4.2. COMMON PHOTODETECTORS 143
Figure 4.8: (a) An APD together with the electric-field distribution inside various layers under
reverse bias; (b) design of a silicon reach-through APD.
that accelerates electrons and holes. Figure 4.7 showsαeandαhfor several semi-
conductors [24]. Values∼ 1 × 104 cm−^1 are obtained for electric fields in the range
2–4× 105 V/cm. Such large fields can be realized by applying a high voltage (∼100 V)
to the APD.
APDs differ in their design from that ofp–i–nphotodiodes mainly in one respect:
an additional layer is added in which secondary electron–hole pairs are generated
through impact ionization. Figure 4.8(a) shows the APD structure together with the
variation of electric field in various layers. Under reverse bias, a high electric field
exists in thep-type layer sandwiched betweeni-type andn+-type layers. This layer
is referred to as themultiplication layer, since secondary electron–hole pairs are gen-
erated here through impact ionization. Thei-layer still acts as the depletion region
in which most of the incident photons are absorbed and primary electron–hole pairs
are generated. Electrons generated in thei-region cross the gain region and generate
secondary electron–hole pairs responsible for the current gain.
The current gain for APDs can be calculated by using the two rate equations gov-
erning current flow within the multiplication layer [23]:
die
dx
=αeie+αhih, (4.2.3)−dih
dx=αeie+αhih, (4.2.4)whereieis the electron current andihis the hole current. The minus sign in Eq. (4.2.4)
is due to the opposite direction of the hole current. The total current,
I=ie(x)+ih(x), (4.2.5)