7.6 Light-emitting diodes

Light-emitting diodes (LEDs) convert electrical energy into light using the properties of semiconductors. They're one of the most direct applications of band theory and carrier dynamics in condensed matter physics, and understanding how they work ties together concepts from p-n junctions, quantum confinement, and radiative recombination.

This guide covers LED operating principles, materials, electrical and optical characteristics, fabrication, advanced designs, and applications.

Principles of LED operation

At its core, an LED is a forward-biased p-n junction designed so that when electrons and holes recombine across the junction, they release energy as photons rather than heat. The color of light depends on the semiconductor's band gap, and the efficiency depends on how well you can promote radiative recombination over competing non-radiative processes.

Band gap in semiconductors

The band gap is the energy difference between the valence band and the conduction band. In an LED, this gap sets the energy of the emitted photon:

$E_{photon} = \frac{hc}{\lambda}$

A larger band gap means a shorter wavelength (bluer light); a smaller band gap means a longer wavelength (redder light). Some reference values:

• GaAs: 1.42 eV (infrared, ~870 nm)
• GaP: 2.26 eV (green/yellow region)
• GaN: 3.4 eV (near-UV, ~365 nm)

By alloying semiconductors (e.g., varying the indium fraction in InGaN), you can tune the band gap continuously to target a specific emission wavelength.

Radiative recombination process

Radiative recombination occurs when an electron in the conduction band drops into a hole in the valence band and the energy difference is emitted as a photon. This is the process you want in an LED.

It competes with non-radiative pathways that waste energy as heat:

• Auger recombination: the recombination energy is transferred to a third carrier instead of producing a photon
• Defect-assisted (Shockley-Read-Hall) recombination: carriers recombine through mid-gap trap states associated with crystal defects

The balance between these processes is captured by the internal quantum efficiency (IQE):

$\eta_{IQE} = \frac{R_{rad}}{R_{rad} + R_{nrad}}$

where $R_{rad}$ is the radiative recombination rate and $R_{nrad}$ is the total non-radiative rate. Maximizing IQE means minimizing defects and suppressing Auger processes.

Carrier injection mechanisms

Forward biasing the p-n junction lowers the potential barrier at the depletion region, allowing electrons from the n-side and holes from the p-side to be injected across the junction as minority carriers. Once they meet in the active region, they can recombine radiatively.

Carrier transport involves both drift (driven by electric fields) and diffusion (driven by concentration gradients). The carrier concentration evolves according to the continuity equation:

$\frac{\partial n}{\partial t} = G - R + \frac{1}{q}\nabla \cdot J_n$

where $G$ is the generation rate, $R$ is the recombination rate, and $J_n$ is the electron current density.

Heterostructures (junctions between different semiconductors) are used to confine carriers in the active region. The band offsets at the interfaces act as potential barriers that keep electrons and holes from escaping, which increases the probability of radiative recombination.

LED materials and structures

The choice of semiconductor material and device geometry directly determines an LED's emission wavelength, efficiency, and reliability.

III-V compound semiconductors

These are compounds formed from group III elements (Ga, In, Al) and group V elements (As, P, N). They dominate LED technology because most of them have direct band gaps, meaning the conduction band minimum and valence band maximum occur at the same crystal momentum. This makes radiative recombination far more probable than in indirect-gap materials like silicon.

• GaAs / AlGaAs: infrared and red LEDs
• InGaP / AlGaInP: red, orange, and yellow LEDs
• InGaN / GaN: blue, green, and UV LEDs

Band gap engineering through alloying lets you smoothly adjust emission across a wide spectral range. These materials also have high electron mobilities and strong light-matter coupling, making them well-suited for high-performance devices.

Organic vs inorganic LEDs

Organic LEDs (OLEDs) use carbon-based molecular or polymeric emitters as the active layer. Their advantages include mechanical flexibility, large-area fabrication on flexible substrates, and broad color tunability. The trade-offs are shorter operational lifetimes, lower peak brightness, and greater sensitivity to moisture and oxygen.

Inorganic LEDs (the III-V devices discussed above) offer higher brightness, longer lifetimes (often exceeding 50,000 hours), and better thermal stability. They're the standard choice for high-power lighting and outdoor displays.

