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Semiconductors can be n-type or p-type, meaning that if current is flowing in them, either electrons or holes are carrying the current. As these charge carriers move, they can scatter off of, that is, transfer momentum to, "phonons" which are the quanta of vibrational energy, i.e. heat in a crystalline lattice. In other words, as the charges flows, it sweeps the heat along with it. You can arrange a bunch of these things between two plates, alternating p-type and n-type, such that as the current snakes back and forth between the little elements, nevertheless, the charge carriers are all going in the same direction, and all sweep the heat in the same way.

When you operate one of these devices (by simply passing a current through it - connect it to a battery) the current itself dissipates some heat in the material, but that heat and some of the heat on the "cold" side get swept to the other side, the "hot" side. If you pinch one of the devices between your fingers and run it, one finger gets hot and the other cold. Materials with low thermal conductivity but good electrical conductivity have the highest figure of merit, and it turns out that the winners are made of bismuth and tellurium, especially. (Silicon has excellent thermal conductivity - no good here, it short-circuits the temperature difference.)

Incidentally, if you hook up the battery backwards, it simply reverses the cold and hot sides, with equal efficiency. And if you actively heat one face and cool the other face, it's an (inefficient!) electrical generator - in this case, the heat is being forced to flow, and the charge carriers are what get swept along for the ride.

[ Incidentally, if you hook up the battery backwards, it simply reverses the cold and hot sides, with equal efficiency. And if you actively heat one face and cool the other face, it's an (inefficient!) electrical generator - in this case, the heat is being forced to flow, and the charge carriers are what get swept along for the ride. ]

Thanks... Excellent... First thing that crossed my mind..