Carrier relaxation time modelling of monolayer black phosphorene
- Author(s): Ali H. Pourasl 1 ; Mohammad T. Ahmadi 1, 2 ; Razali Ismail 1
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View affiliations
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Affiliations:
1:
Computational Nanoelectronic Research Group (CoNE), Faculty of Electrical Engineering , Universiti Teknologi Malaysia , 81310 Skudai, Johor , Malaysia ;
2: Nanotechnology Research Center Nanoelectronic Group, Physics Department , Urmia University , 57147 Urmia , Iran
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Affiliations:
1:
Computational Nanoelectronic Research Group (CoNE), Faculty of Electrical Engineering , Universiti Teknologi Malaysia , 81310 Skudai, Johor , Malaysia ;
- Source:
Volume 12, Issue 10,
October
2017,
p.
758 – 762
DOI: 10.1049/mnl.2017.0242 , Online ISSN 1750-0443
Phosphorene as an innovative structure that can be exfoliated similarly to the graphene with a direct, inherent and suitable bandgap presents exceptional prospects for future generations of electronic devices. Phosphorene possess high carrier mobility, therefore, in this work its carrier statistics in the form of monolayer phosphorene in the non-degenerate limit is analytically modelled and the mobility relation with carrier relaxation time is investigated. Energy dispersion relation is used to develop and calculate the required parameters for carrier relaxation time model which is an important parameter in conduction theory. On the other hand, the dependency of carrier velocity and mobility to voltage, normalised Fermi energy and temperature are modelled. Finally, the carrier relaxation time as a function of carrier mobility is modelled and its dependency towards temperature and normalised Fermi energy is discussed. It is shown that the relaxation time is strongly dependent on the carrier mobility which increases by increasing the mobility.
Inspec keywords: phosphorus; monolayers; carrier relaxation time; elemental semiconductors; carrier mobility; Fermi level
Other keywords: electronic devices; carrier relaxation time; conduction theory; monolayer black phosphorene; carrier velocity; bandgap; P; Fermi energy; carrier mobility; energy dispersion relation
Subjects: Charge carriers: generation, recombination, lifetime, and trapping (semiconductors/insulators); Elemental semiconductors; Low-field transport and mobility; piezoresistance (semiconductors/insulators); Electronic structure of elemental semiconductors (thin films, low dimensional and nanoscale structures); Monolayers and Langmuir-Blodgett films; Electrical properties of elemental semiconductors (thin films, low-dimensional and nanoscale structures)
References
-
-
1)
-
20. Slater, J., Koster, G., Wood, J.: ‘Symmetry and free electron properties of the gallium energy bands’, Phys. Rev., 1962, 126, (4), p. 1307 (doi: 10.1103/PhysRev.126.1307).
-
-
2)
-
36. Mousavi, S.M., Ahmadi, M.T., Sadeghi, H., et al: ‘Bilayer graphene nanoribbon carrier statistic in degenerate and non degenerate limit’, J. Comput. Theor. Nanosci., 2011, 8, (10), pp. 2029–2032 (doi: 10.1166/jctn.2011.1921).
-
-
3)
-
2. Yuanbo, Z., Yan-Wen, T., Stormer, H.L., et al: ‘Experimental observation of quantum hall effect and berry's phase in graphene’, Nature, 2005, 438, pp. 201–204 (doi: 10.1038/nature04235).
-
-
4)
-
21. Berger, C., Song, Z., Li, T., et al: ‘Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics’, J. Phys. Chem. B, 2004, 108, (52), pp. 19912–19916 (doi: 10.1021/jp040650f).
-
-
5)
-
6. Bao, W., Cai, X., Kim, D., et al: ‘High mobility ambipolar MoS2 field-effect transistors: substrate and dielectric effects’, Appl. Phys. Lett., 2013, 102, (4), p. 042104 (doi: 10.1063/1.4789365).
-
-
6)
-
41. Datta, S.: ‘Quantum transport: atom to transistor’ (Cambridge University Press, 2005).
-
-
7)
-
37. Ahmadi, M.T., Ismail, R., Tan, M.L., et al: ‘The ultimate ballistic drift velocity in carbon nanotubes’, J. Nanomater., 2008, 2008, pp. 1–8 (doi: 10.1155/2008/769250).
-
-
8)
-
2. Yan, Z., Nika, D.L., Balandin, A.A.: ‘Thermal properties of graphene and few layer graphene: applications in electronics’, IET Circuits Devices Syst., 2015, 9, (1), pp. 4–12 (doi: 10.1049/iet-cds.2014.0093).
