[en] Two-dimensional materials have great potential for applications as high-performance electronic devices and efficient thermal rectificators. Among them, pristine phosphorene, a single layer of black phosphorus, has shown promising properties such as ultrahigh charge mobility, a tunable band gap, and mechanical flexibility. However, the introduction of extended structural defects such as grain boundaries (GBs) has, in general, a detrimental influence on the electronic and thermal transport properties by causing additional scattering events. In this computational study, based on a combination of a density-functional parametrized tight-binding approach with the Landauer theory of quantum transport, we show that applying a strain can help to partially counteract this effect. We exemplify this by addressing the electronic and phononic transmission of two specific grain boundaries containing 5|7 (GB1) and 4|8 (GB2) defects, respectively. Under uniaxial strain, the electronic band gaps can be reduced for both types of GB, while the respective thermal conductance is only weakly affected despite rather strong changes in the frequency-resolved phonon transmission. The combination of both effects mainly produces an increase of about a factor of 2 in the thermoelectric figure of merit ZT for a GB2 system. Hence, our results provide insights into the manipulation of transport properties as well as the generation of potential thermoelectric materials based on phosphorene.
Materials science & engineering
Author, co-author :
Rodríguez Méndez, Alvaro; Technical University of Dresden - TU Dresden > Institute for Materials Science and Max Bergmann Center of Biomaterials
Medrano Sandonas, Leonardo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Dianat, Arezoo; Technical University of Dresden - TU Dresden > Institute for Materials Science and Max Bergmann Center of Biomaterials
Gutierrez, Rafael; Technical University of Dresden - TU Dresden > Institute for Materials Science and Max Bergmann Center of Biomaterials
Cuniberti, Gianaurelio; Technical University of Dresden - TU Dresden > Institute for Materials Science and Max Bergmann Center of Biomaterials
External co-authors :
Electronic and thermal signatures of phosphorene grain boundaries under uniaxial strain
Publication date :
17 November 2022
Journal title :
Physical Review Materials
American Physical Society (APS), New York, United States - New York
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306, 666 (2004) 0036-8075 10.1126/science.1102896.
N. Briggs, S. Subramanian, Z. Lin, X. Li, X. Zhang, K. Zhang, K. Xiao, D. Geohegan, R. Wallace, L.-Q. Chen, M. Terrones, A. Ebrahimi, S. Das, J. Redwing, C. Hinkle, K. Momeni, A. van Duin, V. Crespi, S. Kar, and J. A. Robinson, A roadmap for electronic grade 2D materials, 2D Mater. 6, 022001 (2019) 2053-1583 10.1088/2053-1583/aaf836.
Z. Xiong, L. Zhong, H. Wang, and X. Li, Structural defects, mechanical behaviors and properties of two-dimensional materials, Materials 14, 1192 (2021) 10.3390/ma14051192.
P. Ares and K. S. Novoselov, Recent advances in graphene and other 2d materials, NMS 4, 3 (2022), special issue on Graphene and 2D Alternative Materials 10.1016/j.nanoms.2021.05.002.
M. Xu, T. Liang, M. Shi, and H. Chen, Graphene-like two-dimensional materials, Chem. Rev. 113, 3766 (2013) 0009-2665 10.1021/cr300263a.
R. Mas-Ballesté, C. Gómez-Navarro, J. Gómez-Herrero, and F. Zamora, 2d Materials: To graphene and beyond, Nanoscale 3, 20 (2011) 2040-3364 10.1039/C0NR00323A.
M. Galluzzi, Y. Zhang, and X.-F. Yu, Mechanical properties and applications of 2D black phosphorus, J. Appl. Phys. 128, 230903 (2020) 0021-8979 10.1063/5.0034893.
B. Li, C. Lai, G. Zeng, D. Huang, L. Qin, M. Zhang, M. Cheng, X. Liu, H. Yi, C. Zhou, F. Huang, S. Liu, and Y. Fu, Black phosphorus, a rising star 2D nanomaterial in the post-graphene era: Synthesis, properties, modifications, and photocatalysis applications, Small 15, 1804565 (2019) 1613-6810 10.1002/smll.201804565.
J. R. Brent, N. Savjani, E. A. Lewis, S. J. Haigh, D. J. Lewis, and P. O'Brien, Production of few-layer phosphorene by liquid exfoliation of black phosphorus, Chem. Commun. 50, 13338 (2014) 1359-7345 10.1039/C4CC05752J.
