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I've studied the Kronig–Penney model and learned about the effective mass theory and I know that at the top of the valence band the effective mass of electrons are negative, this is just an introduction about the information I know to ask the question properly.

My question is: In case of semiconductor an empty state is called hole and it has an positive charge and positive effective mass also, but what really is a hole and how did we introduce this concept and how to understand it? Because a lot of textbooks gives different interpretations to it and I can't understand it correctly.

Qmechanic
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Mans
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    With all due respect, please take more time write/ type the question. There were a lot of typos etc.. This makes the question harder to read for everyone. Moreover, a good formatted question will likely attract more people, raising the chances of obtaining a good answer, I'd say. – Tobias Fünke Mar 18 '23 at 11:05
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    Related: https://physics.stackexchange.com/q/755026/2451 and links therein. – Qmechanic Mar 18 '23 at 11:14
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    You shouldn't see different interpretations as a problem. They are stories about the phenomena. As long as they are experimentally consistent with the phenomena, they are all good stories, with different insights to be be had. – John Doty Mar 18 '23 at 12:36
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    Does this answer your question? What is the concept of hole in semiconductor physics? – Roger V. Mar 18 '23 at 12:40
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    There are different levels of introducing a hole: from describing a jumping vacancy, to effective mass approximation, to obtaining it as a quasiparticle pole in green's function. I post this as a comment, since I have already given an answer in the question linked by @Qmechanic. But I would be glad to expand it, if more precision is required. – Roger V. Mar 18 '23 at 12:44

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