"Introduction". In: Fiber-Optic Communication Systems

134 CHAPTER 4. OPTICAL RECEIVERS

Figure 4.1: A semiconductor slab used as a photodetector.

the incident optical powerPin, i.e.,

Ip=RPin, (4.1.1)

whereRis theresponsivityof the photodetector (in units of A/W).
The responsivityRcan be expressed in terms of a fundamental quantityη, called
thequantum efficiencyand defined as

η=

electron generation rate

photon incidence rate

=

Ip/q

Pin/hν

=

hν

q

R, (4.1.2)

where Eq. (4.1.1) was used. The responsivityRis thus given by

R=

ηq

hν

≈

ηλ

1. 24

, (4.1.3)

whereλ≡c/νis expressed in micrometers. The responsivity of a photodetector in-
creases with the wavelengthλsimply because more photons are present for the same
optical power. Such a linear dependence onλis not expected to continue forever be-
cause eventually the photon energy becomes too small to generate electrons. In semi-
conductors, this happens forhν<Eg, whereEgis the bandgap. The quantum efficiency
ηthen drops to zero.
The dependence ofηonλenters through the absorption coefficientα. If the facets
of the semiconductor slab in Fig. 4.1 are assumed to have an antireflection coating, the
power transmitted through the slab of widthWisPtr=exp(−αW)Pin. The absorbed
power can be written as

Pabs=Pin−Ptr=[ 1 −exp(−αW)]Pin. (4.1.4)

Since each absorbed photon creates an electron–hole pair, the quantum efficiencyηis
given by
η=Pabs/Pin= 1 −exp(−αW). (4.1.5)