An Investigation of the Size Effect on the Heat Transfer in Silicon and Germanium
Date Issued
2010
Date
2010
Author(s)
Kang, Ting-Yu
Abstract
The phonon transport phenomenon in solids was simulated via a Monte-Carlo(MC) simulator , which solves the phonon Boltzmann transport equation under the single mode relaxation time approximation and the gray medium approximation. Physical models for heterogeneous interfaces and numerical boundary conditions are properly designed and implemented. Most of all, we take advantage of the geometric symmetry that exists in a system to reduce the computational amount. We focus our work on investigating the effect of the heterogeneous interfaces and boundaries on the thermal conductivity of Si/Ge nanocomposites and the size effect on the spreading thermal resistance.
For Si/Ge nanocomposites, the investigation results indicate the thermal conductivity significantly reduces with increasing interface density when the interfaces are totally diffuse. When the interfaces are smooth, the thermal conductivities are dominated not only by the interface density but also the intrinsic properties of the components of composites. A critical density ratio is thus resulted with a corresponding minimum thermal conductivity. Furthermore, the investigation results also show that a lower thermal conductivity can be expected by using lower thermal conductivity material in matrix and the higher in wire.
For the size effect on the spreading thermal resistance, the simulated system is a silicon film heated by a narrow heating wire placed on the top surface of the film and cooled by the ambient atmosphere with a constant temperature and convection heat transfer coefficient on the bottom surface. Comparisons were made between the simulation results at micro-scale and the analytical solutions of the thermal diffusion equation as well as between films at micro- and nano- scales. The former verifies the importance of the anisotropy and temperature dependence of the film thermal conductivity. The latter shows an increased spreading-resistance fraction of the total film thermal resistance when the system is scaled down due to the ballistic behaviors of phonons. This paper reveals the importance of spreading resistance in applications at nanoscale.
Subjects
Monte-Carlo simulation
thermal conductivity
nanocomposite
interface density
size effect
spreading resistance
convection heat transfer coefficient
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