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Optical Receivers 211

The expression for F is given by
[ 2 ]
(M − 1)
F = M ⋅ 1 −(1 − k) ⋅ = kM(1 − k)(2 − 1∕M). (5.45)
M 2
′
Here, k is replaced by either k eff or k :
eff
k − k 2 1
2
k = , (5.46)
eff
1 − k
2
k eff
k ′ = , (5.47)
eff 2
k
1
and
∫ W (x) ⋅ M(x)dx
k = 0 W , (5.48)
1
∫ (x) ⋅ M(x)dx
0
∫ W (x) ⋅ M (x)dx
2
k = 0 W . (5.49)
2
∫ (x) ⋅ M (x)dx
2
0
For the case of a uniform electric field in the multiplication region, it turns out that k = ∕ and k ′ = ∕.
eff eff
From the computed results of excess noise factor F vs. gain M, it can be shown that, for lower excess noise,
the carriers with higher ionization coefficient should be injected. Also, the ionization coefficients for electrons
and holes should be significantly different for better performance of the APD. An APD provides gain with-
out the need for an amplifier. However, its main limitation comes from its bandwidth. Because of the long
avalanche build-up time, the inherent bandwidth of APDs is small. But APDs are very important because
their internal gain is suitable for long-haul communication systems with a minimum number of repeaters,
and also for dense wavelength-division multiplexing systems. Special structures can be used to improve the
high-frequency performance. Unlike pin-PDs, even for moderate or high applied bias, the absorption layer
may be at a low bias. This is because the multiplication layer should be under a high field for impact ioniza-
tion. Therefore, the absorption and multiplication regions should be decoupled. The separate absorption and
multiplication (SAM) structure with a bulk InP multiplication layer and an InGaAs absorption layer is shown
in Fig. 5.17. Here, the objective is to make avalanche multiplication occur in a wider band-gap layer, such as
InP, but for absorption to occur in a narrower band-gap layer, such as InGaAs.
To improve the performance of a SAM APD, a grading (G) layer is introduced in order to smooth out a band
discontinuity between InP and InGaAs. This reduces a hole pile-up at the interface and, therefore, improves
its frequency response at low biasing voltage [25–27]. Next, a charge (C) layer is used to control the electric
field distribution between the absorption and multiplication layers. This is necessary because the electric field
should be high enough to initiate impact ionization in the InP multiplication layer, and low enough to suppress
ionization in the absorption layer, which could lead to a lower bandwidth. Depending on the particular design,
different layers can be merged to perform the same tasks. For example, the charge layer can be merged with the
multiplication layer, resulting in a very narrow multiplication layer. This leads to the SAGCM APD, which,
despite its complexity, has an electric field profile that can be optimized for gain–bandwidth performance. It
offers the most flexibility in terms of tuning the electric field profile for a particular application. Also, edge
breakdown is suppressed because the charge sheet density is higher in the center of the device due to the mesa
structure, which results in a higher electric field in the center of the device than in its periphery.
In order for this structure to operate properly as an APD, some practical conditions must be satisfied. For
example, the electric field at the InGaAs/InP heterointerface should be smaller than 15 V/μm at operating