22.3 Photodiodes
601
η =
I ph /e
P opt /(hν)
,
(22.23)
where I ph = A j ph is the photogenerated current over the surface A. The responsivity R λ of the photodiode (for monochromatic radiation) is defined as
R λ =
I ph
P opt
=
e
hν
η ≈
λ
1.24 μm
η .
(22.24)
For a modulated light intensity P opt must be replaced by m P opt /
√
2. The equivalent circuit including
noise sources for a photodiode is shown in Fig. 22.15b.
Random processes lead to shot noise i
2
S (Sect. K.3.3). Besides the photocurrent I ph itself, the
background radiation (I B , in particular for infrared detectors) and the thermal generation (dark current,
I D ) of carriers contribute:
i
2
S = 2 e
I ph + I B + I D
B ,
(22.25)
with B being the bandwidth. Additionally, the parallel resistances cause thermal noise
i
2
T = 4 kT B/R eq .
(22.26)
The resistance R eq is given by the resistance of the depletion layer (junction) R j , the load R L and the
input of the amplifier R i as R
−1
eq = R
−1
j + R
−1
L + R
−1
i . The series resistance R s of the photodiode can
be usually ignored in this context.
For a fully modulated signal the signal-to-noise ratio of the photodiode is given by
S/N =
i
2
ph
i
2
S + +i
2
T
=
e η P opt / hν
2 /2
2e
I ph + I B + I D
B + 4 kT B/R eq
.
(22.27)
Therefore the NEP is given by
NEP =
2 hν B
η
1 +
1 +
I eq
e B
.
(22.28)
The current I eq is given by I eq = I B + I D + 2kT /(eR eq ). If I eq /eB 1, the NEP is determined by the
shot noise of the signal itself. In the other limit I eq /eB 1 the detection is limited by the background
radiation or thermal noise. In this case, the NEP is (for B = 1 Hz, in W cm
2 Hz
1/2 )
NEP =
√
2
hν
η
I eq
e
.
(22.29)
In Fig. 22.16 the situation is shown for a silicon photodiode as a function of R eq . The diode has a
quantum efficiency of 75% at λ = 0.77 µm. A high value of R eq ∼ 1 G is necessary to ensure
detection limited by dark current.
601
η =
I ph /e
P opt /(hν)
,
(22.23)
where I ph = A j ph is the photogenerated current over the surface A. The responsivity R λ of the photodiode (for monochromatic radiation) is defined as
R λ =
I ph
P opt
=
e
hν
η ≈
λ
1.24 μm
η .
(22.24)
For a modulated light intensity P opt must be replaced by m P opt /
√
2. The equivalent circuit including
noise sources for a photodiode is shown in Fig. 22.15b.
Random processes lead to shot noise i
2
S (Sect. K.3.3). Besides the photocurrent I ph itself, the
background radiation (I B , in particular for infrared detectors) and the thermal generation (dark current,
I D ) of carriers contribute:
i
2
S = 2 e
I ph + I B + I D
B ,
(22.25)
with B being the bandwidth. Additionally, the parallel resistances cause thermal noise
i
2
T = 4 kT B/R eq .
(22.26)
The resistance R eq is given by the resistance of the depletion layer (junction) R j , the load R L and the
input of the amplifier R i as R
−1
eq = R
−1
j + R
−1
L + R
−1
i . The series resistance R s of the photodiode can
be usually ignored in this context.
For a fully modulated signal the signal-to-noise ratio of the photodiode is given by
S/N =
i
2
ph
i
2
S + +i
2
T
=
e η P opt / hν
2 /2
2e
I ph + I B + I D
B + 4 kT B/R eq
.
(22.27)
Therefore the NEP is given by
NEP =
2 hν B
η
1 +
1 +
I eq
e B
.
(22.28)
The current I eq is given by I eq = I B + I D + 2kT /(eR eq ). If I eq /eB 1, the NEP is determined by the
shot noise of the signal itself. In the other limit I eq /eB 1 the detection is limited by the background
radiation or thermal noise. In this case, the NEP is (for B = 1 Hz, in W cm
2 Hz
1/2 )
NEP =
√
2
hν
η
I eq
e
.
(22.29)
In Fig. 22.16 the situation is shown for a silicon photodiode as a function of R eq . The diode has a
quantum efficiency of 75% at λ = 0.77 µm. A high value of R eq ∼ 1 G is necessary to ensure
detection limited by dark current.