Effect Of Surface Roughness On Thermal Conductivity Of Silicon Nanowires By Bond Order Theory

Understanding and tuning thermal transport in nanostructures is very important for the development of thermoelectric devices and the thermal management of microand nano-electronics devices.Because of high surface-to-volume ratio,the most prominent size effect limiting thermal transport originates from phonon-surface scattering in nanostructures.However the precise effects of surfaces on thermal transport have remained unclear because the mechanism of phonon-surface scattering is still not well understood,and investigation is in great desirable.We present a novel mechanism of phonon-surface scattering due to bond order imperfections on surface of nanostructures.The coordination number of atoms in surface skin is lower than that of atoms in the bulk,bonds of the under-coordinated atoms on surface become shorter and stronger,which results in perturbation of Hamiltonian of lattice system,and causes phonon scattering.Based on theory of bond order and quantum perturbation,phonon scattering rate of this mechanism is derived.By incorporating this scattering mechanism to phonon Boltzmann transport equation,we reproduce the ultra low thermal conductivity of intentionally roughened vapor-liquid-solid silicon nanowires below the Casimir limit,and reveal that the obvious reduction of thermal conductivity originates from the severe suppression of high-frequency phonons by surface bond order imperfections scattering.Furthermore,we investigate the effect of morphological parameters,such as diameter,root mean square of roughness,correlated length of roughness,and surface-to-volume ratio on the thermal conductivity of rough silicon nanowires.The effect of autocorrelation function(exponential or Gaussian)of random rough surface is also studied.We find that surface-to-volume ratio is the most important parameter to affect the thermal conductivity of rough silicon nanowires.The nanowires with exponential surface have considerably more small-scale and high-frequency roughness,resulting in larger surface-to-volume ratio and lower thermal conductivity than nanowires with Gaussian surface.Our findings are helpful not only in understanding the mechanism of phonon-surface scattering,but also in modulating thermal conductivity of nanostructures by surface engineering.