In fig. 5.12, the measured values displayed in fig. 5.11 are rearranged according to the es- timated kinetic energy Ekin at primary particle impact referring to eq. 5.7 and eq. 5.8. For the determination of the 87Rb-ion impact energies in fig. 5.12(a), an average value of diCEM= 12.22 mm is chosen in eq. 5.7 as determined from the relative flight time differences in subsection 5.3.1 (fig. 5.9). For the electron impact energies in fig. 5.12(b), a CEM channel hit is assumed at a distance31 d
e = 10 mm for a typical channel impact in the e−-CEM. For analysis and comparison of the rearranged efficiency data with the cascaded dynode multiplier efficiency model of section 2.2 and the literature, a least-squared fit according to eq. 2.10 is performed on both data sets as shown in fig. 5.12(a) and (b) (straight and dashed lines).
For the least-square fit, a uniform secondary electron yield of δ = 2 is assumed for the consecutive stages g2..m and both CEM detectors. This choice results from the generalized conditions of the single emission process at the consecutive stages g2..m in the CEM as illus- trated in section 2.1 and described by [48]. For the ion-CEM and the corresponding efficiencies ηi(Ekin), a maximum yield energy ofEδ0,max= 10 keVis further chosen as fixed value for the
least-squared fit of the 87Rb-ion efficiencies. However, the latter choice is to some extend artificial and results as the measured efficiency values ηi(Ekin) in fig. 5.12(a) do not show a
31
The minmum possible distance in the CEM until a primary impact in the active CEM surface isde= 4.25 mm
(cone hit), whereas the minimum distance for a channel hit isde ≈7 mmand the maximum distance is
de ≈13.1 mm (see Appendix A.4). Therefore, a distance ofde = 10 mmis chosen for a common channel
5.4. Absolute detection efficiencies
defined maximum within the observed kinetic energy range as generally expected by eq. 2.10. Nevertheless, the experimental evidence from related experiments of [88, 105, 106, 123, 135] with similar incident ions at comparable impact energiesEkin<15 keV strongly suggests the choice of such a value for the least-squared fit of ion efficiencies [88]. Note further that the ion efficiency data is fitted starting with impact energies Ekin≥0.2 keV corresponding to acceler- ation voltage values of∆Uacc>1.6 kVin accordance to the considerations of subsection 5.3.1.
Ion efficiencies
The measured ion efficienciesηi(Ekin)shown in fig. 5.12(a) depict the quasi-linear increase up to a certain saturation level as observed by various previous efficiency calibration measure- ments [88, 89, 93, 95, 97, 98, 101, 102, 105, 106, 123, 124, 135]. A similar increase and satu- ration level is also continuously observed for multi-channel plates32(MPCs) (e.g., [123, 243]). However, the measured valuesηi(Ekin) depicted in fig. 5.12(a) display a significantly higher efficiency up to a factor of two to three compared to related previous calibration experiments in the literature, using ions with a similar mass-to-charge ratio and within the same energy range (e.g., the krypton isotopes 82,83,84Kr+ in [123] with ηi(Ekin) ∼ 30 % at Ekin = 2 keV; orAr+,Xe+ for Ekin ≤ 2.5 keV in [105] and for Ekin <10 keV in [88, 135]). Nevertheless, if one assumes a channel impact for the primary ions as initially intended by the CEM detector design (see subsection 4.2.4) and not a CEM cone hit (dashed curve, fig. 5.12(a)), the observed factor is consistent with generally measured, enhanced efficiencies in the literature for channel impacts compared to cone hits [87, 88, 133, 134].
In more detail, the least-squared fit shown in fig. 5.12(a) yields a primary particle yield of the87Rb-ion of δ0 = 6.5±0.1. By comparison of this value to commonly observed primary yield valuesδ0 for related active surfaces and kinetic energiesEkin [66, 73, 77, 83, 244], such a high value will only be explained by a87Rb-ion impact under grazing incidences θ in the CEM. As a common cone hit yields an incident particle angle ofθ= 60◦(see subsection 2.4.3), an average incident angle ofθ≈80◦ can be assumed for a typical CEM channel hit (fig. 2.8). Using identical kinetic energies at primary particle impact for both cases, the primary particle yield values δ0(60◦) and δ0(80◦) for a cone or a channel hit will differ only by a fixed factor as indicated by eq. 2.12. For an acceleration voltage of ∆Uacc = 3.8 kV, corresponding to an impact energy of Ekin = 2.044 keV (fig. 5.12), with Eδ0,max = 10 keV and δ = 2, this
will result, e.g., in a calculated absolute efficiency of ηdet(δ0(60◦)) = 0.559 compared to ηdet(δ0(80◦)) = 0.905according to eq. 2.10.
For a comparison of typical cone to channel impacts, a fictitious curveηdet(δ0(60◦)) for a sample cone hit underθ = 60◦ withδ0(60◦) = 2.3 is illustrated33 in fig. 5.12(a). In relation to a CEM channel impact (dashed curve), this reference curve is additionally plotted to the observed data as usually only CEM cone impacts are observed in most CEM detector calibra- tion measurements. Compared to the literature data, the observed values of the measurement thus represent a typical channel hit in the CEM. The latter observation is also consistent with the observed ion flight timesti in subsection 5.3.1, further suggesting a CEM channel impact and not a cone hit.
