Abstract
A method is described for cooling conductive channels to below ambient temperature. The thermodynamic induction principle dictates that the electrically biased channel will cool if the electrical conductance decreases with temperature. The extent of this cooling is calculated in detail for both cases of ballistic and conventional transport with specific calculations for carbon nanotubes and conventional metals, followed by discussions for semiconductors, graphene, and metal–insulator transition systems. A theorem is established for ballistic transport stating that net cooling is not possible. For conventional transport, net cooling is possible over a broad temperature range, with the range being size-dependent. A temperature clamping scheme for establishing a metastable nonequilibrium stationary state is detailed and followed with discussion of possible applications to on-chip thermoelectric cooling in integrated circuitry and quantum computer systems.
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References
F. Pobell, Matter and Methods at Low Temperatures, 2nd edn. (Springer, Berlin, 1996)
T.W. Hänsch, A.L. Schawlow, Opt. Commun. 13, 68 (1975)
D.J. Wineland, R.E. Drullinger, F.L. Walls, Phys. Rev. Lett. 40, 1639 (1978)
M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)
W. Ketterle, N.J. Van Druten, in Advances in Atomic, Molecular, and Optical Physics, ed. by B. Bederson, H. Walther (Academic Press, London, 1996)
S.N. Patitsas, Phys. Rev. E 89, 012108 (2014)
S.N. Patitsas, Phys. A 436, 604 (2015)
N.W. Ashcroft, D.N. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976)
S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (Dover Publications, New York, 1984)
F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw Hill, New York, 1965)
L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1 (Elsevier, New York, 1980)
S. Datta, Quantum Transport: Atom to Transistor (Cambridge, New York, 2005)
R. Landauer, Philoso. Mag. 21, 863 (1970)
H.-L. Engquist, P.W. Anderson, Phys. Rev. B 24, 1151 (1981)
M.Y. Azbel, D.P. DiVincenzo, Phys. Rev. B 30, 6877 (1984)
M. Büttiker, Y. Imry, R. Landauer, S. Pinhas, Phys. Rev. B 31, 6207 (1985)
P.C. Martin, J. Schwinger, Phys. Rev. 115, 1342 (1959)
L.P. Kadanoff, G. Baym, Quantum Statistical Mechanics (Benjamin/Cummings, New York, 1962)
L.V. Keldysh, Sov. Phys. JETP 20, 1018 (1965)
Y. Lu, J.Y. Huang, C. Wang, S. Sun, J. Lou, Nat. Nanotechnol. 5, 218 (2010)
A.C. Ehrlich, J.T. Schriempf, Solid State Commun. 14, 469 (1974)
A.J. Barber, A.D. Caplin, J. Phys. F Metal Phys. 5, 679 (1975)
E.R. Rumbo, J. Phys. F Metal Phys. 6, 85 (1976)
J.F. Kos, J. Phys. Condens. Matter 2, 4859 (1990)
B.R. Barnard, A.D. Caplin, M.N.B. Dalimin, J. Phys. F Metal Phys. 12, 719 (1982)
R. Matula, J. Phys. Chem. Ref. Data 8, 1147 (1979)
S. Sze, Physics of Semiconductor Devices, 2nd edn. (Wiley, New York, 1981)
K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, Solid State Commun. 146, 351 (2008)
W. Pan, J.-S. Xia, V. Shvarts, D.E. Adams, H.L. Stormer, D.C. Tsui, L.N. Pfeiffer, K.W. Baldwin, K.W. West, Phys. Rev. Lett. 83, 3530 (1999)
D. Laroche, G. Gervais, M.P. Lilly, J.L. Reno, Nat. Nanotechnol. 6, 793 (2011)
F. Hartmann, P. Pfeffer, S. Höfling, M. Kamp, L. Worschech, Phys. Rev. Lett. 114, 146805 (2015)
X. Obradors, L.M. Paulius, M.B. Maple, J.B. Torrance, A.I. Nazzal, J. Fontcuberta, X. Granados, Phys. Rev. B 47, 12353 (1993)
M. Imada, A. Fujimori, A. Tokura, Rev. Mod. Phys. 70, 1039 (1998)
A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido, Y. Tokura, Phys. Rev. B 51, 14103 (1995)
H. Kawano, R. Kajimoto, M. Kubota, H. Yoshizawa, Phys. Rev. B 53, R14709 (1996)
I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, D. Koester, R. Alley, R. Venkatasubramanian, Nat. Nanotechnol. 4, 235 (2009)
W. Hafez, M. Feng, Appl. Phys. Lett. 86, 152101 (2005)
Y.-M. Lin, C. Dimitrakopoulos, K.A. Jenkins, D.B. Farmer, H.-Y. Chiu, A. Grill, P. Avouris, Science 327, 662 (2010)
A. Imamoglu, D.D. Awschalom, G. Burkard, D.P. DiVincenzo, D. Loss, M. Sherwin, A. Small, Phys. Rev. Lett. 83, 4204 (1999)
I. Garate, I. Affleck, Phys. Rev. Lett. 106, 156803 (2011)
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I thank Cathy J. Meyer for her assistance in editing the manuscript.
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Patitsas, S.N. Cooling by Thermodynamic Induction. J Low Temp Phys 186, 316–346 (2017). https://doi.org/10.1007/s10909-016-1711-9
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DOI: https://doi.org/10.1007/s10909-016-1711-9