NONEQUILIBRIUM PHONON AND ELECTRON TRANSPORT IN HETEROSTRUCTURES AND SUPERLATTICES

Electron and phonon transport in nanostructures is characterized by interface effects and can deviate significantly from the assumption of local thermal equilibrium underlying the transport equations at macroscale. In this paper, we elucidate some basic nonequilibrium characteristics for phonon and electron transport in thin films and superlattices. Based on a discussion of the thermal boundary resistance at a single interface, the nonequilibrium nature of phonon transport and the consistency of temperature definition are emphasized. Using a consistent definition for temperature, we obtain simplified expressions for phonon transport in thin films, superlattices and give examples to illustrate the effectiveness of the approximation by comparing the thermal conductivity of thin films and superlattices obtained from solving the Boltzmann equation with the current approximation. Similar nonequilibrium processes occur for the electron transport in nanostructures. An example is given on concurrent electron and phonon transport in double junction heterostructures, considering the nonequilibrium transport processes within both the electron and the phonon subsystems and in between them. Finally, the ballistic-diffusive approximation to the Boltzmann equation is introduced, which should be applicable to transport problems from nano- to mascroscales, as well as for fast temporal processes.