I'm having some trouble finding details on just how the Peltier effect (also known as the Peltier-Seebeck effect or the thermoelectric effect) works on a physical level. Am I correct in thinking that it has something to do with the small energy barriers that occur at ohmic contacts? I've searched extensively and the best information I can find is either lacking in details or hidden behind a paywall I can't afford.
What I mostly want to know here is: What causes the charge carriers on the cold side to pick up energy from the crystal lattice? What phonon-electron or phonon-hole interaction occurs?
The Seebeck effect (converting temperature to a potential difference) makes more intuitive sense to me, as diffusion-driven high-energy/high-density charge carriers move across the semiconductor (or metal), but this would seem to imply that it would be something that occurs in the bulk of the material, rather than at the junctions. And I don't know if just reversing that even makes sense to explain the Peltier effect (which is the reverse, current to temperature). Since the Peltier and Seebeck effects are considered to be the same thing operating in two different directions, a diffusion-based explanation would seem not to work.