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200 Fiber Optic Communications

choice for the antireflection coating. Note that if we do not use an antireflection coating, then the reflectivity
of silicon at 680 nm is ∼0.32. This means that ∼68% of the incident light is transmitted into the silicon
photoactive region. Note that the reflection coefficient R is computed using,
p
( ) 2
n ()− 1
Si
R = . (5.21)
p
n ()+ 1
Si
In addition to the antireflection coating, we also need to design a suitable absorption layer thickness (W)
or appropriately select the reverse-bias voltage of the photodiode to be large enough so that adequate light
is absorbed. However, as will be shown later, if the absorption region is too thick, then the speed of a
transit-time-limited photodetector will be degraded. A good rule of thumb is to have the absorption layer
thickness satisfy the following inequality:
2 1
< W < . (5.22)

where is the absorption coefficient and its inverse (1/) is the penetration depth of the incident light.
For the above example of a silicon detector used for 680-nm light, the inverse of the absorption coefficient is
3
1∕(2.21 × 10 )≅ 4.5 μm. Therefore, according to the design rule in Eq. (5.22), the absorption layer thickness
should be between 4.5 and 9 μm. However, in practice, using standard silicon semiconductor technology, this
large a thickness may be difficult to achieve, so the QE would be degraded.

5.2.4 Dark Current
The dark current is the current generated in the photo-detector without an incident optical signal or when it
is in the dark. This current originates from the generation of an ehp due to thermal radiation or stray light.
Here, we briefly introduce typical theoretical current expressions for three mechanisms that contribute to
the dark current in a photodetector under reverse bias. The main mechanisms of transport in a reverse-bias
homojunction diode are diffusion of minority carriers J diff , generation–recombination current (for example,
due to trap-assisted and band-to-band tunneling) J GR , or surface leakage J . These three mechanisms can be
S
described by the following expression:
( √ √ )
2
qn i 1 D n 1 D p
J = + [exp ( ∕ kT)− 1], (5.23)
qV
diff
A N N
A n D p
qn W
i
qV
J GR = [exp ( ∕ 2kT)− 1], (5.24)
A GR
and
B VT 3∕2
s
J = exp ( −E g∕ 2kT). (5.25)
S
A
In these expressions, A is the area of the photodiode, W is the depletion width at reverse-bias voltage V, n is
i
the intrinsic carrier concentration, N and N are acceptor and donor densities, respectively, E is the band-gap
A D g
energy, D’s and ’s are minority carrier diffusion constants and lifetimes, and B is a fitting parameter. The
s
corresponding D’s and diffusion lengths L can be calculated using the Einstein relation D∕ = kT∕q where
= mobility and T = absolute temperature. Note that if dislocations are present, we also need to include a
model for the leakage current originating from the dislocations.