(a) 3D drawing of the complete analyzer system, showing its five main parts: (1) electron gun, (2) input lens, (3) HDA, (4) detector CEM assembly, and (5) movable supporting rail. The electron gun and input lens are seen to be assembled on the same movable supporting rail. (b) Photograph of the actual setup also showing the vertical gas nozzle jet target (6). Here, the electron gun is seen to lie across the analyzer while in the measurements it was used at 90°. The supporting rail can be moved up or down along the direction of the double arrows, effectively changing the entry position of the analyzer R 0.
Analyzer circuit used to operate the analyzer. V 5a is used to retard the electrons down to the pass energy E 0 which was kept fixed during spectrum scans.
Electron kinetic energy spectra showing the elastic scattering peak from 200 eV electrons incident on a Helium target for R 0 = 84 mm (left), R 0 = 100 mm (middle), and R 0 = 112 mm (right). The spectrometer was set to pass electrons with a kinetic energy of E 0 = 50 eV corresponding to 0 energy loss. The y-axis represents normalized counts.
(Left) HDA overall base energy resolution R Bs0 = ΔE B/E s0 plotted as a function of the biasing parameter γ for a source energy E s0 = 200 eV and pass energy E 0 = 50 eV. Data points: experimental results by spectrum scan for fixed pass energy. Error bars: estimated at ±20% of R Bs0 to account for possible “mechanical imperfections.” 18 Straight lines: theoretical calculations for an ideal HDA: (full) based on Eq. (5) and α max = 6.5° (black dashed-dotted) and 0° (red). (Dashed lines) Optimal resolution based on Eq. (7) . SIMION simulations: (blue line) exit beam width formula based on Eqs. (4) and (6) . (Dotted green line) Spectrum scan for fixed pass energy as in actual measurements. The parameters listed in Table I were used in the formulas and simulations. The conventional HDA entry is marked by a circle at R 0 = 100 mm and γ = 1.0 for clear reference. (Right) Schematic of SIMION simulations in the Y = 0 dispersion plane of the spectrometer. Electron trajectories are shown in red and equipotentials in green for specified values of γ.
List of most important geometric parameters used in both experimental setup and theoretical modeling (SIMION simulations and ideal field theoretical calculations).
Overall base energy resolution R Bs0 results for an electron source energy E s0 = 200 eV and pass energy E 0 = 50 eV. Comparison of lowest experimentally determined values to those from SIMION simulations and ideal field HDA theory. Values of parameters from Table I were used. A conservative estimate of 20% of R Bs0 was assigned to the experimental values to reflect absolute errors due to possible mechanical imperfections (see text). Resolution gain is computed with respect to the experimental resolution of the conventional fringing field HDA (R 0 = 100 mm, γ = 1). The HDA voltages used were computed from Eq. (1) . Lens voltages used were fixed at V 1a = 0, V 2a = 114.0 V, V 3a = −104.7 V, V 4a = 144.0 V.
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