136 CHAPTER 4. OPTICAL RECEIVERS
the time taken by electrons and holes to travel to the electrical contacts. It also depends
on the response time of the electrical circuit used to process the photocurrent.
The rise timeTrof a linear electrical circuit is defined as the time during which the
response increases from 10 to 90% of its final output value when the input is changed
abruptly (a step function). When the input voltage across anRCcircuit changes instan-
taneously from 0 toV 0 , the output voltage changes as
Vout(t)=V 0 [ 1 −exp(−t/RC)], (4.1.6)whereRis the resistance andCis the capacitance of theRCcircuit. The rise time is
found to be given by
Tr=(ln 9)RC≈ 2. 2 τRC, (4.1.7)
whereτRC=RCis the time constant of the RC circuit.
The rise time of a photodetector can be written by extending Eq.(4.1.7) as
Tr=(ln 9)(τtr+τRC), (4.1.8)whereτtris the transit time andτRCis the time constant of the equivalentRCcircuit.
The transit time is added toτRCbecause it takes some time before the carriers are col-
lected after their generation through absorption of photons. The maximum collection
time is just equal to the time an electron takes to traverse the absorption region. Clearly,
τtrcan be reduced by decreasingW. However, as seen from Eq. (4.1.5), the quantum
efficiencyηbegins to decrease significantly forαW<3. Thus, there is a trade-off be-
tween the bandwidth and the responsivity (speed versus sensitivity) of a photodetector.
Often, theRCtime constantτRClimits the bandwidth because of electrical parasitics.
The numerical values ofτtrandτRCdepend on the detector design and can vary over a
wide range.
The bandwidth of a photodetector is defined in a manner analogous to that of a RC
circuit and is given by
∆f=[ 2 π(τtr+τRC)]−^1. (4.1.9)
As an example, whenτtr=τRC=100 ps, the bandwidth of the photodetector is below
1 GHz. Clearly, bothτtrandτRCshould be reduced below 10 ps for photodetectors
needed for lightwave systems operating at bit rates of 10 Gb/s or more.
Together with the bandwidth and the responsivity, the dark currentIdof a pho-
todetector is the third important parameter. Here,Idis the current generated in a pho-
todetector in the absence of any optical signal and originates from stray light or from
thermally generated electron–hole pairs. For a good photodetector, the dark current
should be negligible (Id<10 nA).
4.2 Common Photodetectors
The semiconductor slab of Fig. 4.1 is useful for illustrating the basic concepts but such
a simple device is rarely used in practice. This section focuses on reverse-biasedp–n
junctions that are commonly used for making optical receivers. Metal–semiconductor–
metal (MSM) photodetectors are also discussed briefly.