Hybrid organic-inorganic approaches attempt to combine the processing advantages of organics with the performance of inorganic emitters, though this remains an active area of research.

Quantum well structures

A quantum well is a thin layer (typically a few nanometers) of a lower-band-gap material sandwiched between higher-band-gap barrier layers. Carriers are confined in two dimensions within this well, which has two major effects:

1. The confinement increases the overlap between electron and hole wavefunctions, boosting the radiative recombination rate.
2. The emission wavelength can be tuned by adjusting the well thickness, since quantum confinement shifts the effective energy levels.

Most modern LEDs use multiple quantum well (MQW) structures, which distribute carriers across several wells to avoid overcrowding any single well and improve overall efficiency. Deliberate strain in the quantum wells (from lattice mismatch) can also be used to modify the band structure and polarization of emitted light.

Electrical characteristics

The electrical behavior of an LED governs how efficiently it converts injected current into light, and how it integrates into drive circuits.

Current-voltage relationships

An LED follows the standard diode equation:

$I = I_s\left(e^{qV/nkT} - 1\right)$

where $I_s$ is the reverse saturation current, $q$ is the electron charge, $n$ is the ideality factor (typically 1–2), $k$ is Boltzmann's constant, and $T$ is temperature.

The turn-on voltage roughly corresponds to the band gap energy divided by the electron charge. Larger band gaps mean higher turn-on voltages:

• Red LEDs (AlGaInP): ~1.8 V
• Blue LEDs (InGaN): ~3.0 V

At high currents, series resistance from the bulk semiconductor and contacts causes the voltage to increase linearly beyond the exponential regime, leading to additional power dissipation as heat.

Carrier transport mechanisms

Several transport processes operate in an LED:

• Drift-diffusion: the primary model for carrier movement through the bulk and active regions
• Thermionic emission: carriers surmount potential barriers at heterojunction interfaces by thermal energy
• Quantum mechanical tunneling: becomes important in thin barriers, highly doped junctions, or quantum well structures
• Carrier overflow: at high injection levels, carriers can escape the active region without recombining, reducing efficiency
• Space-charge limited current: can dominate in organic LEDs where carrier mobilities are low

Efficiency droop phenomenon

Efficiency droop is the decrease in IQE that occurs as drive current increases beyond a certain point. It's especially pronounced in InGaN-based blue and green LEDs.

The leading proposed causes include:

• Auger recombination, which scales as the cube of carrier density and becomes dominant at high injection
• Carrier leakage out of the active region due to insufficient confinement
• Poor hole injection into the quantum wells, since holes in GaN have low mobility

Mitigation strategies focus on redesigning the active region (wider wells, graded barriers), improving p-type doping, and using electron-blocking layers to reduce carrier overflow.

Optical properties

The optical output of an LED depends not just on how efficiently photons are generated internally, but also on how effectively they escape the device.

Emission spectrum and color

The emission spectrum is determined by the band gap and quantum well structure. Key parameters include:

• Peak wavelength: set by the band gap of the active region
• Full width at half maximum (FWHM): typically 20–30 nm for inorganic LEDs, broader for OLEDs
• Color coordinates: specified using CIE chromaticity for display and lighting applications

White light from LEDs is produced in two main ways:

1. Phosphor conversion: a blue LED excites a yellow phosphor (commonly YAG:Ce), and the combination of blue and yellow appears white
2. RGB mixing: separate red, green, and blue LEDs are combined

For lighting, the color rendering index (CRI) measures how accurately colors appear under the light source, and the correlated color temperature (CCT) describes whether the light appears warm or cool.

Light extraction techniques

A major challenge in LED design is total internal reflection (TIR). Because semiconductors have high refractive indices (GaN ≈ 2.5), most internally generated photons hit the semiconductor-air interface at angles beyond the critical angle and are trapped inside the chip.

