Skip to main content Accessibility help
×
Home
  • Print publication year: 2017
  • Online publication date: June 2017

21 - Theoretical Overview of Black Phosphorus

from Part III
21.7
[1]Castellanos-Gomez, A., Black phosphorus: narrow gap, wide applications. J. Phys. Chem. Lett., 6 (2015), 42804291.
[2]Keyes, R., The electrical properties of black phosphorus. Phys. Rev., 92 (1953), 580584.
[3]Liu H, H., Du, Y., Deng, Y., and Peide, D. Y.. Semiconducting black phosphorus: synthesis, transport properties and electronic applications. Chem. Soc. Rev., 44 (2015), 27322743.
[4]Xia, F., Wang, H., and Jia, Y., Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nat. Commun., 5 (2014), 4458.
[5]Koenig, S. P., Doganov, R. A., Schmidt, H., Neto, A. H. Castro, and Özyilmaz, B., Electric field effect in ultrathin black phosphorus. Appl. Phys. Lett., 104 (2014), 103106.
[6]Li, L., Yu, Y., Ye, G. J., Ge, Q., Ou, X., Wu, H., Feng, D., Chen, X. H., and Zhang, Y., Black phosphorus field-effect transistors. Nat. Nanotechnol., 9 (2014), 372377
[7]Castellanos-Gomez, A., Vicarelli, L., Prada, E., Island, J. O., Narasimha-Acharya, K. L., Blanter, S. I., Groenendijk, D. J., Buscema, M., Steele, G. A., Alvarez, J. V., Zandbergen, H. W., Palacios, J. J., and van der Zant, H. S. J., Isolation and characterization of few-layer black phosphorus. 2D Materials, 1(2) (2014), 025001.
[8]Liu, H., Neal, A. T., Zhu, Z., Luo, Z., Xu, X., Tomanek, D., and Ye, P. D., Phosphorene: an unexplored 2D semiconductor with a high hole mobility. ACS Nano, 8 (2014), 40334041.
[9]Rudenko, A. N. and Katsnelson, M. I.. Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus. Phys. Rev. B, 89 (2014), 201408.
[10]Qiao, J., Kong, X., Hu, Z.-X., Yang, F., and Ji, W., High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat. Commun., 5 (2014), 4475.
[11]Low, T., Rodin, A. S., Carvalho, A., Jiang, Y., Wang, H., Xia, F., and Neto, A. H. Castro, Tunable optical properties of multilayer black phosphorus thin films. Phys. Rev. B, 90 (2014), 075434.
[12]Buscema, M., Groenendijk, D. J., Blanter, S. I., Steele, G. A., van der Zant, H. S., and Castellanos-Gomez, A.. Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors. Nano Lett., 14 (2014), 33473352.
[13]Low, T., Engel, M., Steiner, M., and Avouris, P.. Origin of photoresponse in black phosphorus phototransistors. Phys. Rev. B., 90 (2014), 081408.
[14]Engel, M., Steiner, M., and Avouris, P., Black phosphorus photodetector for multispectral: high-resolution imaging. Nano Lett., 14 (2014), 6414.
[15]Yuan, H., Liu, X., Afshinmanesh, F., Li, W., Xu, G., Sun, J., Lian, B., Curto, A. G., Ye, G., Hikita, Y., and Shen, Z.. Polarization-sensitive broadband photodetector using a black phosphorus vertical p–n junction. Nat. Nanotechnol., 10 (2015), 707713.
[16]Hahn, T. and Paufler, P., International Tables for Crystallography, Vol. A. Space-Group Symmetry. Dordrecht: D. Reidel Publishing Co. (1984).
[17]Sengupta, A., Audiffred, M., Heine, T., and Niehaus, T. A., Stacking dependence of carrier transport properties in multilayered black phosphorous. J. Phys.: Condens. Mat., 28 (2016), 075001.
[18]Fei, R. and Yang, L., Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett., 14 (2014), 28842889.
[19]Rodin, A. S., Carvalho, A., and Neto, A. H. Castro, Strain-induced gap modification in black phosphorus. Phys. Rev. Lett., 112 (2014), 176801.
