The Effect of Surface Roughness on the Universal Thermal Conductance

Details The Effect of Surface Roughness on the Universal Thermal Conductance The Effect of Surface Roughness on the Universal Thermal Conductance

2000-11-28

arxiv.org/abs/cond-mat/0011473v2

Phys. Rev. B 63, 184306 (2001)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 5 figures. Ref. added, typo corrected

Scientific paper

10.1103/PhysRevB.63.184306

We explain the reduction of the thermal conductance below the predicted universal value observed by Schwab et al. in terms of the scattering of thermal phonons off surface roughness using a scalar model for the elastic waves. Our analysis shows that the thermal conductance depends on two roughness parameters: the roughness amplitude $\delta $ and the correlation length $a$. At sufficiently low temperatures the conductance decrease from the universal value quadratically with temperature at a rate proportional to $\delta ^{2}a$. Values of $\delta$ equal to 0.22 and $a$ equal to about 0.75 of the width of the conduction pathway give a good fit to the data.

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