  We investigate thermoelectric transport through interfaces with inelastic
scatterings by developing a quantum theory, which has been extensively
validated by existing theories. We find that under temperature bias, while a
two-terminal conductor-insulator interface behaves only as a thermal resistor,
a three-terminal conductor-insulator-conductor interface can function as an
electricity generator caused by phonon-mediated electron scatterings with
heat-charge current separation. Unlike conventional thermoelectrics which is a
property of a bulk caused by the Seebeck effect, this thermoelectric behavior
is a property of an interface driven by electron-phonon scatterings.
