Page 220 - Fiber Optic Communications Fund

Optical Receivers 201

5.2.5 Speed or Response Time
The speed of response or bandwidth of a pin photodetector, shown in Fig. 5.8, depends on the following
factors.

1. The transit time of the photogenerated carriers through the depletion or active region, given by
t
W
= , (5.26)
t

where is the speed of the carrier. If the carriers are not traveling at their saturation velocity , then
sat
= E where is the mobility of the carrier traveling in an electric field E. The electric field intensity
is in turn computed from E ∼ V∕W, where V is the voltage across the depletion region W. Therefore, we
can write as
t
{
W∕ , for carriers traveling at their saturation velocity
sat
= (5.27)
t
2
W ∕(μV), for carriers traveling below their saturation velocity.
2. The slower (relative to drifting carriers) diffusion of carriers occurs outside the depletion region. To min-
imize this diffusion time effect, generally the depletion region is made as large as possible. For example,
a pin photodiode (Fig. 5.8) may be used instead of a pn photodiode where the i-region is much larger
than a typical reverse-biased depletion region. Also, because the doping concentration in the i-region is
significantly lower than that in the p- or n-regions in a pin photodiode, then most of the depletion width is
the i-region and the carrier transit time is drift dominated.
3. The RC time constant is due to the resistance R (the sum of the diode’s parasitic resistance R and the
RC S
load resistance R ) and the capacitance C of the diode. In this case, the RC time constant is given by
L
RC = RC. (5.28)

Therefore, the total response time tot can be written as the root-mean-square value
√
2
2
tot = RC + . (5.29)
t

p +

+
Reverse-bias
voltage V R ‒
i-layer

n +
Load resistor R L

Figure 5.8 Schematic representation of a pin photodiode showing the photoactive region where electron–hole pairs are
generated.