Photoelectron Collection Efficiency in
Mixtures of Noble Gases with CF4
J. M. D. Escada, P. J. B. M. Rachinhas, T. H. V. T. Dias, J. A. M. Lopes, F. P. Santos,
C. A. N. Conde, Member, IEEE, and A. D. Stauffer

Abstract--The collection efficiency f for the photoelectrons
emitted from a CsI photocathode into CF4 and into Ar-CF4 and
Ne-CF4 mixtures is investigated by Monte Carlo simulation. The
dependence of f on the reduced electric field E/N in the 0.1-40 Td
range, on incident photon energy Eph in the 6.8-9.8 eV (183127 nm) range and on mixture composition is analyzed. Electron
drift parameters in CF4, Ar-CF4 and Ne-CF4 are also presented.
I.
INTRODUCTION
models the emission of photoelectrons from a CsI photocathode
using the photoelectron energy distributions from [7] for
incident monoenergetic VUV photons, and from [8] for the
VUV Hg lamp. The emitted photoelectrons are followed along
their free paths in the gas taking into account multiple elastic
and inelastic collisions, and the probability that a photoelectron
is transmitted is the collection efficiency f, obtained as the ratio
f = m/m0 between the number m of photoelectrons that are
transmitted when m0 are injected into the gas (f =1 in vacuum).
ollowing previous Monte Carlo simulation work for
Fpure
noble gases, noble gas mixtures, and mixtures of
Ar - - - CF4 ——
10
sion
2
cm )
sm
-16
sm
(10
CF4 v4 TEST FIT TUDO
sd

1
CF4 MT TEST FIT TUDO
CF4 v3 TEST FIT TUDO
 sion
CF4 v indirect FIT TUDO
CF4 ATTACH FIT TUDO
sexc
sn ind
s
noble gases with CH4 [1]-[5], results are now presented for the
collection efficiency f of the photoelectrons emitted from a CsI
photocathode into CF4 and into Ar-CF4 and Ne-CF4 mixtures,
where f is the fraction of the number of photoelectrons
transmitted in the gas compared to vacuum. The addition of
CH4 or CF4 to noble gases efficiently increases photoelectron
transmission and drift velocity, due to the important role played
by the vibrational excitation of the molecules at low electron
impact energies. Results are calculated in pure CF4 and in ArCF4 and Ne-CF4 mixtures, for applied electric fields E/N
ranging from 0.1 to 40 Td (N is the gas number density and
1 Townsend = 10-17 V cm2) and incident photon energy Eph. We
have considered both monoenergetic VUV photons in the 6.89.8 eV (183-127 nm) range and irradiation with a continuous
VUV lamp peaked at 6.7 eV (185 nm). Electron drift velocities
w are also calculated, and w and f are compared with
experimental measurements where available.
100
CF4 ND TEST FIT TUDO
CF4 ION TEST FIT TUD
Ar MT 10-16cm2
ArgonIon 10-16cm2
ArgonExc 10-16cm2
Dummy for sec.Scale
0.1
sn 4
0.01
0.01
sn 3
0.1
sa
1
10
Electron energy e (eV)
100
100
↑
Ne - - - CF4 ––––
Ne SIGm: SPLINEa
2keV; 10-16*12676
1.7231) até10keV
Ne ExcZecca 31.7&1
LN (MC after June2
10
Ne_ION: SPLINE at
10-16*77.35826326*
0.773523838) até10k
CF4 MT TEST FIT T
sm
2
cm )
II. MONTE CARLO SIMULATION
This work was carried out at Centro de Instrumentação do Departamento de
Física da Universidade de Coimbra, Portugal (Research Unit 217/94), and
received support from FEDER and POCI2010 programs, through FCT
(Fundação para a Ciência e Tecnologia) project POCI/FP/63418/2005.
J. Escada, P.J.B.M. Rachinhas, T.H.V.T. Dias, J.A.M. Lopes, F.P. Santos,
and C.A.N. Conde are with Departamento de Física da Universidade de
Coimbra, Portugal (e-mail: fteresa@gian.fis.uc.pt). P.J.B.M. Rachinhas is also
with Serviço de Radioterapia, Hospitais da Universidade de Coimbra,
Portugal. J.A.M. Lopes is also with Instituto Superior de Engenharia de
Coimbra, Portugal. A. D. Stauffer is with Department of Physics and
Astronomy, York University, Toronto, Canada.
