Research Papers: Micro/Nanoscale Heat Transfer

Hierarchical Modeling of Heat Transfer in Silicon-Based Electronic Devices

[+] Author and Article Information
Javier V. Goicochea

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

Marcela Madrid

 Pittsburgh Supercomputing Center, Pittsburgh, PA 15213

Cristina Amon

Department of Mechanical and Industrial Engineering, University of Toronto, ON, M5S 1A4, Canada

J. Heat Transfer 132(10), 102401 (Jul 23, 2010) (11 pages) doi:10.1115/1.4001644 History: Received May 08, 2008; Revised April 13, 2010; Published July 23, 2010; Online July 23, 2010

A hierarchical model of heat transfer for the thermal analysis of electronic devices is presented. The integration of participating scales (from nanoscale to macroscales) is achieved by (i) estimating the input parameters and thermal properties to solve the Boltzmann transport equation (BTE) for phonons using molecular dynamics (MD), including phonon relaxation times, dispersion relations, group velocities, and specific heat, (ii) applying quantum corrections to the MD results to make them suitable for the solution of BTE, and (iii) numerically solving the BTE in space and time subject to different boundary and initial conditions. We apply our hierarchical model to estimate the silicon out-of-plane thermal conductivity and the thermal response of an silicon on insulator (SOI) device subject to Joule heating. We have found that relative phonon contribution to the overall conductivity changes as the dimension of the domain is reduced as a result of phonon confinement. The observed reduction in the thermal conductivity is produced by the progressive transition of modes in the diffusive regime (as in the bulk) to transitional and ballistic regimes as the film thickness is decreased. In addition, we have found that relaxation time expressions for optical phonons are important to describe the transient response of SOI devices and that the characteristic transport regimes, determined with Holland and Klemens phonon models, differ significantly.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Step 1: Estimation of different properties and relaxation times with MD

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Figure 2

Steps 2 and 3: Quantum correction of MD properties and solution of the BTE

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Figure 3

Mode specific heat after quantum corrections. Arrows indicate the frequency range of each mode.

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Figure 4

Effect of the isotope scattering term in the phonon mean free path. The thin dotted line presents the edge of the BZ.

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Figure 5

One-dimensional domain used to estimate the out-of-plane thermal conductivity

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Figure 6

Silicon thin film out-of-plane thermal conductivity as a function of film thickness at 220 K

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Figure 7

Variation in Knudsen number with respect to frequency for a film thickness of 1000 nm at 220 K (a) and 1000 K (b). The dashed line represents the edge of the BZ.

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Figure 8

Variation in mode thermal conductivity as a function of film thickness at 220 K

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Figure 9

Mode thermal conductivity contribution as a function of thickness

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Figure 10

One-dimensional domain used to model the silicon layer of a SOI transistor

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Figure 11

Temperature evolution at the center of the hotspot for a film of 100 nm. (a) Heat generated is distributed over all phonon modes, (b) Heat generated is distributed only in LO mode.

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Figure 12

Temperature evolution at the center of the hotspot for different film thicknesses. Hotspot size is 1/10 of the thickness of the film. Heat generated is distributed over all phonon modes (a) and through the LO mode (b).

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Figure 13

Contribution of the TA, LA, LO, and TO modes to the reduced phonon total energy as a function of reduced time for films thicknesses of 10 nm (a) and 100 nm (b)

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Figure 14

Temperature at the center of the hotspot for a film of 100 nm as a function of time, obtained from Holland, and Han and Klemens phonon relaxation times models




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