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RESEARCH PAPERS: Micro/Nanoscale Heat Transfer

# Simulation of Interfacial Phonon Transport in Si–Ge Heterostructures Using an Atomistic Green’s Function Method

[+] Author and Article Information
W. Zhang

School of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907

T. S. Fisher

School of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907tsfisher@purdue.edu

N. Mingo

NASA-Ames Center for Nanotechnology, 229-1, Moffett Field, CA 94035

1

Corresponding author.

J. Heat Transfer 129(4), 483-491 (May 30, 2006) (9 pages) doi:10.1115/1.2709656 History: Received December 15, 2005; Revised May 30, 2006

## Abstract

An atomistic Green’s function method is developed to simulate phonon transport across a strained germanium (or silicon) thin film between two semi-infinite silicon (or germanium) contacts. A plane-wave formulation is employed to handle the translational symmetry in directions parallel to the interfaces. The phonon transmission function and thermal conductance across the thin film are evaluated for various atomic configurations. The contributions from lattice straining and material heterogeneity are evaluated separately, and their relative magnitudes are characterized. The dependence of thermal conductance on film thickness is also calculated, verifying that the thermal conductance reaches an asymptotic value for very thick films. The thermal boundary resistance of a single $Si∕Ge$ interface is computed and agrees well with analytical model predictions. Multiple-interface effects on thermal resistance are investigated, and the results indicate that the first few interfaces have the most significant effect on the overall thermal resistance.

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## Figures

Figure 1

Schematic diagram of a five-unit-cell thin film between two semi-infinite contacts. The definitions of different groups of atoms are shown. In this case, Region D includes three unit-cell layers.

Figure 2

The 2D direct lattice (left) and reciprocal lattice (right) in a fcc structure. A 10×10 mesh is placed on the first Brillouin zone in the right subfigure.

Figure 3

Comparisons of full-spectrum transmission functions

Figure 4

Comparison of the straining effect with the heterogeneous-material effect on phonon transmission functions across a one-unit-cell thin film at low frequencies

Figure 5

Comparison of the thermal conductances of heterogeneous materials and those of homogeneous materials across a one-unit-cell thin film

Figure 6

Thickness dependence of thermal conductance in the Ge∕Si∕Ge configuration. Each unit cell is 2.69Å.

Figure 7

Comparison of the thermal boundary resistance across a Si∕Ge interface calculated by atomistic Green’s function method to that by the acoustic mismatch model (41)

Figure 8

The effect of multiple interfaces on thermal resistance

Figure 9

Comparison of the thermal conductance of Si–Ge superlattice samples with 3nm period at 200K. The experimental result is from Lee (38).

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