Improved Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2009 ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation ◽  
Thermal Conductivities

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time phonon BTE model employs a single-mode relaxation time idea, but the relaxation time is a function of wave-vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior as well as relaxation times satisfying conservation rules. A critical issue in the model development is the accounting for the role of three-phonon N scattering processes. Direct inclusion of N processes into the anisotropic relaxation time model is not possible because such an inclusion would engender thermal resistance. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulation by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted bulk thermal conductivities of silicon and silicon thin-film thermal conductivities with experimental measurements.

Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Thermal Transport ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.

DSMC for Phonon Transport in Solid Thin Films

2009 ◽  
Author(s):  
Mitsuhiro Matsumoto ◽  
Masaya Okano
Keyword(s):  
Heat Transfer ◽  
Thin Films ◽  
Relaxation Time ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Thermal Design ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Phonon Dynamics ◽  
Solid Thin Films

As the scale of electronic devices decreases, heat transfer analysis and thermal design becomes more important. In particular, heat transfer through various solid thin films is strongly affected by thickness dependence of thermal conductivity and interfacial thermal resistance. Analysis of phonon dynamics based on a linearized Boltzmann transport equation, or the so-called relaxation time approximation, has been widely used, but detailed analysis using molecular dynamics simulation reveals that couplings among various phonon modes can affect the energy transfer. In this study, we propose a DSMC scheme to simulate phonon dynamics starting from the original Boltzmann transport equation. In contrast to the linearized model, this scheme requires no relaxation time as an input parameter, and we can investigate the couplings among phonons with different modes, although we have to assume some appropriate model of phonon-phonon collisions. As a test calculation, energy flux was evaluated for model thin films of various thicknesses, and a phenomenon similar to the Casimir limit was retrieved. This scheme will enable us to include other factors, such as phonon-electron couplings.

Modeling Nanoscale Thermal Transport via the Boltzmann Transport Equation

2004 ◽  
Author(s):  
Cristina H. Amon ◽  
Jayathi Y. Murthy ◽  
Sreekant V. J. Narumanchi
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Group Velocity ◽  
Phonon Dispersion ◽  
Dispersion Model ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Solution Methods

In modern microelectronics, where extreme miniaturization has led to feature sizes in the sub-micron and nanoscale range, Fourier diffusion has been found to be inadequate for the prediction of heat conduction. Over the past decade, the phonon Boltzmann transport equation (BTE) in the relaxation time approximation has been employed to make thermal predictions in dielectrics and semiconductors at micron and nanoscales. This paper presents a review of the BTE-based solution methods widely employed in the literature. Particular attention is given to the problem of self-heating (hotspot) in sub-micron transistors. First, the solution approaches based on the gray formulation of the BTE are presented. In this class of solution methods, phonons are characterized by one single group velocity and relaxation time. Phonon dispersion is not accounted for in any detail. This is the most widely employed approach in the literature. The semi-gray BTE approach, moments of the Boltzmann equation, the lattice Boltzmann approach, and the ballistic-diffusive approximation are presented. Models which incorporate greater details of phonon dispersion are also discussed. This includes a full phonon dispersion model developed recently by the authors. This full phonon dispersion model satisfies energy conservation, incorporates the different phonon modes, and well as the interactions between the different modes, and accounts for the frequency dependence for both the phonon group velocity and relaxation times. Results which illustrate the differences between some of these models reveal the importance of developing models that incorporate substantial details of phonon physics.

Modeling of Localized Heating Effect in Sub-Micron Silicon Transistors

2003 ◽  
Author(s):  
Keivan Etessam-Yazdani ◽  
Sadegh M. Sadeghipour ◽  
Mehdi Asheghi
Keyword(s):  
Transport Equation ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Heat Diffusion ◽  
Normal Operation ◽  
Heating Effect ◽  
Boltzmann Transport ◽  
Heat Diffusion Equation ◽  
Localized Heating

The performance and reliability of sub-micron semiconductor transistors demands accurate modeling of electron and phonon transport at nanoscales. The continued downscaling of the critical dimensions, introduces hotspots, inside transistors, with dimensions much smaller than phonon mean free path. This phenomenon, known as localized heating effect, results in a relatively high temperature at the hotspot that cannot be predicted using heat diffusion equation. While the contribution of the localized heating effect to the total device thermal resistance is significant during the normal operation of transistors, it has even greater implications for the thermoelectrical behavior of the device during an electrostatic discharge (ESD) event. The Boltzmann transport equation (BTE) can be used to capture the ballistic phonon transport in the vicinity of a hot spot but many of the existing solutions are limited to the one-dimensional and simple geometry configurations. We report our initial progress in solving the two dimensional Boltzmann transport equation for a hot spot in an infinite media (silicon) with constant temperature boundary condition and uniform heat generation configuration.

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.

Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics Simulations and Theoretical Calculation

2011 ◽  
Vol 55-57 ◽  
pp. 1152-1155 ◽  
Author(s):  
Xing Li Zhang ◽  
Zhao Wei Sun
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Dynamics Simulation ◽  
Boltzmann Transport ◽  
Silicon Thin Films ◽  
Simulation Results ◽  
Dynamics Simulations ◽  
Good Agreement

Molecular, dynamics simulation and the Boltzmann transport equation are used respectively to analyze the phonon transport in Si thin film. The MD result is in good agreement with the theoretical analysis values. The results show that the calculated thermal conductivity decreases almost linearly as the film thickness reduced and is almost independent of the temperature at the nanoscale. It was observed from the simulation results that there exists the obvious size effect on the thermal conductivity.

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