Page 233 - Fiber Optic Communications Fund

214 Fiber Optic Communications

One possible solution to this trade-off is to use a RCE structure such as a Fabry–Perot cavity with a very
thin active layer for a large bandwidth, and multiple passes of light in the absorption layer in the resonant
cavity to increase the quantum efficiency. In this structure, a thin absorption region is placed in an asymmetric
Fabry–Perot cavity (see Section 3.3). The top and bottom reflectors, which can be fabricated by DBRs, form
the cavity. Below, we discuss some relevant details of the resonant cavity structure.
The Fabry–Perot cavity generally has two parallel mirrors comprised of quarter wavelength stacks (QWS)
with a periodic modulation of the refractive index. That is, we use alternating materials that have different
refraction indices in a multilayer form, which results in reflection at the interfaces. This multilayer structure is
exploited to create optical mirrors, which reflect the light back to the optical absorption layer, thus effectively
increasing the absorption width of the otherwise physically thin layer. Having mirrors on both sides of the
absorption layer, the light gets “trapped” in the “cavity” between the mirrors until absorbed. The resonant
frequency of a Fabry–Perot cavity is given by Eq. (3.43),

= 2L∕integer, (5.50)
n
where is the light wavelength in vacuum, n is the refraction index of the material in the cavity, so that
∕n is the light wavelength in the material, and L is the distance between the mirrors. Owing to the electro-
magnetic wave property of the light, the “cavity” of mirrors can cause constructive or destructive summation
of the waves, depending on the ratio of the distance between the mirrors to the wavelength of the light.
Therefore, the spectrum of the enhancement becomes a quasi-oscillatory function of the light wavelength.
The peak-to-valley ratio also depends on the energy loss between the mirrors, or more precisely, the photon
absorption. For particular wavelengths, there is electromagnetic resonance in the cavity, which is the origin
of the term “resonant cavity enhancement”.
The classical arrangement of a RCE photodetector structure shown in Fig. 5.19(b) has a DBR as the front
mirror on the side where the light is incident and a metal reflector as the back mirror on the other side for
better reflection. Both mirrors can be electrically conductive, or one can place additional conductive sheets on
the sides of the absorption layer with width W, and the photogenerated carriers are swept out by the bias of the
photodetector traversing the structure once, thus, the transit time of the photodetector is virtually unaffected
by the optical mirrors. A requirement is for the incident light to pass through the front mirror, and then to be
reflected by the front mirror when traveling back into the cavity. Unfortunately, such a “diode-like” behavior
of optical mirrors is not strong, although it can be achieved with proper selection of anti-reflection coating of
the surface of the photodetector. Therefore, the front mirror is semitransparent, having similar reflectivities
for incident and cavity light, R ≈ R < 1, and consequently, similar transmissivities (1 − R )≈(1 − R ) < 1
1
S
S
1
in both directions. Ideally, the back mirror should have a very high reflectivity, R ∼ 1. The materials (Si and
2
Ge) in the cavity and in the absorption layer usually have similar refractive indices, weakly dependent on
bias and charge or doping concentrations; so, we can neglect reflections inside the cavity. For other materials,
this can be different; for example, in III–V semiconductors, organic semiconductors. The operation of the
photodiode in a RCE was analyzed in Ref. [41], and the responsivity is given in Refs. [41, 42].
I ph { q [ ] }
= × 1 − exp (−W) ×(1 − R ) × RCE,
S
P opt hf 0
where (5.51)
1 + R 2
exp(W)
RCE = √
R 1 R 2 R 1 R 2
1 − 2 cos (2L +Ψ +Ψ )+
exp(W) 1 2 exp(2W)
with (q∕hf ) the responsivity of the absorption material of infinite thickness, W the width of the absorption
0
layer with absorption coefficient , and R ≈ R the reflection from the photodiode surface. Thus, (1 − R )
S
S
1