Energy bands

In an isolated atom an electron's energy is fixed by its orbit. In a solid the atoms are so close that outer orbits of neighbours come near or overlap, which changes how electrons move.

No two electrons in a crystal see exactly the same surrounding charges, so each has a slightly different energy. These closely spaced levels merge into energy bands that vary almost continuously.

The band holding the valence electrons' levels is the valence band; the band above it is the conduction band. With no outside energy, the valence electrons all stay in the valence band.

Si's outermost electrons are in the n = 3 orbit and Ge's in n = 4. Each atom has 4 outer electrons but room for 8, so a crystal of N atoms has 4N valence electrons and 8N available states.

At the atomic spacing of Si and Ge, the 8N states split into two bands of 4N each, separated by an energy gap Eg. At absolute zero the lower band (valence band) is completely full and the upper band (conduction band) is completely empty.

EC is the bottom of the conduction band and EV the top of the valence band. The band gap is Eg = EC − EV; it can be large, small or zero depending on the material.

Metals: the conduction band is partly filled, or the two bands overlap, so many electrons are free to move. Resistance is low.

Insulators: Eg > 3 eV. The conduction band is empty and heat cannot lift electrons across so wide a gap, so no conduction occurs.

Semiconductors: Eg < 3 eV. At room temperature a few electrons gain enough thermal energy to cross into the conduction band, so the resistance is far below an insulator's.

When an electron is lifted across the gap it also leaves an empty level in the valence band, so conduction can happen both in the conduction band and through the vacancies in the valence band.