# Responsivity of photodetector

a) Define the responsivity $\rho$ and quantum efficiency $\eta$ of a photo-detector and show that they are related by

$\rho= (\eta*e*\lambda)/(h c)$

(b) For $0.92 eV$ photons, a photodiode has responsivity $0.35 A/W$. Calculate the quantum efficiency of the photo-diode.

__a) __

__Responsivity__is kind of the “total efficiency” of a photo-detector**. **

**Its precise definition: it is the rapport between the output electric current over the input power of photons.**

If we multiply the Responsivity with the output Voltage we obtain EXACTLY the total efficiency of the photo-detector.

$\mathbf{\rho =\frac{I(out)}{P(in)}}$

$P(in) =\frac{N}{t}*h\nu =\frac{N}{t}*\frac{h c}{\lambda}$

For $N$ incoming photons there are generated $\eta*N$ electrons. Therefore

$\rho = \frac{\eta*e}{h\nu}=\frac{\eta*e\lambda}{h c}$

b)

If the energy of the incoming photon is $E =(h c)/\lambda= 0.92 eV$ then the quantum efficiency is

$\eta =\frac{h c}{\lambda}*\frac{1}{e}*\rho =0.92*0.35=0.322$