How do semiconductors behave?
Some semiconductors are well-behaved and have these nice bands that make things simple. Galllium arsenide, zinc oxide, magnesium oxide and other materials are like this. Then there are indirect semiconductors. Among these are silicon, germanium, and gallium phosphide. What this translates to is that electrons can easily jump up or down between ground and active states in direct bandgap (DB), but they need some push in indirect bandgaps (IB). Starting from here, let’s take a deeper look.
Electrons can only have certain discrete energies as described by specific states. Since electrons are wavelike, we can describe electrons using wavelengths, or more specifically, wavevectors. Wavevectors are wavelengths with specific directions. The energy versus wavevector graph describes what energy states electrons can exist in at certain wavevectors. I.e., an electron at one wavelength can exist in one state. The graphs shown describe this behavior.
While all solids have these graphs, semiconductors exhibit a characteristic gap between bands. All solids have these curves. Metals have curves that overlap and thus they effectively have no bandgap. If a single valence and conduction curve were isolated for a metal, a gap would in fact be present. This individual pair of curves are clearly defined and are called Brillouin zones. In semiconductors, the curves will of course overlap, but there will be a gap in between the bands. The bandgap describes the energy states in which electrons cannot occupy. It is defined using the highest valence value and the lowest conduction value. How close together these two points are describe how easily electrons can move into the conduction band (CB). Insulators are solids with very large bandgaps, for example.
Direct versus indirect bandgaps
When the lowest point in a CB is directly above the highest point of the valence band (VB), the solid has a direct bandgap (DB). DB semiconductors make it easy for electrons to move into the CB, since they can do so directly. It should be noted that electrons can move down from another point on the CB to a point in the VB directly below it. It is just easier to go from trough to peak. It is because of this DB that radiative recombination is much more prevalent in DB semiconductors. To change wavevector (move horizontally on the graph), the electron needs to change its momentum. This is not as easy nor as simple, but it happens and it happens to be quite useful.
Unlike DB semiconductors, indirect bandgap (IB) semiconductors require phonons for electrons to jump down (or up). Note that phonon interaction can cause electrons to jump down and across different momentum values; however, it occurs not nearly as often. In IB semiconductors, it is the primary mechanism for electrons to jump bands. It is because of some semiconductors’ IBs that make radiative recombination nearly negligible.