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In the Peltier effect, we consider charge carriers being able to carry heat. As for electrons or ions, this attitude makes sense, since external electric potential drives particles with mass in a direction and effectively transfers heat from one point of material to another.

But for holes, this situation is only virtual, holes moving in a direction is only reformulation of the fact that the electron making up the hole environment are traveling opposite direction. I just cannot grasp the concept that the holes can indeed carry heat.

I know one can argue that the holes have effective mass, but effective mass is only a measure of how much can you accelerate / decelerate the electron (or hole) in a crystal field.

Can you help me out please?

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If an electron is cold and it travels one way, can't we imagine that as a hole carrying heat the other way? – Jim Apr 26 '13 at 13:46
Well, if the electron is consistently moving one way, it should be hotter than the rest, since it has bigger mean velocity. But I am afraid that this model (classical gas approximation) totally breaks down in crystal structure when it comes to heat transport. – Jan Hirschner Apr 26 '13 at 14:54
Ok, I was just curious. – Jim Apr 26 '13 at 15:18
I wrote a more detailed explanation of what holes are at… - that may help answer your question. – Steve B Apr 26 '13 at 17:30
Thank you Steve, it helped me a lot. Especially the note about dispersion relation which I have happened to completely omit. – Jan Hirschner Apr 27 '13 at 6:15

Both free electrons and holes in semiconductor are excitations, i.e. quasiparticles which can propagate under influence of external electric field or temperature due to diffusion or drift. Don't forget that electrons are also characterized by the effective mass. In p-doped semiconductors a gradient of the temperature creates a region where hoping of real electrons between sites of the crystal lattice are more intensive than in other part of the device. Due to diffusion they tend to spread over all volume.

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It seems that it comes down to the fact I cannot precisely define how the electrons carry heat in crystal band structure, I only used the idea of classical gas - if we accelerate the electrons we increase their mean velocity thus increase their thermal energy. Can you shortly comment on more precise way of defining the heat transport by electrons in crystal structures? – Jan Hirschner Apr 26 '13 at 14:52

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