Phonon Transport in a Thin Film due to Temperature Oscillation at the Film Edge
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H. Ali
Abstract
Transient response of phonon transport in a two-dimensional silicon thin film due to temperature disturbance at the film edge is investigated. Temperature oscillations with different frequencies are incorporated at the high-temperature edge of the film while uniform temperature is assumed initially in the film. The size of heat source, due to temperature oscillation, is varied at the film edge to investigate the coupling effect of oscillation frequency and the heat source size on the phonon transport in the film. Equivalent equilibrium temperature is introduced to assess the phonon transport characteristics for different temperature disturbance conditions. A numerical method incorporating the discrete ordinate method is used to solve the Boltzmann transport equation with the appropriate boundary conditions. It is found that equivalent equilibrium temperature oscillates in the region close to the high-temperature edge of the film; however, oscillation characteristics in terms of frequency and amplitude do not follow temperature oscillation at the film edge. Heat source size and oscillation frequency influence significantly equivalent equilibrium temperature in the film, which is more pronounced in the late heating periods.
Funding statement: Funding: The authors would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project no. RG1301.
Nomenclature
- C
Volumetric specific heat capacity of the dielectric material
- I
Phonon intensity
- I++
Phonon intensity in the first quadrant
- I–+
Phonon intensity in the second quadrant
- I+–
Phonon intensity in the third quadrant
- I––
Phonon intensity in the fourth quadrant
- Io
Equilibrium phonon intensity
- k
Wavenumber
- Lx
Thickness of the dielectric material film
- Lz
Width of the dielectric material film
- t
Time
- T
Equivalent equilibrium phonon temperature
- ν
Speed of phonons
- ws
Heat source thickness
- x
Cartesian coordinate x-direction
- z
Cartesian coordinate z-direction
- Δx
Grid spacing in the x-direction
- Δz
Grid spacing in the z-direction
- Greek Symbols
Phonon mean free path
Polar angle
Azimuthal angle
Relaxation time
- Subscripts
- A
Acoustic
- k
Wavenumber
- L
Longitudinal
- O
Optical
- T
Transverse
- x
x-Axis
- z
z-Axis
References
1. B. S. Yilbas and S. B. Mansour, Phonon transport in thin film: Ballistic phonon contribution to energy transport, Numer. Heat Trans. Appl. 64 (2013), 800–819.10.1080/10407782.2013.798571Search in Google Scholar
2. B. S. Yilbas and S. B. Mansoor, Phonon and electron transport in aluminum thin film: Influence of film thickness on electron and lattice temperatures, Phys. B 407 (2012), 4643–4648.10.1016/j.physb.2012.09.006Search in Google Scholar
3. A. J. Minnich, G. Chen, S. Mansoor and B. S. Yilbas, Quasi-ballistic heat transfer studied using the frequency-dependent Boltzmann transport equation, Phys. Rev. B 84 (2011), 23.10.1103/PhysRevB.84.235207Search in Google Scholar
4. B. S. Yilbas and S. B. Mansour, Phonon transport and equivalent equilibrium temperature in thin silicon films, J. Non-Equilib. Thermodyn. 38 (2013), 153–174.10.1515/jnetdy-2012-0026Search in Google Scholar
5. S. B. Mansoor and B. S. Yilbas, Phonon transport in silicon-silicon and silicon-diamond films: consideration of thermal boundary resistance at interface, Phys. B 406 (2011), 2186–2195.10.1016/j.physb.2011.03.028Search in Google Scholar
6. S. B. Mansoor and B. S. Yilbas, Radiative phonon transport in silicon and collisional energy transfer in aluminum films due to laser short-pulse heating: Influence of laser pulse intensity on temperature distribution, Opt. Laser Technol. 44 (2012), 43–50.10.1016/j.optlastec.2011.05.014Search in Google Scholar
7. S. B. Mansoor and B. S. Yilbas, Heat transfer across silicon-aluminum-silicon thin films due to ultra-short laser pulse irradiation, J. Enhanced Heat Transfer 19 (2012), 259–270.10.1615/JEnhHeatTransf.2012003327Search in Google Scholar
8. H. S. Sim, S. H. Lee and K. G. Kang, Femtosecond pulse laser interactions with thin silicon films and mater formation considering optical phonons and wave interference, Microsyst. Technol. 14 (2008), 1439–1446.10.1007/s00542-007-0554-3Search in Google Scholar
9. D. Terris, K. Joulain and D. Lemonnier, Heat pulse propagation in silicon nanostructures by solving phonon transport equation, in: Proceedings of the ASME Micro/Nanoscale Heat Transfer International Conference, MNHT 2008, Part A, 31–40, 2008.10.1115/MNHT2008-52220Search in Google Scholar
