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
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©2015 by De Gruyter
Artikel in diesem Heft
- 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
Artikel in diesem Heft
- 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
