# Do holes conduct electricity in metal?

1. Sep 1, 2016

### Happiness

1. The problem statement, all variables and given/known data
The conduction band of a metal is partially filled.

When an electron of a metal from a lower band is excited and becomes mobile, the metal conducts electricity. The excitation also leaves behind a hole in the lower band.

Q1. Does this hole contribute to the electrical conductivity of a metal?

Q2. What is the energy level an electron must be excited to for it contribute to conductivity? Is it any level above the Fermi energy? The Fermi energy is the highest energy level of an electron of a metal at 0 Kelvin.

2. Relevant equations
This is NOT a homework question. I just want to clarify my concepts.

3. The attempt at a solution

Q1. Both holes and electrons contribute to conductivity of semiconductors. So I guess this is true for metals too. A metal is made up of metal cations in a sea of delocalised electrons. The electrons in the lower band (those that are not delocalised) from a metal cation can move to an adjacent metal cation and fill up its holes. Or maybe they can't move. If so, then why those in a semiconductor atom can move to an adjacent atom to fill up its holes? Doesn't this produce a contradiction?

Q2. By suggesting that the minimum energy required is the Fermi energy, that is already my attempt to answer my question. Clearly, I'm not an expert in band theory. If I am, I won't be asking these questions. If the answer is no, it's not Fermi energy, then we will just call it something else, like conduction energy. And it should be higher than Fermi energy.

This is my own question. I just want to clarify my concepts.

[Moderator's note: non-pertinent content edited]

Last edited by a moderator: Sep 1, 2016
2. Sep 4, 2016

### Staff: Mentor

In a metal, the concept of holes doesn't work as well as it does for semiconductor because there is no gap that would separate the energy levels into two different regions.

Holes in metals could be interpreted as unoccupied low-energetic electron states below the Fermi level. Those contribution to conduction, sure.

You don't see the localized electrons in this picture, their energy is even lower.
It is close to the Fermi energy - within the range where the occupancy is neither "nearly 100%" nor "nearly 0".