[20]Tran, V., Soklaski, R., Liang, Y., and Yang, L., Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B, 89 (2014), 235319.
[21]Çak1r, D., Sevik, C., and Peeters, F. M., Significant effect of stacking on the electronic and optical properties of few-layer black phosphorus. Phys. Rev. B, 92 (2015), 165406.
[22]Rudenko, A. N., Yuan, S., and Katsnelson, M. I., Toward a realistic description of multilayer black phosphorus: From GW approximation to large-scale tight-binding simulations. Phys. Rev. B, 92 (2015), 085419.
[23]Li, P. and Appelbaum, I., Electrons and holes in phosphorene. Phys. Rev. B, 90 (2014), 115439.
[24]Pereira, J. M. Jr. and Katsnelson, M. I., Landau levels of single layer and bilayer phosphorene. Phys. Rev. B, 92 (2015), 075437.
[25]Cai, Y., Zhang, G., and Zhang, Y.-W., Layer-dependent band alignment and work function of few-layer phosphorene. Sci. Rep., 4 (2014), 6677.
[26]Hu, Z.-X., Kong, X., Qiao, J., Normanda, B., and Ji, Wei, Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus. Nanoscale, 8 (2016), 27402750.
[27]Dai, J. and Zeng, X. C., Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells. J. Phys. Chem. Lett., 5 (2014), 12891293.
[28]Kittel, C.. Introduction to Solid State Physics. Wiley (2005).
[29]Giuliani, G. and Vignale, G., Quantum Theory of the Electron Liquid. Cambridge: Cambridge University Press (2005).
[30]Low, T., Roldán, R., Wang, H., Xia, F., Avouris, P., Moreno, L. M., and Guinea, F., Plasmons and screening in monolayer and multilayer black phosphorus. Phys. Rev. Lett., 113 (2014), 106802.
[31]Low, T. and Avouris, P., Graphene plasmonics for terahertz to mid-infrared applications. ACS Nano, 8 (2014), 10861101.
[32]Grigorenko, A. N., Polini, M., and Novoselov, K. S., Graphene plasmonics. Nature Photonics, 6 (2012), 749758.
[33]Bludov, Y. V., Ferreira, A., Peres, N. M., and Vasilevskiy, M. I.. A primer on surface plasmon-polaritons in graphene. Int. J. Mod. Phys. B, 27 (2013), 1341001.
[34]Koppens, F. H., Chang, D. E., and de Abajo, F. J. Garcia. Graphene plasmonics: a platform for strong light–matter interactions. Nano Lett., 11 (2011), 33703377.
[35]Mikhailov, S. A. and Ziegler, K.. New electromagnetic mode in graphene. Phys. Rev. Lett., 99 (2007), 016803.
[36]Mishchenko, A., Cao, Y., Yu, G. L., Woods, C. R., Gorbachev, R. V., Novoselov, K. S., Geim, A. K., and Levitov, L. S.. Nonlocal response and anamorphosis: the case of few-layer black phosphorus. Nano Lett., 15 (2015), 69916995.
[37]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, 90 (2014), 085433.
[38]Manjanath, A., Samanta, A., Pandey, T., and Singh, A. K., Semiconductor to metal transition in bilayer phosphorene under normal compressive strain. Nanotechnology, 26 (2015), 075701.
[39]Xiao, J., Long, M., Zhang, X., Ouyang, J., Xu, H., and Gao, Y., Theoretical predictions on the electronic structure and charge carrier mobility in 2D phosphorus sheets. Sci. Rep., 5 (2015), 09961.
[40]Berkelbach, T. C., Hybertsen, M. S., and Reichman, D. R.. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B, 88 (2013), 045318.
[41]Chernikov, A., Berkelbach, T. C., Hill, H. M., Rigosi, A., Li, Y., Aslan, O. B., Reichman, D. R., Hybertsen, M. S., and Heinz, T. F.. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett., 113 (2014), 076802.
[42]Tran, V., Fei, R., and Yang, L.. Quasiparticle energies, excitons, and optical spectra of few-layer black phosphorus. 2D Mater., 2 (2015), 044014.
