Photoelectron angular distribution (PAD)

Chapter 2. Experimental methods

2.4 Data analysis

2.4.3 Photoelectron angular distribution (PAD)

Figure 2.9 shows an example of photoelectron image of Kr obtained for free electron laser (Fig. 2.9 case A) and He(I) (Fig. 2.9 case B). As mentioned in chapter 1, for one-photon ionization with polarized light, a PAD is expressed by equation (1-4) and cylindrically symmetric about the polarization axis of light, as shown in Fig. 2.9 (A). The angle () is measured between the polarization axis of light and the outgoing photoelectron velocity.

Therefore, positive and negative  corresponds to the preferential ejection of electrons parallel and perpendicular to the ionization laser polarization. With unpolarized light, a PAD is expressed by equation (1-10) and cylindrically symmetric about the light propagation direction, as shown in Fig. 2.9 (B). In this case, the angle (’) is measured between the light propagation direction and the outgoing photoelectron velocity. Positive and negative  corresponds to the preferential ejection of electrons perpendicular and parallel to the light propagation direction. As shown in fig. 2.9, after the inverse Abel transform, the slice image can be transform to polar plot. Then, the photoelectron angular distribution (PAD) for a specific velocity can be obtained by integration over the selected radial region (for example, the yellow dotted rectangle in Fig. 2.9) and the anisotropy parameter is analyzed using

equation (1-4) or equation (1-10) for polarized or unpolarized light, respectively.

Figure 2.1 (a) W-M type electrode consists of one flat plate and two flat grids. (b) Velocity mapping type electrodes are the W-M type electrodes with annular holes instead of grids.

Figure 2.2 The schematic diagram of image analysis.

Figure 2.3 (a) Slice pattern of 3D distribution through fixed z in xy-plane. (b) 3D slice image at z2. (c) The projection of (b) maps the electrons onto a line on the detector.

Figure 2.4 (a) The raw projection image of N2. (b) The 3D slice image after inverse Abel transformation. (c) The 3D slice image after p-BASEX reconstruction.

Figure 2.5 The schematic drawing of He(I) discharge lamp: (a) with a linear polarizer; (b) the linear polarizer was replaced by 0.8mm-diameter capillary.

Figure 2.6 The schematic drawing of the entire vacuum chamber which is originally designed for droplet experiment.

Figure 2.7 (a) The cross-sectional view of the ionization chamber and the imaging system. (b) The cross-sectional view and field lines for the electrostatic lens system. The electrode gap between repeller and extractor electrode is denoted as d. In the original design, d = 6 mm.

Figure 2.8 The schematic view of the new vacuum chamber.

Figure 2.9 (a) and (c) are the PEI of Kr obtained for free electron laser and He(I), respectively:

the left half is the raw image and the right half is the slice image obtained by taking the inverse Abel transform. (b) and (d) are the polar plots of slice images obtained from (a) and (c), respectively.

2.5 References

1 Chandler, D. W.; Houston, P. L. J. Chem. Phys. 1987, 87, 1445.

2 Wiley, W. C. and McLaren, I. H.; Rev. Sci. Instrum. 1955, 26, 1150.

3 Eppink, A. T. J. B. and Parker, D. H. Rev. Sci. Instrum. 1997, 68, 3477.

4 Wrede, E. et al. J. Chem. Phys. 2001, 114, 2629.

5 Bordas, C.; Paulig, f.; Helm, H.; Huestis, D. L. Rev. Sci. Instrum. 1996, 67, 2257.

6 Manzhos, S. and Loock, H.-P. Comput. Phys. Commun. 2003, 154, 76.

7 Dribinski, V. et al. Rev. Sci. Instrum. 2002, 73, 2634.

8 Garcia, G. A.; Nahon, L.; Powis, I. Rev. Sci. Instrum. 2004, 75, 4989.

9 Smith, L. M.; Keefer, D. R.; Sudharsanan, S. I. J. Quant. Spectrosc. Radiat. Transf. 1988, 39, 367.

10 Tikhonov, A. N. Sov. Math. Dokl. 1963, 4, 1035.

11 Schönhense, G.; Heinzmann, U. J. Phys. E: Sci. Instrum., 1983, 16, 74.

12 Hancock, W. H.; and Samson, J. A. R. J. Electron. Spectrosc. Relat. Phenom. 1976, 9, 211.

Chapter 3 Designing a Photoelectron Imaging Spectrometer for He(I) Light Source

Photoelectron imaging (PEI) has been performed on a number of molecular systems using nanosecond and femtosecond lasers. However, since He(I) radiation generated by a discharge lamp has much poorer beam characteristics than these coherent laser radiation, successful PEI experiments with He(I) radiation requires redesigning of the apparatus. The major problem of He(I) radiation is that it has a large divergence angle and cannot be focused as tightly as laser beams. This causes two practical problems. One is background photoemission from the apparatus caused by scattered light. The other is a large ionization volume that limits the electron energy resolution of PEI.

In this chapter, I describe the procedures taken to identify the source of background photoemission and to improve the performance of the apparatus. A new design of electron acceleration electrodes successfully reduces background photoemission and achieve sufficiently high electron energy resolution for He(I) PEI.

3.1 He(I) PEI experiment using an old vacuum chamber

In the initial stage of this work, I have used the apparatus originally designed for laser spectroscopy of liquid droplets. The schematic view of the experimental setup is shown in Fig.

