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My confusion starts with HALL EFFECT. If Hall Effect is really true then holes should have a positive charge. But I have always and everywhere read that holes are just the electron deficiency and they move relatively, in the sense that electron moves in there position and hence relatively they move in opposite direction to the electron. So are holes "really" positive?

P.S. How can the Hall effect ever show positive charge carriers? this discussion didn't help.

Also What are "electron holes" in semiconductors? - I don't completely agree with this answer, as this answer says that electrons in valence band have negative mass, but according to what I have read 'holes' when considered as electrons in the valence band are said to have negative mass and not 'electrons'.

elle
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First of all, holes are not particles, as electrons were treated as in condensed matter physics. Holes are just positively charged vacancies created due to the absence of an electron in a bond. When an atom loses an electron, quite naturally, there will be an excess of positive charge on the atom, which we call as an ion.

Since the removal of an electron causes a reduction in the charge on the atom (or a bond), we can consider these vacant sites as carrying a positive charge, something counter to the electron, and called as holes. These positive sites causes the neighboring bonded electrons to get attracted to this site. Then the vacant site is filled, but a new vacant site is created. In this way, the holes can be visualized as moving from one lattice site to another; but the actual motion is that created by the jumping of the bonded electrons to the neighboring vacant sites.

In short, the free electrons are free in the sense that they can roam anywhere in the crystal. However, the holes are attached to the parent atoms. They are not detached from the atoms. Still they can travel from one lattice site to another, the actual motion being credited to the bonded electrons.

UKH
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    Incorrect. The holes are indeed 'missing' electrons in the valence band. But, that directly implies that they are also in extended Bloch states, just like the electrons are. They certainly are not attached to atoms. Further, holes are also present in many (if not most) metal band structures, and under appropriate conditions Hall effect measurements can indicate positive charge carriers. – Jon Custer Aug 24 '17 at 12:33