Insight into holes as charge carriers in semiconductors

Question

I can't seem to get my head around the idea that both electrons and holes are charge carriers in semiconductors.

Surely holes are just lack of electrons.

Is it true to say that there are two independent flows of charge (that of the electrons and that of the holes) which together give the resultant current?

Are the holes accessible to the free electrons or are they on completely different energy levels or something?

For example in the case of silicon doped with boron. Is it true to say that there are free electrons and holes in this substance but the free electrons do not go into the holes?

I read somewhere that the holes flow by some quantum mechanical means between the boron atoms. Is there some truth to this?

When a hole flows from a boron atom does an electron take it's place (if so then where did it come from?) or does a different hole replace that hole and hence a flow of holes?

Can someone shed some light on my confusion?

Answer 1

Holes are just a term to indicate a vacancy of an electron.
For understanding you can visualize it as follows: (But what actually happens is complicated and this visualization cannot cope with that)

The electron just knocks another electron out of it's place which knocks another and you've got electrons moving around. This is what happens in (A).
In (B), now consider an empty space where an electron's missing. That's what we call a hole. Another electron in the lattice abandons it's own position and jumps into the hole (because it's easier than to knock another electron). Now the place where the electron was originally is now empty and hence it has become a hole. The process continues with many electrons. If you now look at this as a big picture, it's actually the holes that are moving. It looks like the holes (like the electrons) move around in the lattice.

The holes somehow seem to promote motion of charges. And more holes means more electrons can jump easily into them and more movement of charges. Hence both electrons and holes are considered as charge carriers. (hole assumed to bear +1)

I think that answers most of your worries. If you have a doubt do share in the comments.

Answer 2

Regarding the fact that both conducting electrons and holes can coexist in a semiconductor, I can understand how this might seem improbable. After all, since a hole is just the absence of an electron, why don’t the electrons simply fall into the holes, neutralizing both?

The answer here is that electrons do in fact fall into holes; this is called recombination. But this recombination can potentially take a long time because semiconductors have a band gap. A band gap is a range of energies that an electron cannot have in the semiconductor, and it exists due to the quantum mechanical (wave-like) nature of electrons in the crystal. A consequence of this is that if an electron is in a state above the band gap energy range (in the “conduction band”), and a hole is in a state below the band gap (in the “valence band”), then the electron needs to lose a lot of energy at once to “jump” the band gap and recombine with the hole. Since this process can take awhile, electrons and holes can coexist for some time (but not forever; this is a non-equilibrium state). In a solar cell, the energy from absorbed light promotes electrons from the valence band to the conduction band. This leaves electrons and holes both in the semiconductor at the same time. The trick for high efficiency is to collect those conducting particles before they recombine.

Now you asked about doped semiconductors, and in particular boron-doped silicon. The way to think about dopants is that they are little defects in the crystal that either steal electrons from the valence band (leaving behind holes) or they put extra electrons in the conduction band. Boron steals electrons from the valence band. But here’s the thing: if all of the electrons are in the valence band, none of them have any room to move (so to speak, it’s related to the Pauli exclusion principle). So a full valence band is inert, it doesn’t conduct, similarly to how in a crowded room no one can move around easily. As boron takes electrons out from the filled band, the other ones can move more easily. In a sense, during conduction, electrons are in fact continually falling into holes within the same band, but since the electrons that moved will leave new holes where the electrons had been, it is as if the holes are moving.