Acoustic Softening and Acoustic Stiffening: Modifications of Thermal Conductivity from Altered Dispersion Relations in Si and ZnO Nanostructures

Abstract

At the nanoscale both thermal conductivity and the elastic modulus become size dependent. In silicon, the observed reduction in the elastic modulus has been used to explain anomalously low thermal conductivities in nanostructures with critical dimensions below 20nm. However, these explanations focus on the phonon group velocity and neglect other factors of thermal conductivity such as scattering rates and the heat capacity. My work focuses on modeling the effects of changes in the elastic modulus at the nanoscale on thermal conductivity. Results from both molecular dynamics and modeling are presented for materials that soften with decreasing size (Si) and materials that stiffen with decreasing size (ZnO). When only considering velocity effects, softening causes a reduction in thermal conductivity proportional to the change in the reduction in the elastic modulus. However, by incorporating more rigorous models I identified that effects on factors other than velocity may compete. In the cases studied I found that the effects on the scattering rates could, in part, counter the velocity effects. Additionally, the effects from heat capacity served to shift the peak thermal conductivity, increasing the low temperature thermal conductivity for softening and decreasing the low temperature thermal conductivity for stiffening. This work can help guide the selection of materials where stiffening and softening effects should be most apparent in the measurement of thermal conductivity.