He(I) PEI experiment using a new vacuum chamber

The schematic view of the new experimental setup is shown in Fig. 2.8. The linear polarizer of He(I) discharged lamp was replaced with a 0.8-mm-diameter capillary to increase the photon flux (see Fig. 2.5b).

3.2.1 Testing three electrode design by Eppink and Parker

As described in the earlier sections of this chapter, the electrode gap should be as large as possible to allow the VUV radiation to pass through without scattering. Furthermore, the previous electrostatic lens design following Wrede et al. seemed rather complicated.

Therefore, we tested the conventional three-electrode design by Epping and Parker,⁴ which is widely used in charged particle imaging. The advantage of the Wrede design over the Eppink/Parker design was reduced chromatic and spherical aberrations. The Eppink/Paker design consisted of a repeller, extractor and ground electrode. The repeller voltage Vrep

primarily determines the image size on the detector and is usually set to maximize the radius of the image. The extractor voltage Vext is carefully adjusted to focus electrons with the same initial velocity vector onto the same point on the imaging detector, as shown in Fig. 3.8 (a). If all photoelectrons are created at a point, high-imaging resolution is easily achieved. However, in reality, they are produced within a finite volume defined by the overlap of the molecular and photon beams. The shape of the electron source is approximately cylindrical, as depicted

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in Fig 3.8 (b). In the case of He(I) experiment, the molecular beam (x-axis) and VUV light beam (y-axis) were respectively 8.5 and 4.2 mm in diameter at the interaction region. Since the diameter of VUV beam and molecular beam are different, the shape of the ionization region is asymmetric. This asymmetry results in slightly different focusing for the parallel (y-axis) and perpendicular (z-axis) direction with respect to the VUV beam axis in the imaging plane; the y resolution is altered by the width of the molecular beam. Notice that the velocity resolution is defined as R/R, where R is the radius of the image and R is the width of the distribution. In order to achieve the highest resolution possible, while minimizing the difference between the y and z resolution, we ran electron trajectory calculations on a personal computer with the SIMION 3D software package (Scientific Instrument Services).

We assumed the outer diameter of electrodes to the maximum possible value (170 mm).

Figure 3.9 shows the velocity resolution (/) in two directions (y, z) and their difference as a function of the electrode gap. We found a larger gap provides a higher resolution in both directions, and the resolution difference was minimized with the spacing of 39 mm and the outer diameter of 170 mm. The inner diameter of the electrode was optimized to be 60 mm for the fixed electrode spacing of 39 mm, as shown in Fig. 3.10.

The dimensions of the optimized electrostatic lens are shown in Fig. 3.11. The electrodes are 0.5-mm-thick stainless steel plates of 170 mm in diameter mounted with 39-mm-length insulator spacer (polyimide-CEPLA). The inner holes in the extractor and the ground electrode are 60 mm, and the repeller electrode contains a small hole (5 mm dia.) for propagation of the molecular beam. Figure 3.12 shows the velocity resolution as a function of V_ext/V_rep calculated for He(I) and FEL experiment. The molecular beam diameter was estimated to be 5.8 mm, and the diameter of He(I) and FEL were respectively 4.2 and 0.1 mm in diameter. At the optimal ratios of Vext/Vrep, the best velocity resolutions of y and z are 2.7

% and 2.2 % for He(I) case; 0.06 % and 0.01 % for FEL case. The broad focusing curve and poor resolution in He(I) PEI is attributed to its large ionization volume.

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Figure 3.13 (a)-(c) shows the photoelectron images of Ar measured with the three-electrode design. A repeller electrode had punching holes, and the overall open area was 20 %. The background signal was quite high, and the background component could not be eliminated by subtraction of the background image from the signal image (see Fig. 3.13(c)).

The shape of the background signal is symmetric and did not change with the repeller voltage, which implied that those photoelectrons do not have the velocity components in the imaging plane. Therefore, the background photoemission must be arising from the repeller plate. We replaced the repeller with a mesh (open area = 88 %) and succeeded in reducing the background signal level. The mesh reduced the cross-section of the electrode by one order of magnitude compared with a solid plate, which suppresses background photoemission from this electrode; however, the background feature could never be eliminated by subtraction of the background image from the signal image, as shown in Fig. 3.13 (d)-(f).

3.2.2 A new electrostatic lens

Based on the experimental results presented above, I designed new electrodes. The basic features of this new design are summarized as follows.

