The toolkit

Everything in this course happens at a scale you will never see directly, so it is worth fixing it first. The unit is the nanometre: a millionth of a millimetre, or 0.000 001 mm.

Some landmarks help. A human hair is about 70,000 nanometres across. A bacterium is about 2,000, a flu virus about 100, and the DNA in your cells about 2 nanometres wide. A single atom is smaller still: a few tenths of a nanometre across.

A 2D material is a crystal one or a few atoms thick. One layer of graphene is 0.335 nanometres thick, so a sheet of office paper is as thick as about 300,000 of them stacked up. Counting one layer a second, you would need three and a half days to count that stack.

Because the numbers are so far apart, scientists compare sizes in steps of ten. The ladder below goes down one step of ten at a time; from paper to a single layer of graphene is more than five such steps.

Everything around you is made of atoms, and every atom follows the same plan: a tiny, heavy nucleus in the middle, made of protons and neutrons, surrounded by much lighter electrons. Protons carry a positive charge and electrons an equal negative one, so a whole atom is neutral. Almost all of an atom is empty space: if the nucleus were a pea in the middle of a football stadium, the electrons would be spread over the stands.

What makes one element different from another is the number of protons. Carbon has 6, sulfur 16, molybdenum 42. The periodic table lists the elements in that order, and elements in the same column behave alike – which is why sulfur, selenium and tellurium turn up in the same kinds of crystal again and again.

For this course the electrons matter most. The outermost ones decide how an atom bonds to its neighbours, whether a material conducts electricity, and which colours of light it absorbs. Each electron also carries a tiny built-in magnet, its spin, which is where magnetism comes from.

Electrons do not circle the nucleus like planets. They can only have certain energies – like the floors of a building, which you can stand on but not between – and a jump from one allowed energy to another takes in or gives out a fixed amount of energy. That one fact explains much of what the later levels describe.

Atoms stick together because of their electrons, and they do it in a few distinct ways. In a covalent bond, two neighbouring atoms share a pair of electrons. Covalent bonds are strong and point in fixed directions, which is why diamond is so hard – and why a sheet of graphene, held together entirely by them, is the strongest material ever measured.

In an ionic bond, one atom hands an electron to another. The first becomes positive, the second negative, and the two attract. Table salt is built this way, from sodium and chlorine. In a metal, every atom gives up one or more electrons to a shared sea that flows between them – which is also why metals conduct electricity so well.

There is also a much weaker attraction that acts between almost any atoms or molecules that come close: the van der Waals force. It is tens of times weaker than a chemical bond, or more, yet added up over millions of tiny hairs it lets a gecko walk up a pane of glass.

Layered crystals combine the two extremes. Inside each layer, strong covalent or ionic bonds hold the atoms firmly; between the layers there is only the weak van der Waals attraction. Pull on such a crystal and it splits between its layers, not through them. That is what makes 2D materials possible.

A crystal is a solid whose atoms sit in a pattern that repeats, over and over, in every direction. Salt, sugar, quartz, diamond, the silicon in a computer chip and almost every metal are crystals, even when they do not look like the neat shapes in a mineral collection.

Because the pattern repeats, you only need to describe one small piece of it: the unit cell, the smallest block that builds the whole crystal when you copy it side by side – like the one motif that covers a whole roll of patterned wallpaper. Its edges are a few tenths of a nanometre to about a nanometre long.

The same atoms can repeat in different patterns, and the pattern can matter as much as the atoms. Diamond and graphite are both pure carbon. In diamond each atom bonds to four neighbours in three dimensions, making the hardest natural material and an electrical insulator. In graphite each atom bonds to three neighbours in a flat honeycomb, and the honeycomb sheets stack loosely, making a soft, grey conductor that leaves a mark on paper – the ‘lead’ in a pencil.

One of those honeycomb sheets, on its own, is graphene. The later levels come back to crystal patterns again and again, because what a 2D material does starts with how its atoms are arranged in the sheet, and how the sheets sit on each other.

Light is a wave, and the distance from one crest to the next – its wavelength – sets its colour: about 700 nanometres for red, 530 for green, 450 for blue. Shorter than about 400 nanometres is ultraviolet, which we cannot see; longer than about 750 is infrared, which we feel as warmth.

Light also comes in packets, called photons, and the energy of each packet depends only on the colour: the shorter the wavelength, the more energy per photon. That is why ultraviolet light can give you sunburn and red light, however bright, cannot. A material takes in a photon only if the photon brings enough energy for one of the jumps its electrons can make.

Scientists measure these energies in electronvolts, eV for short: the energy one electron gains when it is pushed through one volt. It is the natural unit for everything electrons do. A red photon carries about 1.8 eV and a blue one about 2.8 eV, and there is a handy rule to convert: divide 1240 by the wavelength in nanometres to get the energy in electronvolts.

You will meet the electronvolt on almost every page about 2D materials – as the size of a band gap, the energy of the light a layer gives off, or how tightly two particles are bound together.

Materials fall into three families by how they treat an electric current. In a metal such as copper, many electrons are free to move, and the smallest voltage sets them flowing: it is a conductor. In an insulator such as glass or plastic, every electron is held in place, and almost no current flows however hard you push. Semiconductors such as silicon sit in between – and, crucially, can be switched from one behaviour to the other.

The reason lies in the energies the electrons are allowed. In a crystal they come in ranges called bands, separated by gaps where no electron can be. In an insulator the lower band is completely full and the next one is far above it: no electron can move, because there is nowhere for it to go, and lifting one across the gap takes a lot of energy. In a metal a band is only partly full, so electrons move easily. A semiconductor is like an insulator with a small gap, so a little energy, a voltage or a few added atoms bring free electrons into play.

That switchability is what every transistor in a computer chip relies on, and the size of the gap also decides which colours of light a material takes in and gives out. Level 4 returns to bands in detail. For now, keep the three families in mind, because every 2D material belongs to one of them: graphene behaves almost like a metal, boron nitride is an insulator and MoS₂ a semiconductor.