-
-
9)
-
8. Novoselov, K., McCann, E., Morozov, S., et al: ‘Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene’, Nat. Phys., 2006, 2, (3), pp. 177–180 (doi: 10.1038/nphys245).
-
-
10)
-
42. Frey, J. (Ed.): ‘Ballistic transport in semiconductor devices’. 1980 Int. IEEE Electron Devices Meeting, 1980.
-
-
11)
-
3. Das, S., Demarteau, M., Roelofs, A.: ‘Ambipolar phosphorene field effect transistor’, ACS Nano, 2014, 8, (11), pp. 11730–11738 (doi: 10.1021/nn505868h).
-
-
12)
-
18. Brown, A., Rundqvist, S.: ‘Refinement of the crystal structure of black phosphorus’, Acta Crystallogr., 1965, 19, (4), pp. 684–685 (doi: 10.1107/S0365110X65004140).
-
-
13)
-
1. Liao, L., Lin, Y.C., Bao, M., et al: ‘High-speed graphene transistors with a self-aligned nanowire gate’, Nature, 2010, 467, pp. 305–308 (doi: 10.1038/nature09405).
-
-
14)
-
40. Lundstrom, M., Guo, J.: ‘Nanoscale transistors: device physics, modeling and simulation’ (Springer Science & Business Media, 2006).
-
-
15)
-
45. Amin, N.A., Johari, Z., Ahmadi, M.T., et al: ‘Low-field mobility model on parabolic band energy of graphene nanoribbon’, Mod. Phys. Lett. B, 2011, 25, (04), pp. 281–290 (doi: 10.1142/S0217984911025584).
-
-
16)
-
23. Dai, J., Zeng, X.C.: ‘Bilayer phosphorene: effect of stacking order on bandgap and its potential applications in thin-film solar cells’, J. Phys. Chem. Lett., 2014, 5, (7), pp. 1289–1293 (doi: 10.1021/jz500409m).
-
-
17)
-
1. Novoselov, K.S., Geim, A.K., Morozov, S.V., et al: ‘Electric field effect in atomically thin carbon films’, Science, 2004, 306, (5696), pp. 666–669 (doi: 10.1126/science.1102896).
-
-
18)
-
16. Reich, E.S.: ‘Phosphorene excites materials scientists’, Nature, 2014, 506, (7486), pp. 19 (doi: 10.1038/506019a).
-
-
19)
-
34. Guinea, F., Neto, A.C., Peres, N.: ‘Interaction effects in single layer and multi-layer graphene’, Eur. Phys. J. Spec. Top., 2007, 148, (1), pp. 117–125 (doi: 10.1140/epjst/e2007-00231-7).
-
-
20)
-
14. Liu, H., Neal, A.T., Zhu, Z., et al: ‘Phosphorene: an unexplored 2D semiconductor with a high hole mobility’, ACS Nano, 2014, 8, (4), pp. 4033–4041 (doi: 10.1021/nn501226z).
-
-
21)
-
31. Xia, F., Wang, H., Jia, Y.: ‘Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics’, Nat. Commun., 2014, 5.
-
-
22)
-
35. Arora, V.K.: ‘Nanoelectronics: quantum engineering of low-dimensional nanoensembles’ (CRC Press, 2015).
-
-
23)
-
15. Li, L., Yu, Y., Ye, G.J., et al: ‘Black phosphorus field-effect transistors’, Nat. Nanotechnol., 2014, 9, (5), pp. 372–377 (doi: 10.1038/nnano.2014.35).
-
-
24)
-
33. Li, P., Appelbaum, I.: ‘Electrons and holes in phosphorene’, Phys. Rev. B, 2014, 90, (11), pp. 1–12, doi: https://doi.org/10.1103/PhysRevB.90.115439.
-
-
25)
-
11. Karmakar, S., Gogna, M., Suarez, E., et al: ‘Novel three state quantum dot gate FET in Silicon-on-insulator’, IET Circuits Devices Syst., 2015, 9, (1), pp. 1–8 (doi: 10.1049/iet-cds.2014.0371).
-
-
26)
-
11. Yoon, Y., Ganapathi, K., Salahuddin, S.: ‘How good can monolayer MoS2 transistors be?, Nano Lett., 2011, 11, (9), pp. 3768–3773 (doi: 10.1021/nl2018178).
