Numerical Simulation of the Thermal Stresses of Layered Molybdenum Disulfide

Zhongtao Lin; Lianchun Long; Yang Yang; Wuguo Liu

doi:10.3788/LOP202158.1516028

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 15 >Page 1516028 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 15, 1516028 (2021)

Numerical Simulation of the Thermal Stresses of Layered Molybdenum Disulfide

Zhongtao Lin¹, Lianchun Long¹, Yang Yang^2、*, and Wuguo Liu²

Author Affiliations

¹Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China

²Institute of Physics, Chinese Academy of Sciences, Beijing 100089, China

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DOI: 10.3788/LOP202158.1516028 Cite this Article Set citation alerts

Zhongtao Lin, Lianchun Long, Yang Yang, Wuguo Liu. Numerical Simulation of the Thermal Stresses of Layered Molybdenum Disulfide[J]. Laser & Optoelectronics Progress, 2021, 58(15): 1516028 Copy Citation Text

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Schematic of SiO2 based MoS2 film model. （a） Schematic of substrate supported MoS2 model；（b） schematic of the suspended MoS2 model

Fig. 1. Schematic of SiO₂ based MoS₂ film model. （a） Schematic of substrate supported MoS₂ model；（b） schematic of the suspended MoS₂ model

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Thermal expansion coefficients of MoS2 and SiO2. （a） Thermal expansion coefficient as a function of temperature；（b） gradient of thermal expansion coefficient changed with temperature

Fig. 2. Thermal expansion coefficients of MoS₂ and SiO₂. （a） Thermal expansion coefficient as a function of temperature；（b） gradient of thermal expansion coefficient changed with temperature

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Fig. 3. Thermal stress distribution. （a） Suspended MoS₂ at 293 K；（b） substrate supported MoS₂ at 293 K；（c） suspended MoS₂ at 200 K；（d） substrate supported MoS₂ at 200 K；（e） suspended MoS₂ at 100 K；（f） substrate supported MoS₂ at 100 K

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Fig. 4. Thermal stress distribution in MoS₂from the center to the edge

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Fig. 5. Temperature dependence of the thermal stress at central point of MoS₂

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Fig. 6. Thickness dependence of the thermal stress at the central point of MoS₂

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Fig. 7. Thermal stress distribution at central point of MoS₂. （a）The dependence of the thermal stress at central point on the thickness of substrate；（b） gradient of the thermal stress at central point as a function of the thickness of substrate

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Material	MoS₂	SiO₂
Thermal expansion coefficient /K^-1	$10^{- 7} + 3.5 \times 10^{- 8} \times T - 3.9 \times 10^{- 11} \times T^{2}, 100 \leq T \leq 500$ ^［30］	$- 1.7 \times 10^{- 6} + 1.5 \times 10^{- 8} \times T - 3.3 \times 10^{- 11} \times T^{2} + 3.2 \times 10^{- 14} \times T^{3} - 1.2 \times 10^{- 17} \times T^{4}, 100 \leq T \leq 500$
Thermal conductivity / （W·m^-1·K^-1）	104.7^［31］	$\{\begin{array}{l} 0.1 + 4.3 \times 10^{- 5} \times T^{2} - 2.3 \times 10^{- 7} \times T^{3} + \\ 3 \times 10^{- 10} \times T^{4}, 50 \leq T < 280 \\ - 0.1 - 5.3 \times 10^{- 5} \times T^{2} + 7.6 \times 10^{- 8} \times T^{3} - \\ 5.06 \times 10^{- 11} \times T^{4} + 1.3 \times 10^{- 14} \times T^{5}, 280 \leq \\ T \leq 500 \end{array}$
Density /（Kg·m^-3）	4800^［32］	$2219.4 - 4.7 \times 10^{- 5} \times T^{2} + 7 \times 10^{- 8} \times T^{3} - 11 \times 10^{- 11} \times T^{4} + 1.4 \times 10^{- 14} \times T^{5}, 100 \leq T \leq 500$
Young modulus /GPa	229^［33］	$\{\begin{array}{l} 7.8 - 8 \times 10^{7} \times T + 1200039 \times T^{2} - \\ 7440.2 \times T^{3} 22 \times 10^{- 6} \times T^{4}, 100 \leq T \leq 170 \\ 7 \times 10^{- 10} + 1.2 \times 10^{7} \times T + 11447.5 \times T^{2} - \\ 26 \times T^{3} - 3 \times 10^{- 6} \times T^{5}, 170 \leq T \leq 500 \end{array}$
Poisson's ratio	0.25^［33］	$\{\begin{array}{l} 0.2 - 3.5 \times 10^{- 4} \times T + 5.4 \times 10^{- 6} \times T^{2} - \\ 2.8 \times 10^{- 8} \times T^{3} + 4.9 \times 10^{- 11} \times T^{4}, 100 \leq \\ T < 170 \\ 0.1 + 2.3 \times 10^{- 4} \times T - 9.3 \times 10^{- 7} \times T^{2} + \\ 1.8 \times 10^{- 9} \times T^{3} - 1.6 \times 10^{- 12} \times T^{4} + 5.4 \times \\ 10^{- 16} \times T^{5}, 170 \leq T \leq 500 \end{array}$
Heat capacity at constant pressure /（J·kg^-1·K^-1）	$- 235.1 + 5.5 \times T - 0.01 \times T^{2} + 4 \times 10^{- 5} \times T^{3} - 4.6 \times 10^{- 8} \times T^{4} + 2.9 \times 10^{- 11} \times T^{5} - 7.4 \times 10^{- 15} \times T^{6}, 100 \leq T \leq 500$	$61.5 + 1.9 \times T - 1.7 \times 10^{- 5} \times T^{3} + 1.9 \times 10^{- 8} \times T^{4} - 7.1 \times 10^{- 12} \times T^{5}, 100 \leq T \leq 500$

Table 1. Physical properties of materials

Zhongtao Lin, Lianchun Long, Yang Yang, Wuguo Liu. Numerical Simulation of the Thermal Stresses of Layered Molybdenum Disulfide[J]. Laser & Optoelectronics Progress, 2021, 58(15): 1516028

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