Biophotonics_Concepts_to_Applications

Solution: From Eq. (5.7) the long-wavelength cutoff is

g¼

number of electronhole pairs generated

number of incident absorbed photons

¼

5 : 4  106

6  106

¼ 0 : 90

Thus for this device the quantum efficiency at 1300 nm is 90 %.

The performance of a photodiode is often characterized by theresponsivity
R. This is related to the quantum efficiency by

R¼

ip

Pin

¼

gq

hm

ð 5 : 8 Þ

The responsivity parameter is quite useful because it specifies the photocurrent
generated per unit of optical power.

Example 5.5Consider the case in which photons of energy 1.53× 10 −^19 J

are incident on a photodiode that has a responsivity of 0.65 A/W. If the input

optical power level is 10μW, what is the photocurrent?

Solution: From Eq. (5.8) the photocurrent generated is

ip¼RPin¼ð 0 :65 A=WÞð 10 lWÞ¼ 6 : 5 lA

Typicalpinphotodiode responsivity values as a function of wavelength are
shown in Fig.5.4. Representative values are 0.65 A/W for silicon at 900 nm and
0.45 A/W for germanium at 1.3μm. For InGaAs, typical values are 0.9 A/W at
1.3μm and 1.0 A/W at 1.55μm.
In most photodiodes the quantum efficiency is independent of the power level
falling on the detector at a given photon energy. Thus the responsivity is a linear
function of the optical power. That is, the photocurrent ipis directly proportional to
the optical power Pinincident upon the photodetector, so that the responsivity is
constant at a given wavelength (a given value of energy hν). Note, however, that the
quantum efficiency is not a constant at all wavelengths because it varies according
to the photon energy. Consequently, the responsivity is a function of the wave-
length and of the photodiode material (since different materials have different
bandgap energies). For a given material, as the wavelength of the incident photon
becomes longer, the photon energy becomes less than that required to excite an
electron from the valence band to the conduction band. The responsivity thus falls
off rapidly beyond the cutoff wavelength, as can be seen in Fig.5.4.

5.1 ThepinPhotodetector 125