A schematic picture of a magnetic bottle spectrometer is displayed in Figure 5.2. As the electrons are made to perform helical motion around the magnetic field lines of the solenoid magnet, their trav-elled distance increases, and therefore also their time–of–flight. That increases energy resolution and collection efficiency. A conical per-manent magnet pole close to the interaction region guides electrons into the spectrometer. The magnetic bottle spectrometer is particu-larly well suited for electron coincidence experiments; recently even for experiments with simultaneous electron and ion detection[112].
However, no position or angular information can be extracted from data. The long flight–times, severalµs [109, 113], put hard restric-tions on the repetition rate of the light source. These flight–times are considerably longer than the single–bunch frequency of typical storage rings. A shorter spectrometer can be constructed to reduce the flight–time, at the expense of resolution[114]. For fast electrons the pulse length can become the limiting factor for achievable energy resolution. Eland et al. used a 20 ns pulse during home lab experi-ments and noted that energy resolution was limited by the light pulse for electron energies above 20 eV[109]. Typical pulses from a storage ring are significantly shorter.
5.2 The angle–resolved time–of–flight (ARTOF)
5.2 The angle–resolved time–of–flight (ARTOF) instrument
Figure 5.3. The ARTOF 10k.
(©VG Scienta AB. Reproduced with permission.)
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Figure 5.5. Schematic depiction of the delay–line detector from above.
Impinging electrons create an MCP avalanche which induces a signal on the delay-lines. The signal travels in both directions through the meandering delay-line and can be picked up by a TDC. The relative timing of the two signals determines the hit position on the detector. Two delay-lines give the position in two dimensions.
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Position sensitive detector
Figure 5.4. Schematic illustration of typical flight paths for electrons through the ARTOF lens. Here, the instrument works in angle–resolved mode (angle–to–point). It is obvious that monoenergetic electrons traveling on the outer paths have longer flight times than on–axis electrons.
in angle resolving mode. In this mode the electrons are distributed on the detector according to their emission angle. Electrons fol-low quite complicated trajectories which must be calculated using electrostatic simulations. It should be noted that a parallel–to–point transformation takes place early in the lens and a focal plane is cre-ated. This focal plane is imaged to the detector with the remaining part of the lens[100].
The lens accepts electrons in a selected energy window, typically 10% of the centre energy. Due to chromatic aberrations, the reso-lution of the instrument decreases as energies depart far from the centre energy; the transformation matrix becomes degenerate and an assignment of electron energies is no longer possible. The ARTOF allows detection of electrons within a±15◦emission cone. The trans-mission of the instrument is thus much higher than for hemispher-ical analysers at comparable energy resolution. The ratio can be es-timated by comparing the area of a circle with diameter equal to the length of the entrance slit to the area of the same slit[107]. For high resolution experiments, where the hemispherical analyser entrance slit would typically have a very narrow width, this can imply up to 300 times increase in transmission. Electrons entering the lens are re-tarded to prolong flight time, and to increase energy resolution. The lens also acts as an energy filter where low energy electrons are not accepted.
A RoentDek position–sensitive delay–line–detector is utilized for time and position detection. A 40 mm Chevron-stacked MCP pre-cedes the delay lines (Figure 5.5). Position is determined by compar-ing relative times of the signals from the delay–lines. The detection time can be determined either by the MCP-signal or by the mean
ar-rival time of the delay–line pulses. The MCP signal is, however, the most precise due to its short rise time. In total the detector produces five signals which are preamplified outside vacuum. The signals are sent to constant fraction discriminators (CFDs) where they are trans-formed to NIM-pulses2. The pulses are fed into a time-to-digital con-verter (TDC) from which they can be read by the computer. The tim-ing at the detector is critical for the instrument; energy resolution is related to time resolution in a complicated way, but can be estimated using the formula[107]
∆E =Æ(αE3/2∆t )2+ (β∆dγE)2 (5.4) where∆t and ∆d are the time-resolution for the electronics and the detector, andα,β,γ are properties of the transformation matrix for the selected centre energy E .
To assure ultimate resolution, the sample must be placed in the focal spot of the lens which is situated along the ARTOF axis at a pre-determined distance from the first lens element. This implies that the ARTOF axis, the light beam and the sample must coincide in one point in space. The ARTOF must also be calibrated to the timing of the light source. If the ARTOF is used with a suitable pulsed light source (storage ring in single–bunch mode), the acquisition should be synchronized to its internal time reference (ring clock). Scattered photons from the sample or sample holder can be used as an abso-lute time–stamp.
The high transmission and data acquisition rate gives rise to ex-tensive amounts of data. Each event is stored as a vector with the x , y and t coordinates. The analysed data is consequently stored as a vector with E ,φ and θ coordinates. The initial analysis can be performed with software provided by the manufacturer. In addition, we have used a set of scripts developed within the ARTOF project to analyse data, for example, in k-space. These extensions provide means of analysis for ARPES and other applications.
For applications in electron spectroscopy, the benefits of ARTOF stem primarily from its high transmission in combination with high energy resolution. A good overview of ARTOF application areas is given in Ref.[107]. The ARTOF allows mapping of the whole momen-tum space in three dimensions (3D-ARPES). For example, the study by King et al.[117] shows 3D-ARPES on Bi2Se3. In this study, the sam-ple was cleaved and the evolution of band structure was studied in real time. ARTOF also opens up for experiments with very low radi-ation doses: In single–bunch modes, the sample is irradiated with a much lower mean intensity. This would typically be a drawback since fewer electrons are emitted, but this is rather a benefit for ra-diation sensitive samples. A study by Vollmer et al. presents results
2The Nuclear Instrument Module (NIM) is a standard set of specifications for elec-tronic modules. The standard also specifies levels for logic signals and associated equipment.