Band Theory for Conductors

Q1: What's the difference between conduction and valence electrons?
A1: Conduction electrons are not associated with particular atoms, and hence move freely and conduct current. Valence electrons are associated with particular atoms, and do not necessarily move as freely.

Q2: What are some of the key ideas of band theory?
A2: Band theory introduces the concepts of the conduction band, valence band, and energy gap.
The conduction band arises from the cumulative effect of having enough conduction electrons at different energy levels.
The valence band arises from the cumulative effect of having enough valence electrons at different energy levels.
For both the conduction and valence bands, the energy levels are so close together that they can be treated as a continuum (and hence, the term "band").
The energy gap is the difference in energy from the bottom of the conduction band to the top of the valence band.

Q3: How does band theory explain conductors, insulators, and semiconductors?
A3: Conductors have no energy gap; in fact there is overlap between the valence and conduction band, meaning that some of the valence electrons are free to conduct.
Insulators have a large energy gap, so their valence electrons are not free to conduct.
Semiconductors have a smaller energy gap, which would suggest that they too would be unable to conduct. In fact, this is the case at 0K. But at room temperature, there's usually enough thermal excitation to bump some of the valence electrons in to conduction band.

Q4: Why is this smaller energy gap important for semiconductors?
A4: As mentioned in A3, the smaller energy gap enables some of the valence electrons to feasibly reach the conduction band at room temperature. But the smaller threshold also explains helps to explain doping. Consider the energy gap of a PN junction. The p-type semiconductor puts holes at the bottom of the energy gap, which makes it easier for valence electrons to enter these extra energy levels. The n-type semiconductor puts extra electrons at the top of the energy gap, which makes it easier for electrons at these energy levels to enter the conduction band.