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Optical Receivers 197

(b) Using Eq. (5.13), with R = 0, the photon absorption rate is
p
R abs = R incident [1 − exp (−W)]
9
−4
4
= 2.77 × 10 ×[1 − exp (−10 × 3 × 10 )] photons/s
9
= 2.63 × 10 photons/s.
(c) The quantum efficiency is given by Eq. (5.15),
=(1 − R )[1 − exp (−W)]
p
4 −4
= 0.9 ×(1 − exp (−10 × 3 × 10 ))
= 0.855.

5.2.2 Responsivity or Photoresponse
The responsivity or photoresponse (sometimes also called sensitivity) is a measure of the ability of the pho-
todetector to convert optical power into an electrical current or voltage. It depends on the wavelength of
the incident radiation, the type of photoresponsive (or active) material in the detector, and the structure and
operating conditions of the photodetector. It is defined as
I PC
R = , (5.16)
P
I
where I PC is the photocurrent and P is the input optical power.
I
The photocurrent, in turn, depends on the absorption characteristics of the active (photoresponsive) material
on the photodetector and the quantum efficiency. In a photodetector, the intrinsic quantum efficiency is the
number of ehps generated per incident photon. In the ideal case, the quantum efficiency, which is a measure
of the number of photogenerated ehps per incident photon, is 1 or 100%, that is, each photon of appropriate
energy (equal to or greater than the energy band gap E of the active semiconductor material) generates one
g
ehp. For a pn photodiode, using Eq. (5.10) in Eq. (5.16), we find
q
R = . (5.17)
hf 0
If we insert the numerical values for q, c, and h and with f = c∕ , Eq. (5.17) may be rewritten as
0 0
(μm)
0
R(A/W)= . (5.18)
1.24
Note that the responsivity is proportional to both the quantum efficiency and the free-space wavelength .
0
Fig. 5.7 shows schematically how the responsivity varies with wavelength. Notice that the responsivity curve
falls at both longer and shorter wavelengths for all three photoresponsive materials. The long-wavelength drop
is related to the energy band gap of the semiconductor. For example, for silicon, the energies of photons with
wavelengths approaching 1.1 μm are close to its indirect band-gap energy, beyond which silicon is transparent.
At the other extreme, at short wavelengths, as mentioned before, the quantum efficiency decreases rapidly due
to surface recombination effects as most of the light is absorbed close to the surface.