Coherent phonon scattering effects on thermal transport in thin semiconductor nanowires

The thermal conductance by phonons of a quasi-one-dimensional solid with\nisotope or defect scattering is studied using the Landauer formalism for\nthermal transport. The conductance shows a crossover from localized to Ohmic\nbehavior, just as for electrons, but the nature of this crossover is modified\nby delocalization of phonons at low frequency. A scalable numerical\ntransfer-matrix technique is developed and applied to model\nquasi-one-dimensional systems in order to confirm simple analytic predictions.\nWe argue that existing thermal conductivity data on semiconductor nanowires,\nshowing an unexpected linear dependence, can be understood through a model that\ncombines incoherent surface scattering for short-wavelength phonons with nearly\nballistic long-wavelength phonons. It is also found that even when strong\nphonon localization effects would be observed if defects are distributed\nthroughout the wire, localization effects are much weaker when defects are\nlocalized at the boundary, as in current experiments.\n