Thermal Conductivity of Graphene Layers Encased in Oxide

Author(s):  
Zhen Chen ◽  
Wanyoung Jang ◽  
Wenzhong Bao ◽  
Chun Ning Lau ◽  
Chris Dames

Experimental knowledge of the heat flow along graphene layers encased by oxide is essential for future graphene-based nanoelectronics, interconnects, and thermal management structures. We used a “heat spreader method” to study the heat dissipation performance of encased graphene. Fitting the experimental data with a three-dimensional finite-element method (FEM) allows the in-plane thermal conductivity of the graphene layers to be extracted. The method is validated on samples with metal films of known thermal conductivity, as determined from electrical resistance measurements and the Wiedemann-Franz law.

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Siva P. Gurrum ◽  
William P. King ◽  
Yogendra K. Joshi ◽  
Koneru Ramakrishna

A technique to extract in-plane thermal conductivity of thin metallic films whose thickness is comparable to electron mean free path is described. Microscale constrictions were fabricated into gold films of thicknesses 43nm and 131nm. A sinusoidal voltage excitation across the constriction results in a local temperature rise. An existing technique known as scanning joule expansion microscopy, measures the corresponding periodic thermomechanical expansion with a 10nm resolution and determines the local temperature gradient near the constriction. A three-dimensional finite-element simulation of the frequency-domain heat transfer fits the in-plane thermal conductivity to the measured data, finding thermal conductivities of 82±7.7W∕mK for the 43nm film and 162±16.7W∕mK for the 131nm film, at a heating frequencies of 100kHz and 90kHz, respectively. These values are significantly smaller than the bulk thermal conductivity value of 318W∕mK for gold, showing the electron size effect due to the metal-dielectric interface and grain boundary scattering. The obtained values are close to the thermal conductivity values, which are derived from electrical conductivity measurements after using the Wiedemann–Franz law. Because the technique does not require suspended metal bridges, it captures true metal-dielectric interface scattering characteristics. The technique can be extended to other films that can carry current and result in Joule heating, such as doped single crystal or polycrystalline semiconductors.


Volume 1 ◽  
2004 ◽  
Author(s):  
Eric N. Schmierer ◽  
Jason Paquette ◽  
Arsalan Razani ◽  
Kwang J. Kim

Geometric models are used to simplify the complex, three-dimensional geometry of metal foams for calculations of effective thermal conductivity. The first is based on a conventional three-dimensional cubic lattice and the second is a tetrakaidecahedronal model. The models consist of interconnecting ligaments with a spherical node at their intersections. The geometry of the foam is determined based on two dimensionless parameters: 1) the porosity and 2) the product of the specific surface area of the foam and the length of the interconnecting ligaments. A free parameter represents the size of the lumps at the ligament interconnections. It is shown that the remaining unknown geometric parameters of the models can be obtained as a solution of a cubic equation that has only one acceptable solution. From the cubic lattice model, a one-dimensional heat conduction analytical model is used to find the effective thermal conductivity of fully saturated metal foam. A three-dimensional finite element calculation of the effective thermal conductivity for the cubic lattice is then compared to the one-dimensional model. In the case of the tetrakaidecahedronal model, a similar three-dimensional finite element calculation is performed to find the effective thermal conductivity. Anisotropy of the models is explored. The results of the models are compared with experimental results from this study and the literature to substantiate their accuracy. The experimental results are reported for fully saturated aluminum metal foam in air, water, and oil. Results show that both the cubic lattice model, which is less complex, and the tetrakaidecahedronal model can both be used to represent one-dimensional effective thermal conductivity. Finally, the dimensionless surface areas for each geometric model are compared. The models produce significantly different surface areas, and therefore do not both represent the density and specific surface area of foam accurately.


2007 ◽  
Vol 35 (3) ◽  
pp. 226-238 ◽  
Author(s):  
K. M. Jeong ◽  
K. W. Kim ◽  
H. G. Beom ◽  
J. U. Park

Abstract The effects of variations in stiffness and geometry on the nonuniformity of tires are investigated by using the finite element analysis. In order to evaluate tire uniformity, a three-dimensional finite element model of the tire with imperfections is developed. This paper considers how imperfections, such as variations in stiffness or geometry and run-out, contribute to detrimental effects on tire nonuniformity. It is found that the radial force variation of a tire with imperfections depends strongly on the geometrical variations of the tire.


1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.


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