Abstract
Nanostructuring provides a viable route to improve the thermoelectric performance of materials, even of those that in bulk form have very low figure of merit. This strategy would potentially enable the fabrication of thermoelectric devices based on silicon, the cheapest, most integrable and easiest to dope Earth-abundant semiconductor. A drastic reduction of the thermal conductivity, which would lead to a proportional enhancement of the figure of merit, was observed for silicon low-dimensional nanostructures, such as nanowires and ultra-thin membranes. Here we provide a detailed analysis of the phononic properties of the latter, and we show that dimensionality reduction alone is not sufficient to hinder heat transport to a great extent. In turn, the presence of surface roughness at the nanoscale reduces the thermal conductivity of sub-10 nm membranes up to 10 times with respect to bulk.
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References
A. Majumdar, Science 303, 777 (2004)
A. Majumdar, Nat. Nanotechnol. 4, 214 (2009)
L.D. Hicks, M.S. Dresselhaus, Phys. Rev. B 47, 16631 (1993)
A. Balandin, Phys. Low-Dim. Struct. 1, 2, 1 (2000)
J.H. Lee, G.A. Galli, J.C. Grossman, Nano Lett. 8, 3750 (2008)
G.J. Snyder, E.S. Toberer, Nat. Mater. 7, 105 (2008)
M.S. Dresselhaus et al., Adv. Mater. 19, 1043 (2007)
A.I. Boukai et al., Nature 451, 168 (2008)
J.K. Yu et al., Nat. Nanotechnol. 5, 718 (2010)
J. Tang et al., Nano Lett. 10, 4279 (2010)
A. Balandin, K.L. Wang, Phys. Rev. B 58, 1544 (1998)
G. Chen, Int. J. Therm. Sci. 39, 471 (2000)
G. Chen, J. Nanopart. Res. 2, 199 (2000)
G. Chen, A. Narayanaswamy, C. Dames, Superlattice Microstrut. 35, 161 (2004)
A.A. Balandin, J. Nanosci. Nanotechnol. 5, 1015 (2005)
C.J. Vineis, A. Shakouri, A. Majumdar, M.G. Kanatzidis, Adv. Mater. 22, 3970 (2010)
J.F. Li, W.S. Liu, L.D. Zhao, M. Zhou, NPG Asia Mater. 2, 152 (2010)
J. Cuffe et al., Nano Lett. 12, 3569 (2012)
M. Asheghi, Y.K. Leung, S.S. Wong, K.E. Goodson, Appl. Phys. Lett. 71, 1798 (1997)
Y.S. Ju, K.E. Goodson, Appl. Phys. Lett. 74, 3005 (1999)
W. Liu, M. Asheghi, J. Appl. Phys. 98, 123523 (2005)
X. Liu, X. Wu, T. Ren, Appl. Phys. Lett. 98, 174104 (2011)
E. Chávez-Ángel et al., APL Mater. 2, 012113 (2014)
J.A. Johnson, A.A. Maznev, J. Cuffe, J.K. Eliason, A.J. Minnich, T. Kehoe, C.M. Sotomayor Torres, G. Chen, K.A. Nelson, Phys. Rev. Lett. 110, 025901 (2013)
J.E. Turney, A.J.H. McGaughey, C.H. Amon, J. Appl. Phys. 107, 024317 (2010)
C.J. Gomes, M. Madrid, J.V. Goicochea, C.H. Amon, J. Heat Transfer 128, 1114 (2006)
P. Heino, Eur. Phys. J. B 60, 171 (2007)
Y.S. Ju, K. Kurabayashi, K.E. Goodson, Thin Solid Films 339, 160 (1999)
W. Liu, M. Asheghi, Appl. Phys. Lett. 84, 3819 (2004)
C.N. Liao, C. Chen, K.N. Tu, J. Appl. Phys. 86, 3204 (1999)
H. Ikeda, F. Salleh, Appl. Phys. Lett. 96, 012106 (2010)
