Which of the following statement is true for a wavelength of 1000 nm. A p-n photodiode is fabricated from a semiconductor with band gap of 1.9 eV.

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  1. The photodiode can detect signal once the energy of signal is increased.
  2. The energy of a signal of given wavelength is more than the specified band gap
  3. The photodiode can easily detect signal
  4. The photodiode cannot detect signal

Answer (Detailed Solution Below)

Option 4 : The photodiode cannot detect signal
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Detailed Solution

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Concept
A p-n photodiode can only detect those signals whose excitation energy is greater than the band gap energy of the p-n photodiode.

Energy associated with a wave is calculated by the formula

\(E = \frac{hc}{λ}\)

where, 

h = plank's constant

c = velocity of the wave i.e. light

λ = wavelength of the signal

Calculation
Given λ = 1000nm = 10-6m

h = 6.6 ×10-34 m2kg/s

c = 3×10m/s

\(E = \frac{6.6× 10^{-34}× 3× 10^8}{10^{-6}}\)

E = 1.98×10-18J

Now we know that 1eV = 1.6×10-19J

\(E =\frac{1.98× 10^{-19}}{1.6× 10^{-19}}\)

E = 1.23eV

Es < 1.9eV band gap)

Since the energy of the signal is 1.23eV less than the energy band gap (1.9eV) of the semiconductor, Hence the signal cannot be detected by the p-n photodiode.

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