Cross-plane heat conduction in nanoporous silicon thin films by phonon Boltzmann transport equation and Monte Carlo simulations

2017 ◽  
Vol 111 ◽  
pp. 1401-1408 ◽  
Author(s):  
Yu-Chao Hua ◽  
Bing-Yang Cao
Keyword(s):  
Thin Films ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Monte Carlo Simulations ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Nanoporous Silicon ◽  
Silicon Thin Films

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films: Role of Optical Phonons

2009 ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Optical Phonons ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

The Monte Carlo (MC) method has found prolific use in the solution of the Boltzmann Transport Equation (BTE) for phonons for the prediction of non-equilibrium heat conduction in crystalline thin films. This paper 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 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 > 200K), 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. At room temperature, optical modes are found to carry about 25% of the energy at steady state in Silicon thin films. Most importantly, inclusion of optical phonons results in better match with experimental observations for Silicon thin-film thermal conductivity.

Thermal Conductivity and Phonon Engineering in Low-Dimensional Structures

1998 ◽  
Vol 545 ◽  
Author(s):  
G. Chen ◽  
S. G. Volz ◽  
T. Borca-Tasciuc ◽  
T. Zeng ◽  
D. Song ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Model Based ◽  
Conduction Mechanisms ◽  
Interface Scattering ◽  
Low Dimensional

AbstractUnderstanding phonon heat conduction mechanisms in low-dimensional structures is of critical importance for low-dimensional thermoelectricity. In this paper, we discuss heat conduction mechanisms in two-dimensional (2D) and one-dimensional (1D) structures. Models based on both the phonon wave picture and particle picture are developed for heat conduction in 2D superlattices. The phonon wave model, based on the acoustic wave equations, includes the effects of phonon interference and tunneling, while the particle model, based on the Boltzmann transport equation, treats the internal as well interface scattering of phonons. For 1D systems, both the Boltzmann transport equation and molecular dynamics simulation approaches are employed. Comparing the modeling results with experimental data suggest that the interface scattering of phonons plays a crucial role in the thermal conductivity of low-dimensional structures. We also discuss the minimum thermal conductivity of low-dimensional structures based on a generalized thermal conductivity integral, and suggest that the minimum thermal conductivities of low-dimensional systems may differ from those of their corresponding bulk materials. The discussion leads to alternative ways to reduce thermal conductivity based on the propagating phonon modes.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Arpit Mittal ◽  
Sandip Mazumder
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Phonon Scattering ◽  
Computational Domain ◽  
Optical Phonons ◽  
Phonon Modes ◽  
Silicon Thin Film ◽  
Silicon Thin Films

Abstract The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper 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 to 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.

scholarly journals Spherical Harmonic Modeling of a 0.05 μm Base BJT: A Comparison with Monte Carlo and Asymptotic Analysis

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 147-151 ◽  
Author(s):  
C.-H. Chang ◽  
C.-K. Lin ◽  
N. Goldsman ◽  
I. D. Mayergoyz
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Band Structure ◽  
Asymptotic Analysis ◽  
Energy Distribution ◽  
Transport Equation ◽  
Spherical Harmonic ◽  
Boltzmann Transport Equation ◽  
System Of Equations ◽  
Boltzmann Transport

We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm base BJT. We find the SH and the MC methods give very similar results for the energy distribution function, using an analytical band-structure, at all points within the tested devices. However, the SH method can be as much as seven thousand times faster than the MC approach for solving an identical problem. We explain the agreement by asymptotic analysis of the system of equations generated by the SH expansion of the BTE.

Prediction of Non-Equilibrium Heat Conduction Using Parallel Computation of the Phonon Boltzmann Transport Equation

2014 ◽  
Author(s):  
Syed A. Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Parallel Computation ◽  
Large Scale ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Computational Time ◽  
Spectral Space ◽  
Boltzmann Transport ◽  
Non Equilibrium

Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In this article, strategies and algorithms for large-scale parallel computation of the phonon BTE are presented. An unstructured finite volume method for spatial discretization is coupled with the control angle discrete ordinates method for angular discretization. The single-time relaxation approximation is used to treat phonon-phonon scattering. Both dispersion and polarization of the phonons are accounted for. Three different parallelization strategies are explored: (a) band-based, (b) direction-based, and (c) hybrid band/cell-based. Subsequent to validation studies in which silicon thin-film thermal conductivity was successfully predicted, transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral cells. The angular space was discretized using 400 angles, and the spectral space was discretized into 40 spectral intervals (bands). This resulted in ∼9.7×109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-based and hybrid band/cell-based parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy — about 88% — was found to be superior to that of the direction-based strategy, and is recommended as the preferred strategy for even larger scale computations.

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