The thermal expansion of 2H-MoS2and 2H-WSe2between 10 and 320 K

Murray, Roger K.; Evans, B.

doi:10.1107/s0021889879012528

Cited by 93 publications

(98 citation statements)

References 17 publications

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“…We find the behavior of the rate of change of α c with T to be different from that of α a , where the former increases rapidly at low T while the latter increases more gradually with T . Murray and Evans 22 have pointed out that the lattice constant a (c) increases linearly (nonlinearly) with temperature, which is consistent with our TEC results at low T .…”

Section: Resultssupporting

confidence: 82%

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Gan

Liu

2016

Phys. Rev. B

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Using density-functional perturbation theory and the Grüneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS2 in the crystallographic a and c directions. The TEC calculation depends critically on the evaluation of a temperature-dependent quantity Ii(T ), which is the integral of the product of heat capacity and Γi(ν), of frequency ν and strain type i, where Γi(ν) is the phonon density of states weighted by the Grüneisen parameters. We show that to determine the linear TECs we may use minimally two uniaxial strains in the z direction, and either the x or y direction. However, a uniaxial strain in either the x or y direction drastically reduces the symmetry of the crystal from a hexagonal one to a base-centered orthorhombic one. We propose to use an efficient and accurate symmetry-preserving biaxial strain in the xy plane to derive the same result for Γ(ν). We highlight that the Grüneisen parameter associated with a biaxial strain may not be the same as the average of Grüneisen parameters associated with two separate uniaxial strains in the x and y directions due to possible preservation of degeneracies of the phonon modes under a biaxial deformation. Large anisotropy of TECs is observed where the linear TEC in the c direction is about 1.8 times larger than that in the a or b direction at high temperatures. Our theoretical TEC results are compared with experiment. The symmetry-preserving approach adopted here may be applied to a broad class of two lattice-parameter systems such as hexagonal, trigonal, and tetragonal systems, which allows many complicated systems to be treated on a first-principles level.

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Section: Resultssupporting

confidence: 82%

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Gan

Liu

2016

Phys. Rev. B

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“…Alternatively, one can understand the red shift of the exciton mode as a strain-induced effect owing to the hot temperatures in the furnace at which CVD growth takes place, while ML samples prepared by exfoliation at RT have very similar emission energies to one another. Since CVD ML are formed on the hot surface out of the vapor phase at elevated temperatures, the consecutive cooling after growth leads to tensions caused by the mismatch of the thermal expansion coefficients (TECs) of WSe 2 (in plane coefficient) TEC = (1.1 × 10 [69,70] and sapphire TEC = (5 × 10 −6 /K-8.3 × 10 −6 /K) [71] at the relevant temper atures (300-900 K), which differ by a factor of 1.5-2. Qualitatively, the TEC of sapphire is less than that of WSe 2 over this temperature range.…”

Section: Resultsmentioning

confidence: 99%

Influence of the substrate material on the optical properties of tungsten diselenide monolayers

et al. 2017

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Monolayers of transition-metal dichalcogenides such as WSe 2 have become increasingly attractive due to their potential in electrical and optical applications. Because the properties of these 2D systems are known to be affected by their surroundings, we report how the choice of the substrate material affects the optical properties of monolayer WSe 2 . To accomplish this study, pump-density-dependent micro-photoluminescence measurements are performed with time-integrating and time-resolving acquisition techniques. Spectral information and power-dependent mode intensities are compared at 290K and 10K for exfoliated WSe 2 on SiO 2 /Si, sapphire (Al 2 O 3 ), hBN/Si 3 N 4 /Si, and MgF 2 , indicating substrate-dependent appearance and strength of exciton, trion, and biexciton modes. Additionally, one CVD-grown WSe 2 monolayer on sapphire is included in this study for direct comparison with its exfoliated counterpart. Time-resolved micro-photoluminescence shows how radiative decay times strongly differ for different substrate materials. Our data indicates exciton-exciton annihilation as a shortening mechanism at room temperature, and subtle trends in the decay rates in correlation to the dielectric environment at cryogenic temperatures. On the measureable time scales, trends are also related to the extent of the respective 2D-excitonic modes' appearance. This result highlights the importance of further detailed characterization of exciton features in 2D materials, particularly with respect to the choice of substrate.

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“…In Fig. 4 we plot the a lattice constant assembling published data in the literature [35][36][37][38] in order to span the temperature range of interest for MoS 2 , MoSe 2 , and sapphire. The solid lines are secondorder polynomial fits which we use to calculate the strain versus temperature.…”

Section: B the Influence Of Strainmentioning

confidence: 99%

“…Strain modifies the ratio of the effective masses in the valence and the conduction bands giving rise to an intercellular [35][36][37][38]. Note that for the low temperature MoS 2 data, scatter was reduced by taking points corresponding to the linear fit to the data in Ref.…”

Section: B the Influence Of Strainmentioning

confidence: 99%

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Magnetoexcitons in large area CVD-grown monolayerMoS2andMoSe2on sapphire

et al. 2016

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Magnetotransmission spectroscopy was employed to study the valley Zeeman effect in large area monolayer MoS 2 and MoSe 2 . The extracted values of the valley g factors for both A and B excitons were found to be similar with g v −4.5. The samples are expected to be strained due to the CVD growth on sapphire at high temperature (700• C). However, the estimated strain, which is maximum at low temperature, is only 0.2%. Theoretical considerations suggest that the strain is too small to significantly influence the electronic properties. This is confirmed by the measured value of the valley g factor, and the measured temperature dependence of the band gap, which are almost identical for CVD and mechanically exfoliated MoS 2 .

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The thermal expansion of 2H-MoS₂and 2H-WSe₂between 10 and 320 K

Cited by 93 publications

References 17 publications

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Direct calculation of the linear thermal expansion coefficients ofMoS2via symmetry-preserving deformations

Influence of the substrate material on the optical properties of tungsten diselenide monolayers

Magnetoexcitons in large area CVD-grown monolayerMoS2andMoSe2on sapphire

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