Light-Emitting Diodes

Introduction

An LED is a forward-biased semiconductor junction designed so that injected electrons and holes recombine by emitting photons. The material's band structure sets an approximate photon-energy scale, while alloy composition lets engineers tune emission. Device brightness also depends on how many carriers recombine radiatively and how much internally generated light escapes. A direct-gap alloy helps, but an LED is a whole optical and electrical device, not just a band-gap number.

Core explanation

Forward bias lowers the junction barrier. Electrons enter the p-side region and holes enter the n-side region, or both are injected into a designed active layer. When a conduction electron drops into an available valence-band hole, the lost electronic energy may leave as a photon: radiative recombination . The photon energy is often near a relevant band-edge transition, though spectra broaden through temperature, carrier distributions, alloy disorder and quantum-well states. The approximate wavelength relation λ(nm) ≈ 1240/E(eV) is a useful energy scale, not an exact LED colour specification. MIT's LED lecture distinguishes radiative and nonradiative pathways.

Direct-gap materials support strong near-edge radiative transitions because a phonon is not needed to reconcile different band-edge wave vectors. Compound semiconductor alloys allow composition to alter band-edge energies. For example, changing the relative amounts of elements in a III–V active region can tune the transition wavelength, while layers with wider gaps can confine carriers and photons. Composition may also change lattice parameter, defect density and crystal stability; a desired gap alone does not guarantee a fabricable high-efficiency junction. Heterostructures and quantum wells can keep injected carriers near one another in the active region, increasing the chance of useful recombination.

Nonradiative paths convert electronic energy into phonons or other excitations rather than emitted light. Defects and surfaces can create recombination centres; very high carrier densities may support Auger processes in which energy goes to a third carrier. Internal quantum efficiency describes photon creation within the active material relative to injected carriers under a specified convention. Extraction efficiency describes how many of those photons escape. A semiconductor's high refractive index causes total internal reflection at interfaces, so device shape, surface texture and encapsulation matter. External efficiency combines the electrical injection, internal recombination and optical escape processes.

Not every colour-producing LED emits that colour directly from its semiconductor. A white LED commonly uses a shorter-wavelength LED and wavelength-converting phosphors; the observed spectrum is a mixture. Temperature can shift emission and reduce efficiency through changed band gap and recombination balance. MIT's optical-semiconductor lecture explains why gap type influences light emission.

Step-by-step reasoning

1. Identify the forward-biased junction and active material. 2. Trace injected electrons and holes into the active region. 3. Compare radiative and nonradiative recombination channels. 4. Estimate photon wavelength from a transition energy, keeping broadening in mind. 5. Assess extraction and thermal performance before judging total device efficiency.

Visual explanation

Draw a conduction-band electron and valence-band hole meeting in a central active layer; a wavy arrow leaves as a photon. Draw a competing downward arrow ending in phonons at a defect. Surround the layer with wider-gap confinement regions and mark an escaping ray and an internally reflected ray. This separates photon generation from photon extraction.

Real-world analogy

Imagine a factory that makes lamps. The fraction of workers that actually make a lamp resembles internal radiative efficiency, and the fraction of finished lamps that leave the warehouse resembles extraction efficiency. A productive factory with a locked loading bay still delivers little light. The analogy does not describe the quantum transition, but it clarifies why two efficiencies multiply.

Real-world example

Blue-emitting semiconductor chips combined with phosphor coatings can yield white lighting. Some blue photons leave unchanged; others excite a phosphor that re-emits at longer wavelengths. The mix appears white to an observer. This device can be bright and efficient even though the primary junction is not a hypothetical “white-gap” semiconductor.

Why?

Why does alloying tune LED colour? Replacing a fraction of atoms changes the periodic potential and therefore the energy and character of electronic band states. The active region's radiative transition energy shifts, changing photon wavelength. The dependence is rarely a perfectly linear average of endpoint gaps because alloy bowing, strain and confinement may matter.

Common misconception

“Every electron crossing the junction produces one escaped photon” ignores leakage, nonradiative recombination and optical trapping. “An LED's emitted wavelength is always exactly hc/E g” ignores spectral broadening, quantum confinement and band-tail or excitonic effects. “White LEDs emit one white photon” confuses a broadband perceived colour with a single photon energy.

Worked example

An active region emits around 2.07 eV. A rough central wavelength is λ ≈ 1240/2.07 ≈ 599 nm , in the orange spectral region. Suppose 80% of injected carriers recombine radiatively and 40% of internal photons leave the package. In a simplified one-carrier-pair-per-photon picture, the extracted-photon fraction is 0.80 × 0.40 = 0.32 , or 32%. The remaining 68% is not all heat from one cause; it includes both nonradiative loss and internally trapped photons, some of which may later be reabsorbed.

Quick check

1. Why does a direct-gap semiconductor generally favour band-edge LED emission? Answer: Electron and hole band-edge states share approximately the same crystal wave vector, so radiative recombination need not also involve a phonon for momentum balance.

Exam focus

Separate injection, radiative recombination and extraction. Use the gap to estimate an energy scale, not a perfectly sharp spectrum. Mention nonradiative defects and high-index optical trapping when discussing efficiency. Explain alloy colour tuning through changed band structure rather than simply “mixing colours.”

Advanced insight

Quantum wells place carriers in thin active layers, changing allowed subband energies and enhancing overlap. Polarisation fields in some nitride heterostructures can separate electron and hole wavefunctions and affect recombination rates. Measuring electroluminescence, photoluminescence and current together helps separate electrical injection from intrinsic optical quality.

Summary

An LED turns injected electron–hole recombination into light. Direct-gap materials and composition-controlled heterostructures support efficient, tunable emission. Actual output depends on nonradiative losses and extraction, so band gap alone cannot predict brightness.

Practice questions

1. Estimate the wavelength of a 3.1 eV emitted photon. Answer: About 1240/3.1 = 400 nm, near the violet edge of visible light. 2. What does a nonradiative recombination event produce instead of the desired emitted photon? Answer: It transfers energy to lattice vibrations or another carrier or excitation, depending on the mechanism. 3. If internal photon creation is 50% and extraction is 20%, what simplified fraction exits? Answer: 0.50 × 0.20 = 0.10, or 10% of the relevant injected-pair count. 4. Why can a phosphor-coated blue LED appear white? Answer: The original blue light combines with longer-wavelength phosphor emission to produce a broad perceived mixture.