We present a theoretical investigation of the magnitude and temperature variation of the recently measured [Phys. Rev. B 66, 045302 (2002)] thermal conductivity of undoped and doped $\mathrm{GaAs}$ nanobeams of cross sections $100\mathrm{nm}\times 250\mathrm{nm}$ and $150\mathrm{nm}\times 250\mathrm{nm}$, respectively. The calculations have been performed by employing Callaway’s theoretical model and Srivastava’s rigorous treatment of three-phonon interactions, based on an isotropic continuum phonon dispersion relation. It is found that an increased rate of diffuse surface scattering in undoped nanobeams explains the attenuation of the thermal conductivity below that of bulk $\mathrm{GaAs}$ well. The drop in thermal conductivity of doped nanobeams compared to that of the undoped beams arises from electron-phonon scattering and additional phonon scattering from a large number of point impurities due to the presence of dopant atoms. It is further shown that specular reflection of phonons from rough surfaces plays only a minor role in controlling the thermal conductivity of the nanobeams. The present calculations also allow for estimating the contributions of the longitudinal phonon branches and the three-phonon $N$-drift term towards the total conductivity.

• Received 6 January 2006

DOI:https://doi.org/10.1103/PhysRevB.73.205308