Heat transfer and energy conversion in electronic and thermoelectric devices often involve multiple length scales ranging from nanometer to millimeters. For example, heat is typically generated in a nanometer-scale region at the drain of a MOSFET and is subsequently conducted through the millimeter thick substrate to the surroundings. As another example, cooling in a thermoelectric device occurs at one interface while the heat is rejected at the other end millimeter away. Modeling the energy transport and conversion processes in such multiple length scale devices is very challenging. Boltzmann equation-based approaches for phonons and electrons transport, although appropriate, are time consuming and not practical in near term. In this paper, we will summarize two approximations we have recently introduced to model transport processes, particularly for phonons, from nano to macroscales. One is the diffusion-transmission interface condition that attributes size effects to the interfacial region only. The other are the ballistic-diffusive equations that group the energy carriers into a ballistic and a diffusive component and that are much easier to solve than the Boltzmann equation. Examples on phonon heat conduction will be given to demonstrate the effectiveness of these two approaches. The approximations can also be extended to electron transport.

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