Effect of size and dimension dependent specific heat on thermal conductivity of nanostructured semiconductors

A thermodynamic model is proposed to study the collective effect of size and dimension dependent specific heat capacity along with phonon surface scattering on thermal conductivity as well as on diffusivity of nanostructured semiconductors. Thermal conductivity and diffusivity of pure and compound semiconducting nanomaterials for partially smooth and rough surfaces of different sizes and dimensions have been calculated. Thermal conductivity and diffusivity decrease with size and increases while moving towards the specular surfaces. Incorporation of size and dimension effect of specific heat capacity with phonon-interface scattering gives the better explanation of thermal conductivity, whereas classical approach alone is inadequate. To validate the obtained results, we have compared our results with the experimental data and other model reported in the literature.