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This is related to the Peltier effect.

Using N-type semiconductor as a thermoelectric material, when a voltage is applied across it the majority charge carriers (electrons) move from the negative side to the positive side carrying heat. This makes the negative side cooler and the positive side hotter.

But when the same is done to a P-type semiconductor, the majority charge carriers (holes) move from positive side to the negative side carrying heat. This makes the negative side hotter and the positive side cooler.

Now my question is, since positive carriers (holes) are just the absence of electrons , they are physically nothing . So how can they carry heat .

Peltier elements

The full document http://www.nano.physik.uni-muenchen.de/education/praktika/f1_thermoelectrics.pdf

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    $\begingroup$ They are not physically nothing - as you say, they are the absence of an electron, so hole motion is also movement of an unoccupied state within a sea of electrons. $\endgroup$
    – Jon Custer
    Jan 11, 2017 at 19:01

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The holes can be said to have some potential energy, as an electron can fall in the hole, and some heat is produced when that happens.

As the holes move they carry that potential energy with them.

Inside the semiconductor electrons are constantly falling into holes, and new holes are constantly being created as those electrons leave holes behind. Heat is produced when a hole and an electron combine. Same amount of heat is turned into potential energy when a new hole is created.

At the hot junction a hole can combine with an electron without any new hole appearing anywhere nearby, so net heat energy is produced at the hot junction.

At the cold junction, with the help of heat energy and energy from the voltage source, electrons leave the semiconductor leaving holes behind, so some heat energy gets converted into potential energy of holes and electrons.

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