596
22 Light-to-Electricity Conversion
Fig. 22.9 QWIP
geometries: a 45 ◦ edge
coupled with multiple
quantum-well (MQW)
absorber and b grating
coupled with GaAs
substrate, AlAs reflector
and metal grating on top.
Grey areas are highly
n-doped contact layers
h
MQW
h
(a)
(b)
GaAs
AlAs
GaAs
Fig. 22.10 Part of a
256 × 256 QWIP focal
plane array (FPA) with
grating coupler (area of one
pixel: 37 µ m 2 ).
From [1832]
where η w is the quantum efficiency of a single quantum well (including the escape rate) and is the
photon flux per time and unit area. During the transport of the charge carriers through the barrier they
can be (re-)captured by the QW with the probability p c . The capture probability decreases exponentially
with the applied bias. The total photocurrent (including generation and recapture) is
I ph = (1 − p c ) I ph + i ph =
i ph
p c
.
(22.15)
If the quantum efficiency is small, the efficiency of N w quantum wells η ≈ N w × η w . With this
approximation the total photocurrent of N w quantum wells is given by
I ph = e η η g ,
(22.16)
where g is termed the gain of the structure and is given by
g =
1
p c
η w
η
≈
1
N w p c
.
(22.17)
The dark current can be calculated from thermionic emission and agrees fairly well with experiment
(Fig. 22.11a). When the voltage is increased further, avalanche multiplication can occur while the
carriers are transported through the barrier(s). This mechanism provides further gain as shown in
Fig. 22.11b.
22 Light-to-Electricity Conversion
Fig. 22.9 QWIP
geometries: a 45 ◦ edge
coupled with multiple
quantum-well (MQW)
absorber and b grating
coupled with GaAs
substrate, AlAs reflector
and metal grating on top.
Grey areas are highly
n-doped contact layers
h
MQW
h
(a)
(b)
GaAs
AlAs
GaAs
Fig. 22.10 Part of a
256 × 256 QWIP focal
plane array (FPA) with
grating coupler (area of one
pixel: 37 µ m 2 ).
From [1832]
where η w is the quantum efficiency of a single quantum well (including the escape rate) and is the
photon flux per time and unit area. During the transport of the charge carriers through the barrier they
can be (re-)captured by the QW with the probability p c . The capture probability decreases exponentially
with the applied bias. The total photocurrent (including generation and recapture) is
I ph = (1 − p c ) I ph + i ph =
i ph
p c
.
(22.15)
If the quantum efficiency is small, the efficiency of N w quantum wells η ≈ N w × η w . With this
approximation the total photocurrent of N w quantum wells is given by
I ph = e η η g ,
(22.16)
where g is termed the gain of the structure and is given by
g =
1
p c
η w
η
≈
1
N w p c
.
(22.17)
The dark current can be calculated from thermionic emission and agrees fairly well with experiment
(Fig. 22.11a). When the voltage is increased further, avalanche multiplication can occur while the
carriers are transported through the barrier(s). This mechanism provides further gain as shown in
Fig. 22.11b.