We study the extent of ballistic and diffusive thermal transport and the range of application of the Casimir and Fourier theories in semiconductor materials by using a theoretical model based on the Boltzmann transport equation. We show that combined effects of length scale, temperature, and boundary roughness are responsible for thermal transport transitions in silicon nanowires and thin films. We also introduce a more accurate principle for ballistic transport that considers the balance between internal and surface scattering.Phonon quantum confinement effects as well as the conditions for phonon wave interference in nanoscale heat transport are discussed.
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