-16
sion
(10
CF4 v4 TEST FIT T
2º
sd
1
s
Detailed descriptions of the simulation model used in the
calculations can be found in [1]-[6]. As in our previous studies
of electron back-scattering effects [2]-[5], the simulation
CF4 v3 TEST FIT TU
sion
sn ind
sm
CF4 ATTACH FIT TU
CF4 ND TEST FIT T
0.1
CF4 ION TEST FIT T
0.01
0.01
0.1
CF4 v indirect FIT TU
sexc
sn 3
sn 4
Dummy for Seconda
sa
1
Electron energy
e
10
100
(eV)
Fig. 1. Electron scattering cross-sections in Ar, Ne and CF4 used in the
Monte Carlo simulation: elastic momentum transfer (σm), vibrational excitation
(σν4, σν3, σνind ), electron attachment (σa), dissociation (σd), excitation (σexc), and
ionization (σion).
w (106 cm/s
This work (Monte Carlo)
10
ekL (eV) M
1
ekT (eV) M
w
e
e kT
0.1
0.01
0.01
0.1
eT Christ. e
1
10
eKL (eV) C
LG and Qlth
Phys Chem.
100
E/N (Td)
Fig. 2. Monte Carlo (continuous curves) and experimental values (symbols)
in CF4 for the electron mean energy e , drift velocity w, and characteristic
energies εkL=eDL/µ and εkT=eDT/µ, where DL and DT are the longitudinal and
transverse diffusion coefficients and µ=w/E is the electron mobility.
WHunter et al.
100
□,●, Christophorou et al. 1979 [18], ● 20%CF4
a)
∆,○ Hunter et al. 1985 [19]
+ Nakamura and Kurachi 1988 [20]
* Schmidt and Polenz 1988 [21]
W (106cm/s) 90
W (106cm/s) 80
CF4
10
30
20
w (106 cm s-1)
B. Collection efficiency : results for monoenergetic VUV
incident photons
This section describes the Monte Carlo photoelectron
collection efficiencies obtained for monoenergetic incident
photons with 7 different energies Eph in the range 6.8-9.8 eV.
The results for f in CF4 are shown in Fig. 4 as a function of E/N
for different Eph, together with the results previously obtained
for Ne [2],[5], Ar [2],[3] and CH4 [3]. In Fig. 5, f is presented
as a function of Eph and different E/N values for mixtures of Ne
and Ar with a 10% concentration of CF4. In Figs. 6 a), b) and
c), the f curves obtained for Eph = 6.8, 7.6 and 9.8 eV and
different E/N values in Ne-CF4 and Ar-CF4 mixtures are
represented as a function of CF4 concentration η.
Fig. 4 a) shows that transmission in CF4 is always higher and
increases more steeply with E/N than in Ne and Ar, due to the
vibrational excitation of the CF4 molecules at low electron
energies, similar to previously results for CH4 [3]. While crosssections for vibrational excitation of CF4 (Fig. 1) are in general
larger than for CH4 (Fig. 1 in [3]), it is found that transmission
in CF4 or mixtures with CF4 is not always higher than in CH4 or
equivalent mixtures with CH4. As an example, Fig. 4 b) shows
that f in CF4 is only higher than in CH4 for the higher photon
energies Eph. On the other hand, while the efficiency f is always
higher in Ne than in Ar (see Fig. 4 a), f in a Ne-CF4 mixture
may be lower than in the equivalent Ar-CF4 mixture.
Emed (eV)
e kL
RESULTS
A. Electron drift parameters
The Monte Carlo results for the electron drift velocity w,
mean energy e and characteristic energies εkL and εkT in CF4
are shown in Fig. 2 as a function of the density-reduced electric
field E/N, and drift velocities in Ar-CF4 and Ne-CF4 mixtures
are shown in Fig. 3 at different CF4 concentrations. The
agreement between the Monte Carlo results (continuous curves)
with data from the literature (symbols) in Fig. 2 and Fig. 3 is a
test to our simulation model and of the choice of cross-sections
for the scattering of electrons by CF4 molecules. Fig. 3 shows
that drift velocity w tends to be higher in CF4 and Ar-CF4 or
Ne-CH4 mixtures than in the pure noble gases, a behaviour
similar to the observed for CH4 and mixtures of noble gases
with CH4.
