This makes no sense to me and i think it's more of a convention. Even though we prefer talking about holes that are the majority carriers in p-type semiconductors, they have no charge and are not particles to be electrically charged. When an electron moves from a Si atom to a B atom, for example, the latter will get a stable configuration with 10 electrons. (5 of its own, 4 from covalences with 4 other Si atoms and the last one, just 'received'). The donor particle, Si, lacks now an electron and it can be considered (at least partially) positive. And what makes an electron move again is the attraction to this positive charge the Si particle has now. Why is the hole considered positively charged? And I have one more thing in mind. I have read that holes can be considered particles with a charge of +e (the electron's charge, but of opposite sign). I can understand it only this way: instead of speaking of an electron of charge -e moving from A to B, let's say, we choose to talk about a hypothetical particle of charge +e moving from B to A. All the associated notions give the same results when you try to determine them, in terms of numerical values. Is it correct what I think?
Holes are considered positively charged because of the relation between their velocity and the electric current: when they move right, the current points right.
It is theoretically possible to only work in terms of electrons: conduction band electrons and valence band electrons. However, electrons in the valence band behave in a strange way. Because of their interaction with the lattice, they don't respond to forces the way free electrons do. In fact, they accelerate in the opposite direction to the applied force. If you're only looking at electromagnetic forces, that looks remarkably like they had positive charge.
The other aspect is the current of a nearly-full band: the valence band in a semiconductor is almost completely occupied by electrons. Wikipedia can explain this better than me, but supose the band has place for electrons with speed -2, -1, 0, 1, 2.
Full band: all those states are occupied with electrons. Then the net current is 0: for each electron going one way there's one going the opposite way, contributing the opposite current.
1 missing electron: Look at the electron with speed 2. Its contribution to the current is (-1)*2 = -2, with the leading -1 because of its negative charge. This current is balanced by the electron with speed -2, whose current is (-1)*(-2) = 2. If you remove the electron with speed 2, there's nothing balancing the -2 electron so you get a total current of 2. Generally, removing an electron which contributes current j increases the net current by -j.
Rather than adding the currents of an almost full valence band (with a lot of cancellation), it's easier to just look at the current due to the missing electrons and take the opposite sign.
Think if it like this:
- You have a material consisting of neutral atoms. That means, they have equal amounts of electrons and protons.
- A new atom is now added, which as you explain it steals an electron from one of the other atoms in order to become coherent with them to "fit in" in the lattice.
- Therefor a neighbour atom now has one less electron. It therefor lost an amount of charge of $-q$. It is therefore not neutral anymore since it has one proton too many. It therefore has a net charge of $+q$ which is the proton and electron charge (they are equal).
- Because of this net charge it might steel an electron from another neighbour in order to become neutral again. This neighbour therefore looses an electron and the same thing repeats itself through many atoms.
From outside it doesn't look like any electrons are moving. They just move one atom to their neighbour, which is not much. But the hole, which is just a missing electron, looks like it is moving from atom to atom to atom. It seems to be propagating. That's why it can be thought of as a particle in itself even though it actually only is a missing electron.
The hole works as a positive charge, because it will move towards a negative charge (if a negatively charged area is introduced, electrons will move away and filling up all holes ad far away as possible, which of course means that the holes are pushed back to that negatively charged area).
I hope this helps the intuitive understanding.
Quantum mechanics is weird. Phonons (crystal lattice vibrations), for example, are not real particles, but they have quantum mechanical properties like superposition and uncertainty. Although we physically describe a hole as an unfilled electron energy state in the conduction band, we can just as well pretend that it's a real particle/wave with all of the usual weird behaviors. In that case, the hole acts like a positively charged particle with a mass (or rather, inertia) somewhere around twice that of an electron.
I'm sorry, but to my understanding, they're not charged, because the netto charge is 0, there's no unbalance. A particle is charged if the amount of protons are not equal to electrons.
We're talking about holes or free electrons, because we doped Si with some atoms that have one missing electron in the outer shell (to make it a complete band) or just a single electron in the outer shell. When 1 electron really moves to another atom and stays there, we than talk about an ion, which is negatively charged because protons are not equal to electrons anymore!
When we talk about negative charged particle, we talk about an electron. A positive charged particle is an atom (because of the proton in it). Finally, it's not important which is the - or +, that is once agreed for convention. Otherwise you have like in the UK you drive on the left side with your car and in Europe on the right side.