Light-emitting diode (LED)

A light-emitting diode (LED) is a forward-biased p-n junction in a direct-gap semiconductor in which injected electrons and holes recombine and emit photons with energy close to the bandgap. The process is electroluminescence by spontaneous emission, so the output is incoherent and spectrally broad compared with a laser: a single-color LED typically has a spectral width of 20–40 nm FWHM, and its emission spreads over a wide angle from the chip. The peak wavelength follows from the photon energy, $\lambda \approx 1239.8\ \mathrm{nm\,eV}/E_g$, so a GaAs emitter (1.424 eV) sits near 870 nm; InGaN covers the violet to green, AlGaInP the amber to red, and AlGaN the ultraviolet.

Spectrum and linewidth

Carriers in the conduction and valence bands are spread over a thermal energy range, so the emission spectrum of an ideal bulk junction has a width in photon energy of about $1.8\,kT$, 46.5 meV at 300 K. Converted to wavelength,

$$\Delta\lambda \approx \frac{1.8\,kT\,\lambda^2}{hc},$$

which gives 27 nm at 850 nm and 15 nm at 630 nm. Blue InGaN LEDs are broader than the 7.6 nm this formula predicts at 450 nm, typically around 20 nm, because fluctuations in indium content broaden the transition. Heating shifts the peak to longer wavelength as the bandgap shrinks, and broadens the spectrum further.

Efficiency

The external quantum efficiency (EQE) is the number of photons leaving the device per electron passing through it,

$$\eta_\mathrm{ext} = \frac{P/h\nu}{I/e} = \eta_\mathrm{int}\,\eta_\mathrm{extr},$$

the product of the internal quantum efficiency and the light-extraction efficiency. An 850 nm LED emitting 5 mW at 20 mA has an EQE of 17 %; at a forward voltage of 1.5 V its wall-plug efficiency is also about 17 %, since the photon energy (1.46 eV) is close to the voltage drop.

Extraction was historically the largest loss. Light generated inside a high-index semiconductor escapes a flat surface only within the critical-angle cone; for GaAs ($n \approx 3.5$) that cone holds 2.1 % of the isotropic emission through one face, and 1.4 % after Fresnel reflection at normal incidence. Shaped and roughened chips, reflective back contacts, removal of absorbing substrates and encapsulation in epoxy or silicone domes (n ≈ 1.5) raise extraction to well above 50 % in modern devices. Internal efficiency falls at high current density in InGaN LEDs, the effect called efficiency droop, which is widely attributed to Auger recombination.

White LEDs and lighting

Almost all white LEDs pair a blue InGaN chip with a yellow-emitting phosphor, commonly cerium-doped YAG, that converts part of the blue light; the mixture appears white. The Stokes shift in conversion from 450 nm to 560–580 nm costs about 20 % of the converted energy. Luminous efficacy, the visible output weighted by the eye's response per electrical watt, is the figure used in lighting; the relation between radiant and luminous quantities is described under radiometry vs photometry. The efficient blue LED, made possible by p-type doping and high-quality growth of gallium nitride, earned Akasaki, Amano and Nakamura the 2014 Nobel Prize in Physics.

Comparison with laser diodes

An LED and a laser diode share the junction and the materials; the laser adds an optical cavity and operates above threshold, where stimulated emission dominates. The LED therefore has no threshold, a broad spectrum, low coherence and a large emission area and angle. Its large étendue limits how much of its power can be coupled into a single-mode fiber or focused to a small spot. The modulation bandwidth is set by the spontaneous carrier lifetime $\tau$ through $f_{3\,\mathrm{dB}} \approx 1/(2\pi\tau)$: 16 MHz for $\tau$ = 10 ns and 160 MHz for 1 ns, sufficient for short multimode links, remote controls and visible-light communication.

Pitfalls

Output power depends strongly on junction temperature, so datasheet values measured with short pulses at 25 °C overstate continuous output on a warm heat sink; red and amber AlGaInP devices lose output particularly fast with heating. An LED must be driven by a current source or through a series resistor, since its current rises exponentially with voltage. For photometric measurements the wide angular pattern and non-Lambertian profile make total-flux measurement in an integrating sphere more reliable than a single power meter reading.

Common questions

Why do LEDs not need a cavity like a laser?

Spontaneous emission needs only carriers recombining radiatively; no feedback is required. A cavity is needed only to build up stimulated emission into a narrow, directional beam.

What sets the color of an LED?

The bandgap of the active layer, chosen through alloy composition (for example the indium fraction in InGaN) and quantum-well thickness. White and many pastel colors come from phosphor conversion instead.

How efficient are LEDs?

Commercial white LEDs commonly reach 100–200 lumens per watt, against about 15 lm/W for an incandescent lamp. The best blue InGaN chips at moderate current convert over half of their electrical input to light.

References: E. F. Schubert, Light-Emitting Diodes 2nd ed. (Cambridge University Press, 2006); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics 3rd ed. (Wiley, 2019); S. Nakamura, T. Mukai and M. Senoh, Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes, Appl. Phys. Lett. 64, 1687 (1994).