2 The Interaction of Radiation with Matter
39
Table 2.3 Asymptotic W
values and Fano factors for
different gases and for solid
silicon (at T = 300 K)
W [eV]
F
Ne
35.4 ± 0.9 [101]
0.13–0.17 [104]
Ar
26.4 ± 0.5 [101]
0.15–0.17 [104]
Kr
24.4 ± 0.3 [101]
0.17–0.21 [104]
Xe
22.1 ± 0.1 [101]
0.124–0.24 [104]
CO 2
33.0 ± 0.7 [101]
0.32 [104]
CH 4
27.3 ± 0.3 [101]
0.22–0.26 [104]
iC 4 H 10 23.4 ± 0.4 [101]
0.261 [106]
CF 4
34.3 [107]
Si
3.67 ± 0.02 [108] <0.1 [104]
Except for CF 4 , the values shown are for measurements using electrons
and, with emphasis on noble gases, in Ref. [105]. Parameters for silicon and some
commonly used gases are listed in Table 2.3.
Analogously to Eqs. (2.40) and (2.41) one can define W values and Fano factors
characterising the distribution of the number of electrons produced by a heavy
charged particle (provided that it is stopped completely in the medium) or by the
absorption of a photon. The asymptotic W values for electrons and photons at high
energies are in general very similar.
In gas mixtures without excitation transfers, the W value and Fano factor are,
to a good approximation, given by the values in the pure gases, weighted by their
respective concentrations. In mixtures where one of the components has excited
states with energies exceeding the ionisation threshold of another component,
excitation transfer can lead to a significant reduction of W and F with respect to
the pure gases (“Jesse effect” [109]). Results for a number of binary gas mixtures
from measurements with α particles can be found in Ref. [110].
2.6.3 Range
The spatial distribution of secondary ionisations produced by a delta electron can be
characterised in terms of the electron range, i.e. the typical path length travelled by
an electron before its energy falls below the ionisation threshold. In the literature,
a number of different definitions of “range” exist, two of which—the fractional
ionisation range R x and the practical range R p —are illustrated in Fig. 2.17. If
the cross sections (including those for elastic scattering) are known, the range of
delta electrons and, more generally, the ionisation pattern produced by a chargedparticle collision, can be calculated using Monte Carlo techniques. As an example,
Fig. 2.18 shows measurements of the 95% range in CH 4 as a function of the primary
electron energy [102], together with calculated values based on the cross sections
implemented in MAGBOLTZ.
39
Table 2.3 Asymptotic W
values and Fano factors for
different gases and for solid
silicon (at T = 300 K)
W [eV]
F
Ne
35.4 ± 0.9 [101]
0.13–0.17 [104]
Ar
26.4 ± 0.5 [101]
0.15–0.17 [104]
Kr
24.4 ± 0.3 [101]
0.17–0.21 [104]
Xe
22.1 ± 0.1 [101]
0.124–0.24 [104]
CO 2
33.0 ± 0.7 [101]
0.32 [104]
CH 4
27.3 ± 0.3 [101]
0.22–0.26 [104]
iC 4 H 10 23.4 ± 0.4 [101]
0.261 [106]
CF 4
34.3 [107]
Si
3.67 ± 0.02 [108] <0.1 [104]
Except for CF 4 , the values shown are for measurements using electrons
and, with emphasis on noble gases, in Ref. [105]. Parameters for silicon and some
commonly used gases are listed in Table 2.3.
Analogously to Eqs. (2.40) and (2.41) one can define W values and Fano factors
characterising the distribution of the number of electrons produced by a heavy
charged particle (provided that it is stopped completely in the medium) or by the
absorption of a photon. The asymptotic W values for electrons and photons at high
energies are in general very similar.
In gas mixtures without excitation transfers, the W value and Fano factor are,
to a good approximation, given by the values in the pure gases, weighted by their
respective concentrations. In mixtures where one of the components has excited
states with energies exceeding the ionisation threshold of another component,
excitation transfer can lead to a significant reduction of W and F with respect to
the pure gases (“Jesse effect” [109]). Results for a number of binary gas mixtures
from measurements with α particles can be found in Ref. [110].
2.6.3 Range
The spatial distribution of secondary ionisations produced by a delta electron can be
characterised in terms of the electron range, i.e. the typical path length travelled by
an electron before its energy falls below the ionisation threshold. In the literature,
a number of different definitions of “range” exist, two of which—the fractional
ionisation range R x and the practical range R p —are illustrated in Fig. 2.17. If
the cross sections (including those for elastic scattering) are known, the range of
delta electrons and, more generally, the ionisation pattern produced by a chargedparticle collision, can be calculated using Monte Carlo techniques. As an example,
Fig. 2.18 shows measurements of the 95% range in CH 4 as a function of the primary
electron energy [102], together with calculated values based on the cross sections
implemented in MAGBOLTZ.