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Research Papers: Micro/Nanoscale Heat Transfer

Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces

[+] Author and Article Information
Dhruv Singh1

Mem. ASME e-mail: singh36@purdue.edu

Jayathi Y. Murthy2

Mem. ASME e-mail: jmurthy@ecn.purdue.eduMem. ASME e-mail:tsfisher@ecn.purdue.edu School of Mechanical Engineering and Birck Nanotechnology Center,  Purdue University, West Lafayette, IN 47907; Air Force Research Laboratory, Thermal Sciences and Materials Branch (AFRL/RXBT), Wright-Patterson AFB, OH 45433-7750

Timothy S. Fisher

Mem. ASME e-mail: jmurthy@ecn.purdue.eduMem. ASME e-mail:tsfisher@ecn.purdue.edu School of Mechanical Engineering and Birck Nanotechnology Center,  Purdue University, West Lafayette, IN 47907; Air Force Research Laboratory, Thermal Sciences and Materials Branch (AFRL/RXBT), Wright-Patterson AFB, OH 45433-7750

1

Present address: Intel Corporation, Hillsboro, OR 97124.

2

Corresponding author.

J. Heat Transfer 133(12), 122401 (Oct 05, 2011) (11 pages) doi:10.1115/1.4004429 History: Received May 14, 2010; Accepted June 03, 2011; Published October 05, 2011; Online October 05, 2011

We report finite-volume simulations of the phonon Boltzmann transport equation (BTE) for heat conduction across the heterogeneous interfaces in SiGe superlattices. The diffuse mismatch model incorporating phonon dispersion and polarization is implemented over a wide range of Knudsen numbers. The results indicate that the thermal conductivity of a Si/Ge superlattice is much lower than that of the constitutive bulk materials for superlattice periods in the submicron regime. We report results for effective thermal conductivity of various material volume fractions and superlattice periods. Details of the nonequilibrium energy exchange between optical and acoustic phonons that originate from the mismatch of phonon spectra in silicon and germanium are delineated for the first time. Conditions are identified for which this effect can produce significantly more thermal resistance than that due to boundary scattering of phonons.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 7

Fractional contribution to heat flux of various phonon groups for L = 400 nm. x* = 0.5 represents the position of the interface between Si and Ge.

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Figure 8

Fractional contribution to heat flux of various phonon groups for L = 10 nm. x* = 0.5 represents the position of the interface between Si and Ge.

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Figure 9

Lattice, acoustic phonon, and optical phonon temperature across the superlattice unit cell for LP  = 20 and 1000 nm and ϕ = 0.5

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Figure 10

Fractional heat flux versus nondimensional position for LSi  = 10 nm, 60 nm, and 100 nm at ϕ = 0.5

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Figure 11

Thermal conductivity of superlattice (at 300 K) as a function of the period length at various values of Si volume fraction ϕSi

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Figure 1

(a) Domain for single interface simulation and (b) periodic unit cell of the superlattice

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Figure 2

Schematic of phonon transport across a Si–Ge interface

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Figure 3

Comparison of empirically calculated relaxation time using Eq. 15 versus those computed from molecular dynamics in Ref. [48] for phonons in [100] direction of silicon at 300 K

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Figure 4

(a) Phonon dispersion in Si and Ge along [100] direction and (b) mean free path of phonons in Si and Ge

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Figure 5

Heat flux across the domain for varying L

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Figure 6

Lattice, acoustic phonon, and optical phonon temperature across the domain for L = 10 nm, 50 nm, and 400 nm

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