Answer :
Final answer:
The responsivity of a p-i-n photodiode is calculated by dividing the power by the photon energy, multiplying by the electron charge, and adjusting for quantum efficiency. The responsivity increases at longer wavelengths because the energy of photons decrease as wavelength increases, resulting in more photons per watt and higher responsivity with constant quantum efficiency.
Explanation:
The responsivity of a p-i-n photodiode is a measure of its electrical response to optical input, typically in amperes per watt (A/W). The responsivity depends on the wavelength of the incident light and the quantum efficiency of the photodiode. The quantum efficiency (η) is the ratio of the number of charge carriers generated to the number of incident photons and can be expressed as a percentage.
To calculate the responsivity (R), we can use the following relation:
At a wavelength of 1.3 μm:
R = (eΦpη) = (1.602 x 10-19 C)(1 W/E)(0.8) =
At a wavelength of 1.55 μm:
R = (eΦpη) = (1.602 x 10-19 C)(1 W/E)(0.8)
The responses for both wavelengths would then be calculated by plugging in the respective values for λ (1.3 μm and 1.55 μm) into the formula for E, and then using them to find Φp and subsequently R.
The photodiode is more responsive at 1.55 μm because the energy of a photon is inversely proportional to its wavelength (λ). As the wavelength increases, the photon energy decreases, which means more photons per watt at longer wavelengths, and with a fixed quantum efficiency, that translates to a higher responsivity.
