I.Definition
A Light-Emitting Diode (LED) is a solid-state semiconductor device centered around a PN junction. When an electric current passes through the chip, electrons from the N-type region and holes from the P-type region undergo radiative recombination at the junction. This process releases energy in the form of photons, achieving the direct conversion of electrical energy into light.

The energy band gap of the semiconductor material determines the emission wavelength, allowing LEDs to directly produce a wide spectrum of light—including red, yellow, blue, green, cyan, orange, and violet—as well as white light. Characterized by high luminous efficacy, extended operational life, fast response, and environmental sustainability, LEDs are extensively applied in general lighting, display systems, optical communications, and smart city infrastructure.

Fig. 1. LEDs of various colors. The emission color is determined by the energy band gap of the semiconductor material. Source:https://en.wikipedia.org/wiki/List_of_light_sources#/media/File:RBG-LED.jpg

II.Energy Levels and Bands
A. Energy Levels
The light-emitting mechanism of semiconductors is rooted in the energy state distribution of microscopic particles:

• Discrete Energy Levels: According to the Bohr model, electrons in isolated atoms (such as low-pressure gases) move only in specific, discontinuous orbits with fixed, discrete energy levels.
  
• Level Splitting: In solid crystals, atoms are densely packed. Under the constraints of the Pauli Exclusion Principle, no two electrons can occupy identical quantum states. This causes isolated energy levels to split into a multitude of closely spaced, quasi-continuous energy levels.
  

Fig. 2. Evolution from discrete energy levels to energy bands. In an isolated atom, energy levels are discrete (left). As atoms aggregate into a solid, the Pauli Exclusion Principle causes these levels to split and form bands (right). Source:https://en.wikipedia.org/wiki/File:Metals_and_insulators,_quantum_difference_from_band_structure.ogv

B. Energy Bands
Energy Band Formation: Atomic level splitting in solids creates quasi-continuous energy bands. The electronic properties of semiconductors are governed by the interaction between the valence band and the conduction band, which are separated by a forbidden energy gap, while the Fermi level dictates the statistical distribution of electrons.

• Valence Band: The lower energy band typically filled with electrons.
• Conduction Band: The higher energy band where mobile electrons enable electrical conductivity.
• Band Gap: The forbidden energy region between the valence and conduction bands. The energy difference between them is defined as the bandgap width. Electrons must gain sufficient energy to bridge this gap; conversely, falling from the conduction to the valence band releases a photon equal to the gap energy.
• Fermi Level: The statistical reference for electron occupancy. Doping shifts its position to create N-type (near the conduction band) or P-type (near the valence band) semiconductors.

III. LED Structure
The fundamental architecture of an LED is a PN junction, created through the precise doping of III-V compound semiconductors (e.g., GaN):

• N-type Semiconductor Layer: Created by doping the intrinsic substrate with Group IV elements (e.g., Silicon, Germanium) to substitute for Group III atoms (e.g., Gallium). Since Group IV atoms possess an extra valence electron, they provide a free electron to the lattice.
• P-type Semiconductor Layer: Created by doping the substrate with Group II elements (e.g., Magnesium, Beryllium) to substitute for Group III atoms. As Group II atoms lack one valence electron, they generate a hole.
• PN Junction and Depletion Layer：When P-type (hole-rich) and N-type (electron-rich) semiconductors are joined, a depletion layer forms at the interface, creating a built-in electric field. At equilibrium, this layer blocks carriers from crossing the junction.

Fig. 4.Key elements for III-V semiconductor doping in LEDs.The periodic table highlights Group III/V base elements and Group II/IV dopants used to form the PN junction of an LED. Source:https://en.wikipedia.org/wiki/Chemical_element#/media/File:32-column_periodic_table.png

IV. Operating Principle
1.Carrier Injection
Doping creates free electrons in the N-region and holes in the P-region. Applying a forward bias (P-side positive, N-side negative) weakens the built-in field, injecting carriers into the depletion region.
2.Excitation and Transition
Under electrical and thermal excitation, valence electrons gain energy to cross the bandgap. They transition to the conduction band, leaving holes in the valence band.
3.Radiative Recombination
Unstable electrons in the conduction band spontaneously drop back to the valence band to recombine with holes.
4.Spontaneous Emission The excess energy is released as photons. This spontaneous emission achieves the direct conversion of electrical energy into light.
Fig. 5.Schematic of the LED light-emitting process. Source:https://en.wikipedia.org/wiki/Light-emitting_diode_physics#/media/File:PnJunction-LED-E.svg

V. Performance Determinants
The emission characteristics of an LED are primarily governed by the physical properties of the semiconductor materials:
1.Band Gap and Emission Wavelength
The band gap energy ($E_g$) is the primary factor determining the peak emission wavelength. According to the Planck-Einstein relation ($E = h\nu$) and the wave equation ($c = \lambda\nu$), the emitted wavelength ($\lambda$) is inversely proportional to the band gap energy.

• High band gap: Produces high-energy photons, shifting the color toward blue/violet.
• Low band gap: Produces low-energy photons, shifting the color toward red/yellow.

2.Band Gap Engineering (Composition Control)
The emission wavelength can be controlled by adjusting the composition of III–V semiconductor alloys. For example:

• Aluminum (Al) increases the band gap.
• Indium (In) decreases the band gap.

This allows for spectral coverage from the ultraviolet to the infrared region.

3.Spectral Width and Monochromaticity
While the band gap determines the peak emission wavelength, the conduction and valence bands are not discrete energy levels but energy bands with a finite distribution. As a result, electron–hole recombination occurs over a range of energies.

Consequently, LED emission is not strictly monochromatic, but exhibits a narrow spectral distribution characterized by a finite Full Width at Half Maximum (FWHM).