32
MCPs generally yield similar active secondary emitting surfaces as CEMs.
33
The data of the fictitious curve yields the identical fit parameters of the channel hit curve, but using
δ0(60◦) =δ0(80◦)(sec(60◦)/sec(80◦) = 2.3as deduced from eq. 2.10 instead ofδ0(80◦) = 6.5as obtained
Maximum ion detection efficiency The least-squared fit according to eq. 2.10 displays a good agreement with the observed efficiency values (fig. 5.12(a); black line). Extending the theoretical fit curve to higher kinetic energiesEkin, the calculated ion efficiency will already raise to ηi,fit(5 keV) = 0.989 at an impact energy of Ekin = 5 keV. From the fit, a maximum ion detection efficiency of ηi,fit(10 keV) = 0.9943 is expected at an impact energy of Ekin =
10 keV for previously stated parameters of δ0, Eδ0,max, and δ (eq. 2.10; see section 2.4).
Unfortunately, such kinetic energy values cannot be observed with the current UHV glass cell setup as eventual current breakthroughs contain the system to acceleration voltage differences
∆Uacc<3.9 kV (see section 4.2).
Note that for a chosen value ofδ= 3in eq. 2.10, the fitted primary ion yield is stillδ0 = 5.5 for the measured ion efficiency values with a chosen Eδ0,max = 10 keV. These values are
in accordance with the theoretically obtained yield values of subsection 2.5. However, the secondary avalanche in the CEM will then undergo only m = 16 stages of amplification in correspondence to commonly observed gain values of G0 = 5×107, using eq. 3.2 and the values δ0 = 5.5 and δ = 3. As a result, the transit time ttransit of the secondary electron avalanche in the CEM will be subsequently altered by the fewer amplification stages, yielding shorter transit times than stated by the manufacturer (see subsection 3.2.1). Therefore, the initial assumption of δ = 2 seems to be generally reasonable for the CEM detectors used in the context of this thesis, and as a reference parameter for any curved CEMs [48].
Electron efficiencies
In contrast to the ion efficiencies, the observed electron detection efficiency ηe displayed in fig. 5.12(b) shows only a low increase, almost remaining constant for the given impact energies Ekin. In comparison to the literature (see subsection 2.4.2), the measured efficienciesηe(Ekin) lie well within the usually stated range of efficiency values fromEkin = 0.1−5 keVfor incident electrons (see extensive compilation by [48]). However, our measured values indicate a slight increase even for impact energiesEkin>1 keVin contrast to many CEM detector calibrations in the literature.
Maximum electron detection efficiency The least-squared fit of the electron efficiencies ηe(Ekin)according to eq. 2.10 displays a very good agreement to the measured data (fig. 5.12(b); red line). For comparison, a sample efficiency curve for incident electrons is additionally shown34(fig. 5.12(b); dashed curve). The sample curve illustrates the observed efficiencies for a common CEM cone impact as reported by [48, 66, 87, 133], and being generally displayed as standard reference of the CEM efficiency response for incident electrons in common CEM operating manuals (e.g., [85]). From the fit as depicted in fig. 5.12(b), a primary electron yield value of δ0 = 2.8±0.1and a fitted impact energy Eδ0,max= 2.2±0.2 keVfor maximum
efficiency is determined. From this, a maximum detection efficiency of ηe,fit(2.2 keV) = 0.8940 at a kinetic energy of Eδ0,max = 2.2 keV is deduced (eq. 2.10; see section 2.4). The fitted
primary electron yield value of δ0 = 2.8 agrees to extensive studies for the primary electron yield δ0 and hydrogen reduced lead glass (δ0 = 2.6−3.5; [63, 66]), and for common values assumed for CEM detectors by [48, 87]. However, the position of the maximum efficiency Eδ0,max according to the fit is significantly shifted to higher kinetic energies Ekin compared
to these studies, where the maximum is usually situated at Eδ0,max= 0.35−0.4 keV.
34The displayed curve is derived from eq. 2.10, using common parameter values ofδ
0,max= 3.6andEδ0,max= 0.4for a typical CEM cone impact [63, 66].
5.4. Absolute detection efficiencies
The origin of this shift to higher kinetic energy valuesEδ0,max is difficult to determine. In
general, the primary particle yield δ0 for different emissive surfaces with their corresponding reduced yield curve characteristic is shifted to higher energy values for grazing incident angles θ of the primary particles [62, 127]. Therefore, the shifted maximumEδ0,max of the efficiency
towards higher impact energies suggests a channel impact35 of the primary electrons in the CEM detector under a grazing angle (θ > 80◦), compared to a CEM cone hit (θ ≈ 60◦). However, this cannot be specifically proven in our experiments as the actual impact position of the incident primary electrons in thee−-CEM is rather undefined (see subsection 4.4.1). Nevertheless, the 2D-scan measurements of section 5.5 indicate by the spatial characteristic of the observed efficiencies in the e−-CEM also a channel impact (fig. 5.14). Moreover, a shifted maximum Eδ0,max similar to our observed values for CEM channel to cone hits is explicitly
measured for sample CEMs by [87], and for primary electron yield valuesδ0 by [63, 66].