Physics and Engineering of Radiation Detection

404 Chapter 6. Scintillation Detectors and Photodetectors

there is a flux Φγof photons having frequencyνuniformly illuminating the surface
of a semiconductor detector of surface areaAper unit time (Φγhas dimensions of
photons per second.). The number of charge pairs generated per unit volume can
then be written as

N=η

φγ

hν

, (6.5.50)

whereηis the quantum efficiency of the detector, which is simply the number of
charge carriers generated per photon. The total current due to these charges, each
having a chargeq,isgivenby

iγ = qN

= qη

φγ

hν

. (6.5.51)

We saw in the previous Chapter that some of these charge pairs recombine with
an average rate of 1/τ(see equation 5.1.20), whereτis the average lifetime of the
charges. Hence the above equation is an overestimation and in order to determine
the actual current we must include the recombination rate into the equation as
well. Ifnis the average number of charge pairs per unit volume, then their average
generation rate can be written as

G =

n

τ

= τ

η(φγ/hν)

Ad

, (6.5.52)

where d is the detector thickness. This equation can be used to determine the
average charge densityn.

n=

η(φγ/hν)

τAd

. (6.5.53)

To determine the current due to these charges we make use of Ohm’s law, which
states that the current density is proportional to the electric field, i.e.,

J=σE

whereσis the conductivity of the material. Usingi=JA, we find that the actual
measurable currentisis given by

is = σEA

= qμnEA. (6.5.54)

Hereμis the charge mobility. We have assumed that the electrons and holes have
same mobility, something that is not really true but is not expected to have a large
effect on our derivation. Substitutingnfrom equation 6.5.53 in the above relation
gives

is=q

τηφγμE

dhν

(6.5.55)