J.H. Lee, J.C. Grossman, J. Reed, G. Galli, Appl. Phys. Lett. 91, 223110 (2007)
Y. He et al., ACS Nano 5, 1839 (2011)
D. Li et al., Appl. Phys. Lett. 83, 2934 (2003)
R. Chen, A.I. Hochbaum, P. Murphy, J. Moore, P. Yang, A. Majumdar, Phys. Rev. Lett. 101, 105501 (2008)
K. Hippalgaonkar et al., Nano Lett. 10, 4341 (2010)
A. Shchepetov et al., Appl. Phys. Lett. 102, 192108 (2013)
C.J. Glassbrenner, G.A. Slack, Phys. Rev. 134, A1058 (1964)
M.G. Holland, Phys. Rev. 132, 2461 (1963)
E.H. Sondheimer, Adv. Phys. 1, 1 (1952)
D.A. Broido et al., Appl. Phys. Lett. 91, 231922 (2007)
J.A. Appelbaum, G.A. Baraff, D.R. Hamann, Phys. Rev. B 14, 588 (1976)
D.J. Chadi, Phys. Rev. Lett. 43, 43 (1979)
J.E. Northrup, Phys. Rev. Lett. 54, 815 (1985)
P.C. Weakliem, E.A. Carter, J. Chem. Phys. 96, 3240 (1992)
D. Donadio, G. Galli, Phys. Rev. Lett. 102, 195901 (2009)
F.H. Stillinger, T.A. Weber, Phys. Rev. B 31, 5262 (1985)
M.Z. Bazant, E. Kaxiras, Phys. Rev. Lett. 77, 4370 (1996)
J. Tersoff, Phys. Rev. B 39, 5566 (1989)
P.C. Kelires, J. Tersoff, Phys. Rev. Lett. 63, 1164 (1989)
K.L. Whiteaker, I.K. Robinson, J.E. Van Nostrand, D.G. Cahill, Phys. Rev. B 57, 12410 (1998)
G. Pernot et al., Nat. Mater. 9, 491 (2010)
L.P. Solie, B.A. Auld, J. Acoust. Soc. Am. 54, 50 (1973)
J.M. Ziman, Electrons and Phonons: the Theory of Transport Phenomena in Solids (Clarendon Press, Oxford, 2001)
H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976)
R. Zwanzig, Ann. Rev. Phys. Chem. 16, 67 (1965)
F. Müller-Plathe, J. Chem. Phys. 106, 6082 (1997)
P. Schelling, S. Phillpot, P. Keblinski, Phys. Rev. B 65, 144306 (2002)
E. Lampin, Q.H. Nguyen, P. Francioso, F. Cleri, Appl. Phys. Lett. 100, 131906 (2012)
C. Melis, R. Dettori, S. Vandermeulen, L. Colombo, Eur. Phys. J. B 87, 96 (2014)
D.P. Sellan et al., Phys. Rev. B 81, 214305 (2010)
Y. He, I. Savic, D. Donadio, G. Galli, Phys. Chem. Chem. Phys. 14, 16209 (2012)
S. Plimpton, J. Comput. Phys. 117, 1 (1995)
S. Nosé, J. Chem. Phys. 81, 511 (1984)
R. Kremer et al., Solid State Commun. 131, 499 (2004)
M. Asheghi et al., J. Heat Transfer 120, 30 (1998)
W. Liu, M. Asheghi, J. Appl. Phys. 98, 123523 (2005)
B.L. Davis, M.I. Hussein, Phys. Rev. Lett. 112, 055505 (2014)
D. Donadio, G. Galli, Nano Lett. 10, 847 (2010)
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Contribution to the Topical Issue “Silicon and Silicon-related Materials for Thermoelectricity”, edited by Dario Narducci.
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Neogi, S., Donadio, D. Thermal transport in free-standing silicon membranes: influence of dimensional reduction and surface nanostructures. Eur. Phys. J. B 88, 73 (2015). https://doi.org/10.1140/epjb/e2015-50677-5
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DOI: https://doi.org/10.1140/epjb/e2015-50677-5