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Review of the Physics
of Semiconductor Detectors Creation of Electron-Hole Pairs in Semiconductor Detectors
by Ionizing Radiation
Average Energy Necessary to Create an Electron-Hole PairThe energy lost by ionizing radiation in semiconductor detectors
ultimately results in the creation of electron-hole pairs. Details of the processes
through which incoming radiation creates electron-hole pairs are not well known, but the
average energy e necessary to create an electron-hole pair in a
given semiconductor at a given temperature is independent of the type and the energy of
the ionizing radiation. The values of e are: 3.62 eV in silicon
at room temperature; 3.72 eV in silicon at 80 K, and 2.95 eV in germanium at 80 K.
Since the forbidden bandgap value is 1.115 eV for silicon at room
temperature and is 0.73 eV for germanium at 80 K, it is clear that not all the energy of
the ionizing radiation is spent in breaking covalent bonds. Some of it is ultimately
released to the lattice in the form of phonons.The constant value of e for different types of
radiation and for different energies contributes to the versatility and flexibility of
semiconductor detectors for use in nuclear spectroscopy. The low value of e compared with the average energy necessary to create an
electron-ion pair in a gas (typically 15 to 30 eV) results in the superior spectroscopic
performance of semiconductor detectors.
The Fano FactorIf all of the energy lost by ionizing radiation in a semiconductor were
spent breaking covalent bonds in the detector's sensitive volume, no fluctuations would
occur in the number of electron-hole pairs produced by ionizing radiation of a given
energy. At the other extreme, if that energy entering the semiconductor detector that is
partitioned between breaking covalent bonds and lattice vibrations or phonon production
were completely uncorrelated, Poisson statistics would apply.
The variance in the number of electron-hole pairs n would then be
<n>2 = n. In fact, neither of these suppositions simulates
reality. As the incoming ionizing radiation gives up energy, a large shower of hot
electrons is created. After many generations, the energy of these hot electrons gets close
to the ionization energy necessary to create an electron-hole pair in the semiconductor
detector, so that there are several possible competing mechanisms for energy loss. Thus
the Fano factor F is introduced to modify the more familiar Poisson relation for this
case. The equation for the variance can be written as
In the case where there are no fluctuations in the number of
electron-hole pairs, F would be zero; in the case where Poisson statistics apply, F would
be equal to 1. Since the energy necessary to create electron-hole pairs in semiconductor
detectors is much smaller than that of the incoming ionizing radiation, it can be
concluded that F is closer to zero than to 1. The true value of F for silicon and
germanium is still unknown; the conflicting theories on the subject do not lead to
experimentally distinguishable results. However, by assuming a value of 0.1 for F in both
silicon and germanium, satisfactory agreement with measured results is found in most
cases.
By assuming a value of 0.1 for the Fano factor, the following formula
gives the germanium detector resolution at LN2 temperature:
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(3) |
with E measured in eV.
DE must be summed in quadrature with the FWHM
keV noise; DN in order to obtain the measured energy resolution
DES:
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(4) |
The value of K for silicon at room temperature is of little interest
because, in such conditions, other factors than fundamental statistics dominate energy
resolution values. These simple formulas show that, as expected from the better statistics
due to the lower value of e , when the energy resolution
is dominated by the detector contribution, germanium detectors have an advantage over
silicon detectors. |
