Andrew P Horsfield et al 2004 J. Phys.: Condens. Matter 16 3609 doi:10.1088/0953-8984/16/21/010
Andrew P Horsfield1, D R Bowler1,2, A J Fisher1,2, Tchavdar N Todorov3 and M J Montgomery3
Show affiliationsModelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested.
85.35.-p Nanoelectronic devices
73.63.-b Electronic transport in nanoscale materials and structures
Issue 21 (2 June 2004)
Received 1 March 2004
Published 14 May 2004
Andrew P Horsfield et al 2004 J. Phys.: Condens. Matter 16 3609
Andrew P Horsfield et al 2004 J. Phys.: Condens. Matter 16 8251
Andrew P Horsfield et al 2004 J. Phys.: Condens. Matter 16 L65
Robert B Mann et al 2008 Class. Quantum Grav. 25 225019
Maria Werner and Erik Aurell 2009 Phys. Biol. 6 046007
M A Nielsen 2001 J. Phys. A: Math. Gen. 34 6987
Andrea Capocci and Guido Caldarelli 2008 J. Phys. A: Math. Theor. 41 224016
B Abbott et al 2008 Class. Quantum Grav. 25 245008
L Baggio et al 2008 Class. Quantum Grav. 25 095004
Amit J Nimunkar and John G Webster 2009 Physiol. Meas. 30 101