Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes (original) (raw)
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Physical review letters, 2015
The electron-phonon interaction is well known to create major resistance to electron transport in metals and semiconductors, whereas fewer studies are directed to its effect on phonon transport, especially in semiconductors. We calculate the phonon lifetimes due to scattering with electrons (or holes), combine them with the intrinsic lifetimes due to the anharmonic phonon-phonon interaction, all from first principles, and evaluate the effect of the electron-phonon interaction on the lattice thermal conductivity of silicon. Unexpectedly, we find a significant reduction of the lattice thermal conductivity at room temperature as the carrier concentration goes above 10^{19} cm^{-3} (the reduction reaches up to 45% in p-type silicon at around 10^{21} cm^{-3}), a range of great technological relevance to thermoelectric materials.
Nature Materials, 2010
The ability to precisely control the thermal conductivity (κ) of a material is fundamental in the development of on-chip heat management or energy conversion applications. Nanostructuring permits a marked reduction of κ of single-crystalline materials, as recently demonstrated for silicon nanowires. However, silicon-based nanostructured materials with extremely low κ are not limited to nanowires. By engineering a set of individual phonon-scattering nanodot barriers we have accurately tailored the thermal conductivity of a single-crystalline SiGe material in spatially defined regions as short as ∼15 nm. Single-barrier thermal resistances between 2 and 4 × 10 −9 m 2 K W −1 were attained, resulting in a room-temperature κ down to about 0.9 W m −1 K −1 , in multilayered structures with as little as five barriers. Such low thermal conductivity is compatible with a totally diffuse mismatch model for the barriers, and it is well below the amorphous limit. The results are in agreement with atomistic Green's function simulations.
Journal of Electronic Materials, 2013
We study the thermal properties of ultra-narrow silicon nanowires (NW) with diameters from 3 nm to 12 nm. We use the modified valence-force-field method for computation of phononic dispersion and the Boltzmann transport equation for calculation of phonon transport. Phonon dispersion in ultra-narrow 1D structures differs from dispersion in the bulk and dispersion in thicker NWs, which leads to different thermal properties. We show that as the diameter of the NW is reduced the density of long-wavelength phonons per cross section area increases, which increases their relative importance in carrying heat compared with the rest of the phonon spectrum. This effect, together with the fact that low-frequency, low-wavevector phonons are affected less by scattering and have longer mean-free-paths than phonons in the rest of the spectrum, leads to a counter-intuitive increase in thermal conductivity as the diameter is reduced to the sub-ten-nanometers range. This behavior is retained in the presence of moderate boundary scattering.
Prediction of thermal conductivity of nanostructures: Influence of phonon dispersion approximation
International Journal of Heat and Mass Transfer, 2009
In this study, the influence of phonon dispersion approximation on the prediction of in-plane and out-ofplane thermal conductivity of thin films and nanowires is shown. Results obtained using the famous Holland dispersion approximation and the Brillouin zone boundary condition (BZBC) dispersion curves are compared. For (in-plane and out-of-plane) thermal conductivity predictions based on BZBC dispersion curves, new relaxation time parameters fitted from experimental data of bulk silicon thermal conductivity are reported. The in-plane thermal conductivity of nanostructures (films of thicknesses 20 nm, 100 nm, and 420 nm and nanowires of widths 22 nm, 37 nm, and 100 nm) in the temperature range 20-1000 K is calculated from the modified bulk thermal conductivity model by scaling the bulk phonon mean free path (MFP) by the Fuch-Sondheimer factor of boundary scattering developed for nanostructures with rectangular cross-section. The pseudo out-of-plane thermal conductivity of films of thicknesses 20 nm, 100 nm, and 420 nm and in the temperature range 150-1000 K is calculated from the solution of the Boltzmann transport equation (BTE) for phonons by using the Discrete ordinate method (DOM), and the Monte Carlo (MC) simulation. In order to confirm the current results, the calculated in-plane thermal conductivity of silicon thin films and silicon nanowires are compared with existing experimental data. Moreover, due to lack of experimental and theoretical data of out-of-plane thermal conductivity of thin films, comparison of the DOM and MC simulation is performed. The current work shows that a drastic simplification of dispersion curves can lead to wrong prediction of both in-plane and out-of-plane thermal conductivities of nanostructures, especially for ultra thin nanostructures and/or at high temperatures. Comparison with experimental data of in-plane thermal conductivity of silicon thin films and silicon nanowires proves that more refined dispersion approximation such as the BZBC is well adequate for phonon transport calculations when confinement has negligible effect. Moreover, the comparison between the thermal conductivity in the out-of-plane direction and that in the inplane direction enables one to quantify the anisotropy of thermal conductivity of the film.