M. Akhtar, G. Anderson, R. Zhao, A. Alruqi, J. E. Mroczkowska, G. Sumanasekera, and J. B. Jasinski, Recent advances in synthesis, properties, and applications of phosphorene, npj 2D Mater. Appl. 1, 5 (2017) 2397-7132 10.1038/s41699-017-0007-5.
L. Liang, J. Wang, W. Lin, B. G. Sumpter, V. Meunier, and M. Pan, Electronic bandgap and edge reconstruction in phosphorene materials, Nano Lett. 14, 6400 (2014) 1530-6984 10.1021/nl502892t.
C. Guo, T. Wang, C. Xia, and Y. Liu, Modulation of electronic transport properties in armchair phosphorene nanoribbons by doping and edge passivation, Sci. Rep. 7, 12799 (2017) 2045-2322 10.1038/s41598-017-13212-7.
Y. Cai, G. Zhang, and Y. W. Zhang, Layer-dependent band alignment and work function of few-layer phosphorene, Sci. Rep. 4, 6677 (2015) 2045-2322 10.1038/srep06677.
J. M. G. Hernandez, J. G. Sanchez, H. N. F. Escamilla, G. H. Cocoletzi, and N. Takeuchi, First-principles studies of the strain-induced band-gap tuning in black phosphorene, J. Phys.: Condens. Matter 33, 175502 (2021) 0953-8984 10.1088/1361-648X/abdd62.
V. Sorkin and Y. W. Zhang, Mechanical properties and failure behavior of phosphorene with grain boundaries, Nanotechnology 28, 075704 (2017) 0957-4484 10.1088/1361-6528/aa537b.
G. S. Rohrer, Grain boundary energy anisotropy: A review, J. Mater. Sci. 46, 5881 (2011) 0022-2461 10.1007/s10853-011-5677-3.
L. Zhang, C. Lu, and K. Tieu, A review on atomistic simulation of grain boundary behaviors in face-centered cubic metals, Comput. Mater. Sci. 118, 180 (2016) 0927-0256 10.1016/j.commatsci.2016.03.021.
H. Vahidi, K. Syed, H. Guo, X. Wang, J. L. Wardini, J. Martinez, and W. J. Bowman, A review of grain boundary and heterointerface characterization in polycrystalline oxides by (scanning) transmission electron microscopy, Crystals 11, 878 (2021) 2073-4352 10.3390/cryst11080878.
F. Gargiulo, Electronic transport across realistic grain boundaries in graphene, arXiv:2107.06784.
M. Khalkhali, A. Rajabpour, and F. Khoeini, Thermal transport across grain boundaries in polycrystalline silicene: A multiscale modeling, Sci. Rep. 9, 5684 (2019) 2045-2322 10.1038/s41598-019-42187-w.
J. Sun, J. Leng, and G. Zhang, The grain boundary effect on mechanical and electronic transport properties of a striped borophene, Phys. Chem. Chem. Phys. 22, 21844 (2020) 1463-9076 10.1039/D0CP04387G.
Y. Guo, S. Zhou, J. Zhang, Y. Bai, and J. Zhao, Atomic structures and electronic properties of phosphorene grain boundaries, 2D Mater. 3, 025008 (2016) 2053-1583 10.1088/2053-1583/3/2/025008.
Z.-L. Zhu, W.-Y. Yu, X.-Y. Ren, Q. Sun, and Y. Jia, Grain boundary in phosphorene and its unique roles on C and O doping, Europhys. Lett. 109, 47003 (2015) 0295-5075 10.1209/0295-5075/109/47003.
Y. Liu, F. Xu, Z. Zhang, E. S. Penev, and B. I. Yakobson, Two-dimensional mono-elemental semiconductor with electronically inactive defects: The case of phosphorus, Nano Lett. 14, 6782 (2014) 1530-6984 10.1021/nl5021393.
Y. Guo, C. Qiao, A. Wang, J. Zhang, S. Wang, W.-S. Su, and Y. Jia, The fracture behaviors of monolayer phosphorene with grain boundaries under tension: A molecular dynamics study, Phys. Chem. Chem. Phys. 18, 20562 (2016) 1463-9076 10.1039/C6CP03655D.
