Page 56 - Photonics Essentials an introduction with experiments

Photodiodes

50 Photonic Devices

1
Spectral Response 0

1.24

= m
E g
Increasing Wavelength
or
Decreasing Energy
Figure 3.6. Idealized spectral response for a photodiode S(E) = 1 if the photon energy is
greater than the band gap. Otherwise S(E) is 0.

I(x) – I(x + x) = –
·I(x)· x

d
I(x) = –
·I(x)
dx
x=x
ln[I(x)] x=x 0 = –
· (x – x 0 )
I(x)
ln = –
· (x)
I(x 0 )

set x 0 = 0, and I(x 0 ) = I 0
I(x) = I 0 e –
x (3.22)
The constant of proportionality
is called the absorption coeffi-
cient. The absorption coefficient is proportional to the spectral re-
sponse function. In Si and other indirect band gap materials,
is
2
about 10 cm –1 at the band gap energy, whereas in GaAs and direct
4
–1
band gap materials,
is about 10 cm , two orders of magnitude
larger. The inverse of the absorption coefficient gives an estimate of
the average distance for absorption of a photon to occur. For exam-
ple, a photon with the band gap energy will penetrate nearly 100 m
into a silicon photodiode on the average before it gets absorbed.
Wherever a photon is absorbed an electron hole pair is created. The

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