Biophotonics_Concepts_to_Applications

generated electron–hole pairs is very short. The generated carriers thus recombine
before they can be collected by the photodetector circuitry.
If the depletion region has a width w, then, from Eq. (5.1), the total power
absorbed in the distance w is

PabsorbedðwÞ¼

Zw

0

asPinexpðÞasxdx¼PinðÞð 1 easw 5 : 5 Þ

When taking into account a reflectivity Rfat the entrance face of the photodiode,
then theprimary photocurrentipresulting from the power absorption of Eq. (5.5)is
given by

ip¼

q

hm

PinðÞ 1 easwðÞð 1 Rf 5 : 6 Þ

where Pinis the optical power incident on the photodetector, q is the electron
charge, and hνis the photon energy.
Two important characteristics of a photodetector are its quantum efficiency and
its response speed. These parameters depend on the material bandgap, the operating
wavelength, and the doping and thicknesses of the p, i, and n regions of the device.
Thequantum efficiencyηis the number of the electron–hole carrier pairs generated
per incident–absorbed photon of energy hνand is given by

g¼

number of electronhole pairs generated

number of incident absorbed photons

¼

ip=q

Pin=hm

ð 5 : 7 Þ

Here, ipis the photocurrent generated by a steady-state optical power Pinincident
on the photodetector.
In a practical photodiode, 100 photons will create between 30 and 95 electron–
hole pairs, thus giving a detector quantum efficiency ranging from 30 to 95 %. To
achieve a high quantum efficiency, the depletion layer must be thick enough to
permit a large fraction of the incident light to be absorbed. However, the thicker the
depletion layer, the longer it takes for the photon-generated carriers to drift across
the reverse-biased junction. Because the carrier drift time determines the response
speed of the photodiode, a compromise has to be made between response speed and
quantum efficiency.

Example 5.4Consider the case when in a 100-ns pulse there are 6× 106

photons at a 1300-nm wavelength that fall on an InGaAspinphotodetector. If

an average of 5.4× 106 electron–hole pairs are generated, what is the

quantum efficiency?

124 5 Fundamentals of Optical Detectors