260 Chapter 5. Solid State Detectors
E.1 IntrinsicEnergyResolution
Equation 5.1.15 gives the observed spread in the number of electron hole pairs pro-
duced by the incident radiation. Since the number of charges produced is related
to the energy delivered, therefore this equation can also be used to determine the
intrinsicspread in the energy deposited by the incident radiation. The term intrin-
sic refers to the fact that here we are dealing with the uncertainty associated with
the physical process of charge pair production. The energy resolution thus obtained
characterizes the best possible resolution that the system can be expected to pos-
sess. In reality there are other factors, such as noise and the resolving power of the
associated electronics, that may deteriorate the resolution significantly. The good
thing about computing the intrinsic resolution is that it tells us the physical limits
of the system.
SinceEdep=wins, therefore the intrinsic uncertainty in energy can be written
as
σE=σ(wins)=wiσi, (5.1.16)
where we have made use of the constancy ofwiunder non-varying working condi-
tions. Hence according to equation 5.1.15, the spread in the energy is given by
σE = ξwiσi
=√
FEdepwi, (5.1.17)where we have usedns=Edep/wi.
Now we are ready to compute the intrinsic energy resolution of the semiconductor
material, which can be written as
R = ξσE
Edep= ξ√
Fwi
Edep. (5.1.18)
Here we have introduced a factorξ, which can be thought of as a yardstick to decide
whether two peaks could be resolved or not. Its value depends mostly on how the
peak looks like, or in other words which distribution it seems to follow. for example
for a perfectly Gaussian peakξ=2
√
2ln(2) = 2.355. This value corresponds to the
Full Width at Half Maximum (or FWHM) of a Gaussian peak. We will discuss this
in more detail in the Chapter on data analysis.
Energy resolution is the most important factor for a radiation detector used for
spectroscopic purposes since it characterizes the detector in terms of how well it can
differentiate between closely spaced energy peaks in the spectrum. for example if a
source emits two photons having an energy difference of 2keV then the spread in
the measured energy must be better than 2keV for the two peaks to be detected
separately. Otherwise the peaks will get superimposed on one another and become
indistinguishable.
√An important point to note is that the energy resolution varies inversely with
Edep. Therefore a material that does not have good energy resolution at a certain
energy might be more efficiently utilized at a higher energy.