142 CHAPTER 4. OPTICAL RECEIVERS
Figure 4.7: Impact-ionization coefficients of several semiconductors as a function of the elec-
tric field for electrons (solid line) and holes (dashed line). (After Ref. [24];©c1977 Elsevier;
reprinted with permission.)
4.2.3 Avalanche Photodiodes.....................
All detectors require a certain minimum current to operate reliably. The current re-
quirement translates into a minimum power requirement throughPin=Ip/R. Detectors
with a large responsivityRare preferred since they require less optical power. The re-
sponsivity ofp–i–nphotodiodes is limited by Eq. (4.1.3) and takes its maximum value
R=q/hνforη=1. Avalanche photodiode (APDs) can have much larger values ofR,
as they are designed to provide an internal current gain in a way similar to photomulti-
plier tubes. They are used when the amount of optical power that can be spared for the
receiver is limited.
The physical phenomenon behind the internal current gain is known as theimpact
ionization[23]. Under certain conditions, an accelerating electron can acquire suffi-
cient energy to generate a new electron–hole pair. In the band picture (see Fig. 3.2) the
energetic electron gives a part of its kinetic energy to another electron in the valence
band that ends up in the conduction band, leaving behind a hole. The net result of
impact ionization is that a single primary electron, generated through absorption of a
photon, creates many secondary electrons and holes, all of which contribute to the pho-
todiode current. Of course, the primary hole can also generate secondary electron–hole
pairs that contribute to the current. The generation rate is governed by two parame-
ters,αeandαh, theimpact-ionization coefficientsof electrons and holes, respectively.
Their numerical values depend on the semiconductor material and on the electric field