Interplay between thermoelectric and thermionic effects in heterostructures

When electrons sweep through a double-heterojunction structure, there exist thermionic effects at the junctions and thermoelectric effects in the film. While both thermoelectric and thermionic effects have been studied for refrigeration and power generation applications separately, their interplay in heterostructures is not understood. This paper establishes a unified model including both thermionic and thermoelectric processes based on the Boltzmann transport equation for electrons and the nonequilibrium interaction between electrons and phonons. Approximate solutions are obtained, leading to the electron temperature and Fermi level distributions inside heterostructures. These quantities are discontinuous at the interfaces as a consequence of the highly nonequilibrium transport when the film thickness is much smaller than the electron mean free path. The electron temperature and Fermi level discontinuities at the interfaces determine the thermionic effect, while their gradients inside the film govern the thermoelectric effect.