How Does Temperature Affect Avalanche Photodiode Performance?

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Temperature significantly impacts the performance of avalanche photodiodes, particularly in terms of quantum efficiency, responsiveness, and noise characteristics. For an InGaAs avalanche photodiode operating at 1310 nm and 300K, key parameters such as gain coefficient, noise factor, and absorption coefficient are crucial for calculations. The quantum efficiency, responsiveness, and noise equivalent power (NEP) can be derived using relevant equations, which are essential for understanding device performance. Additionally, achieving a signal-to-noise ratio of 1000 may require consideration of cooling the detector to reduce thermal noise. Cooling could enhance performance by improving the signal-to-noise ratio, thus justifying its use in specific applications.
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[Moderator's note: Thread moved from a non-homework forum and thus lacks the homework template]

Summary:: It is a small question that my teacher gave me about avalanche diode. Anyone who can help me will be very grateful.

Consider an avalanche photodiode of InGaAs, which operates at the wavelength of 1310 nm, and has a bandwidth of 1GHz. The operating temperature of the device is 300K and its equivalent resistance is 50Ω. The gain coefficient avalanche equals 4 and the noise factor equals 2.
The device has an active region with length 1μm, absorption coefficient of 10^4 cm-1, recombination coefficient 0.9 and refractive index 3.4.
Determine:
(a) The quantum efficiency of the device
(b) The responsiveness of the device
(c) The device's NEP (Noise Equivalent Power)
(d) The flow of photons at the entrance of the device that results in a signal-to-noise ratio equal to 1000
(e) In the previous item, would it be advantageous to cool the detector? Justify.
 
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Apparently this is a homework problem, and should be posted to the appropriate homework forum (suggested: Engineering and Comp Sci Homework Help Forum).

You need to show your own attempt/thinking on the problem before any help can be provided (this is a Physics Forums requirement).

What equations/physical laws are relevant?