Page 58 - Photonics Essentials an introduction with experiments

Photodiodes

52 Photonic Devices

minority carrier of this pair will diffuse toward the p-n junction. If
the p-n junction is located more than a minority carrier diffusion
length from the point of absorption, there is a good chance that the
minority carrier will recombine with a majority carrier. If this hap-
pens, there will be no contribution to the external current from the
absorption of the photon.

3.4.2 Quantum Efficiency
The ratio of the number of photocarriers to the number of incident
photons is called the quantum efficiency. If the absorption of every
photon resulted in a minority carrier reaching the p-n junction, the
quantum efficiency would be unity. If the p-n junction is too far away
from the point of absorption, then the quantum efficiency could be
considerably less than unity. In a well-designed photodiode, the rela-
tionship between the absorption coefficient and the diffusion length is
taken into account so that nearly all photocarriers are collected by the
p-n junction. The resulting quantum efficiency is close to unity.
The photocurrent is just the product of the number of electrons per
second (= n e ) and the charge on each electron (= q)

I photocurrent = q·n e
so

I photocurrent
n e = electrons/sec (3.23)
q
The optical power is the number of photons per second (= n ) times
the energy per photon (= ):
P optical = n ·
so

P optical
n = photons/sec (3.24)

The quantum efficiency for a photodiode is defined as Q = n e /n . In an
experiment, you will measure I photocurrent and P optical , and not n e or n .
Using Eqs. 3.23 and 3.24,

I/q I photocurrent ·
n e
Quantum efficiency = Q = = = (3.25)
n P/ P optical · q
and
qP optical Q
I photocurrent = (3.25a)

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