Strategies to improve light extraction include:

• Surface texturing: roughening the surface to randomize photon angles and increase the escape probability
• Photonic crystal structures: periodic patterns that use Bragg scattering to redirect trapped photons outward
• Resonant cavity designs: placing the active region inside an optical cavity to enhance emission in preferred directions
• Transparent conductive oxides (e.g., ITO): serve as current-spreading layers while being optically transparent

Quantum efficiency factors

Several efficiency metrics characterize LED performance:

• External quantum efficiency (EQE) = IQE × light extraction efficiency. This is the fraction of injected electrons that produce photons that actually leave the device.
• Wall-plug efficiency (WPE): the ratio of optical output power to total electrical input power. It accounts for resistive losses and is always lower than EQE.
• Phosphor conversion efficiency: relevant for white LEDs, since the Stokes shift during wavelength down-conversion introduces additional energy loss.

All of these efficiencies degrade with increasing temperature (due to enhanced non-radiative recombination) and at high current densities (due to droop).

LED fabrication methods

Fabrication quality directly determines defect density, interface sharpness, and ultimately device performance.

Epitaxial growth techniques

Epitaxy is the process of growing crystalline semiconductor layers on a substrate, atom by atom. The main techniques are:

• Metal-Organic Chemical Vapor Deposition (MOCVD): the workhorse of LED manufacturing. Precursor gases (e.g., trimethylgallium, ammonia) react on a heated substrate to deposit thin films. It offers good throughput and scalability.
• Molecular Beam Epitaxy (MBE): uses beams of atoms or molecules in ultra-high vacuum. It provides atomic-level control of layer thickness and composition, but at lower throughput than MOCVD.
• Hydride Vapor Phase Epitaxy (HVPE): used to grow thick GaN layers, often as free-standing substrates for vertical LED structures.
• Atomic Layer Deposition (ALD): deposits material one atomic layer at a time, useful for conformal coatings on nanostructures.

Strain management during growth is critical. Lattice mismatch between layers generates dislocations that act as non-radiative recombination centers, so buffer layers and graded compositions are used to minimize defect density.

Doping and junction formation

• In-situ doping during epitaxial growth is the most common approach, giving precise control over carrier concentrations throughout the structure.
• Ion implantation allows selective-area doping for more complex device geometries.
• P-type doping of GaN is notoriously difficult. Magnesium is the standard p-type dopant, but it forms complexes with hydrogen during MOCVD growth. A post-growth activation step (thermal annealing or electron beam irradiation) is required to break these complexes and activate the Mg acceptors.
• Graded doping profiles near the junction can optimize carrier injection and reduce series resistance.

Device packaging considerations

Packaging has a major impact on LED reliability and optical performance:

• Thermal management: high-power LEDs generate significant heat. Heat sinks, thermal interface materials, and thermally conductive substrates are essential to prevent efficiency loss and degradation.
• Encapsulation: epoxy or silicone encapsulants protect the chip from moisture and mechanical damage while also serving as a refractive index bridge to improve light extraction.
• Electrical connections: wire bonding (top-contact) or flip-chip bonding (contacts face down onto a submount) provide the current path.
• Phosphor integration: for white LEDs, phosphor can be applied as a conformal coating on the chip, as a remote phosphor plate, or embedded in ceramic converters.
• Optics: lenses and reflectors shape the output beam for the target application.

Advanced LED technologies

White LEDs and phosphors

The most common white LED architecture pairs a blue InGaN LED with a YAG:Ce (cerium-doped yttrium aluminum garnet) yellow phosphor. The blue photons excite the phosphor, which emits a broad yellow spectrum. The combination of transmitted blue and phosphor-emitted yellow produces white light.

Limitations of single-phosphor designs include a relatively low CRI (typically 70–80) due to weak red emission. Multi-phosphor approaches add red and green phosphors to fill spectral gaps and push CRI above 90.

Quantum dot color converters are an emerging alternative. Their narrow emission linewidths (~30 nm FWHM) enable high color purity and wide color gamuts, though long-term stability remains a challenge.

Remote phosphor configurations place the phosphor layer away from the LED chip, reducing thermal quenching and improving color uniformity.

High-power LED designs

Scaling LEDs to high power requires addressing current spreading, heat extraction, and light extraction simultaneously:

• Vertical LED structures: the growth substrate is removed and replaced with a thermally and electrically conductive submount, improving both heat dissipation and current uniformity
• Patterned sapphire substrates (PSS): periodic patterns on the sapphire growth substrate scatter light that would otherwise be trapped, while also reducing threading dislocation density during GaN growth
• Chip-scale packaging (CSP): eliminates the traditional lead frame, reducing thermal resistance and package size
• Photonic crystal integration: surface or embedded photonic crystals enhance extraction efficiency beyond what texturing alone achieves

Micro-LED displays

Micro-LEDs are individual LED pixels scaled down to the micrometer range (typically 1–100 μm). Each pixel is a self-emissive inorganic LED, combining the brightness and lifetime advantages of inorganic LEDs with the per-pixel control of OLED displays.

