UC Berkeley

With the evolution of semiconductor technology toward nanometer size and gigahertz frequency, the traditional diffusive Fourier's law of heat conduction can no longer be applied. To engineer new methods for chip cooling or thermoelectric power generation, understanding the non-diffusive heat transfer in both the length and time domains is important. In this dissertation, the phonon transport at nanometer lengths or gigahertz heating frequencies is investigated using the Boltzmann Transport Equation (BTE).

Regarding length scale effects, a systematic theory of the phonon thermal conductivity accumulation function was developed to show which phonon mean free paths are important for heat transfer. I show that the nanostructure thermal conductivity can be obtained with only the bulk mean free path spectrum and nanostructure geometry as independent inputs. This theory has been applied to nanowire and in-plane thin film systems. In addition, the length scale effect on the effective conductivity in randomly oriented superlattice polycrystals, which are potential thermoelectric materials, has also been investigated.

Regarding time scale effects, I derived an analytical solution to the BTE under the gray mean free time assumption, and extended the solution to the non-gray regime. With this theory, I can explain the experiments measuring a heating frequency dependent thermal conductivity of semiconductor alloys. I also build up a framework which can be used to extract a phonon accumulation function with respected to mean free time. The similarities and differences of both length and time effects have also been compared and discussed.