Pore-size dependence of the thermal conductivity of porous silicon: A phonon hydrodynamic approach (original) (raw)
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A Phenomenological Study of Pore-Size Dependent Thermal Conductivity of Porous Silicon
Acta Applicandae Mathematicae, 2012
A phonon-hydrodynamics approach is used to analyze the influence of porosity and of pore size on the reduction of the thermal conductivity in porous silicon. Different geometrical arrangements of the pores have been considered. For any given value of the porosity, the theoretical results show that for increasing Knudsen number (i.e., decreasing pore size) the effective thermal conductivity decreases whatever the geometrical arrangement of the pores is.
Thermal conductivity across nanostructured porous silicon films
Journal of Physics: Conference Series, 2007
This paper models the effect of pore size, pore arrangement and porosity on room temperature thermal conductivity across low porosity meso-porous silicon (meso-PS) films known as n+ and p+ type PS. Whereas the meso-PS films are simulated using a threedimensional (3D) pore network generator, the heat conduction is modeled using the Monte Carlo method (MCM) recently developed for simulating steady-state phonon transport in submicron structures. The simulations show that (i) the thermal conductivity across mesoporous films decreases when the pore size decreases or the porosity increases, in accordance with past studies. (ii) The thermal conductivity of n+ type pore network is always greater than that of p+ type due to the difference in pore morphology. Finally, the simulations corresponding to p+ type pore network are shown in good agreement with existing experimental data for low porosity p+ type PS. Such comparison confirms the validity of the current 3D modeling.
Thermal conductivity of silicon nanomeshes: Effects of porosity and roughness
Journal of Applied Physics, 2014
We theoretically investigate thermal conductivity in silicon nanomeshes using Monte Carlo simulations of phonon transport. Silicon membranes of 100nm thickness with randomly located pores of 50nm diameter are considered. The effects of material porosity and pore surface roughness are examined. Nanomesh porosity is found to have a strong detrimental effect on thermal conductivity. At room temperature, a porosity of 50% results in ~80% reduction in thermal conductivity. Boundary roughness scattering further degrades thermal conductivity, but its effect is weaker. Thermal transport can additionally be affected by the specific arrangement of the pores along the transport direction.
Nanoscale nature and low thermal conductivity of porous silicon layers
Applied Surface Science
Recently discovered phenomenon of low thermal conductivity of porous silicon (PS) layers is discussed in detail. A proposed theoretical model explains the considerable decrease of the thermal conductivity of nanoscale PS in comparison with meso-PS and bulk silicon. The thermal conductance dependence of Si/porous Si structures on the formation conditions of PS layers has been studied. By varying the values of anodisation current density and anodisation time it is possible to optimize the thermal conductance values of the Si/porous Si structures. In this way, an efficient thermal isolation can be obtained by forming thick PS layers.
Monte Carlo simulation of cross-plane thermal conductivity of nanostructured porous silicon films
Journal of Applied Physics, 2008
This paper presents a Monte Carlo ͑MC͒ modeling of heat conduction in heavily doped ͑p + and n + ͒ porous silicon ͑PS͒ films known as mesoporous silicon ͑meso-PS͒. A three-dimensional pore network generator is developed to better reproduce the structure of low porosity ͑f v Ͻ 50% ͒ meso-PS. The submicron scale heat conduction modeled by the Boltzman transport equation is simulated using the MC method in which the nonlinear phonon dispersion curves of bulk silicon and the phonon lifetime dependent on temperature, frequency, and polarization are taken into account. The proposed method has been applied to predict the effect of the porosity ͑10%-47%͒, pore sizes ͑10-20 nm͒, pore arrangement ͑p + -and n + -type͒, temperature ͑50-500 K͒, and film thickness ͑50 nm-1 m͒ on the cross-plane thermal conductivity of meso-PS films. Moreover, the simulation results enable to deduce the scattering mean free path ͑MFP͒ of phonons in the PS and the scattering MFP due to phonon-pore wall interaction. At room temperature, the thermal conductivity of meso-PS is shown one to two orders of magnitude smaller than that of bulk silicon. A drastic simplification of the phonon dispersion curves and phonon MFP, such as in the Debey approximation, results in an overestimation ͑by about three times͒ of the thermal conductivity of meso-PS. The thermal conductivity decreases when the pore size decreases or the porosity increases. For a given porosity and pore size, the thermal conductivity of doped p + -type PS is much smaller than that of doped n + -type PS. Finally, the simulations of thermal conductivity of doped p + -type PS are shown in good agreement with available experimental data which confirms the validity of the current modeling.
Thermal conductivity of highly porous Si in the temperature range 4.2 to 20 K
Nanoscale research letters, 2014
We report on experimental results of the thermal conductivity k of highly porous Si in the temperature range 4.2 to 20 K, obtained using the direct current (dc) method combined with thermal finite element simulations. The reported results are the first in the literature for this temperature range. It was found that porous Si thermal conductivity at these temperatures shows a plateau-like temperature dependence similar to that obtained in glasses, with a constant k value as low as 0.04 W/m.K. This behavior is attributed to the presence of a majority of non-propagating vibrational modes, resulting from the nanoscale fractal structure of the material. By examining the fractal geometry of porous Si and its fractal dimensionality, which was smaller than two for the specific porous Si material used, we propose that a band of fractons (the localized vibrational excitations of a fractal lattice) is responsible for the observed plateau. The above results complement previous results by the au...
Impact of pore anisotropy on the thermal conductivity of porous Si nanowires
Scientific Reports
Porous materials display enhanced scattering mechanisms that greatly influence their transport properties. Metal-assisted chemical etching (MACE) enables fabrication of porous silicon nanowires starting from a doped Si wafer by using a metal template that catalyzes the etching process. Here, we report on the low thermal conductivity (κ) of individual porous Si nanowires (NWs) prepared from MACE, with values as low as 0.87 W•m −1 •K −1 for 90 nm diameter wires with 35-40% porosity. Despite the strong suppression of long mean free path phonons in porous materials, we find a linear correlation of κ with the NW diameter. We ascribe this dependence to the anisotropic porous structure that arises during chemical etching and modifies the phonon percolation pathway in the center and outer regions of the nanowire. The inner microstructure of the NWs is visualized by means of electron tomography. In addition, we have used molecular dynamics simulations to provide guidance for how a porosity gradient influences phonon transport along the axis of the NW. Our findings are important towards the rational design of porous materials with tailored thermal and electronic properties for improved thermoelectric devices.
Microelectronics Journal, 1999
Recently measured low thermal conductivity of as-prepared and slightly oxidized meso-porous silicon (meso-PS) offers new possibility to apply this promising material for thermal isolation in microsensors and microsystems. We report here a theoretical model describing specific mechanisms of heat transport in as-prepared and oxidized meso-PS. The model is in good agreement with experimental data obtained earlier.
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.