-
-
27)
-
12. Fuhrer, M.S., Hone, J.: ‘Measurement of mobility in dual-gated MoS2 transistors’, Nat. Nanotechnol., 2013, 8, (3), pp. 146–147 (doi: 10.1038/nnano.2013.30).
-
-
28)
-
43. Arora, V.K.: ‘Quantum engineering of nanoelectronic devices: the role of quantum emission in limiting drift velocity and diffusion coefficient’, Microelectron. J., 2000, 31, (11), pp. 853–859 (doi: 10.1016/S0026-2692(00)00085-9).
-
-
29)
-
5. Novoselov, K.S., Geim, A.K., Morozov, S.V., et al: ‘Two-dimensional gas of massless Dirac fermions in graphene’, Nature, 2005, 438, p. 197 (doi: 10.1038/nature04233).
-
-
30)
-
26. Maruyama, Y., Suzuki, S., Kobayashi, K., et al: ‘Synthesis and some properties of black phosphorus single crystals’, Physica B + C, 1981, 105, (1), pp. 99–102 (doi: 10.1016/0378-4363(81)90223-0).
-
-
31)
-
25. Rodin, A., Carvalho, A., Neto, A.C.: ‘Strain-induced gap modification in black phosphorus’, Phys. Rev. Lett., 2014, 112, (17), p. 176801 (doi: 10.1103/PhysRevLett.112.176801).
-
-
32)
-
27. Keyes, R.W.: ‘The electrical properties of black phosphorus’, Phys. Rev., 1953, 92, (3), p. 580 (doi: 10.1103/PhysRev.92.580).
-
-
33)
-
17. Delhaes, P.: ‘Graphite and precursors’ (CRC Press, 2000).
-
-
34)
-
30. Takao, Y., Asahina, H., Morita, A.: ‘Electronic structure of black phosphorus in tight binding approach’, J. Phys. Soc. Jpn., 1981, 50, (10), pp. 3362–3369 (doi: 10.1143/JPSJ.50.3362).
-
-
35)
-
38. Pierret, R.F., Neudeck, G.W.: ‘Advanced semiconductor fundamentals’ (Addison-Wesley, Reading, MA, 1987).
-
-
36)
-
39. Mathewson, A., Rohan, J.: ‘Simulation of semiconductor processes and devices’ (Ireland, Springer, 2001).
-
-
37)
-
32. Morita, A.: ‘Semiconducting black phosphorus’, Appl. Phys. A, 1986, 39, (4), pp. 227–242 (doi: 10.1007/BF00617267).
-
-
38)
-
13. Radisavljevic, B., Kis, A.: ‘Reply to measurement of mobility in dual-gated MoS2 transistors’, Nat. Nanotechnol., 2013, 8, (3), pp. 147–148 (doi: 10.1038/nnano.2013.31).
-
-
39)
-
24. Liu, H., Neal, A.T., Zhu, Z., et al: ‘Phosphorene: a new 2D material with high carrier mobility’, arXiv:14014133, 2014.
-
-
40)
-
29. Asahina, H., Shindo, K., Morita, A.: ‘Electronic structure of black phosphorus in self-consistent pseudopotential approach’, J. Phys. Soc. Jpn., 1982, 51, (4), pp. 1193–1199 (doi: 10.1143/JPSJ.51.1193).
-
-
41)
-
9. Radisavljevic, B., Radenovic, A., Brivio, J., et al: ‘Single-layer MoS2 transistors’, Nat. Nanotechnol., 2011, 6, (3), pp. 147–150 (doi: 10.1038/nnano.2010.279).
-
-
42)
-
33. Schwierz, F.: ‘Graphene transistors’, Nat Nano, 2010, 5, (7), pp. 487–496 (doi: 10.1038/nnano.2010.89).
-
-
43)
-
44. Liao, B., Zhou, J., Qiu, B., et al: ‘Ab initio study of electron–phonon interaction in phosphorene’, Phys. Rev. B, 2015, 91, (23), pp. 235419 (doi: 10.1103/PhysRevB.91.235419).
-
-
44)
-
28. Akahama, Y., Endo, S., Narita, S.-i.: ‘Electrical properties of black phosphorus single crystals’, J. Phys. Soc. Jpn., 1983, 52, (6), pp. 2148–2155 (doi: 10.1143/JPSJ.52.2148).
-
-
45)
-
19. Cartz, L., Srinivasa, S., Riedner, R., et al: ‘Effect of pressure on bonding in black phosphorus’, J. Chem. Phys., 1979, 71, (4), pp. 1718–1721 (doi: 10.1063/1.438523).
-
-
1)