Temperature dependence of specific heat capacity of nanostructures via neuroevolution machine-learned potential

In this study, lattice dynamics calculations based on the Neuroevolution Machine-learned Potential (NEP) were performed for three types of silicon nanostructures: thin films, nanowires, and quantum dots. The temperature and size dependence of the specific heat capacity was systematically examined. The results reveal a significant enhancement in the specific heat capacity of nanostructures at low temperatures compared to bulk silicon, primarily due to phonon confinement, discrete energy spectra, and the emergence of low-frequency surface vibrational modes. These findings underscore the dominant role of nonlinear acoustic phonons at low temperatures, with increasing contributions from optical modes as the temperature rises. Notably, this work reports the temperature-dependent evolution of local fitting exponents in the specific heat scaling relation Cv∼Tn(T) for nanostructured systems. The high accuracy and computational efficiency of the NEP model allow for detailed characterization of the complex phonon behaviors that govern thermal properties at the nanoscale.