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Modeling nanostructure thermal conductivity: effect of phonon distribution function

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Abstract

In this study, the lattice thermal conductivity of nanostructure material is demonstrated using the non-equilibrium phonon distribution function to solve the Boltzmann transport equation in the relaxation time approximation. This model is compared with the experimental data of silicon nanowires (SiNWs) for a wide diameter and temperature range (20–320 K). Phonon scattering is assumed to be by sample boundaries, impurities and other phonons via Normal and Umklapp processes. The predicted lattice thermal conductivity (LTC) values demonstrate sensible concurrence with experimental measurements. The present analysis can clarify the experimental results on the lattice thermal conductivity of nanostructures.

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Abbreviations

a :

Lattice constant

\(K\) :

Lattice thermal conductivity

\(\Delta K\) :

Correction term

\(K_{{\text{B}}}\) :

Boltzmann constant

\(g(\omega )\) :

Density of state

\(C_{{\text{v}}}\) :

Specific heat

\(\overline{k}\) :

Phonon wave vector

\(\hbar\) :

Planck’s constant divided by \(2\pi\)

\(\omega\) :

Phonon angular frequency

\(x\) :

Dimensionless parameter

\(v_{{\text{s}}}\) :

Phase velocity

\(v\) :

Group velocity

\(V_{ \circ }\) :

Volume of the specimen

\(\theta_{{\text{D}}}\) :

Debye temperature

\(\tau_{{\text{C}}}\) :

Combined scattering relaxation rates

\(\tau_{{\text{N}}}\) :

Relaxation rate of normal process

\(\tau_{{\text{U}}}\) :

Relaxation rate of Umklapp process

\(\overline{\lambda }\) :

Arbitrary constant vector

\(N(t)\) :

Non-equilibrium distribution function

\(N_{ \circ }^{{}}\) :

Equilibrium distribution function

T :

Lattice temperature

\(\nabla T\) :

Temperature gradient

\(\tau_{{\text{B}}}^{ - 1}\) :

Boundary scattering relaxation rate

\(\tau_{{{\text{pt}}}}^{ - 1}\) :

Point defects scattering relaxation rate

\(\tau_{{\text{N}}}^{ - 1}\) :

Three phonon normal processes

\(\tau_{{\text{U}}}^{ - 1}\) :

Three phonon Umklapp processes

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  1. Department of Physics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq

    A. H. Awad

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Awad, A.H. Modeling nanostructure thermal conductivity: effect of phonon distribution function. J Therm Anal Calorim 147, 14071–14078 (2022). https://doi.org/10.1007/s10973-022-11693-x

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