X. Wang, Q. Wang, X. Liu, Z. Huang, and X. Liu, Phosphorene grain boundary effect on phonon transport and phononic applications, Nanotechnology 33, 265704 (2022) 0957-4484 10.1088/1361-6528/ac60db.
X. Liu, J. Gao, G. Zhang, J. Zhao, and Y. W. Zhang, Remarkable role of grain boundaries in the thermal transport properties of phosphorene, ACS Omega 5, 17416 (2020) 2470-1343 10.1021/acsomega.0c01806.
Z. Dai, L. Liu, and Z. Zhang, Strain engineering of 2d materials: Issues and opportunities at the interface, Adv. Mater. 31, 1805417 (2019) 0935-9648 10.1002/adma.201805417.
Z. Peng, X. Chen, Y. Fan, D. J. Srolovitz, and D. Lei, Strain engineering of 2D semiconductors and graphene: from strain fields to band-structure tuning and photonic applications, Light Sci. Appl. 9, 190 (2020) 2047-7538 10.1038/s41377-020-00421-5.
S. Yang, Y. Chen, and C. Jiang, Strain engineering of two-dimensional materials: Methods, properties, and applications, InfoMat 3, 397 (2021) 2567-3165 10.1002/inf2.12177.
M. Raeisi, S. Ahmadi, and A. Rajabpour, Modulated thermal conductivity of 2D hexagonal boron arsenide: A strain engineering study, Nanoscale 11, 21799 (2019) 2040-3364 10.1039/C9NR06283A.
K. Nakagawa, K. Satoh, S. Murakami, K. Takei, S. Akita, and T. Arie, Controlling the thermal conductivity of multilayer graphene by strain, Sci. Rep. 11, 19533 (2021) 2045-2322 10.1038/s41598-021-98974-x.
L. M. Sandonas, R. Gutierrez, A. Pecchia, G. Seifert, and G. Cuniberti, Tuning quantum electron and phonon transport in two-dimensional materials by strain engineering: A green's function based study, Phys. Chem. Chem. Phys. 19, 1487 (2017) 1463-9076 10.1039/C6CP06621F.
S. B. Kumar and J. Guo, Strain-induced conductance modulation in graphene grain boundary, Nano Lett. 12, 1362 (2012) 1530-6984 10.1021/nl203968j.
Y. Liu, X. Zou, and B. I. Yakobson, Dislocations and grain boundaries in two-dimensional boron nitride, ACS Nano 6, 7053 (2012) 1936-0851 10.1021/nn302099q.
W. Zhou, X. Zou, S. Najmaei, Z. Liu, Y. Shi, J. Kong, J. Lou, P. M. Ajayan, B. I. Yakobson, and J. C. Idrobo, Intrinsic structural defects in monolayer molybdenum disulfide, Nano Lett. 13, 2615 (2013) 1530-6984 10.1021/nl4007479.
B. Aradi, B. Hourahine, and T. Frauenheim, Dftb+, a sparse matrix-based implementation of the DFTB method, J. Phys. Chem. A 111, 5678 (2007) 1089-5639 10.1021/jp070186p.
Álvaro Rodríguez Méndez, L. M. Sandonas, A. Dianat, R. Gutierrez, and G. Cuniberti, An atomistic study of the thermoelectric signatures of cnt peapods, J. Phys. Chem. C 125, 13721 (2021) 1932-7447 10.1021/acs.jpcc.1c02611.
C. He, G. Liu, W. X. Zhang, Z. Q. Shi, and S. L. Zhou, Tuning the structures and electron transport properties of ultrathin cu nanowires by size and bending stress using DFT and DFTB methods, RSC Adv. 5, 22463 (2015) 2046-2069 10.1039/C4RA15051A.
A. Pecchia, L. Latessa, A. Di Carlo, P. Lugli, and T. Neihaus, Electronic transport properties of molecular devices, Phys. E 19, 139 (2003), fourth International Symposium on Nanostructures and Mesoscopic Systems 1386-9477 10.1016/S1386-9477(03)00300-X.
M. Gaus, Q. Cui, and M. Elstner, DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (scc-dftb), J. Chem. Theory Comput. 7, 931 (2011) 1549-9618 10.1021/ct100684s.
