Valence Band
The valence band is the highest band of electron energies that is completely occupied at absolute zero in an insulator or semiconductor; it is built from the bonding states formed by the valence electrons that hold the crystal together. Because every state in a full band is already taken, its electrons cannot respond to a modest electric field, and a perfect crystal with only a full valence band and an empty band above it carries no current. The band becomes electrically interesting at the moment even one electron leaves, because the single empty state it leaves behind, a hole, lets all the remaining electrons shift and produces conduction.
In silicon the valence band is the sea of bonding electrons, with four per atom filling the lower bands. Each atom's four outer electrons form sp3 hybrid orbitals, and combining the orbitals of all atoms in the crystal produces bonding bands, filled, and antibonding bands, empty, which become the valence and conduction bands. The width of the valence band is on the order of 12 electron-volts from bottom to top, but only the upper few tenths of an electron-volt matter for devices, since that is where holes appear. The top of the band, the valence-band maximum, is the reference from which the band gap is measured: 1.12 electron-volts to the conduction-band minimum in silicon, 0.67 in germanium. In both, the maximum sits at the centre of momentum space, where the crystal momentum is zero.
Holes appear when electrons leave the valence band, and the band's detailed shape decides how those holes behave. In a nearly full band the electrons close to the top have energy that decreases as their momentum grows, which gives them a negative effective mass; treating the missing electrons as holes turns this into a positive mass and a positive charge, a trick that goes back to the 1929-31 work of Rudolf Peierls and Werner Heisenberg. The band's curvature at the top sets how readily holes accelerate, and doping with acceptors such as boron, which supplies levels about 0.045 electron-volts above the maximum in silicon, fills part of the band's top edge with empty states at room temperature. Everyday transistors, solar cells and diodes depend on that handful of empty states.
Near the maximum, silicon has not one valence band but three, with different curvatures. At the zone centre two bands, the heavy-hole and light-hole bands, meet at the same energy, and a third, the split-off band, lies lower by a spin-orbit splitting of about 0.044 electron-volts in silicon and about 0.3 electron-volts in germanium. The heavy-hole band has weak curvature, so its carriers have a large effective mass and move sluggishly, while the light-hole band curves more sharply. This mixing and warping make hole transport more complicated than electron transport and help explain why hole mobility in silicon is lower than electron mobility. Engineers manipulate it deliberately: compressive strain, produced by growing silicon-germanium in the transistor's source and drain regions, splits the heavy and light bands, lowers the effective mass and raises hole mobility, a technique that became standard in processors from about 2003.
Interfaces are defined by how valence-band edges line up, which sets the barriers that holes meet. In a silicon and silicon-dioxide structure the valence-band step is about 4.5 electron-volts, much larger than the roughly 3.1 electron-volt step for electrons, so oxides block holes more strongly than electrons and gates leak and wear differently in n-type and p-type devices. The valence-band edge also fixes the ionization energy, the energy needed to remove an electron from the solid entirely, so it matters in photoemission measurements, in solar-cell design and in matching materials in heterojunctions. In heterostructures grown by epitaxy, such as gallium arsenide with aluminium gallium arsenide, the offset in valence bands creates quantum wells that trap holes just as the conduction-band offset traps electrons.
Typical misunderstandings concern what full means and what moves. A full band conducts nothing, not because its electrons are stationary, but because they cannot reach a new state and their motions cancel; a full band also does not mean every electron is bound to one atom, since the electrons are shared in the whole crystal. The valence band is also not a physical layer in the material: a band diagram plots energy, and the edge is a statement about the allowed energies of the whole lattice. Moreover, when a hole moves the atoms stay in their places; only the pattern of occupied states shifts. The same filled-band physics sits inside every p-type transistor of a processor or AI accelerator.
Read the valence band as the filled floor of the crystal, a full sea of bonding electrons that does nothing until some of it is removed, and whose top edge then defines the gap, the barrier at every interface, and the empty states that act as holes.