Assessment of Fourier-Based Thermal Models Used in Frequency-Domain Thermoreflectance Data Analysis

2012 ◽  
Author(s):  
D. P. Sellan ◽  
V. Mishra ◽  
J. A. Malen ◽  
A. J. H. McGaughey ◽  
C. H. Amon
Keyword(s):  
Data Analysis ◽  
Frequency Domain ◽  
Modulation Frequency ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Temperature Modulation ◽  
Temperature Profiles ◽  
Boltzmann Transport ◽  
Bulk Phonon ◽  
Phonon Relaxation Time

We assess a Fourier-based thermal model used in frequency-domain thermoreflectance data analysis. The Boltzmann transport equation (BTE) is first used to simulate sub-continuum phonon transport in a semi-infinite solid. We then compare the BTE-predicted temperature profiles to those predicted by an analytical solution of the Fourier-based conduction equation. The two models agree well when ωτ < 1, where ω is the surface-temperature modulation-frequency and τ is the bulk phonon relaxation time, but diverge when ωτ > 1.

FREQUENCY DEPENDENT PHONON TRANSPORT IN TWO-DIMENSIONAL SILICON AND DIAMOND THIN FILMS

2012 ◽  
Vol 26 (17) ◽  
pp. 1250104 ◽  
Author(s):  
B. S. YILBAS ◽  
S. BIN MANSOOR
Keyword(s):  
Thin Films ◽  
Boltzmann Transport Equation ◽  
Diamond Films ◽  
Equilibrium Temperature ◽  
Phonon Transport ◽  
Two Dimensional ◽  
Boltzmann Transport ◽  
Frequency Dependent ◽  
Aluminum Films ◽  
The Difference

Phonon transport in two-dimensional silicon and aluminum films is investigated. The frequency dependent solution of Boltzmann transport equation is obtained numerically to account for the acoustic and optical phonon branches. The influence of film size on equivalent equilibrium temperature distribution in silicon and aluminum films is presented. It is found that increasing film width influences phonon transport in the film; in which case, the difference between the equivalent equilibrium temperature due to silicon and diamond films becomes smaller for wider films than that of the thinner films.

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.

Statistical Phonon Transport Model of Thermal Transport in Silicon

2009 ◽  
Vol 1229 ◽  
Author(s):  
Thomas W Brown ◽  
Edward Hensel
Keyword(s):  
Thermal Transport ◽  
Lattice Dynamics ◽  
Transport Model ◽  
Silicon Nanowire ◽  
Boltzmann Transport Equation ◽  
Momentum Conservation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Crystalline Materials ◽  
Statistical Framework

AbstractThermal transport in crystalline materials at various length scales can be modeled by the Boltzmann transport equation (BTE). A statistical phonon transport (SPT) model is presented that solves the BTE in a statistical framework that incorporates a unique state-based phonon transport methodology. Anisotropy of the first Brillouin zone (BZ) is captured by utilizing directionally-dependent dispersion curves obtained from lattice dynamics calculations. A rigorous implementation of phonon energy and pseudo-momentum conservation is implemented in the ballistic thermal transport regime for a homogeneous silicon nanowire with adiabatic specular boundary conditions.

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.

Phonon Transport Across Mesoscopic Constrictions

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Dhruv Singh ◽  
Jayathi Y. Murthy ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Resistance ◽  
Numerical Solution ◽  
Entire Range ◽  
Practical Importance ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Total Thermal Resistance ◽  
Constriction Resistance ◽  
Analytical Expressions

Phonon transport across constrictions formed by a nanowire or a nanoparticle on a substrate is studied by a numerical solution of the gray Boltzmann transport equation (BTE) resolving the effects of two length scales that govern problems of practical importance. Predictions of total thermal resistance for wire/substrate and particle/substrate combinations are made for the entire range of Knudsen number, with an emphasis on resolving transport in the mesoscopic regime where ballistic-diffusive mechanisms operate and analytical expressions are not available. The relative magnitudes of bulk and constriction resistance are established, and a correlation for overall thermal resistance spanning the range of practical Knudsen numbers is provided.

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.

Heat Pulse Propagation in Silicon Nanostructures by Solving Phonon Transport Equation

2008 ◽  
Author(s):  
Damian Terris ◽  
Karl Joulain ◽  
Denis Lemonnier
Keyword(s):  
Transport Equation ◽  
Pulse Propagation ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Isotropic Scattering ◽  
Silicon Nanostructures ◽  
Boltzmann Transport ◽  
Discrete Ordinate ◽  
Rectangular Mesh ◽  
Angle Space

The temperature evolution prediction of silicon nanofilms and nanowires can be useful to safeguard high technology systems of its deterioration. The simulation of a level and a pulse in these nanostructures is then made with Boltzmann Transport Equation (BTE) resolution using the single time approximation. The Discrete Ordinate (DO) method helps to numerate the angle space. BTE is written in cylindrical coordinates which corresponds to wires. Therefore, the cylindrical plane is considered as an isotropic scattering to mimic a nanowire and then, as a specular reflexion (which conserve z momentum) to simulate a nanofilm. Using the axisymmetry done with a specular reflexion, the cylinder is two dimensionally discretized with a regular rectangular mesh.

The first-principles and BTE investigation of phonon transport in 1T-TiSe2

2021 ◽  
Author(s):  
Zhao-Liang Wang ◽  
Guofu Chen ◽  
Xiaoliang Zhang ◽  
Dawei Tang
Keyword(s):  
Density Functional Theory ◽  
Transport Equation ◽  
First Principles ◽  
Density Functional ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Functional Theory

Through the first-principles density functional theory and the phonon Boltzmann transport equation, we investigated the phonon transport characteristics inside 1T-TiSe2.

Validation of a Unified Nondiffusive-Diffusive Phonon Transport Model for Nanoscale Heat Transfer Simulations

2014 ◽  
Author(s):  
Ashok T. Ramu ◽  
Yanbao Ma
Keyword(s):  
Heat Transfer ◽  
Spatial Dependence ◽  
Hot Spots ◽  
Transport Model ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
High Fidelity ◽  
Boltzmann Transport ◽  
Fourier Law ◽  
Limiting Case

Heat transfer in the vicinity of nanoscale hot-spots is qualitatively different from that in the macroscale, which effect stems from the breakdown of Fourier law due to phonon nondiffusive transport. In this work, we validate a recently proposed alternative, high-fidelity phonon transport model, the unified nondiffusive-diffusive (UND) model, which takes into account the mixed ballistic-diffusive nature of heat transport, as well as reduces to the Fourier law as a limiting case. In the UND model, the nondiffusive phonons are treated using the Boltzmann transport equation, while the diffusive phonon gas is treated by the Fourier law. The numerical results of Maznev et al. for the geometry and spatial dependence of variables corresponding to the transient gratings experiments of Johnson et al. are used for validation of the model.

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