Size effect on the phonon heat conduction in semiconductor nanostructures (original) (raw)
Related papers
The lattice thermal conductivity of a semiconductor nanowire
Journal of Applied Physics, 2006
It has been found experimentally as well as theoretically that the lattice thermal conductivity can be largely reduced by the size confinement effect. The significant boundary scattering effect is one of the dominant factors. In most existing lattice thermal conductivity models, an empirical relation is used for this scattering rate. An unconfined or confined phonon distribution obtained based on the phonon Boltzmann equation and the relaxation time approximation is then employed to calculate the lattice thermal conductivity. In this work, we first attempt to derive an analytical form of the boundary scattering rate for phonon conduction in a semiconductor nanowire and then claim two reasonable ways to take it into account correctly. Consistent mathematical models in the sense that the effects of the size confinement on (i) the phonon dispersion relation, (ii) the phonon distribution, (iii) the phonon group and phase velocities, and (iv) the Debye temperature are finally proposed.
Thermal Conductivity in Thin Silicon Nanowires: Phonon Confinement Effect
Nano Letters, 2007
Thermal conductivity of thin silicon nanowires (1.4−8.3 nm) including the realistic crystalline structures and surface reconstruction effects is investigated using direct molecular dynamics simulations with Stillinger−Weber potential for Si−Si interactions. Thermal conductivity as a function of decreasing nanowire diameter shows an expected decrease due to increased surface scattering effects. However, at very small diameter (<1.5 nm), an increase in the thermal conductivity is observed, which is explained by the phonon confinement effect.
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.
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.
Physical Review B, 1998
Lattice thermal conductivity of a quantum well limited by umklapp, impurity, and boundary scattering was investigated theoretically by taking into account dispersion of confined acoustic-phonon modes. We show that strong modification of phonon group velocities due to spatial confinement leads to a significant increase in the phonon relaxation rates. From the numerical calculations, we predict a decrease by an order of magnitude of the lattice thermal conductivity in a 100-Å-wide free-standing quantum well. Our theoretical results are consistent with recent experimental investigations of the lateral thermal conductivity of nitride/silicon/oxide membranes conducted in our group.
Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics
International Journal of Heat and Mass Transfer, 2018
A mathematical model is presented for thermal transport in nanowires with rectangular cross sections. Expressions for the effective thermal conductivity of the nanowire across a range of temperatures and cross-sectional aspect ratios are obtained by solving the Guyer-Krumhansl hydrodynamic equation for the thermal flux with a slip boundary condition. Our results show that square nanowires transport thermal energy more efficiently than rectangular nanowires due to optimal separation between the boundaries. However, circular nanowires are found to be even more efficient than square nanowires due to the lack of corners in the cross section, which locally reduce the thermal flux and inhibit the conduction of heat. By using a temperature-dependent slip coefficient, we show that the model is able to accurately capture experimental data of the effective thermal conductivity obtained from Si nanowires, demonstrating that phonon hydrodynamics is a powerful framework that can be applied in nanosystems even at room temperature.
We present a rigorous analysis of the thermal conductivity of bulk silicon ͑Si͒ and Si nanowires ͑Si NWs͒ which takes into account the exact physical nature of the various acoustic and optical phonon mechanisms. Following the Callaway solution for the Boltzmann equation, where resistive and nonresistive phonon mechanisms are discriminated, we derived formalism for the lattice thermal conductivity that takes into account the phonon incidence angles. The phonon scattering processes are represented by frequency-dependent relaxation time. In addition to the commonly considered acoustic three-phonon processes, a detailed analysis of the role of the optical phonon decay into acoustic phonons is performed. This optical phonon decay mechanism is considered to act as acoustic phonon generation rate partially counteracting the acoustic phonon scattering rates. We have derived the analytical expression describing this physical mechanism which should be included in the general formalism as a correction to the resistive phonon-point-defects and phonon-boundary scattering expressions. The phonon-boundary scattering mechanism is taken as a function of the phonon frequency, incidence angles, and surface roughness. The importance of all the mechanisms we have involved in the model is demonstrated clearly with reference to reported data regarding the isotopic composition effect in bulk Si and Si NW samples. Namely, our model accounts for previously unexplained experimental results regarding ͑i͒ the isotope composition effect on the thermal conductivity of bulk silicon reported by Ruf et al. ͓Solid State Commun. 115, 243 ͑2000͔͒, ͑ii͒ the size effect on ͑T͒ of individual Si NWs reported by Li et al. ͓Appl. Phys. Lett. 83, 2934 ͑2003͔͒, and ͑iii͒ the dramatic decrease in the thermal conductivity for rough Si NWs reported by Hochbaum et al. ͓Nature ͑London͒ 451, 163 ͑2008͔͒.