Thermal conductivity data for rough surface silicon nanowires suggest the breakdown of the Casimir limit which assumes completely diffuse phonon boundary scattering. We show that coherent effects in phonon transport at room temperature indeed lead to such breakdown. Correlated multiple scattering of phonons off the rough surface lead to a reduced thermal conductivity that is dependent not only on the roughness amplitude but more importantly on the roughness correlation length. A correlation length less than the diameter of the wire is typically necessary for lowering the thermal conductivity below the Casimir limit. Our model explains seeming anomalies in data reported for electrolessly etched and electron beam lithography defined nanowires.

• Received 28 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.115450