Physics and Engineering of Radiation Detection

5.1. Semiconductor Detectors 269

general practice, still in principle one could operate a detector at room temperature
at the expense of some added noise in the detector output.
Another parameter of interest for silicon is the intrinsic carrier concentration,
given by
ni=

√

NcNve−Eg/^2 kBT (5.1.30)

whereNc andNvare the density of states in the conduction and valence bands
respectively andkBis the Boltzmann’s constant. The density of states for silicon
can be evaluated from (47)

Nc =6. 2 × 1015 T^3 /^2 cm−^3 (5.1.31)

Nv =3. 5 × 1015 T^3 /^2 cm−^3. (5.1.32)

Except for compensated materials, the intrinsic carrier concentration is the major
source of noise in the detector. Further complication arises from its strong temper-
ature dependence, which stems from the low band gap energy in silicon. This is
another reason to operate the silicon detectors at low temperatures. Substituting
the expressions forNcandNvin equation 5.1.30 we get

ni=4. 66 × 1015 T^3 /^2 e−Eg/^2 kBT (5.1.33)

This equation, withEggiven by equation 5.1.29, has been plotted in Fig.5.1.10.

T (K)

250 260 270 280 290 300 310

-3)

(cmi

n

108

109

1010

Figure 5.1.10: Dependence of

intrinsic charge concentration in

silicon on absolute temperature.

Up until now we have assumed that the band gap in silicon is completely empty.
In reality the situation is not that simple because of the presence of impurities in
the bulk of the material. These impurities could either act as donors or acceptors
depending on where their energy levels lie in the forbidden gap. These energy levels
can trap electrons and holes with the consequence of deterioration of the output
signal. Table.5.1.3 lists some of the commonly encountered impurities in silicon
with their position in the band gap. The reader should note that this list is in no
way exhaustive and other impurities should also be expected in the material, though
in lower concentrations. The fact that no two silicon wafers (wafers are thin slices
of the bulk silicon that are used to produce detector modules) are exactly same, is
well known by detector technologists and researchers. Even detector modules cut
from the same wafer may show different behaviors. However this is not much of a