title: Thermal conductivity of highly porous Si in the temperature range 4.2 to 20 K.
abstract: 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).
  61.43.-j; 63.22.-m; 65.8.-g.
authors.affiliation: NCSR Demokritos/INN, Terma Patriarchou Grigoriou, Aghia Paraskevi, Athens 15310, Greece.
authors.forename: Katerina
authors.initials: K
authors.lastname: Valalaki
authors.affiliation: NCSR Demokritos/INN, Terma Patriarchou Grigoriou, Aghia Paraskevi, Athens 15310, Greece.
authors.forename: Androula Galiouna
authors.initials: AG
authors.lastname: Nassiopoulou
keywords: Cryogenic temperatures; Nanoscale semiconductors; Porous Si; Thermal conductivity
references.citation: Phys Rev Lett. 1996 Oct 28;77(18):3831-3834
references.pmid: 10062319
references.citation: Phys Rev Lett. 1987 Jan 12;58(2):128-131
references.pmid: 10034610
references.citation: Sensors (Basel). 2012 Nov 02;12(11):14838-50
references.pmid: 23202189
references.citation: J Colloid Interface Sci. 2009 Aug 1;336(1):215-25
references.pmid: 19406424
references.citation: Phys Rev B Condens Matter. 1986 Oct 15;34(8):5696-5701
references.pmid: 9940407
references.citation: Nano Lett. 2010 Mar 10;10(3):847-51
references.pmid: 20163124
references.citation: Phys Chem Chem Phys. 2014 Feb 14;16(6):2425-9
references.pmid: 24356280
references.citation: Nanoscale Res Lett. 2012 Jul 31;7(1):427
references.pmid: 22849851
references.citation: Nano Lett. 2008 Nov;8(11):3750-4
references.pmid: 18947211
references.citation: Phys Rev B Condens Matter. 1995 Jan 15;51(4):2199-2213
references.pmid: 9978968
references.citation: Phys Rev B Condens Matter. 1986 Aug 15;34(4):2726-2734
references.pmid: 9939968
references.citation: Phys Rev Lett. 1996 Jan 22;76(4):604-607
references.pmid: 10061501
references.citation: Sensors (Basel). 2013 Oct 10;13(10):13596-608
references.pmid: 24152923
references.citation: Nat Mater. 2008 Nov;7(11):870-7
references.pmid: 18849975
references.citation: Phys Rev B Condens Matter. 1996 Sep 15;54(12):R8373-R8376
references.pmid: 9984598
references.citation: Nanotechnology. 2013 May 24;24(20):205402
references.pmid: 23598565