Why an LED is one colour: the bandgap sets the photon energy

A red LED is red whether you run it dim or bright. Turn the current up and you get more light, but the same red. The colour is not painted on and it is not set by the power supply. It is fixed by the crystal the diode is made from, and one number about that crystal decides it.

What is being claimed

An LED is a junction between two kinds of semiconductor. Forward current pushes electrons into one side and holes into the other. A hole is a missing electron, and it behaves like a positive charge. When an electron meets a hole, the electron drops into the empty place and gives up its extra energy. Chenming Hu writes that the electrons and holes recombine by emitting photons with energy approximately equal to E_g, the bandgap.

The bandgap is the energy step between the band of states an electron occupies when it is free to conduct and the band it falls back into. Every electron that crosses the junction falls down the same step. So every photon comes out with about the same energy, and a photon's energy is its colour.

Why it is worth knowing

It explains why each LED gives one narrow colour rather than a dial you can turn, and why each new colour has meant a new material. It also explains the one colour that took decades. Red and green LEDs were on sale by the late 1960s. Efficient blue arrived in the 1990s and won the 2014 Nobel Prize in Physics for Isamu Akasaki, Hiroshi Amano and Shuji Nakamura.

From a gap to a wavelength

A photon's energy and its wavelength are tied together by Planck's constant and the speed of light. In the units engineers use, Hu gives it as photon energy in electronvolts = 1.24 / wavelength in micrometres. Turn it round and you have his LED rule: wavelength in micrometres ≈ 1.24 / E_g in eV. A bigger gap means more energy per photon, which means a shorter wavelength, moving from infrared through red, yellow and green towards blue and ultraviolet.

Look at what is missing from that rule: current and voltage. Driving an LED harder sends more electrons across the junction each second. The Nobel background defines quantum efficiency as the number of photons emitted per electron passing through, so more electrons give more photons. Each photon still falls down the same gap. The LED gets brighter and stays the same colour.

Why not silicon?

Silicon has a gap of 1.12 eV, which would put its light in the infrared at about 1.1 µm (our arithmetic). But the size of the gap is not enough on its own. In a direct-gap material such as GaAs or GaN, the electron and the hole already have matching momentum and can recombine at once. Silicon's gap is indirect: the electron also has to hand momentum to a vibration of the crystal, called a phonon. Hu gives the difference as nanosecond lifetimes for light in direct-gap material against millisecond lifetimes in indirect-gap material. Given that long a wait, the electron nearly always finds a defect first and recombines there, making phonons, which is heat, not photons. That is why LEDs are made of compound semiconductors such as GaAs and GaN, not silicon.

Colours by recipe

Few pure crystals have a useful gap, so makers mix them. Hu describes blending GaP and GaAs into GaAs_1−xP_x: near pure GaP it glows yellow, and as the arsenic grows it goes orange, red and finally infrared. The Nobel background puts GaAs at 1.4 eV, in the infrared, and GaP at 2.2 eV. GaP's gap is indirect, and in the 1960s red and green GaP LEDs worked by adding impurities.

Why blue was hard

Blue light, around 0.45 to 0.49 µm, needs a gap of roughly 2.5 to 2.8 eV (our arithmetic), and the candidate was gallium nitride, GaN, with a direct gap of 3.4 eV. That is actually a little too wide: 1.24 / 3.4 is 0.365 µm, ultraviolet (our arithmetic). Blue LEDs use InGaN, which Hu's table of common LEDs lists as green–blue; adding indium narrows the gap. The harder problem was making GaN into a diode at all. It was hard to grow as good crystal, and it came out naturally n-type. Making the p-type side failed for years, because hydrogen bonded to the added acceptor atoms and switched them off. The Nobel background says controlled p-doping of GaN was achieved only at the end of the 1980s. In 1994 Nakamura and co-workers reported a quantum efficiency of 2.7% from an InGaN/AlGaN double heterojunction.

Blue also opened the door to white. There is no white semiconductor. A white LED is a blue LED shining on a phosphor, which glows green and red, and the mixture looks white. Another route is red, green and blue LEDs side by side.

In short

Each photon from an LED carries about one bandgap of energy, so its wavelength in micrometres is about 1.24 divided by the gap in electronvolts. More current means more photons, not different ones. To change the colour you have to change the material, and blue waited decades for gallium nitride to become a usable diode.