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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