Band Gap: One Number That Decides Almost Everything
Ask why silicon is used for solar cells, why diamond is transparent, why copper conducts, and why graphene behaves like nothing else, and the answer to all four is the same quantity with four different values. The band gap is the most compressed piece of information in materials science: a single energy that tells you, before anything else, what a material is for.
Where the Gap Comes From
An isolated atom has electrons at discrete energy levels. Bring many atoms together into a crystal and those levels split and broaden into continuous bands, because no two electrons can occupy the same state. The result is ranges of energy electrons can have, separated by ranges they cannot.
The highest band that is full at low temperature is the valence band; the next one up is the conduction band. An electron in a full band cannot move usefully, because moving means changing state and every nearby state is occupied. Only in a partly filled band can charge flow.
The band gap is the energy distance between the top of the valence band and the bottom of the conduction band. If it is zero or the bands overlap, there are always available states and the material is a metal. If it is wide, no ordinary process can lift an electron across, and the material insulates.
Semiconductors occupy the middle, and their usefulness comes entirely from that. The gap is small enough that carriers can be created deliberately - thermally, optically, or by doping - and large enough that they are not there by default. A material whose conductivity you can switch is far more useful than one that simply conducts.
Why the Gap Sets Optical Behaviour
A photon can only be absorbed by promoting an electron across the gap, and it can only do that if it carries at least the gap energy. Photons with less energy pass straight through. This single rule explains a great deal.
Diamond has a gap near 5.5 eV, far above visible light, so no visible photon can be absorbed and the crystal is transparent and colourless. Silicon has a gap of 1.12 eV, below the energy of visible light, so it absorbs the whole visible spectrum and appears grey-black. A material's colour is largely its band gap.
For solar cells this creates a direct trade. A wide gap means high voltage per absorbed photon but many photons pass through unused. A narrow gap absorbs almost everything but wastes most of each photon's energy as heat. The optimum for a single junction under sunlight sits somewhere between 1.1 and 1.4 eV, which is why silicon and gallium arsenide are both close to the ideal.
That trade is the reason for tandem cells, where two materials with different gaps are stacked so each handles the part of the spectrum it suits - the approach that has taken perovskite-silicon devices past the theoretical ceiling for silicon alone.
Direct and Indirect
Electrons in a crystal have momentum as well as energy, and a full description places the bands on both axes. In some materials the top of the valence band and the bottom of the conduction band sit at the same momentum. That is a direct gap, and a photon alone can drive the transition.
In others they sit at different momenta. Then a photon is not enough: the transition also needs a lattice vibration to supply the momentum difference. Requiring two events to coincide makes the process orders of magnitude less likely. That is an indirect gap, and silicon has one.
The consequences are practical rather than subtle. Indirect-gap materials absorb weakly, so they need to be thick. They also emit weakly, which is why silicon cannot easily be made into an LED and why light-emitting devices use direct-gap compounds instead.
This is a good example of why a single number is not enough to characterise a material. Silicon and gallium arsenide have gaps within a few tenths of an electronvolt of each other and behave completely differently optically, because one is direct and the other is not.
The Zero-Gap Case
Graphene is the interesting exception. Its valence and conduction bands touch at a single point, so the gap is exactly zero - but unlike a metal, there is no overlap either. It is a semimetal, and near that touching point its electrons behave as though they had no mass at all.
This gives graphene extraordinary conductivity and mobility. It also means it cannot be switched off, which is the central obstacle to using it as a transistor channel: a device that cannot be turned off is not a switch. A great deal of research has gone into opening a small gap in graphene by straining it, patterning it into narrow ribbons, or stacking it in bilayers.
For absorption the zero gap cuts both ways. Graphene absorbs across a very wide spectrum, including infrared where silicon is transparent, but a single layer absorbs only about 2.3 percent of incident light - remarkable for one atom of thickness, negligible in absolute terms.
In a graphene and silicon multilayer such as the one our research concerns, this contrast is the point rather than a problem. Two materials with completely different band structures placed in contact form a heterojunction, and the behaviour of that junction is not predictable from either material alone. What it does depends on the interface, which is why claims about such a stack have to be supported by measurements of the assembled device rather than by properties of its ingredients.
Frequently asked questions
What exactly is a band gap?
The energy separation between the highest electron states that are occupied and the lowest empty states in which charge can move. An electron must acquire at least that much energy to contribute to a current.
How does it distinguish metals from insulators?
Metals have no gap or overlapping bands, so charge can always move. Insulators have a gap too wide for ordinary processes to bridge. Semiconductors sit between, with a gap small enough that carriers can be created on purpose.
Why does the band gap determine colour?
Because a photon can only be absorbed if it carries at least the gap energy. Diamond's 5.5 eV gap is above visible light, so it is transparent. Silicon's 1.12 eV gap is below it, so silicon absorbs the whole visible range.
What is the difference between a direct and an indirect gap?
In a direct gap the band extremes sit at the same momentum and a photon alone can drive the transition. In an indirect gap they do not, so a lattice vibration is also needed, which makes absorption and emission far less likely.
Does graphene have a band gap?
No. Its bands touch at a point, making it a zero-gap semimetal. That gives it exceptional conductivity but means it cannot be switched off, which is the main obstacle to using it in transistors.
