Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation (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.
Measurement of ballistic phonon conduction near hotspots in silicon
Applied Physics Letters, 2001
The Fourier law for lattice heat conduction fails when the source of heat is small compared to the phonon mean free path. We provide experimental evidence for this effect using heating and electrical-resistance thermometry along a doped region in a suspended silicon membrane. The data are consistent with a closed-form two-fluid phonon conduction model, which accounts for the severe departure from equilibrium at the hotspot. The temperature rise exceeds predictions based on the Fourier law by 60% when the phonon mean free path is a factor of 30 larger than the resistor thickness. This work is improving the constitutive modeling of heat flow in deep-submicron transistors.
Phonon confinement and transport in ultrathin films
Physical Review B, 2020
Thermal transport by phonons in films with thicknesses of less than 10 nm is investigated in a soft system (Lennard-Jones argon) and a stiff system (Tersoff silicon) using two-dimensional lattice dynamics calculations and the Boltzmann transport equation. This approach uses a unit cell that spans the film thickness, which removes approximations related to the finite cross-plane dimension required in typical three-dimensional-based approaches. Molecular dynamics simulations, which make no assumptions about the nature of the thermal transport, are performed to obtain finite-temperature structures for the lattice dynamics calculations and to predict thermal conductivity benchmarks. Thermal conductivity decreases with decreasing film thickness for both the two-dimensional lattice dynamics calculations and the MD simulations, until the thickness reaches four unit cells (2.1 nm) for argon and three unit cells (1.6 nm) for silicon. With a further decrease in film thickness, thermal conductivity plateaus in argon while it increases in silicon. This unexpected behavior, which we identify as a signature of phonon confinement, is a result of an increased contribution from low-frequency phonons, whose density of states increases as the film thickness decreases. Phonon mode-level analysis suggests that confinement effects emerge below thicknesses of ten unit cells (5.3 nm) for argon and six unit cells (3.2 nm) for silicon. These transition points both correspond to approximately twenty atomic layers. Thermal conductivity predictions based on the bulk (i.e., three-dimensional) phonon properties combined with a boundary scattering model do not capture the low thickness behavior. To match the two-dimensional lattice dynamics and molecular dynamics predictions for larger thicknesses, the three-dimensional lattice dynamics calculations require a finite specularity parameter that in some cases approaches unity. These findings point to the challenges associated with interpreting experimental thermal conductivity measurements of ultrathin silicon films, where surface roughness and a native oxide layer impact phonon transport.
Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes
Physical Review B, 2010
We present a calculation of the full thermal conductivity tensor for ͑001͒, ͑111͒, and ͑011͒ surface orientations of the silicon-on-insulator ͑SOI͒ nanomembrane, based on solving the Boltzmann transport equation in the relaxation-time approximation with the full phonon dispersions, a momentum-dependent model for boundary scattering, as well as three-phonon and isotope scattering. The interplay between strong boundary scattering and the anisotropy of the phonon dispersions results in thermal conduction that strongly depends on the surface orientation and exhibits marked in-plane vs out-of-plane anisotropy, as well as slight in-plane anisotropy for the low-symmetry ͑011͒ SOI. In-plane thermal conductivity is highest along ͓100͔ on Si͑011͒ and lowest in Si͑001͒ due to the strong scattering of the highly anisotropic TA modes with ͑001͒ surfaces. The room-temperature in-plane conductivities in ͑011͒ and ͑001͒ nanomembranes with thicknesses around 10 nm differ by a factor of 2, and the ratio can be much higher at lower temperatures or in rougher samples. We discuss surface facet orientation as a means of tailoring thermal conduction in low-dimensional nanostructrures and address the role of out-of-plane thermal conductivities in predicting vertical phonon transport in superlattices.
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.
Joule heating and phonon transport in nanoscale silicon MOSFETs
2007 IEEE International Conference on Electro/Information Technology, 2007
This work examines the generation of heat in silicon MOSFETs using self-consistent Monte Carlo device simulation with full electron bandstructure and a full phonon dispersion computed from the Adiabatic Bond Charge model. We devise an efficient algorithm for the inclusion of full phonon dispersion in order to account for anisotropy and details of heat transport with great accuracy. We compute the density-of-states (DOS) and the lattice thermal energy numerically and use them to generate maps of local temperatures in a representative small-channel MOSFET device. Our results show that most heat is dissipated in the form of optical g-type phonons in a small region in the drain, and that the heat flows in a preferred direction aligned with the flow of the electron current. We also show that the distribution of generated phonons in energy closely follows the phonon DOS.
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...
Journal of Computational Electronics, 2013
Low-dimensional semiconductors are considered promising candidates for thermoelectric applications with enhanced performance because of a drastic reduction in their thermal conductivity, κ l , and possibilities of enhanced power factors. This is also the case for traditionally poor thermoelectric materials such as silicon. This work presents atomistic simulations for the electronic, thermal, and thermoelectric properties of ultrathin Si layers of thicknesses below 10nm. The Linearized Boltzmann theory is coupled: i) to the atomistic sp 3 d 5 s* tight-binding (TB) model for the electronic properties of the thin layers, and ii) to the modified valence-force-field method (MVFF) for the calculation of the thermal conductivity of the thin layers. We calculate the room temperature electrical conductivity, Seebeck coefficient, power factor, thermal conductivity, and ZT figure of merit of ultra-thin p-type Si layers (UTLs). We describe the numerical formulation of coupling TB and MVFF to the linearized Boltzmann transport formalism. The properties of UTLs are highly anisotropic, and optimized thermoelectric properties can be achieved by the choice of the appropriate transport and confinement orientations, as well as layer thickness. Index terms: thermoelectrics, tight-binding, sp 3 d 5 s*, modified valence-force-field, Boltzmann transport, Seebeck coefficient, thermoelectric power factor, silicon ultra-thin layers, ZT figure of merit.
Effect of Phonon Dispersion on Thermal Conduction Across Si/Ge Interfaces
Journal of Heat Transfer-Transactions of the Asme, 2011
We report finite-volume simulations of the phonon Boltzmann transport equation (BTE) for heat conduction across the heterogeneous interfaces in SiGe superlattices. The diffuse mismatch model incorporating phonon dispersion and polarization is implemented over a wide range of Knudsen numbers. The results indicate that the thermal conductivity of a Si/Ge superlattice is much lower than that of the constitutive bulk materials for superlattice periods in the submicron regime. We report results for effective thermal conductivity of various material volume fractions and superlattice periods. Details of the non-equilibrium energy exchange between optical and acoustic phonons that originate from the mismatch of phonon spectra in silicon and germanium are delineated for the first time. Conditions are identified for which this effect can produce significantly more thermal resistance than that due to boundary scattering of phonons.