Band Gaps, Photon Energies and the Joules Behind Them
Semiconductor and photonics work runs almost entirely in electronvolts. A band gap is 1.12 or 3.4, a laser line is quoted by wavelength, an emitter is picked by the colour its junction can produce. The moment that physics has to meet an optical power budget, a detector responsivity in amps per watt or a thermal calculation, the numbers have to become joules — because watts are joules per second and nothing in radiometry is denominated in electronvolts. This page is that one crossing, at the scale where a single photon carries less than a billionth of a billionth of a joule.
What the Electronvolt Is Describing Here
One Volt Across One Elementary Charge
The Gap Sets the Colour
Per Photon, Never Per Beam
Exact, Not Measured
Taking a Band-Gap Figure into SI for a Device Model
Start from whichever number the data sheet actually prints — a gap in eV, a peak wavelength in nm, or a photon energy already in joules — and convert once, at the point where the optical calculation hands over to the electrical one.
Pin down the energy in electronvolts
If the source quotes a wavelength instead, divide 1 239.84 by the wavelength in nanometres. A 1 550 nm telecom line comes out at 0.80 eV; a 460 nm indium gallium nitride emitter at about 2.70 eV.
Type it into the eV field
The joule column resolves as each digit lands. Decimal commas are read the same as points and stray spaces are dropped, so a value lifted out of a European alloy-composition table needs no cleaning first.
Turn it round when the source is already SI
The swap arrows point the pair the other way, which is what you want when a radiometry note gives energy per photon in joules and you would rather see the gap it corresponds to. Either side can also be re-aimed through its searchable unit list, putting keV, MeV and GeV one selection away.
Lift the exponent form into your model
The copy control above each field takes the digits alone, without a unit label, which is the form a TCAD input deck or a Python notebook expects. Ctrl+C inside a field does the same.
Semiconductor Gaps, Emission Wavelengths and Single-Photon Energies
Each row pairs a room-temperature band gap — or a photon energy, where the entry is a light source — with the wavelength it corresponds to and the joule content of one quantum at that energy. The wavelength column comes from 1 239.84 ÷ E(eV); the joule column is the eV figure multiplied by 1.602177e-19.
| Material or source | Energy (eV) | Wavelength (nm) | One photon (J) |
|---|---|---|---|
| Germanium | 0.66 | 1 878.5 | 1.057437e-19 |
| Telecom C-band photon | 0.80 | 1 549.8 | 1.281741e-19 |
| Silicon | 1.12 | 1 107.0 | 1.794438e-19 |
| Gallium arsenide | 1.42 | 873.1 | 2.275091e-19 |
| Red AlGaInP emitter | 1.91 | 649.1 | 3.060157e-19 |
| Blue InGaN emitter | 2.70 | 459.2 | 4.325877e-19 |
| 4H silicon carbide | 3.26 | 380.3 | 5.223096e-19 |
| Gallium nitride | 3.40 | 364.7 | 5.447401e-19 |
Read down the energy column and the whole logic of detector and emitter selection appears at once. Germanium and the telecom photon sit below silicon's gap, which is exactly why a silicon photodiode goes blind past about 1 100 nm and fibre receivers are built from indium gallium arsenide instead. Climb to the other end and gallium nitride's 3.40 eV lands in the ultraviolet — blue emitters reach 460 nm by alloying indium into it to pull the gap back down to roughly 2.7 eV.
What This Pairing Gives a Photonics Calculation
Sub-Attojoule Values Keep Their Exponent
Anything below a millionth of a joule is shown in exponent form rather than as a row of leading zeros, so a single-photon energy stays readable and stays checkable.
keV, MeV and GeV Without Leaving the Page
The searchable list on each side reaches the whole electronvolt ladder alongside the joule family, which matters as soon as the work moves from optical photons up to X-ray energies.
Band-Gap Digits for a Device Deck
Copied output carries no unit text, so an exponent-form joule value drops straight into a simulation parameter or a responsivity spreadsheet without editing.
Swap Back When the Note Is Already in Joules
Radiometry sources give energy per photon in joules; one press reverses the pair so that figure can be read back as the electronvolt value an alloy datasheet would print.
Photonics Questions About Electronvolts, Wavelength and Gap
Where does the 1 240 in E = 1240/λ come from?
It is hc divided by the elementary charge, expressed in electronvolt-nanometres. Planck's constant times the speed of light gives 1.986 445e-25 J·m; divide that by 1.602 177e-19 J per eV and rescale from metres to nanometres, and out comes 1 239.84 eV·nm. Because both constants are now defined exactly, so is that shortcut. Rounding it to 1 240 costs about 0.013 per cent — harmless for a band gap, worth keeping in full for a narrow spectroscopic line.
How many photons per second does a 1 mW laser emit?
Divide the optical power by the energy of one photon. At 1 550 nm each photon is 0.80 eV, or 1.281741e-19 J, so a milliwatt is 1e-3 ÷ 1.281741e-19 ≈ 7.8e15 photons every second. Move to a 532 nm green line at 2.33 eV and each photon costs 3.733921e-19 J, giving about 2.7e15 per second for the same milliwatt. Shorter wavelength, fewer but harder photons — which is why photon-counting rates and shot-noise limits are meaningless unless a wavelength is quoted with them.
Why keep a unit whose joule value has eighteen zeros after the point?
Because the electronvolt puts the interesting numbers between about 0.5 and 4, where a person can compare them at a glance and spot a wrong one. Writing silicon as 1.794438e-19 J instead of 1.12 eV hides the fact that it sits just below the telecom band and just above germanium. The unit also maps onto junction voltage directly, so an engineer reading 3.4 eV already knows roughly what forward bias the diode will want.
What does an LED's forward voltage tell me about its band gap?
Roughly the gap in volts, plus overhead. Each carrier crossing the junction gains one electronvolt per volt applied, so an emitter cannot light up much below Eg ÷ e. A red AlGaInP part at 1.91 eV turns on near 1.9 V; a blue InGaN part near 2.70 eV needs closer to 3 V, and its data sheet usually quotes 3.0–3.4 V at rated current because contact and series resistance sit on top. The difference between turn-on and rated forward voltage leaves as heat, not light.
Why does a wider gap always mean a bluer emission?
Energy and wavelength are inversely related, so pushing the gap up pushes the emitted wavelength down. Gallium arsenide at 1.42 eV radiates at 873 nm and is invisible; widen the gap to 1.91 eV and it is red at 649 nm; widen it again to 2.70 eV and it is blue at 459 nm. That same inverse relationship is why the visible band is so narrow in energy terms — deep red to violet spans barely a factor of two, from about 1.65 to 3.26 eV.
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