WHunter et
A 38 58 (10
CF4
+ Christophorou et al. 1996 [16]
 Christophorou and Olthoff 1999 [17]
W_MC (106cm
10
5
2
1
W_MC (106cm
0.5
W_MC (106cm
1
w Ar MCmt
Ar
Ar-CF4
W 70Ar+30CF4
This work (Monte Carlo)
0,1
0,1
1
10
W 90Ar+10CF4
100
E/N (Td)
W 98Ar+2CF4
100
● Christophorou et al. 1979 [18], ● 10%CF4
b)
This work (Monte Carlo)
W_MC (106cm
Wtab 90Ne-10CF4
w (106 cm/s) 70
(106cm/s)
CF4
10
w (106 cm s-1)
III.
100
w (106 cm s-1), e (eV), e k (eV)
The cross-sections for the scattering of the electrons by Ar
and Ne atoms and CF4 molecules used in the present simulation
are represented in Fig. 1. In Ar and Ne, they are those
previously adopted in [2],[3] for Ar, and in [2],[5] for Ne. A
description of the cross-sections in Ar can be found in [2], [3].
In Ne, the cross-sections for elastic momentum transfer follow
[9] below 20 eV and [10] above 20 eV, and inelastic scattering
cross-sections are based on [11], [12] for excitation, and [13],
[14] for ionization. In CF4, the cross-section data recommended
in [15], [16], [17] are used, neglecting super-elastic collisions.
5
10
2
W MC (106cm/s) 8
30
W 94.92Ar+5.0
Nakamura
W MC (106cm/s)
9
W 99.5Ar+0.5C
W MC (106cm/s)
9
2
W MC (106cm/s) 9
W_MC (106cm
W MC (106cm/s) 7
1
Ne
W_MC (106cm
W MC (106cm/s) N
Ne-CF4
W (106cm/s) 95
W MC (106cm/s)
C
W 80Ar+20CF4
Polenz 88
0.1
0.1
1
10
100
E/N (Td)
Fig. 3. Monte Carlo (continuous curves) and experimental values (symbols)
for the electron drift velocity w: a) in Ar, CF4, and Ar-CF4 mixtures with
0.5%, 1%, 2%, 5%, 10%, 20%, and 30% CF4 concentrations, b) in Ne, CF4,
and Ne-CF4 mixtures with 2%, 5%, 10%, 20% and 30% CF4 concentrations.
w (106 cm/s) C
W 99.505Ar+0.
e Nakamura
CF4
1
E ph
Ne
Ar
(eV)
1
E ph = 6.8 eV
6.8 eV
6.8
0.8
7.6 eV
0.8
40 Td
7.2 eV
7.2
8.2 eV
7.6
0.6
8.8 eV
0.6
8.8
9.2
0.4
9.2 eV
f
f
8.2
0.4
9.8 eV
9.8
f_6,8eV
CF4 MC
f_7,2eV
0.2
CF4 MC
f_7,6eV
CF4 MC
f_8,2eV
0
CF4 MC
0
10
20
30
40
f_8,8eV
E/N (Td)
CF4 MC
f_9,2eV
E ph
CF4 MC
--- CH4
CF4
Series8
1
f_9,8eV
(eV)
CF4 MC
Series9
f_6,8eV
6.8
Ar MC
Series10
0.8
f_7,2eV
7.2
Ar MC
Series11
f_7,6eV
7.6
Ar MC
Series12
0.6
f_8,2eV
8.2
Ar MC
Series13
8.8
f_8,8eV
9.2
Ar MC
Series14
0.4
f_9,2eV
9.8
Ar MC
f_7,2eV
f_9,8eV
CF4
MC
Ar MC
f_7,6eV
0.2
CF4 MC
f_8,2eV
CF4 MC
f_8,8eV
0
CF4 MC
0
10
20
30
40
f_9,2eV
CF4 MC
E/N (Td)
f_9,8eV
Fig. 4. Monte Carlo collection efficiency f as a function of E/N for CF4 MC
photoelectrons emitted from a CsI photocathode into CF4 compared a) with f_6,8eV
Ne and Ar b) with CH4 (data from [2],[5] for Ne; [2],[3] for Ar, [3] for CH4). CF4 MC
0.2
a)
1
0.8
a)
0
0
20
40
60
80
Ne-CF4
Ar-CF4
0.8
b)
40 Td
0.6
f
0.4
0.2
0.1 Td
E ph = 7.6 eV
0
0
20
40
60
80
90%Ne
40
90%Ar
100
CF4 concentration h (%)
1
c)
E ph = 9.8 eV
E/N
(Td)
100
CF4 concentration h (%)
1
f
b)
0.1 Td
Ne-CF4
Ar-CF4
0.8
+ 10%CF4
3
Ne-CF4
Ar-CF4
f
0.6
0.6
f
0.4
40 Td
0.4
0.2
0.1
0.2
0.1 Td
0
0
0
6.5
7.5
8.5
9.5
E ph (eV)
Fig.5. Monte Carlo collection efficiency f for photoelectrons emitted from a
CsI photocathode into 90%Ne-10%CF4 and 90%Ar-10%CF4 mixtures, as a
function of incident photon energy Eph for the reduced electric fields
E/N = 0.1, 3, and 40 Td in CH4.
