The unit of energy for electrons, light and chemical bonds: the energy one electron gains when it is pushed through a voltage of one volt. It is tiny – about 1.6 × 10−19 joules – but it is the natural size for single atoms and electrons. Visible light comes in photons of about 1.6 to 3.3 eV, the band gaps of semiconductors are around 1 to 2 eV and chemical bonds a few eV; smaller effects, such as the energy of heat at room temperature, about 25 meV, are counted in millielectronvolts.
Scientists measure these energies in electronvolts, eV for short: the energy one electron gains when it is pushed through one volt.
Indirect gaps with the conduction band minimum at the zone boundary; PBE underestimates by the better part of an electronvolt, so use hybrids or GW.
Pushing one electron through a potential difference of one volt gives it one electronvolt of energy. In joules that is a tiny number, 1.602 176 634 × 10−19 – exactly, because the charge of the electron has been fixed by definition in the SI units (Tiesinga and colleagues, 2021). The joule suits kettles; for one electron, one photon or one chemical bond the electronvolt gives numbers of a convenient size.
So the scales of the field read naturally in it. Chemical bonds hold their atoms with a few electronvolts. Band gaps run from zero in graphene through about 1–2 eV for the common semiconductors to about 6 eV in hexagonal boron nitride, an insulator. Thinning MoS2 from bulk to a single layer shifts its indirect gap up by more than 0.6 eV, enough to turn it into a direct-gap material that emits light strongly (Mak and colleagues, 2010).
A photon’s energy and wavelength are tied together: the wavelength in nanometres is about 1240 divided by the energy in electronvolts. Red light at 700 nm is 1.77 eV, violet at 400 nm is 3.10 eV, and the 1550 nm light of optical fibre is 0.80 eV. Matching a band gap to a wavelength – to make a detector for telecom light or an emitter for a display – is therefore a sum anyone can do.
Heat is far smaller. The typical thermal energy at room temperature, k_BT, is 25.85 meV, about a fortieth of an electronvolt. A band gap many times larger keeps a semiconductor’s bands empty at room temperature, and the binding energies of excitons in monolayers, hundreds of millielectronvolts, are why they survive there at all.
Every branch of spectroscopy keeps its own unit, and all of them are energies. Raman spectroscopy counts in wavenumbers: 1 meV is 8.066 cm−1, so graphene’s G band near 1580 cm−1 is 0.196 eV. Terahertz work counts in frequency: 1 meV is 0.2418 THz. Low-temperature physics counts in kelvin: 1 meV is 11.60 K. Magnetic splittings are given per tesla – the valleys of WSe2 split by about 0.25 meV for each tesla of field.
All these conversions follow exactly from the defined values of the Planck constant, the speed of light, the elementary charge and the Boltzmann constant, so they never need measuring again.
1 eV = 1.602 176 634 × 10−19 J exactly, the elementary charge being a defined constant of the SI. Exact consequences of the defined constants give the working conversions: a photon of energy E has a vacuum wavelength λ ≈ 1239.84 nm / E[eV]; 1 meV corresponds to 8.066 cm−1, 0.2418 THz and 11.60 K; and k_BT at 300 K is 25.85 meV. Spectroscopies keep their own units – Raman shifts in cm−1 (graphene’s G band near 1580 cm−1 is 0.196 eV), terahertz in THz, magnetic splittings in meV per tesla – so the same energy appears under several names. Thinning MoS2 to one layer raises its indirect gap by more than 0.6 eV and turns it into a direct-gap emitter.
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