[43]Yang, J., Xu, R., Pei, J., Myint, Y. W., Wang, F., Wang, Z., Zhang, S., Yu, Z., and Lu, Y.. Optical tuning of exciton and trion emissions in monolayer phosphorene. Light: Science and Applications, 4 (2015), e312.
[44]Keldysh, L. V., Coulomb interaction in thin semiconductor and semimetal films. JETP Lett., 29 (1978), 658.
[45]Cudazzo, P., Tokatly, I. V., and Rubio, A., Phys. Rev. B, 84 (2011), 085406.
[46]Rodin, A. S., Carvalho, A., and Neto, A. H. Castro. Excitons in anisotropic two-dimensional semiconducting crystals. Phys. Rev. B, 90 (2014), 075429.
[47]Chaves, A., Low, T., Avouris, P., Çakir, D., and Peeters, F. M., Anisotropic exciton Stark shift in black phosphorus. Phys. Rev. B, 91 (2015), 155311.
[48]Giannozzi, P., de Gironcoli, S., Pavone, P., and Baroni, S., Ab initio calculation of phonon dispersions in semiconductors. Phys. Rev. B, 43 (1991), 72317242.
[49]Zhu, L., Zhang, G., and Li, B., Coexistence of size-dependent and size-independent thermal conductivities in phosphorene. Phys. Rev. B, 90 (2014), 214302.
[50]Hu, Z.-X., Kong, X., Qiao, J., Normand, B., and Ji, W., Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus. arXiv:1503.06735 [cond-mat.mtrl-sci] (2015).
[51]Qin, G., Yan, Q.-B., Qin, Z., Yue, S.-Y., Hu, M., and Su, G., Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles. Phys. Chem. Chem. Phys, 17 (2015), 48544858.
[52]Jain, A. and McGaughey, A. J. H., Strongly anisotropic in-plane thermal transport in single-layer black phosphorene. Sci. Rep., 5 (2015), 8501.
[53]Fei, R. and Yang, L., Lattice vibrational modes and Raman scattering spectra of strained phosphorene. Appl. Phys. Lett., 105 (2014), 083120.
[54]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 (2014), 2527225277.
[55]Luo, Z., Maassen, J., Deng, Y., Du, Y., Garrelts, R. P., Lundstrom, M. S., Ye, P. D., and Xu, X., Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus. Nat. Commun., 6 (2015), 8572.
[56]Jeong, C., Datta, S., and Lundstrom, M., Full dispersion versus Debye model evaluation of lattice thermal conductivity with a Landauer approach. J. Appl. Phys., 109 (2011), 073718.
[57]Paul, A., Salamat, S., Jeong, C., Klimeck, G., and Lundstrom, M., An efficient algorithm to calculate intrinsic thermoelectric parameters based on Landauer approach. J. Comput. Electron., 11 (2012), 5666.
[58]Conrad, K., Maassen, J., and Lundstrom, M., LanTraP (2014), https://nanohub.org/resources/lantrap.
[59]Jeong, C., Datta, S., and Lundstrom, M., Thermal conductivity of bulk and thin-film silicon: A Landauer approach. J. Appl. Phys., 111 (2012), 093708.
[60]Lee, S., Yang, F., Suh, J., Yang, S., Lee, Y., Li, G., Choe, H. S., 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 (2015), 8573.
[61]Jang, H., Wood, J. D., Ryder, C. R., Hersam, M. C., and Cahill, D. G., Anisotropic thermal conductivity of exfoliated black phosphorus. arXiv:1510.00051 [cond-mat.mtrl-sci](2015).
[62]He, J., Kanatzidis, M. G., and Dravid, V. P., High performance bulk thermoelectrics via a panoscopic approach. Materials Today, 16 (2013), 166176.
[63]Biwas, K., He, J., Blum, I. D., Wu, C.-I., Hogan, T. P., Seidman, D. N., Dravid, V. P., and Kanatzidis, M. G.. High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature 489 (2012), 414418.