10. A. Q. Wu and X. Xu, Ultrafast diagnostics of coherent phonon excitation and energy transfer, in: Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 – Heat Transfer, 377–379, 2006.10.1115/IMECE2006-13773Search in Google Scholar
11. B. S. Yilbas and S. B. Mansoor, Energy transport in silicon-aluminum composite thin film during laser short-pulse irradiation, Opt. Quant. Electron. 44 (2012), 437–457.10.1007/s11082-012-9567-ySearch in Google Scholar
12. Y. Ma, Heat pulse propagation along silicon nanofilms, in: ASME 2012 3rd International Conference on Micro/Nanoscale Heat and Mass Transfer, MNHMT, pp. 917–922, 2012.10.1115/MNHMT2012-75324Search in Google Scholar
13. R. A. Escobar and C. H. Amon, Influence of phonon dispersion on transient thermal response of silicon-on-insulator transistors under self-heating conditions, J. Heat Transfer 129 (2007), 790–797.10.1115/1.2717243Search in Google Scholar
14. T. S. English, L. Phinney, P. E. Hopkins and J. R. Serrano, Mean free path effects on the experimentally measured thermal conductivity of single-crystal silicon microbridges, J. Heat Transfer 135 (2013), DOI: 10.1115/1.4024357.), DOI: 10.1115/1.4024357Search in Google Scholar
15. L. Guo, S. L. Hodson, T. S. Fisher and X. Xu, Heat transfer across metal-dielectric interfaces during ultrafast-laser heating, J. Heat Transfer 134 (2012), DOI: 10.1115/1.4005255.), DOI: 10.1115/1.4005255Search in Google Scholar
16. S. Pisipati, C. Chen, J. Geer, B. Sammakia and B. T. Murray, Multiscale thermal device modeling using diffusion in the Boltzmann transport equation, Int. J. Heat Mass Transfer 64 (2013), 286–303.10.1016/j.ijheatmasstransfer.2013.04.011Search in Google Scholar
17. B.-Y. Gu and X.-L. Zhang, Characteristics of the localized interface optical-phonon modes in triple-constitution superlattices with defect layers, Int. J. Nonlinear Sci. Numer. Simul. 3 (2002), 581–584.10.1515/IJNSNS.2002.3.3-4.581Search in Google Scholar
18. L.-L. Zhu and X.-J. Zheng, A theory for electromagnetic heat conduction and a numerical model based on Boltzmann equation, Int. J. Nonlinear Sci. Numer. Simul. 7 (2006), 339–344.10.1515/IJNSNS.2006.7.3.339Search in Google Scholar
19. Q. Chen, M. Wang, N. Pan and Z.-Y. Guo, Irreversibility of heat conduction in complex multiphase systems and its application to the effective thermal conductivity of porous media. Int. J. Nonlinear Sci. Numer. Simul. 10 (2009), 57–66.10.1515/IJNSNS.2009.10.1.57Search in Google Scholar
20. P. Yang, N.-B. Liao, C. Li and S.-H. Shang, Multi-scale modeling and numerical analysis of thermal behavior of cu-al interface structure in micro/nano manufacturing, Int. J. Nonlinear Sci. Numer. Simul. 10 (2009), 483–491.10.1515/IJNSNS.2009.10.4.483Search in Google Scholar
21. B. S. Yilbas and S. B. Mansour, Influence of heat source size on phonon transport in thin silicon film, Transp. Theory Stat. Phys. 42 (2014), 2.10.1080/00411450.2013.853193Search in Google Scholar
22. B. S. Yilbas and S. B. Mansoor, Frequency dependent phonon transport in two-dimensional silicon and diamond films, Mod. Phys. Lett. B 26 (2012), 17.10.1142/S0217984912501047Search in Google Scholar
23. S. Z. Shuja, B. S. Yilbas and S. Khan, Laser repetitive pulse heating of tool surfaces, Opt. Laser Technol. 43 (2011), 754–61.10.1016/j.optlastec.2010.12.013Search in Google Scholar
©2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- A Hierarchy of Lattice Soliton Equations Associated with a New Discrete Eigenvalue Problem and Darboux Transformations
- Simulation in System-Level Based on Model Order Reduction for a Square-Wave Micromixer
- Phonon Transport in a Thin Film due to Temperature Oscillation at the Film Edge
- Numerical Solutions for Groundwater Flow in Unsaturated Layered Soil with Extreme Physical Property Contrasts
- Lie Symmetries and Exact Solutions of Shallow Water Equations with Variable Bottom
Articles in the same Issue
- Frontmatter
- A Hierarchy of Lattice Soliton Equations Associated with a New Discrete Eigenvalue Problem and Darboux Transformations
- Simulation in System-Level Based on Model Order Reduction for a Square-Wave Micromixer
- Phonon Transport in a Thin Film due to Temperature Oscillation at the Film Edge
- Numerical Solutions for Groundwater Flow in Unsaturated Layered Soil with Extreme Physical Property Contrasts
- Lie Symmetries and Exact Solutions of Shallow Water Equations with Variable Bottom
