Electrical current in metals | energy bands

[Goodver]

Why electrical current is possible only with the presence of energy BANDs, rather than discrete energy levels.

Thank you.

 

[mfb]

Why do you think discrete energy levels do not allow currents?

 

[Goodver]

As far as I understand now, in case of discrete energy levels, electrons can not jump from one atom to another because it would violate Pauli exclusion principle, but in case of energy bands, it is somehow possible. And I am not sure about why is it possible.

 

[mfb]

They can always go to free states, it does not matter if they are in a band or not. Most solids form bands, and you still have good conductors (like metals, no band gap) and good insulators (with a band gap) there.

 

[Goodver]

Suppose we have Beryllium (2s2). As far as I understand electron can jump to the free state without changing its quantum numbers. In case of Beryllium s orbital is fully occupied, thus electron can not jump to s orbital again, and only possibility if it would jump to p orbital, which will require change of L quantum number and change of electron's state. What makes electron to change it's state?

Insulators topic, seems to be more less clear to me.

 

[yehokhenan]

The electron can change its state by acquiring energy from somewhere. This can be from a photon, a phonon or an applied electrical bias.

 

[Goodver]

The electron can change its state by acquiring energy from somewhere.

Change of energy would mean change of energy level (principal quantum number), as far as I understand, electrical current is due to jump of electrons within degenerate states, that's why electrical current possible in metals and not in insulators (without changing of energy level).

 

[mfb]

The concept of principal quantum numbers does not make sense if the electron is not bound to a specific atom.
Bands are simply energy regions where the states are extremely close together, so even tiny energy changes are sufficient to reach a different state.

 

[Goodver]

Ok, I am confused now. What is meant by the state then? And what determines when the band is fully packed and when not?

As far as I understand, electrons can be in one of the energy bands which are separated by energy gaps (Kronig Penney model). On each energy band/level can be only certain amount of electrons. In insulators we have elements for which energy bands are fully packed, therefore to conduct a current electron must be excited to the higher energy band, which requires overcoming of energy gap. In case of conductors, energy bands are not packed fully, thus electrons do not have to overcome energy gap to conduct.

Is this correct?

 

[mfb]

What is meant by the state then?

An energy level that can get occupied by an electron.

And what determines when the band is fully packed and when not?

The number of electrons compared to the number of available energy levels.

As far as I understand, electrons can be in one of the energy bands which are separated by energy gaps (Kronig Penney model).

The gap does not have to exist.

Right.