1. The repller is made with mesh and placed away from the ionization region.

2. A small retardation field is added to prevent photoelectrons from the mesh transmitted to the acceleration region.

3. Electrons are gradually accelerated in a long distance to achieve high energy resolution.

The dimensions of the electrostatic lens system (outer diameter, inner diameter, and spacing of the electrodes) were optimized by running electron trajectory calculations with the SIMION 3D software. Figure 3.14 shows the final design of the new lens system. A stack of 8 circular electrodes is rigidly held by insulating supports, and the position of each electrode

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plate was fixed by four sets of insulator screws and nuts. The electrode No. 1 is made with a high-transmission (90 %) mesh (70 wires/inch) with a 6-mm-diameter hole in the center for the molecular beam to pass through. The negative voltage of this electrode is set slightly smaller in magnitude than that of the electrodes No. 2 and 3 (see Fig. 3.14). This retardation field prevents photoelectrons produced by stray light of VUV radiation from being transmitted towards the detector. Figure 3.15 shows simulated electron trajectories emitted from the mesh electrode started from six different starting positions spaced 10 mm apart with 5 different ejection angles spaced by 45 (red, blue and orange curve). In order to enhance the visibility of the trajectories, the kinetic energy of each electron was set to 200 eV. In Fig. 3.14, the role of the electrode No. 1 is to shield the system from the ground potential of the bulkhead of the molecular beam source. The electrode No. 2 is held at the same voltage as the electrode No. 3 to avoid the field distortion caused by the large central hole in the electrode No. 3. We refer the electrodes Nos. 3 and 4 as a repeller and an extractor, respectively. Voltages were independently applied to electrodes Nos. 1 to 4 using a computer-controlled multi-port power supply (MBS, A-1 Electronics; 12 kV max), whereas the other electrode voltages were passively regulated by a register (22 MΩ) chain placed outside the vacuum chamber. The gradual change in the voltages applied to electrodes 4-8 achieved energy resolution (E/E) higher than 1% even for a large ionization volume (several millimeters in length of each side of cylinder). The entire assembly can withstand voltages up to 12 kV.

3.2.3 Molecular beam diameter and velocity resolution

The difference in diameter between molecular beam and VUV beam leads to different resolution in y and z. As the diameter of VUV beam (4.3 mm) could not be altered easily, the molecular beam diameter was reduced. Figure 3.16 shows the simulated y and z velocity resolutions as a function of the ratio between the molecular beam and the VUV beam diameters. When the molecular beam diameter is larger than VUV beam diameter (skimmer

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diameter > 1 mm), the cylindrical symmetry axis is along the VUV beam propagation axis (y-axis), as indicated in Fig. 3.16. On the other hand, when the molecular beam diameter is smaller than the VUV beam diameter (skimmer diameter < 1 mm), the cylindrical symmetry axis is along the molecular beam propagation axis (x-axis) that is perpendicular to the MCP surface. As anticipated, when the molecular beams is smaller than the VUV beam in diameter, the y and z resolution are essentially the same. In the actual experiment, I used the 0.8-mm diameter skimmer and created the molecular beam diameter of 3.4 mm at the ionization region. Figure 3.17 shows the velocity resolution simulated as a function of V_ext/V_rep for both He(I) and FEL. In He(I) case, at the optimal ratios of Vext/Vrep, the velocity resolutions of 0.25

% in y-axis and 0.24 % in z-axis are achieved. In FEL case, the diameter of a focused laser beam of ~ 0.1 mm provides the best speed resolution of 0.04 % in y-axis and 0.019 % in z-axis.

3.2.4 Distortion of the photoelectron image

The photoelectron image of Ar measured with this new set of electrodes is shown in Fig.

3.18. Comparing with Fig. 3.13, the background signal was suppressed considerably, and it could be removed completely by subtracting a background photoelectron image. However, the image in Fig. 3.18 is slightly distorted. First I have suspected imperfect alignment of electrode stack; for example, electrode plates are not parallel to each other. I have realigned the electrode stack several times, and I replaced the components with those of higher precision;

however, the image was still distorted, as shown in Fig. 3.19(d). During this process, I found that the way of the distortion changed every time I opened the chamber, which strongly suggested that distortion was caused by charging of the insulators.

In order to examine the effect of insulator charging on PEI, 3-D trajectory calculation of electrons was performed. Figure 3.20 (a) shows the 3-D configuration of the lens with a charged insulator placed between the repeller and the extractor electrode plate. In the

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simulation, I considered only the electrons with the initial velocities parallel to the detector plane. Figure 3.20 (b) shows the simulated images on the MCP detector (X-Y plane) expected for the following three conditions: (i) no charged insulator; (ii) an insulator at a negative potential of -3424 V (same as V_ext); (iii) an insulator at a negative voltage of -2000 V. The result shows that a charged object can cause distortion in a similar way with the observed one.

With a larger voltage difference between the insulator and extractor electrode, larger distortion occurred. Similar distortion was observed when the charged insulator was placed between the electrode Nos. 6 and 7, as shown in Fig. 3.21. The distortion was negligible when a charged object was placed between the electrodes Nos. 1 and 3. Thus, I concluded that the observed distortion was caused by charging of the insulators.

3.2.5 The final design of electrostatic lens

The final design and dimensions of the electrodes are shown in Figure 3.22. The stack consists of 12 circular electrodes. All elements except the first two electrodes are thick rings spaced with 3-mm-diameter ruby balls, and they hide the insulating supports from stray light and electrons. Electrodes 3 to 5 were referred as the repeller, light port, and extractor, respectively. Two 40  35 mm square holes in the light port allow incoherent He(I) radiation to propagate with minimal scattering. The negative voltage of electrode No. 1 is set slightly lower in magnitude than that of the electrodes No. 2 and 3, and the electrode No. 2 is held at the same voltage as No. 3. Voltages were independently applied to electrodes 1 to 5 and other voltages were regulated by a register chain. As shown in Figure 3.23, the best speed resolution was 0.36 % in both directions in the imaging plane. Using trajectory calculations, I examined the effect of the number of electrodes in the acceleration region on the resolution. The geometry of the lenses was slightly simplified by removing the port electrode, as shown in Fig.

