Importance of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon–germanium thermoelectrics

Hua, Chengyun; Minnich, Austin J.

doi:10.1088/0268-1242/29/12/124004

Cited by 65 publications

(42 citation statements)

References 48 publications

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“…In contrast to Si [11][12][13][14][15][16] and SiGe alloys [12,17], systematic studies of the nanostructuring effect on the thermal conductivity are scarce in bismuth. A quasisuppression of the thermal conductivity has been found in bismuth nanowires, but its origin is still debated [2].…”

Section: Introductionmentioning

confidence: 99%

Nanoscale mechanisms for the reduction of heat transport in bismuth

et al. 2016

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Hand-on routes to reduce lattice thermal conductivity (LTC) in bismuth have been explored by employing a combination of Boltzmann's transport equation and ab initio calculations of phonon-phonon interaction within the density functional perturbation theory. We have first obtained the temperature dependence of the bulk LTC in excellent agreement with available experiments. A very accurate microscopic description of heat transport has been achieved and the electronic contribution to thermal conductivity has been determined. By controlling the interplay between phonon-phonon interaction and phonon scattering by sample boundaries, we predict the effect of size reduction for various temperatures and nanostructure shapes. The largest heat transport reduction is obtained in polycrystals with grain sizes smaller than 100 nm.

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Section: Introductionmentioning

confidence: 99%

Nanoscale mechanisms for the reduction of heat transport in bismuth

et al. 2016

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“…Although the precise speedup will depend on the relative size of the detector and source, in the examples considered here, speedups ranging from one to three orders of magnitude were observed. We note that, in consultation with the authors, Hua and Minnich [23] applied the proposed adjoint formulation to the investigation of boundary scattering in nanocrystalline materials. The method allowed them to show that low-frequency phonons, in spite of the nanocrystalline structure, still carry a significant proportion of the heat and that, as a consequence, design of efficient thermoelectric materials should account for such effects.…”

Section: Discussionmentioning

confidence: 99%

“…Obtaining expression (23) from (22) requires use of Eq. (15), integration by parts and, depending on the problem of interest, some manipulation.…”

Section: B Fundamental Relationmentioning

confidence: 99%

Adjoint-based deviational Monte Carlo methods for phonon transport calculations

Péraud

Hadjiconstantinou

2015

Phys. Rev. B

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In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. In this paper, we develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.

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“…The adjoint method has already proven useful in [60] where it is used as a means of calculating the contributions of each phonon frequency mode to heat conduction in nanocrystalline materials (namely, silicon and silicon-germanium). For such calculations, the "forward" method performs poorly in resolving the contributions of low frequency phonons: the latter usually feature a low density of states and thus the occurrence of a particle contributing to the corresponding estimate is rare, resulting in a large statistical uncertainty.…”

Section: Efficient Methods For Linearized Problemsmentioning

confidence: 99%

Deviational methods for small-scale phonon transport

Péraud

Landon

Hadjiconstantinou

2014

Mechanical Engineering Reviews

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Deviational methods are a class of stochastic particle simulation tools for solving kinetic equations. They have been developed [1][2][3] to alleviate the most important, perhaps, disadvantage of MC methods, namely their inability to efficiently simulate low-signal problems, such as small temperature differences. Deviational methods reduce statistical uncertainty by making use of deterministic information, a technique widely known as control-variate variance reduction [4]. In the case of kinetic equations, deviational methods make use of the observation that statistical noise becomes a limitation when transport signals are small, that is, the system state is close to equilibrium. By using that equilibrium state as a control, and using a stochastic method to simulate the deviation therefrom, deviational methods leverage exact solutions and focus the computational resources onto the unknown component of the phonon distribution function. As discussed further in Section 8, the ability to focus computational resources on the non-equilibrium component of the distribution function is very valuable for simulating multiscale problems.In the context of small-scale processes, the need for solving kinetic equations such as the Boltzmann transport equation (BTE), arises from the fact that the more tractable continuum description is only a limiting description valid in the limit of "small" mean free path, where transport is diffusive. Deviation from diffusive transport can be quantified by the Knudsen number, AbstractWe review deviational methods for solving the Boltzmann equation governing phonon transport processes in the context of small-scale, solid-state heat transfer. We briefly discuss the numerical foundations of deviational algorithms as well as basic simulation methodology. Particular emphasis is given to recent developments in the field yielding appreciable efficiency improvements, such as linearized and adjoint formulations, and their applications to complex multiscale problems. Recently developed methods for simulating the ab initio collision operator for applications to phonon transport in novel two-dimensional materials, such as graphene, are also reviewed and discussed.

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Importance of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon–germanium thermoelectrics

Cited by 65 publications

References 48 publications

Nanoscale mechanisms for the reduction of heat transport in bismuth

Nanoscale mechanisms for the reduction of heat transport in bismuth

Adjoint-based deviational Monte Carlo methods for phonon transport calculations

Deviational methods for small-scale phonon transport

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