We introduce a generalized hydrodynamic framework for predicting thermal energy currents in semiconductor nanostructures with characteristic dimensions down to tens of nanometers across a broad temperature range. The evolution of slowly evolving moments of the phonon distribution function is predicted deterministically using a hydrodynamic equation. To accurately capture nonequilibrium effects under extreme confinement, the heat-flux profile is further refined by stochastically modeling higher-order statistical features of the distribution that become significant far from local equilibrium. The formalism, which uses inputs strictly calculated from first principles, is validated against the apparent thermal conductivity of silicon ultrathin films across a wide range of temperatures.

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• Semiconductors
• Ultrathin films
• Boltzmann theory
• Hydrodynamic models