3.24 (a). Without the port electrode, the velocity resolution was slightly improved from 0.36

% to 0.25 %. As shown in Fig. 3.24 (b), the velocity resolution was generally higher at a

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larger number of electrodes; however, it was practically saturated at 7 electrodes. Here we count the number of electrodes behind the extractor (lens No. 5): for instance, the electrodes shown in Fig. 3.22 are 12 in total but the number of electrodes behind the extractor is 7 (No.

6–12). Figure 3.25 shows the photoelectron image of Ar with a new lens set, which exhibits no distortion.

3.2.6 Chromatic aberration

In the above discussion, we optimized the electrode voltages (V_port/V_rep and V_ext/V_rep) to achieve the best energy resolution for a certain electron kinetic energy. However, the electron lens generally has some finite chromatic aberration in that the electrons with different initial kinetic energies receive different focusing by the lens. Then, the energy resolution is determined not only by the spatial resolution of the imaging system but also the chromatic aberration of the lens. Notice that chromatic aberration of an electrostatic lens can only be minimized and not eliminated.⁵ I found that the soft focusing in the acceleration region can alleviate chromatic aberration. I have checked chromatic aberration of our newly designed electrode (see Fig. 3.22) with various number of lens electrode behind the extractor. Similar to the previous section, the port electrode was removed to simplify the voltage optimization procedure (see Fig. 3.24 a). Figure 3.26 compares the calculated energy resolution (E) as a function of the electron kinetic energy (eKE) for our newly designed electrode with different number of lens electrodes. In all cases, the focusing conditions were optimized for a repeller voltage of -4000 V and eKE of 5.461 eV. Electrons were ejected from the region of ionization volume (3.4 o.d.  4.2 mm) with the angles of 90 with respect to the flight axis. The figure shows that chromatic aberration reduces as more lens electrodes are employed. Similar calculation with the conventional three-electrode design (see Fig. 3.11) is also shown in Fig.

3.26 (open green triangle), the result of conventional three-electrode approaches to the result of newly designed electrode with two lens electrode which is difficult to focus electrons with

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high eKE. It clearly demonstrates the advantage of our design over the three electrodes.

3.2.7 He(I) PEI of rare gases with a new lens set (A) Velocity resolution

The performance of our electrostatic lens was examined by He(I) PEI of Kr using a CCD camera (512  512 pixels) without COG calculations. PKED observed at the optimal ratios of Vport/Vrep and Vext/Vrep is shown in Fig. 3.27. The spin-orbit splitting of Kr (0.665 eV) is clearly resolved. As shown in the inset, the least-squares fit using a Gaussian function indicated the full width at half maximum (FWHM) of 210 meV at 7.22 eV, corresponding to the energy resolution E/E (= 2/) of 2.9 %. Figure 3.28 shows the energy resolution determined by PEI of Kr as a function of Vext/Vrep with Vrep = -5000 and Vport = -4319 V; the optimum voltage of V_port was determined experimentally. It is seen that the resolution varies only gradually with Vext/Vrep within the range of ca. 30 V about the best point. This contradicts with a much sharper dependence on the voltage predicted theoretically, and it is attributed to insufficient imaging resolution. In order to evaluate the energy resolution more precisely, we used a super-resolution imaging system using a 4M-pixel CCD camera (2048  2048 pixels)⁶. The subpixel centroiding calculations down to a quarter pixel size achieved an effective imaging resolution of 4096  4096 pixels. The inset of Fig. 3.28 shows the energy resolution evaluated by PEI of Ar at fixed Vrep of -4000 V and Vport of -3464.8 V, respectively: the optimum Vport

was determined experimentally. The energy resolution varied much more sensitively with V_ext in this case, and the resolution clearly degraded on both sides of the best point. The best voltage ratios were V_port/V_rep = 0.8662 and V_ext/V_rep = 0.8557, with which we obtained the energy resolution (E/E) of 0.735 % at 5.461 eV (FWHM: 40 meV) in excellent agreement with the trajectory calculations. The fine structure splitting of Ar was resolved, as shown in Fig. 3.29. The signal count level of He(I) PEI was very high, and I intentionally reduced the gain of MCP to perform COG calculations.

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(B) Photoelectron angular distribution

The photoelectron angular anisotropy was evaluated independently for the four quadrants of one image, as shown in Fig. 3.30. For each quadrant, the anisotropy parameters () were detector. The  determined by both methods are in good agreement with the literature value (1.24 and 1.21 for ²P3/2 and ²P1/2),1which indicates that symmetrization of the raw image prior to analysis does not affect the anisotropy.