In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics
Journal of Heat Transfer, 2006
The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2to217nm and temperatures from 300to1000K. The relation between the bulk phonon mean free path (Λ) and the film thickness (ds) spans from the ballistic regime (Λ⪢ds) at 300K to the diffusive, bulk-like regime (Λ⪡ds) at 1000K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300K. In the ballistic limit, in a...
Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation
Journal of Applied Physics, 2013
We investigate the effect of confinement and orientation on the phonon transport properties of ultra-thin silicon layers of thicknesses between 1 nm − 16 nm. We employ the modified valence force field method to model the lattice dynamics and the ballistic Landauer transport formalism to calculate the thermal conductance. We consider the major thin layer surface orientations {100}, {110}, {111}, and {112}. For every surface orientation, we study thermal conductance as a function of the transport direction within the corresponding surface plane. We find that the ballistic thermal conductance in the thin layers is anisotropic, with the {110}/<110> channels exhibiting the highest and the {112}/<111> channels the lowest thermal conductance with a ratio of about two. We find that in the case of the {110} and {112} surfaces, different transport orientations can result in ∼ 50% anisotropy in thermal conductance. The thermal conductance of different transport orientations in the {100} and {111} layers, on the other hand, is mostly isotropic. These observations are invariant under different temperatures and layer thicknesses. We show that this behavior originates from the differences in the phonon group velocities, whereas the phonon density of states is very similar for all the thin layers examined. We finally show how the phonon velocities can be understood from the phonon spectrum of each channel. Our findings could be useful in the design of the thermal properties of ultra-thin Si layers for thermoelectric and thermal management applications.
Unusually High and Anisotropic Thermal Conductivity in Amorphous Silicon Nanostructures
ACS Nano
Amorphous Si (a-Si) nanostructures are ubiquitous in numerous electronic and optoelectronic devices. Amorphous materials are considered to possess the lower limit to the thermal conductivity κ , which is ~1 W.m-1 K-1 for a-Si. However, recent work suggested that κ of micron-thick a-Si films can be greater than 3 W.m-1 K-1 , which is contributed by propagating vibrational modes, referred to as "propagons". However, precise determination of κ in a-Si has been elusive. Here, we used novel structures of a-Si nanotubes and suspended a-Si films that enabled precise in-plane thermal conductivity (∥) measurement within a wide thickness range of 5 nm to 1.7 µm. We showed unexpectedly high ∥ in a-Si nanostructures, reaching ~3.0 and 5.3 W.m-1 K-1 at ~100 nm and 1.7 µm, respectively. Furthermore, the measured ∥ is significantly higher than the cross-plane on the same films. This unusually high and anisotropic thermal conductivity in the amorphous Si nanostructure manifests the surprisingly broad propagon mean free path distribution, which is found to range from 10 nm to 10 µm, in the disordered and atomically isotropic structure. This result provides an unambiguous answer to the century-old problem regarding mean free path distribution of propagons and also sheds light on the design and performance of numerous a-Si based electronic and optoelectronic devices.
Lattice thermal conductivity of silicon from empirical interatomic potentials
Physical Review B, 2005
We present calculations of the lattice thermal conductivity of silicon that incorporate several commonly used empirical models of the interatomic potential. Second-and third-order force constants obtained from these potentials are used as inputs to an exact iterative solution of the inelastic phonon Boltzmann equation, which includes the anharmonic three-phonon scattering as well as isotopic defect and boundary scattering. Comparison of the calculated lattice thermal conductivity with the experiment shows that none of these potentials provides satisfactory agreement. Calculations of the mode Grüneisen parameters and the linear thermal expansion coefficient help elucidate the reasons for this. We also examine a set of parameters for one of these empirical potentials that produces improved agreement with both the measured lattice thermal conductivity and the thermal expansion data.
2008
The thermoelectric efficiency of a material depends on the ratio of its electrical and thermal conductivity. In this work, the cross-sectional dependence of electron mobility and lattice thermal conductivity in silicon nanowires has been investigated by solving the electron and phonon Boltzmann transport equations. The effects of confinement on acoustic phonon scattering (both electron-phonon and phonon-phonon) are accounted for in this study. With decreasing wire crosssection, the electron mobility shows a non-monotonic variation, whereas the lattice thermal conductivity exhibits a linear decrease. The former is a result of the decrease in intervalley and intersubband scattering due to a redistribution of electrons among the twofold-degenerate ∆ 2 and fourfold-degenerate ∆ 4 valley subbands when the cross-section is below 5 × 5 nm 2 , while the latter is because of the monotonic increase of three phonon umklapp and boundary scattering with decreasing wire cross-section. Among the wires considered, those with a cross-section between 3 × 3 nm 2 and 4 × 4 nm 2 have the maximal ratio of the electron mobility to lattice thermal conductivity, and are expected to provide the maximal thermoelectric figure of merit.