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Thermal conductivity of highly porous Si in the temperature range 4.2 to 20 K.

Valalaki K, Nassiopoulou AG - Nanoscale Res Lett (2014)

Bottom Line: The reported results are the first in the literature for this temperature range.This behavior is attributed to the presence of a majority of non-propagating vibrational modes, resulting from the nanoscale fractal structure of the material.The above results complement previous results by the authors in the temperature range 20 to 350 K.

View Article: PubMed Central - HTML - PubMed

Affiliation: NCSR Demokritos/INN, Terma Patriarchou Grigoriou, Aghia Paraskevi, Athens 15310, Greece.

ABSTRACT

Unlabelled: 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 authors in the temperature range 20 to 350 K. In this temperature range, a monotonic increase of k with temperature is observed, fitted with simplified classical models. The extremely low thermal conductivity of porous Si, especially at cryogenic temperatures, makes this material an excellent substrate for Si-integrated microcooling devices (micro-coldplate).

Pacs: 61.43.-j; 63.22.-m; 65.8.-g.

No MeSH data available.


Related in: MedlinePlus

Temperature dependence of porous Si thermal conductivity. The graphshows experimental results of thermal conductivity of porous Si fortemperatures between 5 and 20 K (present results, full points in themain figure and in the inset) and for temperatures in the range 20 to350 K (open rectangles; previous results by the authors [18]). The plateau-like behavior for the 5 to 20 K temperaturerange is illustrated, with a mean value of 0.04 W/m.K.
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Figure 2: Temperature dependence of porous Si thermal conductivity. The graphshows experimental results of thermal conductivity of porous Si fortemperatures between 5 and 20 K (present results, full points in themain figure and in the inset) and for temperatures in the range 20 to350 K (open rectangles; previous results by the authors [18]). The plateau-like behavior for the 5 to 20 K temperaturerange is illustrated, with a mean value of 0.04 W/m.K.

Mentions: For the extraction of the substrate thermal conductivity, a combination ofexperimental results and finite element method (FEM) analysis was used. The obtainedresults in the temperature range 5 to 20 K are depicted by full black circlesin Figure  2 and in the inset of this figure.Plateau-like temperature dependence at a mean value of approximately 0.04 W/m.Kwas obtained. These results are the first in the literature in the 5 to 20 Ktemperature range. For the sake of completeness, our previous results fortemperatures between 20 and 350 K are also presented in the same figure by openrectangles. A monotonic increase of the thermal conductivity as a function oftemperature is obtained for temperatures above 20 K and up to 350 K,without any maximum as that obtained, in the case of bulk crystalline Si.


Thermal conductivity of highly porous Si in the temperature range 4.2 to 20 K.

Valalaki K, Nassiopoulou AG - Nanoscale Res Lett (2014)

Temperature dependence of porous Si thermal conductivity. The graphshows experimental results of thermal conductivity of porous Si fortemperatures between 5 and 20 K (present results, full points in themain figure and in the inset) and for temperatures in the range 20 to350 K (open rectangles; previous results by the authors [18]). The plateau-like behavior for the 5 to 20 K temperaturerange is illustrated, with a mean value of 0.04 W/m.K.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4109793&req=5

Figure 2: Temperature dependence of porous Si thermal conductivity. The graphshows experimental results of thermal conductivity of porous Si fortemperatures between 5 and 20 K (present results, full points in themain figure and in the inset) and for temperatures in the range 20 to350 K (open rectangles; previous results by the authors [18]). The plateau-like behavior for the 5 to 20 K temperaturerange is illustrated, with a mean value of 0.04 W/m.K.
Mentions: For the extraction of the substrate thermal conductivity, a combination ofexperimental results and finite element method (FEM) analysis was used. The obtainedresults in the temperature range 5 to 20 K are depicted by full black circlesin Figure  2 and in the inset of this figure.Plateau-like temperature dependence at a mean value of approximately 0.04 W/m.Kwas obtained. These results are the first in the literature in the 5 to 20 Ktemperature range. For the sake of completeness, our previous results fortemperatures between 20 and 350 K are also presented in the same figure by openrectangles. A monotonic increase of the thermal conductivity as a function oftemperature is obtained for temperatures above 20 K and up to 350 K,without any maximum as that obtained, in the case of bulk crystalline Si.

Bottom Line: The reported results are the first in the literature for this temperature range.This behavior is attributed to the presence of a majority of non-propagating vibrational modes, resulting from the nanoscale fractal structure of the material.The above results complement previous results by the authors in the temperature range 20 to 350 K.

View Article: PubMed Central - HTML - PubMed

Affiliation: NCSR Demokritos/INN, Terma Patriarchou Grigoriou, Aghia Paraskevi, Athens 15310, Greece.

ABSTRACT

Unlabelled: 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 authors in the temperature range 20 to 350 K. In this temperature range, a monotonic increase of k with temperature is observed, fitted with simplified classical models. The extremely low thermal conductivity of porous Si, especially at cryogenic temperatures, makes this material an excellent substrate for Si-integrated microcooling devices (micro-coldplate).

Pacs: 61.43.-j; 63.22.-m; 65.8.-g.

No MeSH data available.


Related in: MedlinePlus