Problems 121
Problems
5.1 An optical receiver operating at a wavelength of 1,06 jim has an
electrical bandwidth of 1000 MHz, Find the NEP using a high-gain
PIN-FET transimpedance amplifier with an input resistance of 500 Q.
The FET has a g^ of 5 mS, a y of 1.5, and the quantum efficiency of
the PIN is 05,
5.2 What would be the required quantum efficiency of a high-gain pho-
tomultiplier to )deld the same sensitivity as in Problem 5.1? Assume a
noise factor Fof 125,
5.3 The p-i-n photodiode shown in the sketch has thin transparent p
and n regions so that all photoinduced pairs are produced in the intrin-
sic space-charge region.
±
d
T
(a) Write an expression for the quantum efficiency, rj, in terms of
the absorption coefficient a and the thickness d,
(b) Find an expression for d
z;ersws
a,iiri
=
50%.
5.4 Find both the signal-noise-linuted NEP, (NEP)^j^, and the dark-
current-limited NEP,
(NEP)j^j^,
for a photomultiplier with current gain
G and excess noise factor r. Note that the mean square noise current is
given by
2qG^r(i^+
ij^)B,
5.5 A photomultiplier is used to detect individual "photons" (photo-
events) with a time resolution of 10 nsec. With a 50-X2 output load with
T^ = 300 K, find the required gain G for the output current pulse to
have a peak value 10 times the rms noise current. For simplicity,
assume a square output pulse and a bandwidth of
100
MHz,
122 Chapters Real Detect ois
5.6 A photomultiplier with a cut-off wavelength of
1
jjm is cooled to
reduce the dark current. At what temperature will the
(NEP)j^j^
be
reduced by 20
dB (100/1)
fron\ the value at
T = 300 K7
5.7 A unit quantum efficiency ideal detector at a
lO-ium
wavelength is
operated at 77 K with an integral bias resistor of 1000 Q in the same
temperature bath. The detector is coupled by a cable to an external
transimpedance amplifier with input resistance of 300 Q, and effective
input noise current of
2
pA/Hz^^^.
Find:
(a)
R.^
and T^ as seen by the detector.
(b) The overall effective input noise current in
A/Hz^^^.
(c) The
WEP)^i^
for a bandwidth of
1
MHz,
5.8 A mercury-cadmium-telluride (HgCdTe) junction detector is used in
the "photovoltaic" mode to detect 10
iJm
radiation. The detector area is
1
mm^,
the measured zero bias or dark resistance is 100
^2
at 77 K, the
operating temperature, and the bandwidth is
1
MHz, Find:
(a) The diode saturation current
7^.
(b) The (NEP)^ with zero background, with a high-gain
FET
stage,
^m ~ ^'^^
mhos,
7=1, also operated at
77
K,
(c) The linear dynamic range,
P^^JNEP,
where P^^ produces
5.9 An InGaAs APD operating at a
15-iJm
wavelength has a quantum
efficiency of 0,5 and
equal impact ionization
coefficients.
The diode out-
put drives an amplifier with K.^ = 50 Q, T^ = 300 K, and B = 1000
MHz,
(a) Write an expression for the total mean square noise current in
terms of the nonmultiplied signal current, f
^^
M, F, B, T^, and
P^^,
(b) Find
z^^
forfS/N)^=l.
(c) Find and plot the NEP as a function of M from M = 1 to M =
200,
(d) Estimate
NEP^^^
and the associated value of M.

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