Key advantages include very high brightness, excellent contrast ratio (true black from off pixels), fast response times, and low power consumption.

The primary manufacturing challenge is mass transfer: picking up millions of micro-LEDs from a growth wafer and placing them precisely onto a display backplane. Yield management at this scale is extremely demanding.

Full-color displays can be achieved by growing separate red, green, and blue micro-LEDs, or by using blue/UV micro-LEDs with quantum dot or phosphor color converters on each sub-pixel. Applications include AR/VR headsets, smartwatches, and ultra-high-resolution displays.

LED applications

Solid-state lighting

LEDs have largely replaced incandescent and fluorescent lighting in most applications. Modern white LEDs exceed 200 lm/W in efficacy (compared to ~15 lm/W for incandescent bulbs) and last over 50,000 hours.

• Smart lighting systems allow dimming and color temperature adjustment via electronic drivers
• Human-centric lighting tunes the spectral output throughout the day to support circadian rhythms
• Horticultural lighting uses tailored red and blue spectra to optimize photosynthesis in indoor farming

Display technologies

• LED-backlit LCDs: LEDs provide the backlight for liquid crystal displays in TVs and monitors
• Direct-view LED displays: large arrays of LEDs form the image directly, used in outdoor signage and stadium screens
• OLED displays: self-emissive organic LEDs enable thin, flexible screens for smartphones and high-end TVs
• Micro-LED displays: next-generation technology targeting AR/VR and premium consumer electronics
• Quantum dot-enhanced displays: QD films placed over blue LED backlights widen the color gamut

Optical communication systems

LEDs also serve as light sources for data transmission:

• Visible Light Communication (VLC): modulates LED lighting to transmit data, with the room light doubling as a communication channel
• LiFi: a high-speed wireless networking protocol based on VLC
• Infrared LEDs: used in remote controls and short-range data links in consumer electronics
• Fiber optic transmitters: LEDs (typically at 850 nm) serve as sources for short-reach multimode fiber links
• Underwater communication: blue-green LEDs exploit the low-absorption window of seawater for short-range optical links

Challenges and future directions

Efficiency improvements

• Overcoming efficiency droop through novel active region designs (wider wells, improved electron-blocking layers) and better carrier injection schemes
• Enhancing hole injection in III-nitride LEDs, where low hole mobility remains a bottleneck
• Advancing light extraction with nanostructured surfaces and photonic crystal engineering
• Reducing Auger recombination through band structure engineering (e.g., using wider quantum wells to lower carrier density)
• Closing the "green gap": green LEDs (500–560 nm) currently have significantly lower efficiency than both blue and red LEDs, due to challenges with high-indium-content InGaN

Novel materials exploration

• III-nitride nanowires: grown defect-free due to lateral strain relaxation, potentially improving IQE
• Perovskite LEDs: metal halide perovskites offer tunable emission and solution-processable fabrication, though stability is a major concern
• 2D materials (e.g., $MoS_2$, $WS_2$): transition metal dichalcogenides with direct band gaps at monolayer thickness, enabling atomically thin emitters
• Colloidal quantum dot LEDs: narrow linewidth emission (~30 nm) with size-tunable wavelength across the visible spectrum
• Hybrid organic-inorganic systems: aim to combine the easy processing of organics with the efficiency and stability of inorganic emitters

Integration with photonic circuits

• On-chip integration of LEDs with silicon photonics platforms for optical interconnects in data centers
• Electrically injected nanolasers: pushing LED-like structures toward coherent emission for optical computing
• Lab-on-a-chip sensors: LEDs integrated with microfluidic channels and photodetectors for compact biosensing
• Monolithic LED-photodetector integration: enables bidirectional optical communication on a single chip
• Topological photonics: an emerging field exploring whether topologically protected optical modes can improve LED robustness and enable new functionalities