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Help me out here, If thought of as electron sea, there's is no need of holes in modeling conductivity in metals. But it's not that we can deny that there will be positive charge in the nucleus after electron goes in conduction, however small its effect is. ( the effect would be small enough without small interaction electron would never had got easily detached from individual atom) The metallic bonds are some kind of covalent bond more inclusive then covalent bonds in semiconductor which occurs between only neighboring nuclei, there should be a generation of holes. And cause there is a sea of electron in conduction band, there should also be a sea of holes in valence band which can or cannot contribute in conduction (that's specifically i want to know) . Can you add something into this..

arguments maybe not structured so please ask right away

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    $\begingroup$ Yes, holes can and do contribute to conduction in metals. $\endgroup$
    – Jon Custer
    Commented Mar 30, 2020 at 18:18
  • $\begingroup$ Why don't we see it in our books then, as I mentioned there would be two seas of charges actively participating...which should double our drift current, which I hadn't seen $\endgroup$
    – Prabhat
    Commented Mar 30, 2020 at 18:21
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    $\begingroup$ Because your introductory texts try not to be too confusing too early. $\endgroup$
    – Jon Custer
    Commented Mar 30, 2020 at 18:39
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    $\begingroup$ The key point for semiconductors is that, at 0K, the valence band is full and the conduction band is empty. This allows for detailed balance to relate electron and hole concentrations ($np = n_{i}^{2}$), and allows doping to dramatically change those carrier concentrations. In metals, with partially filled bands, detailed balance no longer holds. What flows where comes down to details of the band structure. Once away from 'free-electron-like' bands it becomes quite complicated. $\endgroup$
    – Jon Custer
    Commented Mar 31, 2020 at 16:10
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    $\begingroup$ Does this answer your question? Electron holes in metals $\endgroup$
    – Shub
    Commented Oct 17, 2022 at 0:41

3 Answers 3

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The difference between insulators/semiconductors and metals is that in the former we can distinguish the valence band (completely filled with electrons) and the conduction band (completely empty). These two bands a separated by a gap, so that any change of electron energy requires energy greater than the gap energy $E_g$. As a flow of current is essentially accelerating electrons, i.e. creating electronic excitations of small energy, such materials are insulating.

Due to finite temperature some electrons may be excited to the conduction band, leaving vacant energy states behind, which we call holes. This makes conduction possible. By doping one can create materials that have extra holes in the valence band or extra electrons in the conduction band.

In metals, on the other hand, the last band is only partially filled with electrons. It is usually called the conduction band, but not in the same sense as in insulators. So defining holes and electrons doesn't make much sense. Still, some metals, with a conduction band more than 50% filled, exhibit hole-like conduction.

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  • $\begingroup$ So you're saying.that lithium, the simplest metal, with a single.unpaired free electeon per atom, has a conduction band.that is more.than half filled? Coz it behaves as a p doped conductor. $\endgroup$
    – untreated_paramediensis_karnik
    Commented Sep 25, 2022 at 7:19
  • $\begingroup$ @untreated_paramediensis_karnik the answer does not make any specific claims. I don't know enough about lithium to say whether it is really a counterexample to anything I said. However, the band structure is not solely determined by the number of outer shell electrons. $\endgroup$
    – Roger V.
    Commented Sep 25, 2022 at 7:52
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I'm not an expert in this, but in my imagination....

Imagine you have an electric circuit with a battery and a lamp and an open switch. The battery has a positive charge at one pole and a negative charge at the other. Electrons move from one end (the positive end?) wherever they can go to create a sea of electrons in the wire at that end. Electrons move from wherever they can to the negative end to create a sea of holes in the other wire. They go through the lamp into the wire beyond it to the switch, and they can't go any farther.

The wires are acting kind of like a couple of antennas. They ARE a couple of antennas and they pick up radio waves.

So then the switch is closed. Instead of a sea of electrons on one side and a sea of holes on the other side, it starts to even out.

How fast do the electrons move? Every popular description of it I've seen has been oversimplified. Typically when they figure the average speed of electrons in a copper wire, they count it as 29 electrons per atom, and we presume that 28 of them aren't moving at all. It might make more sense to only count the ones that move. Also, the electric field created by the holes versus the electric field created by the electrons is not a very big force acting on electrons. Maybe the current is more a statistical thing. Electrons happen to move a lot, back and forth, and they move on average more from where there are a lot of them to where there are fewer.

Imagine a freeway. Is it a freeway at rush hour, where lots of cars are moving very slowly? Or is it a freeway with a little traffic moving fast in both directions, and the average speed is just about zero because there are as many cars going one way as the other way?

This could be important. What if it's a lot of electrons traveling at relativistic speeds in both directions, a few more in the direction of the current? Then relativity is affecting all of them.

Maybe this should be its own question rather than an answer to yours, but it looks like you're trying to imagine pictures of it, and so am I.

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Semiconductors can be either N-type or P-type.

In the N-type there are "unattached" electrons, not involved in crystal bonding, which can be nudged away from their parent atom with around a volt or so, into what is known as the conduction band, and are then free to wander.

In the P-type there are not enough electrons to form all the bonds required by the crystal lattice, so there are "holes" left in the lattice where an electron is missing. Again, a volt or two can persuade an electron to jump into a neighbouring hole - but it leaves another hole behind it, as if it were the hole that had moved not the electron. A P-type hole can move approximately as freely as an N-type conduction electron can.

A metal is in some ways like an N-type semiconductor, except that the unattached electrons already have enough energy to go wandering at will, they cannot be stopped, so it is a regular conductor. There are no holes in a metal.

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  • $\begingroup$ Some metals exhibit a positive Hall coefficient. Some, such as beryllium, have different signs depending on the direction of the transport. Metals can be pretty weird. $\endgroup$
    – Jon Custer
    Commented Mar 30, 2020 at 18:38
  • $\begingroup$ Even the simplest metal doesn't behave as an n doped semiconductor: lithium with a single unpaired electron per atom. $\endgroup$
    – untreated_paramediensis_karnik
    Commented Sep 25, 2022 at 7:17

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