20
40
60
80
CF4 concentration h (%)
100
0.3
0.5
1
2
3
5
10
15
25
40
0.1
0.1
0.3
0.5
1
2
3
5
10
15
25
40
0.3
0.5
1
2
3
5
10
15
25
40
0.1
0.1
0.3
0.5
1
2
3
5
10
0.3
15
0.5
1
2
3
5
10
15
25
40
0.1
0.1
0.3
0.5
1
2
3
5
10
15
25
40
Fig. 6. Monte Carlo collection efficiency f for photoelectrons emitted from
a CsI photocathode into Ne-CF4 and Ar-CF4 mixtures as a function of CF4
concentration η, for E/N = 0.1, 0.3, 0.5, 1, 3, 5, 10, 15, 25, 35 and 40 Td and
incident photon energies a) Eph = 6.8 eV, b) Eph = 7.6 eV and c) Eph = 9.8 eV
(data from [2], [5] for Ne; and from [2], [3] for Ar).
This is shown in Fig. 5 for mixtures with 10%CF4, where f in
Ne-CF4 becomes lower than in Ar-CF4 as we move to lower
E/N. The calculations in the mixtures are summarized in Fig. 6
where f is seen to increase in general with E/N and decrease
with Eph. The dependence of f on CF4 concentration η shows a
sharp increase of f at very low η, in some cases going through
maxima where f reaches values above pure CF4, and smoothing
out at intermediate and higher η. In general, the behaviour of
the f curves in CF4, Ne-CF4 or Ar-CF4 and equivalent results
involving CH4, can essentially be explained in terms of the
ratios ς=nν/nt between the number of vibrational excitation
collisions nν and the total number of collisions nt in the gas,
where ς is a measure of the competition between vibrational
excitation of the molecules and elastic scattering.
C. Collection efficiency : results for incident photons from a
continuous VUV Hg(Ar) lamp
In order to compare with available collection efficiencies f
measured when the photocathode is irradiated with a
continuous spectrum Hg(Ar) lamp, we used in the simulation
the photoelectron energy distribution measured in [8] for this
lamp. The Monte Carlo and experimental data in CF4, Ne, Ar
and Xe are compared in Fig. 7. The agreement between
calculated and measured results is satisfactory, considering that
Ne and Ar data are close, and that experimental values are
rather scattered and include scintillation feedback above ~4Td
for the noble gases. Nevertheless, for Ne, Ar and Xe, the
agreement is improved if calculations take into account electron
reflection by using a reflection coefficient r~0.3, though r may
depend on the electron energy [26]. Also photocathode surface
conditions lead to large uncertainties in r and in photoelectron
emission energies ε0 [27], and we know that f depends strongly
on ε0 for incident photons in the energy range of this lamp [3].
1
CF4
0,8
0,6
f
Ne
Ar
0,4
Xe
0,2
0
0
2
4
6
8
10
E/N (Td)
Fig. 7. Collection efficiency f in CF4 , Ne, Ar, and Xe for photoelectrons
emitted from a CsI photocathode irradiated with a continuous VUV Hg(Ar)
lamp with a spectrum peaked at 6.7 eV (185 nm). Curves are our Monte Carlo
data (CF4, present; Xe, Ne [5]; Ar [3]). Symbols are experimental results (CF4:
 [22],  [23]; Xe:  [23]; Ne: ▲ [23]; Ar:  [23], [24],  [25]).
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