# Problem with energy bands

I am getting confused by the energy bands. As far as I know, the outermost shell of an atom is called valence shell. The electrons residing in that shell participate in reactions and conduction of electricity. The valence electrons construct an energy level diagram (for a single atom).

Now in the case of a crystal lattice, there is not one atom but many, and the inter-atomic interaction between the atoms split an energy level into as many energy levels as there are atoms in the crystal. These heavily congested energy levels construct a near-continuous energy band. Similarly, the valence shell electrons construct the valence band.

Now, when an external energy field is applied, the valence electrons jump out of the valence band and roam freely throughout the crystal and participates in electrical conduction, therefore these excited electrons construct a conduction band. There is a forbidden energy gap $E$ between the valence and conduction band, which equals the amount of energy required for an electron to jump from valence to conduction band.

Lets have an example, sodium's electron configuration is $1s^2 2s^2 2p^6 3s^1$, so the outermost shell (M shell) has 1 electron, which is the valence electrons. This will construct the valence band for $3s$.

Question is, somewhere I've read that the conduction band is the next available empty shell.

1. Is the valence band constructed from the outermost shell of the atom, or is that the conduction band?

2. Are all the things I've stated true? Or did I misunderstand the whole thing? If so, please enlighten.

• When the outer band is half (not completely) filled there are many nearby energy levels available for electrons so you have good conduction. When the outer band is full the next band is some energy gala away. If that gap is small you have a semiconductor (some electrons are excited into the conduction band thermally). If the gap is large you have an insulator. – Floris Apr 19 '15 at 21:03

## 1 Answer

What you said is not completely true. Valence electrons are involved in the formation of energy bands, the lower in energy is called "valence" band while the higher in energy is called "conduction" band but they both originate from the valence electrons. According to Pauli's principle only 2N electrons can be found in a band, where N is the number of atoms involved in the band, you can have conduction only if the band is not full so it is possible to have conduction also in the valence band (if the lattice's atoms are monovalent). If the valence band is full and the energy gap between valence and conduction band is small enough, electrons can reach the conduction band (for example through thermal excitations) and the solid becomes a good conductor.