Abstract
A simple band model such as the effective mass approximation (EMA) can be used to quickly obtain the lower-energy region for the band structure of monolayer molybdenum disulfide. But the EMA band model cannot give the correct description for the band structure in the higher-energy region. To address this major issue, we propose an analytical band calculation (ABC) model to study monolayer molybdenum disulfide. Important parameters of the ABC model are obtained by fitting the three-direction band structure of monolayer molybdenum disulfide obtained from the first-principles (FP) method. The proposed ABC model fits well with the FP band structure calculation result for monolayer molybdenum disulfide. We also use the ABC model to calculate physical quantities used in carrier transport such as density of states and group velocity. Our ABC model can be extended and further utilized for calculating the key physical quantities of ballistic transport of 2D semiconductor materials.
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References
IRDS 2020 version, the official website: https://irds.ieee.org/editions/2020
Wang, Q.H., Kalantar-Zadeh, K., Kis, A., Coleman, J.N., Strano, M.S.: Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol. 7, 699 (2011). https://doi.org/10.1038/nnano.2012.193
Li, L.K., Yu, Y.J., Ye, G.J., Ge, Q.Q., Ou, X.D., Wu, H., Feng, D.L., Chen, X.H., Zhang, Y.B.: Black phosphorus field-effect transistors. Nat. Nanotechnol. 9, 372 (2014). https://doi.org/10.1038/nnano.2014.35
Chen, K.-T., Hsieh, M.-H., Yen-Shuo, Su., Lee, W.-J., Chang, S.-T.: Carrier mobility calculation for monolayer black phosphorous. J. Nanosci. Nanotechnol. 19, 6821–6825 (2019). https://doi.org/10.1166/jnn.2019.17126
Chou, A.S., Shen, P.C., Cheng, C.C., Lu, L.S., Chueh, W.C., Li, M.Y., Pitner, G., Chang, W.H., Wu, C.I., Kong, J., Li, L.J., Philip Wong, H.S.: High on-current 2D nFET of 390 µA/µm at VDS = 1V using monolayer CVD MoS2 without intentional doping. In: Symposium on VLSI Technology, Honolulu, HI, paper TN1.7, June 15–19, 2020. https://doi.org/10.1109/VLSITechnology18217.2020.9265040
Shen, P.-C., Su, C., Lin, Y., Chou, A.-S., Cheng, C.-C., Park, J.-H., Chiu, M.-H., Lu, A.-Y., Tang, H.-L., Tavakoli, M.M., Pitner, G., Ji, X., Cai, Z., Mao, N., Wang, J., Tung, V., Li, J., Bokor, J., Zettl, A., Wu, C.-I., Palacios, T., Li, L.-J., Kong, J.: Ultralow contact resistance between semimetal and monolayer semiconductors. Nature 593, 211 (2021). https://doi.org/10.1038/s41586-021-03472-9
Jin, Z., Li, X., Mullen, J.T., Kim, K.W.: Intrinsic transport properties of electrons and holes in monolayer transition-metal dichalcogenides. Phys. Rev. B 90, 045422 (2014). https://doi.org/10.1103/PhysRevB.90.045422
Kaasbjerg, K., Thygesen, K.S., Jacobsen, K.W.: Phonon-limited mobility in n-type single-layer MoS2 from first principles. Phys. Rev. B 85, 115317 (2012). https://doi.org/10.1103/PhysRevB.85.115317
Luisier, M., Szabo, A., Stieger, C., Klinkert, C., Bruck, S., Jain, A., Novotny, L.: First-principles simulations of 2-D semiconductor devices: mobility, I-V characteristics, and contact resistance. In: IEEE International Electron Devices Meeting (IEDM), December 3–7; San Francisco, US. pp. 123–126 (2016). https://doi.org/10.1109/IEDM.2016.7838353
Osanloo, M.R., Van de Put, M.L., Saadat, A., Vandenberghe, W.G.: Identification of two-dimensional layered dielectrics from first principles. Nat. Commun. 12, 5051 (2021). https://doi.org/10.1038/s41467-021-25310-2
Knobloch, T., Illarionov, Y.Y., Ducry, F., Schleich, C., Wachter, S., Watanabe, K., Taniguchi, T., Mueller, T., Waltl, M., Lanza, M., Vexler, M.I., Luisier, M., Grasser, T.: The performance limits of hexagonal boron nitride as an insulator for scaled CMOS devices based on two-dimensional materials. Nat. Electron. 4, 98–108 (2021). https://doi.org/10.1038/s41928-020-00529-x
Li, W., Walther, C.F.J., Kuc, A., Heine, T.: Density functional theory and beyond for band-gap screening: performance for transition-metal oxides and dichalcogenides. J. Chem. Theory Comput. 9, 2950 (2013). https://doi.org/10.1021/ct400235w
Liu, G.-B., Shan, W.-Y., Yao, Y., Yao, W., Xiao, Di.: Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B 88, 085433 (2013). https://doi.org/10.1103/PhysRevB.88.085433
Hosseini, M., Elahi, M., Pourfath, M., Esseni, D.: Strain induced mobility modulation in single-layer MoS2. J. Phys. D: Appl. Phys. 48, 375104 (2015). https://doi.org/10.1088/0022-3727/48/37/375104
Zahid, F., Lei Liu, Yu., Zhu, J.W., Guo, H.: A generic tight-binding model for monolayer, bilayer and bulk MoS2. AIP Adv. 3, 052111 (2013). https://doi.org/10.1063/1.4804936
Kresse, G., Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996). https://doi.org/10.1103/PhysRevB.54.11169
Kresse, G., Furthmüller, J.: Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15 (1996). https://doi.org/10.1016/0927-0256(96)00008-0
Ridley, B.K.: Quantum Processes in Semiconductors, 2ed edn., p. 33. Oxford University Press, Oxford (1988)
Rahman, A., Guo, J., Datta, S., Lundstrom, M.S.: Theory of ballistic nanotransistors. IEEE Trans. Electron Devices 50, 1853 (2003). https://doi.org/10.1109/TED.2003.815366
Kormányos, A., Zólyomi, V., Drummond, N.D., Rakyta, P., Burkard, G., Fal’ko, V.I.: Monolayer MoS2: trigonal warping, the Γ valley, and spin-orbit coupling effects. Phys. Rev. B 88, 045416 (2013). https://doi.org/10.1103/PhysRevB.88.045416
Acknowledgements
This work was supported by the National Science Council, Taiwan, R.O.C., under contract nos. MOST110-2622-8-002-014 and MOST 110-2221-E-005-060. Computing support was provided by the National Center for High-Performance Computing (NCHC), Taiwan. We would like to thank Uni-edit (www.uni-edit.net) for editing and proofreading this manuscript.
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Yang, CH., Chung, YF., Su, YS. et al. Band structure of molybdenum disulfide: from first principle to analytical band model. J Comput Electron 21, 571–581 (2022). https://doi.org/10.1007/s10825-022-01880-2
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DOI: https://doi.org/10.1007/s10825-022-01880-2