I. Definition of LED
LED (Light Emitting Diode) is a solid-state semiconductor device with a PN junction semiconductor chip at its core. When current passes through the chip, electrons from the N-region and holes from the P-region meet in the junction region and undergo radiative recombination, releasing energy in the form of photons and achieving direct conversion from electrical energy to light energy. The emission color is determined by the bandgap width of the PN junction material, enabling direct emission of various visible lights such as red, yellow, blue, green, cyan, orange, purple, and white. It offers advantages such as high efficiency, long lifespan, fast response, and environmental friendliness, and is widely used in lighting, displays, optical communications, and smart city applications.

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

• Discrete Energy Levels: According to the Bohr model, in isolated atoms (such as in low-pressure gases), electrons can only move in specific, discontinuous orbits, possessing definite discrete energy levels.
• Level Splitting: In solid crystals, a large number of atoms are closely packed. Restricted by the Pauli exclusion principle, no two electrons can occupy the exact same quantum state. This causes the originally isolated energy levels to split drastically, evolving into countless quasi-continuous energy levels that are extremely close to each other.

Energy levels of isolated atoms are discrete	Close packing of atoms in solids causes level splitting to form energy bands

(Image source: https://en.wikipedia.org/wiki/File:Metals_and_insulators,_quantum_difference_from_band_structure.ogv)

• Energy Bands: The dense, quasi-continuous collection of energy levels formed by the splitting of atomic energy levels in solids is collectively referred to as energy bands. Among them, the valence band and conduction band play a decisive role in semiconductor properties. They are separated by a bandgap, while the Fermi level determines the distribution state of electrons in the energy bands.
• * Valence Band: The low-energy region typically filled with electrons.
  
• * Conduction Band: The high-energy region where electrons are free from binding and can conduct electricity freely.
  
• * Bandgap: The energy vacuum region between the top of the valence band and the bottom of the conduction band is called the forbidden gap, and the energy difference is the bandgap width. Electrons cannot reside in this region and must acquire sufficient energy to cross the bandgap for transition; when electrons fall back from the conduction band to the valence band, the energy of the emitted photon is equal to this bandgap width.
  
• * Fermi Level: Represents the probability of electrons occupying energy levels under thermal equilibrium. Through doping (introducing impurity atoms), the position of the Fermi level can be artificially altered, thereby converting intrinsic semiconductors into N-type (Fermi level close to the conduction band) or P-type (Fermi level close to the valence band).
  

III. Basic Structure of LEDs
The core structure of an LED is a PN junction formed by precise doping of III-V group compounds (such as GaN):

• N-type Semiconductor Layer: Group IV elements (such as Si, Ge) are doped into the intrinsic substrate to replace Group III atoms (such as Ga). Since Group IV atoms have one extra valence electron, they provide one free electron.
  
• P-type Semiconductor Layer: Group II elements (such as Mg, Be) are doped into the substrate to replace Group III atoms. Since Group II atoms lack one valence electron, they create one hole.
  

(Image source: https://en.wikipedia.org/wiki/Chemical_element#/media/File:32-column_periodic_table.png

• PN Junction and Depletion Region: When P-type (hole-rich) and N-type (electron-rich) materials come into contact, a depletion region is formed at the interface, generating a built-in electric field. The presence of the depletion region prevents charge carriers from passing through under equilibrium conditions.
  

IV. Light Emission Principle of LEDs
The light emission process of an LED is essentially a non-equilibrium energy level transition of electrons driven by an electric field:

1. Carrier Provision and Injection: The doping process pre-provides a large number of free electrons and holes in the N-region and P-region. When a forward voltage is applied to the PN junction (P-region connected to positive, N-region to negative), the external electric field weakens the built-in electric field, breaking the thermal equilibrium state and driving electrons from the N-region and holes from the P-region to inject simultaneously into the depletion region (the light-emitting region).
   
2. Excitation and Transition (from Valence Band to Conduction Band): Under the combined action of electric field injection and thermal excitation, electrons in the valence band gain energy, cross the bandgap, and transition to the high-energy conduction band, becoming non-equilibrium carriers. At this point, high-energy electrons accumulate in the conduction band, leaving holes in the valence band.
   
3. Radiative Recombination (from Conduction Band to Valence Band): Electrons in the high-energy conduction band are highly unstable and undergo spontaneous transitions, crossing the bandgap to fall back to the low-energy valence band, where they recombine with holes.
   
4. Spontaneous Emission and Light Generation: During this radiative recombination process, electrons release excess energy. This energy is radiated outward in the form of photons, a physical phenomenon known as spontaneous emission, thereby achieving direct conversion from electrical energy to light energy.
   

(Image source: https://en.wikipedia.org/wiki/Light-emitting_diode_physics#/media/File:PnJunction-LED-E.svg)

V. Performance Determinants
The light emission characteristics of LEDs are primarily constrained by the physical properties of the semiconductor materials, with the core logic as follows:

• Nature of Light Color (Wavelength): The bandgap width ($E_g$) is the primary factor determining the central wavelength of the LED emission spectrum. According to the quantum mechanics formulas $E = h\nu$ (photon energy is proportional to frequency) and $c = \lambda\nu$ (frequency is inversely proportional to wavelength), it can be deduced that: the larger the bandgap, the higher the photon energy released during recombination, and the shorter the corresponding emission wavelength $\lambda$.
  
• High bandgap materials radiate high-energy particles, resulting in light color shifted towards blue/purple;
• Low bandgap materials radiate low-energy particles, resulting in light color shifted towards red/yellow.

• Material Bandgap Engineering: By doping different intra-group elements into the III-V group substrate (such as using Al to increase the bandgap, or In to decrease it), precise adjustment of the bandgap width can be achieved, thereby covering the entire spectral range from ultraviolet to infrared.
  

• Spectral Width (Monochromaticity): Although the bandgap determines the central wavelength, since the conduction and valence bands in crystals are not single energy levels but quasi-continuous bands with a certain energy distribution, the recombination of electrons and holes occurs within a certain energy interval. Therefore, the emission spectrum of an LED is not an absolutely monochromatic spectrum, but a narrowband spectrum with a certain full width at half maximum (FWHM).