinga M, Grabowski B, Hickel T, Neugebauer J, Wuttig M. A map for phase-change materials. Nature Materials, 2008, 7(12): 972–977
CrossRef
Pubmed
Google scholar
|
[70] |
Matsunaga T, Yamada N, Kojima R, Shamoto S, Sato M, Tanida H, Uruga T, Kohara S, Takata M, Zalden P, Bruns G, Sergueev I, Wille H C, Hermann R P, Wuttig M. Phase-change materials: vibrational softening upon crystallization and its impact on thermal properties. Advanced Functional Materials, 2011, 21(12): 2232–2239
CrossRef
Google scholar
|
/
〈 | 〉 |