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Monte-Carlo Study of Phonon Heat Conduction in Silicon Thin Films

Mittal, Arpit
http://rave.ohiolink.edu/etdc/view?acc_num=osu1259602975

Abstract Details

2009, Master of Science, Ohio State University, Mechanical Engineering.
Heat conduction in crystalline semiconductor materials occurs by lattice vibrations that result in the propagation of quanta of energy called phonons. The Boltzmann Transport Equation (BTE) for phonons is a powerful tool to model both equilibrium and non-equilibrium heat conduction in crystalline solids. Non-equilibrium heat conduction occurs either when the length scales (of the device in question) are small or at low temperatures. The BTE describes the evolution of the number density (or energy) distribution for phonons as a result of transport (or drift) and inter-phonon collisions. The Monte-Carlo (MC) method has found prolific use in the solution of the Boltzmann Transport Equation (BTE) for phonons. This thesis contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions-in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that Transverse Acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T > 200 K), Longitudinal Acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50-200 K) and increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. For thin film thermal conductivity predictions, it has been found that the dimensionality of the computational domain has no impact on the accuracy of the numerical solution. In the diffusion dominated regime, three-dimensional Monte-Carlo calculations are found to be comparable to two-dimensional Monte-Carlo calculations in terms of computational efficiency. It has also been found that irrespective of dimensionality of the computational domain, the impact of the size of the lateral boundaries can be accounted for by tuning the resistance provided by the boundaries, i.e., the degree of specularity. It is also shown that the time averaging of the statistically stationary data can be used to reduce statistical noise and can result in considerable computational savings.
Sandip Mazumder, PhD (Advisor)
Vishwanath Subramaniam, PhD (Committee Member)
99 p.
Mechanical Engineering
Monte Carlo; Boltzmann Transport Equation; thin film; thermal conductivity; optical phonon; silicon

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Citations

  • Mittal, A. (2009). Monte-Carlo Study of Phonon Heat Conduction in Silicon Thin Films [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1259602975

    APA Style (7th edition)

  • Mittal, Arpit. Monte-Carlo Study of Phonon Heat Conduction in Silicon Thin Films. 2009. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1259602975.

    MLA Style (8th edition)

  • Mittal, Arpit. "Monte-Carlo Study of Phonon Heat Conduction in Silicon Thin Films." Master's thesis, Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1259602975

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.
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