The energy an electron needs to jump from a full band, where it is stuck, into an empty one where it can move and carry current – like a car in a packed car park, which can only drive off once it is lifted to the empty deck above. Metals have no gap and always conduct; have a large gap and hardly conduct; sit in between, which is what makes them switchable.
Going deeper
Left: in a metal the highest occupied band is only partly filled, so electrons can always move; a semiconductor has a modest gap and an insulator a wide one. Right: in a direct gap the band edges sit at the same momentum and light alone can lift an electron across; in an indirect gap a lattice vibration (a phonon) has to supply the missing momentum.
Where the gap comes from
An isolated atom has sharp energy levels. Bring many atoms together into a crystal and each level broadens into a band of closely spaced states. Electrons fill these states from the bottom up: the highest band that is completely filled is the valence band, and the next one above it, empty, is the conduction band. The band gap is the range of energies between them in which the crystal has no states at all.
A filled band cannot carry a current, because every state is taken and electrons have nowhere to move. To conduct, an electron has to be lifted across the gap into the empty conduction band – by heat, by absorbing light, or by a strong electric field – leaving behind a hole that conducts too. The size of the gap therefore decides the character of the material: no gap makes a metal, a gap of up to a few electronvolts a semiconductor, and a wider one an insulator.
Direct and indirect gaps
Electrons in a crystal carry momentum as well as energy, so the band edges have a position in momentum as well as a height. When the top of the valence band and the bottom of the conduction band sit at the same momentum, a – which carries almost no momentum – can bridge the gap on its own, and the material absorbs and emits light efficiently. When they sit at different momenta, the jump also needs a lattice vibration to supply the difference, which makes light emission weak.
MoS2 shows both. Bulk MoS2 has an indirect gap of about 1.2–1.3 eV; as it is thinned to a the band edges shift until the monolayer has a direct gap of about 1.9 eV. That crossover is why a monolayer glows brightly under a laser while a thicker flake of the same crystal barely does.
Why a 2D gap needs a qualifier
A monolayer is surrounded by vacuum or a rather than by more of itself, so the electric fields between charges inside it are screened far less than in a bulk crystal. Two consequences follow. The energy needed to create a free electron and a – the – grows, and at the same time electrons and holes attract each other strongly enough to bind into .
The gap seen in an optical measurement is therefore smaller than the quasiparticle gap by the exciton binding energy, which in monolayer is several hundred meV. Both numbers also move with the environment: the same monolayer has a different gap on SiO2, on graphene or in hBN. A band gap quoted for a means little without saying which gap, measured how, and on what.
For specialists
The energy range between the valence-band maximum and the conduction-band minimum in which a crystal has no electronic states. It is direct when both extrema lie at the same crystal momentum and indirect otherwise; monolayer MoS2 is direct while bulk MoS2 is indirect. In 2D the and optical gaps differ strongly because excitons are tightly bound.