Heat transport in ultra-thin dielectric membranes and bridges

Details Heat transport in ultra-thin dielectric membranes and bridges Heat transport in ultra-thin dielectric membranes and bridges

2004-04-28

arxiv.org/abs/cond-mat/0404676v1

Phys. Rev. B 70, 125425 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages and 6 figures

Scientific paper

10.1103/PhysRevB.70.125425

Phonon modes and their dispersion relations in ultrathin homogenous dielectric membranes are calculated using elasticity theory. The approach differs from the previous ones by a rigorous account of the effect of the film surfaces on the modes with different polarizations. We compute the heat capacity of membranes and the heat conductivity of narrow bridges cut out of such membranes, in a temperature range where the dimensions have a strong influence on the results. In the high temperature regime we recover the three-dimensional bulk results. However, in the low temperature limit the heat capacity, $C_V$, is proportional with $T$ (temperature), while the heat conductivity, $\kappa$, of narrow bridges is proportional to $T^{3/2}$, leading to a thermal cut-off frequency $f_c=\kappa/C_V\propto T^{1/2}$.

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