Thermal expansion coefficient of monolayer MoS₂ determined using temperature-dependent Raman spectroscopy combined with finite element simulations

Abstract

The thermal expansion coefficient is an important parameter of monolayer MoS₂ that affects the performance of its related optoelectronic devices. To obtain the thermal expansion coefficient of monolayer MoS₂, suspended and supported MoS₂ are systematically investigated using micro-Raman spectroscopy in a temperature range of 77-557 K. Obvious differences in the temperature-dependent evolution of the Raman peaks between suspended and supported MoS₂ are observed, which result from the thermal expansion coefficient mismatch between MoS₂ and the substrate. With the help of the finite element method, the thermal strain in suspended and supported MoS₂ is calculated and used to deduce the thermal expansion coefficient mismatch-induced Raman shift. By matching the simulation and experimental results, the thermal expansion coefficient of MoS₂ is identified through the numerical inversion calculation. Our results demonstrate that the combination of micro-Raman spectroscopy and finite element simulations is highly effective for identifying the intrinsic thermal expansion coefficient of two-dimensional materials.

Keywords

Monolayer MoS₂ / thermal expansion coefficient / Raman spectroscopy / finite element method

References

[1] Chhowalla M,Zhang H.Two-dimensional transition metal dichalcogenide (TMD) nanosheets..Chem Soc Rev2015;44:2584-6

[2] Lv R,Schaak RE.Transition metal dichalcogenides and beyond: synthesis, properties, and applications of single- and few-layer nanosheets..Acc Chem Res2015;3:897

[3] Huang X,Zhang H.Metal dichalcogenide nanosheets: preparation, properties and applications..Chem Soc Rev2013;42:1934-46

[4] Chhowalla M,Eda G,Loh KP.The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets..Nat Chem2013;5:263-75

[5] Ding Y,Ni J,Shi S.First principles study of structural, vibrational and electronic properties of graphene-like MX2 (M=Mo, Nb, W, Ta; X=S, Se, Te) monolayers..Physica B Condens Matter2011;406:2254-60

[6] Mak KF,Hone J,Heinz TF.Atomically thin MoS₂: a new direct-gap semiconductor..Phys Rev Lett2010;105:136805

[7] Radisavljevic B,Brivio J,Kis A.Single-layer MoS₂ transistors..Nat Nanotechnol2011;6:147-50

[8] Yu Y,Xu C.Engineering substrate interactions for high luminescence efficiency of transition-metal dichalcogenide monolayers..Adv Funct Mater2016;26:4733-9

[9] Dai Z,Zhang Z.Strain engineering of 2D materials: issues and opportunities at the interface..Adv Mater2019;31:e1805417

[10] Yan Z,Khan JM.Graphene quilts for thermal management of high-power GaN transistors..Nat Commun2012;3:827

[11] Sevik C.Assessment on lattice thermal properties of two-dimensional honeycomb structures: Graphene, h-BN, h-MoS₂, and h-MoSe₂..Phys Rev B2014;89:

[12] Ding Y.Thermal expansion tensors, Grüneisen parameters and phonon velocities of bulk MT ₂ (M = W and Mo; T = S and Se) from first principles calculations..RSC Adv2015;5:18391-400

[13] Huang LF,Zeng Z.Correlation between structure, phonon spectra, thermal expansion, and thermomechanics of single-layer MoS₂..Phys Rev B2014;90:

[14] Yuan J,Lu Q,Chen X.First-principles study of the phonon vibrational spectra and thermal properties of hexagonal MoS₂..Solid State Sciences2015;40:1-6

[15] Liang L,Sumpter BG,Tan PH.Low-frequency shear and layer-breathing modes in Raman scattering of two-dimensional materials..ACS Nano2017;11:11777-802

[16] Wang Y,Qiu C.Raman spectroscopy study of lattice vibration and crystallographic orientation of monolayer MoS₂ under uniaxial strain..Small2013;9:2857-61

[17] Saigal N,Čapeta D.Effect of lithium doping on the optical properties of monolayer MoS₂..Appl Phys Lett2018;112:121902

[18] Huang X,Liu L.Raman spectra evidence for the covalent-like quasi-bonding between exfoliated MoS₂ and Au films..Sci China Inf Sci2021;64:

[19] Mouri S,Nanishi Y.Thermal conductivity of van der Waals hetero-bilayer of MoS₂/MoSe₂..Appl Phys Express2020;13:075001

[20] Zhang L,Song Y.Thermal expansion coefficient of monolayer molybdenum disulfide using micro-raman spectroscopy..Nano Lett2019;19:4745-51

[21] Lin Z,Tian S,Huang Y.Thermal expansion coefficient of few-layer MoS₂ studied by temperature-dependent Raman spectroscopy..Sci Rep2021;11:7037

[22] Huang Y,Yang R.Universal mechanical exfoliation of large-area 2D crystals..Nat Commun2020;11:2453

[23] Baek SH,Choi W.Large-area growth of uniform single-layer MoS₂ thin films by chemical vapor deposition..Nanoscale Res Lett2015;10:388 PMCID:PMC4595407

[24] Yang Y,Lin Z.Micro-defects in monolayer MoS₂ studied by low-temperature magneto-Raman mapping..J Phys Chem C2020;124:17418-22

[25] Chakraborty B,Sood AK.Layer-dependent resonant Raman scattering of a few layer MoS₂: Raman scattering of a few layer MoS₂..J Raman Spectrosc2013;44:92-6

[26] Tian S,Liu Z.Temperature-dependent Raman investigation on suspended graphene: Contribution from thermal expansion coefficient mismatch between graphene and substrate..Carbon2016;104:27-32

[27] Huang X,Yang T,Cheng HM.Quantitative analysis of temperature dependence of raman shift of monolayer WS2..Sci Rep2016;6:32236 PMCID:PMC5006054

[28] Chen Y,Zhu Y.Temperature-dependent photoluminescence emission and Raman scattering from Mo1-x W x S2 monolayers..Nanotechnology2016;27:445705

[29] Late DJ,Waghmare UV,Rao CN.Thermal expansion, anharmonicity and temperature-dependent Raman spectra of single- and few-layer MoSe₂ and WSe₂..Chemphyschem2014;15:1592-8

[30] Zouboulis ES.Raman scattering in diamond up to 1900 K..Phys Rev B Condens Matter1991;43:12490-3

[31] Su L,Cao L.In situ monitoring of the thermal-annealing effect in a monolayer of MoS₂..Phys Rev Applied2017;7:

[32] Chakraborty B,Muthu DVS,Waghmare UV.Symmetry-dependent phonon renormalization in monolayer MoS₂ transistor..Phys Rev B2012;85:

[33] Iqbal MW,Akbar R.A review on Raman finger prints of doping and strain effect in TMDCs..Microelectron Eng2020;219:111152

[34] Yoon D,Cheong H.Negative thermal expansion coefficient of graphene measured by Raman spectroscopy..Nano Lett2011;11:3227-31

[35] McCreary A,Amani M.Effects of uniaxial and biaxial strain on few-layered terrace structures of MoS₂ grown by vapor transport..ACS Nano2016;10:3186-97

[36] Zhang H.Electronic, thermal expanding, and optical absorption properties of transition metal dichalcogenides: a first-principles study..J Wuhan Univ Technol-Mat Sci Edit2018;33:1355-9

[37] Hu X,Jokisaari J,Salehi-Khojin A.Mapping thermal expansion coefficients in freestanding 2D materials at the nanometer scale..Phys Rev Lett2018;120:055902