H. Sevinçli, S. Roche, G. Cuniberti, M. Brandbyge, R. Gutierrez, and L. M. Sandonas, Green function, quasi-classical Langevin and Kubo-Greenwood methods in quantum thermal transport, J. Phys.: Condens. Matter 31, 273003 (2019) 0953-8984 10.1088/1361-648X/ab119a.
W. Zhang, T. S. Fisher, and N. Mingo, The atomistic Green's function method: An efficient simulation approach for nanoscale phonon transport, Numer. Heat Transf., Pt. B 51, 333 (2007) 1040-7790 10.1080/10407790601144755.
A. Pecchia, G. Penazzi, L. Salvucci, and A. D. Carlo, Non-equilibrium Green's functions in density functional tight binding: Method and applications, New J. Phys. 10, 065022 (2008) 1367-2630 10.1088/1367-2630/10/6/065022.
L. Medrano Sandonas, R. Gutierrez, A. Pecchia, A. Croy, and G. Cuniberti, Quantum phonon transport in nanomaterials: Combining atomistic with non-equilibrium Green's function techniques, Entropy 21, 735 (2019) 1099-4300 10.3390/e21080735.
O. V. Yazyev and S. G. Louie, Topological defects in graphene: Dislocations and grain boundaries, Phys. Rev. B 81, 195420 (2010) 1098-0121 10.1103/PhysRevB.81.195420.
T. Nakanishi, S. Yoshida, K. Murase, O. Takeuchi, T. Taniguchi, K. Watanabe, H. Shigekawa, Y. Kobayashi, Y. Miyata, H. Shinohara, and R. Kitaura, The atomic and electronic structure of (Equation presented) and (Equation presented) grain boundaries in MOS2, Front. Phys. 7, 59 (2019) 2296-424X 10.3389/fphy.2019.00059.
Y. Lu and J. Guo, Band gap of strained graphene nanoribbons, Nano Res. 3, 189 (2010) 1998-0124 10.1007/s12274-010-1022-4.
N.-C. Ri, J.-C. Kim, and S.-I. Ri, Effect of strain on mechanical, electronic, and transport properties of hybrid armchair graphane/graphene/fluorographane nanoribbon, Chem. Phys. Lett. 765, 138311 (2021) 0009-2614 10.1016/j.cplett.2020.138311.
Y. Zhang, X. Wu, Q. Li, and J. Yang, Linear band-gap modulation of graphane nanoribbons under uniaxial elastic strain: A density functional theory study, J. Phys. Chem. C 116, 9356 (2012) 1932-7447 10.1021/jp301691z.
Q. G. Zhang, X. Zhang, B. Y. Cao, M. Fujii, K. Takahashi, and T. Ikuta, Influence of grain boundary scattering on the electrical properties of platinum nanofilms, Appl. Phys. Lett. 89, 114102 (2006) 0003-6951 10.1063/1.2338885.
M. Schrade, K. Berland, S. N. Eliassen, M. N. Guzik, C. Echevarria-Bonet, M. H. Sørby, P. Jenuš, B. C. Hauback, R. Tofan, A. E. Gunnæs, C. Persson, O. M. Løvvik, and T. G. Finstad, The role of grain boundary scattering in reducing the thermal conductivity of polycrystalline XNISN (x = hf, zr, ti) half-heusler alloys, Sci. Rep. 7, 13760 (2017) 2045-2322 10.1038/s41598-017-14013-8.
F. Wang, I. A. Kinloch, D. Wolverson, R. Tenne, A. Zak, E. O'Connell, U. Bangert, and R. J. Young, Strain-induced phonon shifts in tungsten disulfide nanoplatelets and nanotubes, 2D Mater. 4, 015007 (2016) 2053-1583 10.1088/2053-1583/4/1/015007.
G. J. Snyder and A. H. Snyder, Figure of merit zt of a thermoelectric device defined from materials properties, Energy Environ. Sci. 10, 2280 (2017) 1754-5692 10.1039/C7EE02007D.
L. Medrano Sandonas, D. Teich, R. Gutierrez, T. Lorenz, A. Pecchia, G. Seifert, and G. Cuniberti, Anisotropic thermoelectric response in two-dimensional puckered structures, J. Phys. Chem. C 120, 18841 (2016) 1932-7447 10.1021/acs.jpcc.6b04969.