Physics and Engineering of Radiation Detection

5.1. Semiconductor Detectors 261

Example:

Determine the energy resolution of a silicon detector for 520keV photons

using Fano factor and also by assuming a perfectly Poisson process.

Solution:

Assuming that the photons deposit their full energy in the active volume of

the detector, we haveEdep= 520keV. For silicon we havewi=3. 62 eV and

F =0.1. Forξwe will use the generally usedvalue of 2.355. Substituting

these values in equation 5.1.18 we get

R = ξ

√

Fwi

Edep

=2. 355

[

(0.1)

(

3. 62 × 10 −^3

)

520

] 1 / 2

=1. 9 × 10 −^3.

If we assume the process to be perfectly Poisson, then the energy resolution

will be given by

R = ξ

√

wi

Edep

=2. 355

[

3. 62 × 10 −^3

520

] 1 / 2

=6. 2 × 10 −^3.

E.2 Recombination

We saw earlier that electrons and holes can recombine through an intermediate
energy state created by crystal imperfection or impurity. This is not the only re-
combination mechanism. In fact an electron in the conduction band can also directly
recombine with a hole in the valence band. This process is similar to the process of
electron-ion recombination we studied in the chapter on gas filled detectors except
that in this case the positive charge is a hole and not an ion. The end result of the
process is the removal of an electron from the conduction band and the hole from
the valence band. A point to remember here is that the electron, having a defined
mass, does not annihilate in this process, as is sometimes wrongly concluded. Re-
combination isnotan annihilation process. The free electron simply gets trapped
in the valence band but retains its identity and properties.
The process of recombination can occur in two distinct ways as described below.

Band-Recombination:An electron in the conduction band can fall into the

valence band to recombine with a hole. This is the simplest and most prevalent

form of recombination that occurs in semiconductors. The difference in the

energy of the electron in the two states is then emitted as shown in Fig.5.1.5.

Now this energy can be absorbed by another electron in the conduction band,