# Can electrons have energies between valence and conduction bands?

When looking at pictures of direct band gaps from a crystal lettice I wondered if it really is impossible that electrons, even if its only for a short time, occupy the Energies between the band gaps ? Or is it just that these Energies between the two gaps arent solid energies ? Meaning that an electron have such an energy value but it would want to (and actually do) decrease or increase its energy until its in the valence or conduction band.

• There are no states in the gap to occupy. (In real crystals there are impurities and defects that may have states in the gap, so keep that in mind. Dopants are a special kind of impurity, and they have states in the gap.) Jan 24 at 22:41
• Not in any useful way. If you want to get away from thinking about individual electrons, then you can model how a passing photon causes ripples in the electromagnetic and electron fields, but none of those are electrons. If those ripples add up in the right way, we can talk about an electron jumping to a higher energy level - but there must be such quantized energy level in the first place. I'm not aware of any case where those "disturbances" to the electromagnetic/electron fields would be of any importance to chemistry (unless you count superposition in general, but... don't). Jan 25 at 12:13

This is similar to asking if an electron, in say a hydrogen atom, can occupy an energy level somewhere in between the $$n=1$$ and $$n=2$$ levels.
In this instance, and in the context of your question, the energies of electrons are quantized, and therefore can only possess allowed energies and will occupy only allowed energy levels in the conduction and valence band. So they are forbidden from entering a band gap (provided it is an ideal lattice with no impurities). Certainly, there is no possible states for them to occupy in the band gap to begin with, much like there is no possible state for our electron in the hydrogen atom to be "between $$n=1$$ and $$n=2$$". This is the essence of quantum mechanics.