Picture 1
Three LEDs
Each LED is a chip of crystal a third of a millimetre across, wired to the battery through its own 50-ohm resistor, as real LEDs are: a few tenths of a volt too much across a bare LED sends its current up a thousandfold, and it burns out.
Slide the battery down to zero, then slowly up. Nothing, nothing, and then the infrared one lights, with about 1.1 volts across it; then the red one, at about 1.6; then the blue, at about 2.4. At 3 volts (two AA cells), all three are bright, with 1.26, 1.78 and 2.49 volts across them. Each colour waits for its own voltage. Why?
Picture 2
Inside an LED
Here’s the inside of one chip, its middle 2½ thousandths of a millimetre, drawn as an energy map: up is more energy for an electron. Electrons move along the top band. The places where electrons are missing, called holes, act like positive charges and move along the bottom one. Between the two bands is a gap: in a perfect crystal, no electron can have an energy in it.
The dashed lines are the electrons’ and holes’ levels: how crowded each is, written as an energy. They aren’t places an electron sits, so they can run through the gap. The battery holds them apart: the gap between them is the voltage across the LED, because an electronvolt is the energy one electron gains crossing one volt. Raise the voltage and they split further: electrons crowd in from the n side on the left, holes from the p side on the right, into the thin layer in the middle. There they meet. An electron meeting a hole drops across the gap (the coloured stroke), and its energy leaves as a particle of light, a photon.
Why one colour? The electrons sit just above the floor of their band, within about kT, the crystal’s jiggle energy (0.026 electronvolts at room temperature), and the holes just under the ceiling of theirs. So every drop is nearly the same size, the gap, and so is every photon’s energy. A photon’s energy is its colour. Pick red or blue: the gap widens, each photon carries more energy, and it takes a bigger split, more volts, to crowd the electrons and holes in. A 2.7 electronvolt gap takes about 2.7 volts.
The middle layer is walled in. Its crystal has a narrower gap than the crystal on either side, so the step up on the right stops electrons going on into the p side, and the step on the left stops holes going on into the n side. Caught between the two, they meet: at 20 milliamps, 92 of every 100 electrons make light, and 8 meet holes at flaws and make heat. The walls’ wider gap also lets the light out without swallowing it. Layered crystals like this won Zhores Alferov and Herbert Kroemer a share of the 2000 Nobel Prize in physics, and nearly every LED and laser diode is built this way.
Shows
Where the light comes from, why its energy is the gap, and why the volts follow the gap.
Hides
The light trapped inside the chip; and the crystals real red and blue LEDs are made of.
Picture 3
One colour each
Here is each LED’s light, spread out by colour.
Each peak sits just above its gap, by half the jiggle energy, kT, and is about twice kT wide: for the infrared LED, 28 nanometres. That’s why an LED looks like one pure colour, where a hot filament glows across the whole rainbow and beyond. (Real LEDs are wider than this, often two or three times: heavy doping blurs a crystal’s band edges, and the mixed crystals of red and blue LEDs aren’t quite even.)
Picture 4
The volts
Each LED’s current at every voltage across it, on a scale where each line up is a hundred times more.
All three curves have the same shape, shifted: once it’s lit, each LED’s current rises tenfold for every 60 millivolts more. Each climbs just under its own gap. That steep climb is why each seems to switch on at its own voltage, and why, once it’s on, the extra volts of the battery go to its resistor instead.
So
A solar cell, backwards
An LED is a solar cell run backwards. In a solar cell, light makes electrons and holes, and the junction sorts them to the two wires, as a voltage; electrons and holes meeting again inside are its loss. In an LED, a voltage pushes electrons and holes together, and their meeting is the whole point: in clean crystal, each meeting makes one photon, with the gap’s energy. So the gap sets the colour, and the gap sets the voltage it takes.
And while we’re here
Other questions the pictures answer
Why don’t silicon chips glow?
Silicon has a gap, and its electrons and holes meet all the time, but it almost never makes light. In silicon, the electrons at the bottom of their band and the holes at the top of theirs move with different momentum, and a photon can’t carry the difference away; the crystal has to jiggle at the same moment. (Physicists call this an indirect band gap; gallium arsenide’s is direct.) So an electron among the holes of a doped silicon chip (10¹⁷ per cm³) waits about 2 milliseconds to give off light, where in gallium arsenide it waits 14 nanoseconds. Long before 2 milliseconds, a flaw in the crystal usually catches it, and its energy goes to heat: in ordinary silicon, fewer than 1 in 100 meetings make light (the best silicon LEDs ever made, with great care, only just pass 1 in 100).
Why does a real blue LED need about 3 volts?
This page’s blue LED runs at about 2.5 volts. Real ones need 2.8 to 3.3 volts at 20 milliamps: their p-type gallium nitride conducts poorly, and the layers around their light-making layers add barriers, and those take volts too. Real red LEDs need 1.8 to 2.2, close to this page’s.
Does the light carry more energy than the battery gives?
In this simulation, yes. In picture 2, at 3 volts, the gap is 1.42 electronvolts but the split, the voltage, is 1.26: each photon carries away about 1.46 electronvolts, while the battery gives each electron 1.26. Even with 7 in 100 electrons lost to heat at flaws, this LED gives out 8% more energy as light than it takes in. The difference comes from heat: the electrons and holes that meet sit a little above their levels, put there by the crystal’s jiggling, so an LED with nothing else wasted cools itself a little as it glows. Real LEDs waste far more, in resistance and in light trapped inside, and they warm up. Only warmed, and at tiny currents, has an LED been measured giving out more light than the electrical power put in (P. Santhanam, D. J. Gray and R. J. Ram, Phys. Rev. Lett. 108, 097403 (2012)).
How does a white LED work?
It’s a blue LED coated with a phosphor, a powder that absorbs some of the blue and gives off yellow. Blue and yellow together look white.
Under the hood
How an LED is simulated
The rules alone are textbook physics: a diode’s current grows tenfold for each 60 millivolts at room temperature, and the voltage it needs follows the gap. This page checks against them, and against real LEDs. Its infrared LED takes 1.25 volts for 20 milliamps, as real gallium arsenide LEDs take about 1.2 to 1.3 before their resistance; its light peaks at 863 nm, as gallium arsenide’s does at room temperature (about 870); and 92 of every 100 of its electrons make light, as in good real ones.
What this simulation adds is where: the bands and levels across the chip, where the electrons gather, and how each one ends. It follows the electrons and holes through the chip as they diffuse and drift (the drift–diffusion model, the same rule that runs our solar panels, lithium-ion battery and nerves), and lets them meet two ways: by giving off light, at the standard rate for gallium arsenide, or at flaws in the crystal.
It leaves things out, to run live: the light, once made, simply leaves (none is trapped or reabsorbed); there’s no resistance in the chip or its contacts; the red and blue LEDs are gallium arsenide with only its gap changed, not the crystals real ones are made of; and the colours come from the textbook law, not the simulation.