Validity of the isotropic thermal conductivity assumption in supercell lattice dynamics

Superlattices and nano phononic crystals have attracted significant attention due to their low thermal conductivities and their potential application as thermoelectric materials. A widely used expression to calculate thermal conductivity, presented by Klemens and expressed in terms of the relaxation...

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Bibliographic Details
Published in:Journal of applied physics 2018-02, Vol.123 (6)
Main Authors: Ma, Ruiyuan, Lukes, Jennifer R.
Format: Article
Language:English
Subjects:
Applied physics
Boltzmann transport equation
Brillouin zones
Crystal lattices
Germanium
Heat conductivity
Heat transfer
Lattice vibration
Mathematical analysis
Phonons
Quantum dots
Relaxation time
Silicon
Superlattices
Superstructures
Thermal conductivity
Thermoelectric materials
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Summary:Superlattices and nano phononic crystals have attracted significant attention due to their low thermal conductivities and their potential application as thermoelectric materials. A widely used expression to calculate thermal conductivity, presented by Klemens and expressed in terms of the relaxation time by Callaway and Holland, originates from the Boltzmann transport equation. In its most general form, this expression involves a direct summation of the heat current contributions from individual phonons of all wavevectors and polarizations in the first Brillouin zone. In common practice, the expression is simplified by making an isotropic assumption that converts the summation over wavevector to an integral over wavevector magnitude. The isotropic expression has been applied to superlattices and phononic crystals, but its validity for different supercell sizes has not been studied. In this work, the isotropic and direct summation methods are used to calculate the thermal conductivities of bulk Si, and Si/Ge quantum dot superlattices. The results show that the differences between the two methods increase substantially with the supercell size. These differences arise because the vibrational modes neglected in the isotropic assumption provide an increasingly important contribution to the thermal conductivity for larger supercells. To avoid the significant errors that can result from the isotropic assumption, direct summation is recommended for thermal conductivity calculations in superstructures.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.5007054