Monte Carlo modeling of phonon transport in nanodevices

Lacroix, David; Joulain, Karl; Terris, Damian; Lemonnier, Denis

doi:10.1088/1742-6596/92/1/012078

Cited by 5 publications

(5 citation statements)

References 11 publications

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“…78,80,[82][83][84][85][86] PMC has proven to be an effective tool to study nanoscale thermal transport in systems near equilibrium. 74,[86][87][88][89] It is also straightforward to include nontrivial geometries, such as rough boundaries or edges, in PMC. 43,80,90 The starting point of PMC is equilibrium.…”

Section: Phonon Monte Carlo Methods With Full Dispersionmentioning

confidence: 99%

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

Mei

Maurer

Akšamija

et al. 2014

Journal of Applied Physics

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We simulate phonon transport in suspended graphene nanoribbons (GNRs) with real-space edges and experimentally-relevant widths and lengths (from submicron to hundreds of microns). The full-dispersion phonon Monte Carlo (PMC) simulation technique, which we describe in detail, involves a stochastic solution to the phonon Boltzmann transport equation with the relevant scattering mechanisms (edge, three-phonon, isotope, and grain boundary scattering) while accounting for the dispersion of all three acoustic phonon branches, calculated from the fourth-nearest-neighbor dynamical matrix. We accurately reproduce the results of several experimental measurements on pure and isotopically modified samples [S.

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Section: Phonon Monte Carlo Methods With Full Dispersionmentioning

confidence: 99%

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

Mei

Maurer

Akšamija

et al. 2014

Journal of Applied Physics

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“…With typical semiconductor feature sizes ranging from the nanometer to the millimeter scale [6], phonon transport modeling using a mesoscopic approach such as the BTE is very desirable. Practical applications of interest include the calculation of the thermal conductivity of bulk and nanostructured semiconductors [7][8][9][10][11][12][13][14][15][16], fundamental understanding and manipulation of the thermal properties of semiconducting [17][18][19], as well as low-dimensional materials like graphene [20][21][22] and solution of coupled electronphonon transport problems [23][24][25][26][27][28].…”

Section: Deviational Methods For Small-scale Phonon Transportmentioning

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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“…With typical semiconductor feature sizes in the range of tens of nanometers to almost millimeters, 19 phonon transport can typically be treated semiclassically, using a Boltzmann equation. This approach is currently being used to calculate the thermal conductivity of bulk and nanostructured semiconductors, [20][21][22][23][24][25][26][27][28][29] to predict thermal transport behavior in small-scale and low-dimensional structures that are difficult to probe experimentally, such as graphene, [30][31][32] as well as to solve coupled electron-phonon transport problems. [33][34][35][36][37][38] New measurement techniques for probing the frequency-dependent response of phonon systems have also been aided by solution of the Boltzmann equation.…”

Section: Small-scale Transportmentioning

confidence: 99%

Monte Carlo Methods for Solving the Boltzmann Transport Equation

Péraud

Landon

Hadjiconstantinou

2014

Annual Rev Heat Transfer

101

113

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We review Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons. Our discussion reviews the numerical foundations of Monte Carlo algorithms, basic simulation methodology, as well as recent developments in the field. Examples of the latter include formulations for calculating the effective thermal conductivity of periodically nanostructured materials and variance-reduction methodologies for reducing the computational cost associated with statistical sampling of field properties of interest, such as the temperature and heat flux. Recent developments are presented in the context of applications of current practical interest, including multiscale problems that have motivated some of the most recent developments.

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Monte Carlo modeling of phonon transport in nanodevices

Cited by 5 publications

References 11 publications

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

Deviational methods for small-scale phonon transport

Monte Carlo Methods for Solving the Boltzmann Transport Equation

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