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)

Responsivityis 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

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