Light Emitting Diodes

The Light Emitting Diode (LED) is a forward-biased p-n junction device in which injected minority carriers recombine with majority carriers and release the recombination energy as photons rather than heat. The wavelength of emitted light is directly determined by the bandgap of the semiconductor material, which is why different materials produce different colors.

Core Concept Explanation

In a forward-biased p-n junction, electrons from the n-side are injected into the p-side and holes from the p-side are injected into the n-side. These minority carriers diffuse away from the junction and eventually recombine with majority carriers. In standard silicon or germanium diodes, this recombination is indirect band-to-band recombination, and the energy is released as heat (phonons) because momentum conservation requires phonon assistance. No significant light is emitted.

LED materials such as GaAs, GaP, GaAsP, and GaN are direct bandgap semiconductors (or use isoelectronic traps in indirect gap materials). In direct bandgap materials, the conduction band minimum and valence band maximum occur at the same crystal momentum (k=0). Electrons can recombine with holes directly without needing a phonon, releasing the full bandgap energy as a single photon. The photon energy is E = hf = Eg, so the emitted wavelength is determined by lambda = hc / Eg.

The external quantum efficiency (EQE) of an LED is the ratio of the number of photons emitted outside the device to the number of electron-hole pairs injected. Internal quantum efficiency relates to how many injected carriers recombine radiatively versus non-radiatively. Light extraction efficiency is limited by total internal reflection, which is why LED packages use dome-shaped encapsulants with high refractive index.

Mathematical Expression

The fundamental relation connecting emitted photon wavelength to semiconductor bandgap is:

lambda (nm) = 1240 / Eg (eV). This formula comes from E = hf = hc/lambda combined with E = Eg. It gives a quick way to calculate the emission wavelength from bandgap, or vice versa. For example, GaAs with Eg = 1.42 eV emits at lambda = 1240/1.42 = 873 nm, which is in the near-infrared. Red LEDs from GaAsP with Eg approximately 1.9 eV emit at about 653 nm. Blue GaN LEDs (Eg = 3.4 eV) emit at 365 nm near-UV, and with InGaN alloy the gap is tuned to around 2.7 eV giving 460 nm blue light.

The forward current-voltage relationship of an LED is the standard diode equation I = I0(exp(qV/nkT) - 1). Operating forward currents are typically 10 to 30 mA for standard LEDs. The light output power is roughly proportional to forward current in the linear operating region.

Practical Understanding

The development of high-brightness blue LEDs using GaN (awarded Nobel Prize 2014) enabled the creation of white LEDs by combining a blue InGaN LED with a yellow-emitting cerium-doped YAG phosphor. This approach is now the dominant technology in LED lighting. The human eye perceives the combination of blue and yellow as white light.

In optoelectronics courses and GATE, LEDs are compared with laser diodes in terms of coherence and spectral width. LEDs emit incoherent, broadband light (linewidth 20-100 nm) while laser diodes emit coherent narrowband light. LEDs are used in displays, indicators, and short-range optical fiber links, while laser diodes are used for long-haul fiber optic communication.

Given:
GaAsP LED emitting red light, Eg = 1.85 eV

Why this formula applies:
Photon energy equals bandgap for direct recombination, E = hc/lambda

Formula:
lambda = 1240 / Eg (eV)

Substitution:
lambda = 1240 / 1.85

Calculation:
lambda = 670.3 nm

Verification:
hf = 1.85 eV => f = 1.85 * 1.6e-19 / 6.626e-34 = 4.47e14 Hz
c/f = 3e8 / 4.47e14 = 671 nm (matches)

Final Answer: lambda = 670 nm (red region of visible spectrum)

Exam Tip: Use lambda (nm) = 1240 / Eg (eV) for instant wavelength calculation. Silicon has indirect bandgap so it does NOT emit light efficiently. GaAs, GaN, InGaAs are direct bandgap. GATE frequently asks to identify which material emits a given wavelength or which transition is radiative.

• In direct bandgap materials, conduction band minimum and valence band maximum occur at same crystal momentum k, allowing momentum-conserving direct photon emission.
• In indirect bandgap materials like Si and Ge, a phonon must supply the momentum difference, making radiative recombination rare and inefficient.
• Emitted photon wavelength lambda = 1240/Eg(eV) in nanometers; higher bandgap gives shorter wavelength (higher frequency, more blue/UV).
• External quantum efficiency depends on both internal radiative efficiency and light extraction efficiency, limited by total internal reflection.
• White LEDs use InGaN blue LED plus YAG:Ce phosphor which down-converts blue photons to yellow, the combination appearing white to the human eye.

Quick Revision

• LED requires direct bandgap semiconductor for efficient light emission; Si and Ge are indirect and do not emit light efficiently.
• Wavelength formula: lambda (nm) = 1240 / Eg (eV).
• GaAs (IR, 873nm), GaAsP (Red, ~660nm), GaP:N (Green, ~550nm), GaN (Blue/UV, ~365nm), InGaN (tunable blue-green).
• Forward current 10-30 mA typical; light output proportional to current in linear region.
• EQE = (photons out) / (electron-hole pairs injected); limited by non-radiative recombination and total internal reflection.
• White LED = blue InGaN + yellow phosphor (YAG:Ce).
• Exam trap: Higher bandgap means shorter wavelength, not longer. Also, Si cannot be used as LED material because it has an indirect bandgap.