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Research Papers

Comparison of Atomistic and Continuum Methods for Calculating Ballistic Phonon Transmission in Nanoscale Waveguides

[+] Author and Article Information
Drew A. Cheney

e-mail: dcheney@seas.upenn.edu

Jennifer R. Lukes

e-mail: jrlukes@seas.upenn.edu
Department of Mechanical Engineering and
Applied Mechanics,
University of Pennsylvania,
Philadelphia, PA 19104

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 3, 2012; final manuscript received March 8, 2013; published online July 26, 2013. Assoc. Editor: Pamela M. Norris.

J. Heat Transfer 135(9), 091101 (Jul 26, 2013) (9 pages) Paper No: HT-12-1347; doi: 10.1115/1.4024355 History: Received July 03, 2012; Revised March 08, 2013

We compare two methods for the calculation of mode dependent ballistic phonon transmission in nanoscale waveguides. The first method is based on continuum acoustic waveguide theory and uses an eigenmode expansion to solve for phonon transmission coefficients. The second method uses lattice dynamics (LD)-computed mode shapes to excite guided phonon wavepackets in a nonequilibrium molecular dynamics (MD) simulation and calculates phonon transmission from the final distribution of system energy. The two methods are compared for the case of shear-horizontal (SH) phonons propagating in a planar waveguide with a T-stub irregularity, a geometry which has been proposed for the tuning of phonon transmission and nanostructure thermal conductance. Our comparison highlights advantages and disadvantages of the two methods and illustrates regimes when atomistic effects are prominent and continuum approaches are not appropriate.

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References

Figures

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Fig. 1

T-stub-waveguide geometry

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Fig. 2

Description of supercell. In this figure Ncell = 6. Blue atoms at the upper and lower boundaries are held fixed.

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Fig. 3

Molecular dynamics computational geometry

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Fig. 4

Illustration of wavepacket width for kx = 0.250 (1/σ). Wider wavepackets better approximate phonons of single wavenumber.

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Fig. 5

Dispersion relations of four different atomistic waveguide leads simulated: (a) 2 cells wide, (b) 4 cells wide, (c) 6 cells wide, and (d) 8 cells wide. Only the highlighted branches (SH1-heavy solid line, SH2-heavy dashed line) are investigated in this study.

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Fig. 6

Transmission dependence on wave packet width for 2 cell waveguide. Upper set of data points correspond to SH1 at kx = 0.159 (1/σ). Lower set of data points correspond to SH1 at kx = 0.111 (1/σ). Marker shapes correspond to different domain sizes: triangles (Lwaveguide = 259.2 σ), crosses (Lwaveguide = 518.4 σ), circles (Lwaveguide = 2073.8 σ), squares (Lwaveguide = 2592.2 σ).

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Fig. 7

SH1 transmission dependence on wave packet width for 6 cell waveguide. Results are shown across a range of wavenumber and compared with the continuum result obtained from technique presented in Sec. 2.

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Fig. 8

Snap-shots of z-displacement field for different values of wavenumber for incident SH1 mode. Extrema in transmission correspond to formation of standing waves in T-stub region.

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Fig. 9

Transmission of SH1 mode for different sized waveguide leads. For all cases, hII* = 2.0 and d* = 1.0. Agreement with continuum is best for the thicker waveguide leads (6 cell and 8 cell) and at lower frequencies.

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Fig. 10

Transmission of SH2 mode for different sized waveguide leads

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