610
22 Light-to-Electricity Conversion
Fig. 22.27 a Experimental
time-dependent response of
an InGaAs:Fe MSM
photodetector to a short
light pulse for three
different wavelengths, inset
shows the frequency
response from a Fourier
transform. b Response of
the MSM for two different
finger widths and
separations (both 1 or 2
µ m, respectively), InGaAs
layer thickness 2 µ m,
λ = 1.3 µ m and bias
voltage 10 V. Adapted
from [1841]
(a)
(b)
2
S = 2 e
I ph + I B + I D
2
B .
(22.51)
The term
2
is written as
2 F(M) with F(M) = =M
2
2 being the excess noise factor
that describes the additional noise introduced by the random nature of the impact ionization. For
multiplication started with electron injection, it is given by [1843]
F(M) = k M + (1 − k)
2 −
1
M
,
(22.52)
with k = α p /α n . For hole injection starting the multiplication (22.52) holds with k substituted by
k
= α n /α p . In Fig. 22.29a the excess noise factor is shown vs. the average multiplication for various
values of k and k
.
Experimental data are shown in Fig. 22.29b for a Si APD. For short wavelengths absorption is
preferential at the surface (n-region) and we have the case of hole injection. The data for the excess
noise factor are fairly well fit with k
≈ 5. For longer wavelengths, the data for electron injection are
fit by k ≈ 0.2 = 1/k
.
For a fully modulated signal the signal-to-noise ratio is given by
S/N =
(e η P opt / hν)
2
/2
2 e
I ph + I B + I D
F(M) B + 4 kT B/(R eq M 2 )
.
(22.53)
If S/N is limited by thermal noise, the APD concept leads to a drastic improvement of noise.
22 Light-to-Electricity Conversion
Fig. 22.27 a Experimental
time-dependent response of
an InGaAs:Fe MSM
photodetector to a short
light pulse for three
different wavelengths, inset
shows the frequency
response from a Fourier
transform. b Response of
the MSM for two different
finger widths and
separations (both 1 or 2
µ m, respectively), InGaAs
layer thickness 2 µ m,
λ = 1.3 µ m and bias
voltage 10 V. Adapted
from [1841]
(a)
(b)
2
S = 2 e
I ph + I B + I D
2
B .
(22.51)
The term
2
is written as
2 F(M) with F(M) = =M
2
2 being the excess noise factor
that describes the additional noise introduced by the random nature of the impact ionization. For
multiplication started with electron injection, it is given by [1843]
F(M) = k M + (1 − k)
2 −
1
M
,
(22.52)
with k = α p /α n . For hole injection starting the multiplication (22.52) holds with k substituted by
k
= α n /α p . In Fig. 22.29a the excess noise factor is shown vs. the average multiplication for various
values of k and k
.
Experimental data are shown in Fig. 22.29b for a Si APD. For short wavelengths absorption is
preferential at the surface (n-region) and we have the case of hole injection. The data for the excess
noise factor are fairly well fit with k
≈ 5. For longer wavelengths, the data for electron injection are
fit by k ≈ 0.2 = 1/k
.
For a fully modulated signal the signal-to-noise ratio is given by
S/N =
(e η P opt / hν)
2
/2
2 e
I ph + I B + I D
F(M) B + 4 kT B/(R eq M 2 )
.
(22.53)
If S/N is limited by thermal noise, the APD concept leads to a drastic improvement of noise.