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Phonon heat transport in superlattices: Case of Si/SiGe and SiGe/SiGe superlattices
D. G. Cahil, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
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We present a predictive Boltzmann
model for the cross-plane thermal conductivity in superlattices. The developed model considers particle-like phonons exhibiting wave characteristics at the interfaces and makes the assumption that the phonon
heat transport in a superlattice has a mixed character. Exact Boltzmann equation comprising spatial dependence of phonon distribution function is solved to yield a general expression for the lattice thermal conductivity. The intrinsic phonon scattering rates are calculated from Fermi’s golden rule, and the model vibrational parameters are derived as functions of temperature and crystallographic directions by using elasticity theory-based lattice dynamics approach. The developed theory is then adapted to calculate the cross-plane thermal conductivity of superlattices. It is assumed that the phonons of wavelengths comparable or smaller than the superlattice period or the root mean square irregularity at the superlattice interfaces may be subject to a resistive scattering mechanism at the interfaces, whereas the phonons of wavelengths much greater than the superlattice period undergo ballistic transmission through the interfaces and obey dispersion relations determined by the Brillouin zone folding effects of the superlattice. The accuracy of the concept of mixed phonon
transport regime in superlattices is demonstrated clearly with reference to experimental measurements regarding the effects of period thickness and temperature on the cross-plane thermal conductivity of Si/Si0.7
0.3 and Si0.84
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