Electronic Thermal Conduction in Thin Gold Films

2003 ◽  
Author(s):  
Basil T. Wong ◽  
M. Pinar Mengu¨c¸
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Thermal Conduction ◽  
Gold Film ◽  
Boltzmann Transport Equation ◽  
Gold Films ◽  
Temperature Profiles ◽  
Boltzmann Transport ◽  
Fourier Law ◽  
Thin Gold Film

In this work, electronic thermal conduction in thin gold film is modeled via the Boltzmann Transport Equation (BTE). The BTE is solved using a Monte Carlo Method (MCM). Temperature profiles for various film thicknesses are computed. Results show that the electronic thermal transport in gold is still diffusion-like at film thicknesses as small as 100 nm, implying that the Fourier law of conduction can be applied at this scale to predict the steady-state thermal heat transfer without comprising the physics. However, the Fourier law does not predict the temperature profiles accurately if the film thickness is reduced to 10 nm or below.

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.

scholarly journals Low-Variance Monte Carlo Simulation of Thermal Transport in Graphene

2012 ◽  
Author(s):  
Colin Landon ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Thermal Management ◽  
Numerical Solutions ◽  
Graphene Nanoribbons ◽  
Boltzmann Transport Equation ◽  
Approximate Solutions ◽  
Simulation Method ◽  
Boltzmann Transport ◽  
Kinetic Description

Due to its unique thermal properties, graphene has generated considerable interest in the context of thermal management applications. In order to correctly treat heat transfer in this material, while still reaching device-level length and time scales, a kinetic description, such as the Boltzmann transport equation, is typically required. We present a Monte Carlo method for obtaining numerical solutions of this description that dramatically outperforms traditional Monte Carlo approaches by simulating only the deviation from equilibrium. We validate the simulation method using an analytical solution of the Boltzmann equation for long graphene nanoribbons; we also use this result to characterize the error associated with previous approximate solutions of this problem.

Study the Heat Transfer Process From Electron-Phonon Nonequilibrium in Thin Gold Film to Glass Substrate Through Transient Thermoreflectance Measurements

2010 ◽  
Author(s):  
Weigang Ma ◽  
Haidong Wang ◽  
Xing Zhang ◽  
Wei Wang
Keyword(s):  
Heat Transfer ◽  
Transfer Process ◽  
Borosilicate Glass ◽  
Glass Substrate ◽  
Physical Vapor Deposition ◽  
Gold Film ◽  
Coupling Factor ◽  
Heat Transfer Process ◽  
Thin Gold Film ◽  
Open Question

How the energy transfers during electron-phonon nonequilibrium in thin metal films is still an open question, and how to measure the intrinsic thermal transport properties of the material under the covering layer is another challenge. In this paper, the heat transfer process from electron-phonon nonequilibrium in thin gold film to borosilicate glass substrate has been studied by resorting to different segments of the transient thermoreflectance signal, which is obtained from the rear-pump front-probe transient thermoreflectance technique. The gold film, which has a thickness of 23.1 nm, is deposited on the borosilicate glass substrate using using a physical vapor deposition (PVD) approach. Within the framework of the two-temperature model (TTM), the electron-phonon (e-ph) coupling factors of the gold film, which reflect the strength of heat flow from hot electrons to cold phonons, are derived from the signal taken after the first several picoseconds with different pump fluences, and the measured value is (1.95–2.05)×1016 W m−3 K−1. The electron-phonon coupling factor does not significantly change in response to the pump pulse fluence variation and exhibits little change compared to the bulk gold value 2.4×1016 W m−3 K−1. Furthermore, the thermal conductivity of the glass substrate is obtained through the thermoreflectance signal between 20 to 140 picoseconds and the value is W m−1 K−1.

Study of an Iterative Solution for Boltzmann Transport Equation and Calculation of Thermal Conductivity

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Iterative Method ◽  
Transport Equation ◽  
Linear Systems ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Boltzmann Transport

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.

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.

Modeling Electron-Phonon Nonequilibrium in Gold Films Using Boltzmann Transport Model

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Arvind Pattamatta ◽  
Cyrus K. Madnia
Keyword(s):  
Film Thickness ◽  
Pulse Duration ◽  
Laser Fluence ◽  
Laser Heating ◽  
Gold Film ◽  
Transport Model ◽  
Melting Time ◽  
Gold Films ◽  
Boltzmann Transport ◽  
Energy Carriers

Ultrashort-pulsed laser irradiation on metals creates a thermal nonequilibrium between electrons and the phonons. Previous computational studies used the two-temperature model and its variants to model this nonequilibrium. However, when the laser pulse duration is smaller than the relaxation time of the energy carriers or when the carriers’ mean free path is larger than the material dimension, these macroscopic models fail to capture the physics accurately. In this paper, the nonequilibrium between energy carriers is modeled via a numerical solution of the Boltzmann transport model (BTM) for electrons and phonons, which is applicable over a wide range of lengths and time scales. The BTM is solved using the discontinuous Galerkin finite element method for spatial discretization and the three-step Runge–Kutta temporal discretization. Temperature dependent electron-phonon coupling factor and electron heat capacity are used due to the strong electron-phonon nonequilibrium considered in this study. The results from the proposed model are compared with existing experimental studies on laser heating of macroscale materials. The model is then used to study laser heating of gold films, by varying parameters such as the film thickness, laser fluence, and pulse duration. It is found that the temporal evolution of electron and phonon temperatures in nanometer size gold films is very different from the macroscale films. For a given laser fluence and pulse duration, the peak electron temperature increases with a decrease in the thickness of the gold film. Both film thickness and laser fluence significantly affect the melting time. For a fluence of 1000 J/m2, and a pulse duration of 75 fs, gold films of thickness smaller than 100 nm melt before reaching electron-phonon equilibrium. However, for the film thickness of 2000 nm, even with the highest laser fluence examined, the electrons and phonons reach equilibrium and the gold film does not melt.

LOCALIZED SURFACE PLASMON OF THIN GOLD FILM WITH PERIODIC ARRAYS OF NANOHOLES

2009 ◽  
Vol 23 (02) ◽  
pp. 147-153 ◽  
Author(s):  
ZONG-SUO ZHANG ◽  
XIONG-RUI SU ◽  
JIAN-BO LI ◽  
ZHONG-HUA HAO ◽  
LI ZHOU
Keyword(s):  
Surface Plasmon ◽  
Gold Film ◽  
Dipole Approximation ◽  
Resonance Peak ◽  
Localized Surface Plasmon ◽  
Gold Films ◽  
Thin Gold Film ◽  
Periodic Arrays ◽  
Edge Separation ◽  
Plasmon Polaritons

The localized surface plasmon (LSP) resonances properties of periodic arrays of nanoholes in thin gold films are investigated by using the method of discrete dipole approximation (DDA). The surface plasmon polaritons (SPPs) play important roles in amplification or suppression of the LSP resonances in the film. The LSP-SPP coupling is affirmed based on the extinction spectra calculated by the DDA. The intensity of the LSP resonances can be controlled through changing the edge-to-edge separation distances between nanoholes, the number and the diameter of the nanoholes. The calculations also indicate that the LSP resonance peak decreases with increasing the thickness of the gold film.

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