Optical Sources, Detectors, and Systems

5.2 Semiconductors: Photoconductors and Photodiodes 103

set at 12 times the rms noise current, for example, results in a false

count probability of

10"^

for each pulse interval or an error rate of

10'^/2

X

10-^

or one false count every 2 sec. If the expected pulse

height were a constant, then each electron emitted by the photo-

cathode would be detected. Actually the gain is a random process

as we have discussed in deriving the noise factor, P. In the ex-

treme, we know that there is a finite probability that

no

electron will

be emitted from the first dynode. If the statistics are indeed Poisson,

then from Eq. (4.2), a 5 of 5 yields a probability of nonemission of

p(0,5) =

e'^

«

20'2.

Using an analysis similar to that used earlier for

r, the fractional mean square gain fluctuation is found to he ( 1/5

-h

1/5^

+ ) = (r - 1), For 5 = 5, the mean square fractional

fluctuation is 025, and the rms fluctuation, 05. The gain prob-

ability distribution is not Gaussian but we conclude that the thresh-

old must be set well below

0.5

of the mean pulse height to assure the

detection of a high fraction of the individual photoelectron events.

5.2 Semiconductors: Photoconductors and Photodiodes

We consider primarily the semiconductor junction photodiode in our

systems analyses, but we first review briefly the photoconductor, which

has more specialized uses although it was historically one of the first

solid-state optical detectors. The photoconductor, as its name implies is

a conducting element whose conductance is controlled by incident

infrared or visible radiation. As shown in Figure 5.5, light striking a

homogeneous semiconductor produces holes or electrons or hole-

electron pairs which cause current to flow in the presence of voltage, V.

There are two types of photoconductor, intrinsic and extrinsic, the

former depending on across-the-gap transitions or pair production and

the latter on excitation of carriers from an impurity level in the forbidden

region. In either event, there are two parameters of interest, the

recombination

time

r^

and the transit time

T^,

the time for the carrier to

traverse the distance /in the presence of the electric field Vjl The

photocurrent in the presence of optical power

P,

becomes

104

Chapter 5 Real Detectors

Figure 5.5 Semiconductor photoconductor.

since, as in section 4.2, qv//is the induced current flow at the electrodes

during recombination time r^. The quantum efficiency, rj, is determ-

ined by the reflectivity, p, at the input surface and the bulk absorption

coefficient, a (see problem 5.3). The ratio of the time constants is called

the photoconductive gain G^. Similar to our treatment of the colliding

electrons in section

4.2,

the fractional electron charge contribution in the

first parentheses is given by the ratio of the distance traveled before

recombination to the length of the device. The expression may be seen

to be consistent if, for example, the transit time and recombination times

are equal. Then, on the average, an excited carrier moves the length of

the photoconductor before recombining and contributes one electron

charge to the external circuit. It is apparent that the gain can also be

greater than unity, but this improved performance is accompanied by a

reduced frequency

cut-off,

which is the inverse of the recombination

time.

The induced photocurrent has a mean square fluctuation called g-

r noise for

generation-recombination,

which is given by (Kingston, 1978,

Ch.6)

<i^>=4(qGp)iB

=

4qG}^B

(5.5)

This may be simply interpreted as shot noise due to pulses of charge

(qGJ, an extra factor of two arising from the fluctuation in pulse width

due to the randomness of the recombination process. Intrinsic photo-

conductors are made from a myriad of materials such as PbS, PbSe, PbTe,

CdS,

etc., as well as HgCdTe and the well-known III-Vs, GaAs, etc., and,

of course. Si and Ge. Extrinsic photoconductors are usually made by