How does wavelength affect rise time?
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Figure 2: Typical absorption coefficients and penetration depths for silicon, germanium, and indium gallium arsenide (In0.53Ga0.47As) are plotted. The penetration depth is the reciprocal of the absorption coefficient.
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Figure 1: Different wavelengths of light have different average penetration depths into the PN-junction based detector. The penetration depth is related to the wavelength-dependent absorption coefficient (Figure 2).
When light is incident upon a photodiode, the photons that do not reflect due to the Fresnel reflection from the air / semiconductor interface will travel through the semiconductor material.
A photon will continue to travel until it is absorbed or it reaches the end. When a photon is absorbed, a charge carrier pair will be generated.
Charge carriers generated within the depletion region can contribute almost immediately to photocurrent. However, carriers generated outside of the depletion region must take the extra step of traveling to the depletion region. The duration of this travel is the diffusion time. In Figure 1, the blue and red photons generate carriers in the P-type and N-type regions, respectively. These must diffuse to the depletion region.
The probability of a photon being absorbed once it enters the semiconductor is based on the absorption coefficient. The wavelength-dependent absorption coefficient and penetration depth for various detector materials is shown in Figure 2.
As the incident wavelength increases, the absorption coefficient decreases. This means a longer-wavelength photon can travel a longer average distance within the semiconductor before being absorbed and generating a charge carrier pair. The greater the distance a charge carrier needs to travel to reach the depletion region, the longer the rise time.
Figures 3 through 5 show the measured rise times for a selection of silicon, InGaAs, and germanium photodiodes. In the silicon plot, the slopes of the curves are nearly flat for wavelengths <800 nm. This suggests that the diffusion time for photons absorbed near the surface is negligible. After 800 nm, the rise time increases exponentially. Since the penetration depth for silicon at 800 nm is 9 µm (Figure 2), this suggests that the distance from the top of the sensor and the bottom of the depletion region is less than 9 µm.
Date of Last Edit: Dec. 4, 2019