The relationship between the light absorption depth of silicon materials in image sensors and the wavelength of light can be explained by the physical mechanisms of photon energy and material interaction, as detailed below:
1. The Wave-Particle Duality of Light: Differences in Photon Energy
Light exhibits wave-particle duality, and its energy formula is: E = hc/λ
where: E is the photon energy, h is Planck’s constant, c is the speed of light, and λ is the wavelength of light.
Shorter wavelengths (e.g., blue light, ultraviolet light): Higher photon energy E;
Longer wavelengths (e.g., red light, near-infrared light): Lower photon energy E.
2. The Band Structure of Silicon and the Light Absorption Mechanism
Silicon is a semiconductor material with a bandgap (approximately 1.12 eV) between its valence band and conduction band. When photons strike the silicon material, only photons with energy E >= bandgap can be absorbed, exciting valence band electrons to the conduction band, generating photogenerated carriers (electron-hole pairs).
The absorption process of light in silicon follows the Lambert-Beer Law, with the intensity decay formula as:
I(x) is the light intensity at depth x, I0 is the incident light intensity at the surface, α is the absorption coefficient, and x is the depth in the silicon material.
The absorption coefficient α is directly related to photon energy (or wavelength):
High-energy photons (short wavelengths):
Energy significantly exceeds the bandgap, resulting in more intense interactions with silicon atoms, making photons easier to absorb near the silicon surface, leading to a high absorption coefficient α and a shallow absorption depth (most absorption occurs in the shallow region near the surface).
Low-energy photons (long wavelengths):
Energy approaches the bandgap, resulting in weaker interactions with silicon atoms, requiring photons to penetrate deeper into the silicon layer to be absorbed, leading to a low absorption coefficient α and a deep absorption depth (capable of penetrating deeper into the silicon material).
“Absorption depth” can be simply understood as the distance at which the energy of light is absorbed by approximately 63% (i.e., decaying to 1/e of the incident light intensity, where e is the natural constant ≈ 2.718) while propagating through the material (such as silicon). The absorption depth is typically defined as the inverse of the absorption coefficient (1/α), meaning that when x = 1/α, the light intensity decays to about 37% of its initial value.
3. Intuitive Analogy: The “Penetration Ability” of Different Energy Photons
Short wavelength light (e.g., blue light):
Similar to “high-energy bullets,” high energy but weak penetration ability, quickly colliding with silicon atoms upon incidence and releasing energy, primarily absorbed in the shallow surface layer.
Long wavelength light (e.g., red light):
Similar to “low-energy particles,” low energy but strong penetration ability, capable of propagating further distances in silicon until energy is depleted before being absorbed.
4. Impact on Image Sensors
Spectral Response Characteristics:
The difference in absorption depths of silicon-based image sensors (such as CMOS, CCD) for different wavelengths of light leads to uneven spectral sensitivity:
Short wavelength light (blue light) is primarily absorbed near the PN junction at the silicon surface,
while long wavelength light (red light, near-infrared light) can penetrate deep into the silicon substrate for absorption.
Pixel Structure Design:
To optimize the absorption of short wavelength light, light traps or anti-reflective layers should be designed at the pixel surface (e.g., shallow trench isolation areas),
and to enhance the absorption of long wavelength light, the silicon layer thickness should be increased (e.g., back-illuminated structures) or infrared filters should be used to separate signals.
Crosstalk and Noise:
Deep absorption of long wavelength light may cause photogenerated carriers to be collected by adjacent pixels during diffusion, resulting in crosstalk; while shallow absorption of short wavelength light is more susceptible to surface defects, leading to noise.
5. Conclusion: The Essence of the Relationship Between Wavelength and Absorption Depth
This characteristic is an inherent physical property of silicon materials and is a key basis for optimizing spectral response and improving imaging quality in image sensor design.
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