[64]Jeong, C., Kim, R., Luisier, M., Datta, S., and Lundstrom, M., On Landauer versus Boltzmann and full band versus effective mass evaluation of thermoelectric transport coefficients. J. Appl. Phys., 107 (2010), 023707.
[65]Maassen, J. and Lundstrom, M., A computational study of the thermoelectric performance of ultrathin Bi2Te3 films. Appl. Phys. Lett., 102 (2013), 093103.
[66]Verma, D. and Dumitrică, T., Directional-dependent thickness and bending rigidity of phosphorene. Phys. Rev. B, 94 (2016), 121404.
[67]Zhang, J., Liu, H. J., Cheng, L., Wei, J., Liang, J. H., Fan, D. D., Jiang, P. H., Sun, L., and Shi, J., High thermoelectric performance can be achieved in black phosphorus. arXiv:1508.06834 [cond-mat.mtrl-sci] (2015).
[68]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 (2014), 6452.
[69]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 (2014), 63936399.
[70]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 (2014), 6946.
[71]Flores, E., Ares, J. R., Castellanos-Gomez, A., Barawi, M., Ferrer, I. J., and Sanchez, C., Thermoelectric power of bulk black-phosphorus. Appl. Phys. Lett., 106 (2015), 022102.
[72]Hippalgaonkar, K., Wang, Y., Ye, Y., Zhu, H., Wang, Y., Moore, J., and Zhang, X., Record high thermoelectric powerfactor in single and few-layer MoS2. arXiv:1505.06779 [cond-mat.mtrl-sci] (2014).
[73]Jo, I., Pettes, M. T., Ou, E., Wu, W., and Shi, L., Basal-plane thermal conductivity of few-layer molybdenum disulfide. Appl. Phys. Lett., 104 (2014), 201902.
[74]Jones, R. M., Mechanics of Composite Materials. 2nd edn. Boca Raton, FL : CRC Press (1998).
[75]Zhang, D.-B. and Dumitricã, T., Elasticity of ideal single-walled carbon nanotubes via symmetry adapted tight-binding objective modeling. Appl. Phys. Lett., 93 (2008), 031919.
[76]Zhang, D.-B., Akatyeva, E., and Dumitricã, T., Bending ultrathin graphene at the margins of continuum mechanics. Phys. Rev. Lett., 106 (2011), 255503.
[77]Wei, Q. and Peng, X., Superior mechanical flexibility of phosphorene and few-layer black phosphorus. Appl. Phys. Lett., 104 (2014), 251915.
[78]Lee, C., Wei, X. D., Kysar, J. W., and Hone, J., Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science, 321 (2008), 385388.
[79]Castellanos-Gomez, A., Poot, M., Steele, G. A., van der Zant, H. S. J., Agrat, N., and Bollinger, G. R., Elastic properties of freely suspended MoS2 nanosheets. Adv. Mat., 24 (2012), 772775.
[80]Jiang, J.-W. and Park, H. S., Negative Poisson’s ratio in single-layer black phosphorus. Nature Comm., 5 (2014), 47274731.
[81]Yang, Y., Yu, H., York, D., Elstner, M., and Cui, Q., Description of phosphate hydrolysis reactions with the self-consistent-charge density-functional-tight-binding (SCC-DFTB) theory: 1. Parameterization. J. Chem. Theory Comput., 4 (2008), 20672084.
[82]Kou, L., Ma, Y., Smith, S. C., and Chen, C., Anisotropic ripple deformation in phosphorene. J. Phys. Chem. Lett. 6 (2015), 15091513.
[83]Sha, Z.-D., Pei, Q.-X., Ding, Z., Jiang, J.-W., and Zhang, Y. W., Mechanical properties and fracture behavior of single-layer phosphorene at finite temperatures. J. Phys. D. 48 (2015), 395303.
[84]Hopcroft, M. A., Nix, W. D., and Kenny, T. W., What is the Young’s modulus of silicon? J. Microelectromech. Syst. 19 (2010), 229238.
[85]Wang, Z. and Feng, P. X.-L., Design of black phosphorus 2D nanomechanical resonators by exploiting the intrinsic mechanical anisotropy. 2D Mater. 2 (2015), 021001.