Physics and Engineering of Radiation Detection

258 Chapter 5. Solid State Detectors

Eimp

Eg

Radiation

Incident

Valence Band

E

Conduction Band

Electron Hole

Figure 5.1.4: Production mechanisms of

electron hole pairs by incident radiation in

a semiconductor.

it would mean that the variance in the number of ionization and excitations can be
written as

σi =

√

ni and

σx =

√

nx.

These two variances are normally not equal because of difference in the thresholds
for excitation and ionization processes. However if we weight them with their cor-
responding thresholds, they should be equal for a large number of collisions, i.e.,

iσi = xσx or

i

√

ni = x

√

nx.

Combining this with equation 5.1.12 gives

σi=

x

i

[

Edep

x

−

i

x

ni

] 1 / 2

(5.1.13)

Let us now denote the average energy needed to create an electron-hole pair bywi.
Note that this energy includes the contribution from all other non-ionizing processes
as well. This means that it can be obtained simply by dividing the total deposited
energy by the number of electron-hole pairs detectedns. Hence we can write

wi =

Edep

ns

or

ns =

Edep

wi

.

If we have a perfect detection system that is able to count all the charge pairs
generated, then we can safely substitutensforni. In this case the above expression
forσiyields

σi=

[

x

i

(

wi

i

− 1

)(

Edep

wi

)] 1 / 2

. (5.1.14)

UsingEdep/wi=ns, this can be written as

σi=

√

Fns. (5.1.15)