Abstract
With the advances in fabrication of materials with feature sizes at the order of nanometers, it has been possible to alter their thermal transport properties dramatically. Miniaturization of device size increases the power density in general, hence faster electronics require better thermal transport, whereas better thermoelectric applications require the opposite. Such diverse needs bring new challenges for material design. Shrinkage of length scales has also changed the experimental and theoretical methods to study thermal transport. Unsurprisingly, novel approaches have emerged to control phonon flow. Besides, ever increasing computational power is another driving force for developing new computational methods. In this review, we discuss three methods developed for computing vibrational thermal transport properties of nano-structured systems, namely Green function, quasi-classical Langevin, and Kubo–Green methods. The Green function methods are explained using both nonequilibrium expressions and the Landauer-type formula. The partitioning scheme, decimation techniques and surface Green functions are reviewed, and a simple model for reservoir Green functions is shown. The expressions for the Kubo–Greenwood method are derived, and Lanczos tridiagonalization, continued fraction and Chebyshev polynomial expansion methods are discussed. Additionally, the quasi-classical Langevin approach, which is useful for incorporating phonon–phonon and other scatterings is summarized.
Highlights
One requires good thermal conduction in order to get rid of the excess heat because the device temperature limits the operation speed
nonequilibrium Green functions (NEGF) was used by Meir and Wingreen [21] to study electronic transport, and later used to address phonon transport. [22–24]
Computing phonon transport using Green function (GF) technique for ensembles of isotopically disordered structures, the authors reported that conductance of straight graphene nanoribbon (s-graphene nanoribbons (GNRs)) at room temperature was reduced from 0.566 nW K−1 nm−2 to 0.460 nW K−1 nm−2 when the isotope density was the same (50%) but the distribution of isotopes was changed from atomic to precursor
Summary
Thermal transport plays a central role in most of the state-of-the-art technological applications. The entire phonon spectrum is involved in thermal transport, in general, a wide range of length scales are relevant for phonon transport. The relation between length scales and thermal transport is important for understanding the effects of nano-structuring on phonon transport, and because nano-structuring has the potential to bring novel concepts and applications involving phonons One such concept of fundamental nature is the quantum of thermal conductance, which is observed in suspended insulating nano-structures at very low temperatures. [6–9] Classical molecular dynamics (MD) simulations, Boltzmann formalism, equilibrium and nonequilibrium Green function (GF) methods, generalized quasi-classical Langevin (QCL) approach, master equation formalism and the real-space Kubo-Greenwood (KG) methodology are among the widely used methodologies to compute phonon transport at the nano-scale. Disordered carbon nanotubes, edge disordered graphene nanoribbons and graphene/BN heterostructures are the examples reviewed using this method
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