Page 55 - Photonics Essentials an introduction with experiments

Photodiodes

Photodiodes 49

gap energy are absorbed. Furthermore, all of these energetic photons
have an equal chance of being absorbed. The photodiode acts there-
fore as a threshold discriminator: all photons having an energy
greater than or equal to the band gap are absorbed and all the rest
are not absorbed.
We can define a spectral response function S(E). For this simple
model:
S(E) = S( ) = 1 if E( ) Eg
S(E) = S( ) = 0 if E( ) < Eg (3.19)

When you measure the response in the laboratory, you will find it
more convenient to modify this relationship so that it is expressed in
terms of the photon wavelength. This is because almost all spectrome-
ters continue to be calibrated in terms of optical wavelength rather
than photon energy. The origin of this difference is both historical and
functional, being related to the wavelength interference that is the
basis for the operation of the diffraction grating inside the spectrome-
ter.
Optical absorption, however, is not a phenomenon related to wave-
length. It has its physical basis in the quantum nature of light and
conservation of energy. A single photon must have enough energy to
break a single bond. Two photons each having three-quarters the
needed energy will not suffice even though the combined energy of
these two photons would exceed the bond energy. Fortunately, there
is a simple relationship between the energy of a photon and its wave-
length in air:
·2 c hc
E photon = = = (3.20)

And, as we showed in Chapter 1, the relationship between the photon
energy in eV and the wavelength of the photon in air is expressed as
1.24 eV 1.24 m
E photon = , or
= (3.21)

(microns) E photon (eV)
In the ideal model, we can plot the spectral response as a function
of energy or wavelength as shown in Fig. 3.6. The spectral response
function for real photodiodes is not too different from this model, as
shown in Fig. 3.7.
Photons that are incident on the photodiode continue to propagate
into the diode until they are absorbed. The number of photons, or in-
tensity I(x) – I(x + x) that is absorbed in the region x (as dia-
grammed in Fig. 3.8) is proportional to the incident intensity:

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