2.6 and 2.7. A light source was the He(I) discharge lamp equipped with a rotatable

three-mirror polarizer (see Fig. 2.5a).

3.1.1 Reduction of background noise

Figure 3.1(a) shows the first photoelectron image of Ar measured with He(I) radiation.

The outer rings seen in the raw image are photoionization signal of Ar, while the inner part of the image exhibits a background photoemission signal that was observed even without a molecular beam. The background has never occurred in photoelectron imaging (PEI) with a well-collimated laser beam. The background signal disappeared when the acceleration electric field was turned off, which indicated that background signal is not carried by photons but the photoelectrons from the apparatus. In order to reduce the scattered light inside the chamber, graphite powder (Areodag) was painted on the entire inner surface of the ionization chamber and the PEI electrodes. A He(I) beam dumper was also attached to the ionization chamber to minimize the back reflection of He(I) radiation from its exit port (see Fig. 2.6). However, the background was not eliminated by those modifications.

On the other hand, I found that the background signal decreased by reducing the diameter of the He(I) radiation (see Fig. 2.5a). Figure 3.1 shows the photoelectron images of Ar for different aperture diameters (a) 6 mm and (b) 2 mm of the He(I) lamp. The result clearly indicates that He(I) radiation illuminates some vacuum components adjacent to its light path, causing background photoemission. Thus, we suspected that the acceleration electrodes of electrons are the source of the background.

To reduce the background, I have enlarged the gap between the electrodes to allow the He(I) radiation passes through without scattering. Figures 3.2(a)–(c) show the photoelectron images of Kr measured with the electrode gaps (denoted as d in Fig. 2.7b) of 6, 9 and 12 mm, respectively. In Figs. 3.2 (b) and (c), the aperture diameter of He(I) was also reduced from 2 to 1.3 mm. In order to estimate the diameter of the He(I) radiation in the ionization chamber, I introduced the emission from a high intensity halogen lamp along the same path with the He(I)

radiation. The diameter (FWHM) of the photon beam was 3.0 and 2.5 mm at the exit side of the electron acceleration lens for the aperture sizes 2 and 1.3 mm for the photon beam, respectively. Therefore, Fig. 3.2 (c) indicates that the electrode gap should be 5 times larger than the estimated VUV beam diameter to suppress the background photoemission. This means that a considerable intensity of a halo exists around the VUV beam. The results clearly show that the broad background feature in the center gradually diminishes when increasing the electrode gap.

3.1.2 He(I) photoelectron images of supersonic beams of Ar, Kr and N₂ (A) Determination of polarization degree of He(I) radiation

The polarization degree of He(I) radiation has to be determined for the analysis of photoelectron angular distribution. Since the gold-coated mirror surfaces in the polarizer may be contaminated and/or degraded, it is possible that the polarization degree may vary with time. We measured photoelectron images of rare gases and analyzed the images and determined the polarization degree as to reproduce the anisotropy parameter  reported in the literature. Figure 3.3 shows the difference between the literature value (1.24)¹ for Kr (²P_3/2) and the value extracted from p-BASEX analysis of our image by assuming different polarization degrees of light. The best agreement was obtained at the polarization degree of 74%.

(B) Examination of cluster formation in supersonic beams

The images of Kr and Ar presented above were obtained at a stagnation pressure of 2.2 MPa for supersonic jet expansion. The high stagnation pressure was used to compensate considerable dilution of the gas density at the ionization point that is far (380 mm) from the nozzle. Since these rare gas atoms may form clusters and exhibit different anisotropy parameters from that of free atoms, the pressure dependence of photoelectron images was

investigated. Clusters can be identified from smaller ionization energies than that of free atoms, because the ionized atom is stabilized by solvation in the clusters.² However, as shown in Fig. 3.4, the PKEDs in the He(I) photoionization of Ar are almost unchanged for different stagnation pressures of 0.4, 1.1, and 2.2 MPa, and the angular anisotropy parameters determined for the main peak in PKED were 0.93, 0.92 and 0.94, respectively. Thus, the cluster formation in our supersonic beam had negligible influence on the determination of the polarization degree of the He(I) radiation.

(C) Results

The images presented in the previous section were recorded by integrating the signal intensity from the CCD chip without any image processing. In this simple integration mode, an image of the light spot due to electron appears much larger than one pixel size of a CCD and degredes the energy resolution of PEI. The center-of-gravity (COG) calculation of each light enhances the resolution. Figure 3.5 shows photoelectron images observed by He(I) photoionization of supersonic beams of Ar, Kr and N2 with COG calculations. In COG calculations, if the light spots overlap each other in an image frame, COG of light spots and their number of hits are miscalculated; therefore, COG calculation must be performed at sufficiently low signal count levels. In this particular experiment to obtain Fig. 3.5, the background photoelectron signal was strong, and we lowered the gain of MCP to achieve the optimum condition for COG calculations. Consequently, each of the integration time of the signal and the background images were 4.5 hours, 5.5 hours and 17.7 hours for Ar, Kr and N2, respectively.

Figure 3.6 shows the PKEDs of Ar and Kr extracted from these images. The spin-orbit splitting of Kr (0.665 eV) is clearly resolved: the best-fit Gaussian function had the FWHM of 0.248 eV at 7.22 eV, which corresponds to an energy resolution (E/E) of 3.4 %. This resolution is insufficient to resolve the fine structure splitting of Ar (0.178 eV). Figure 3.7(a)

shows the PKEDs of N2, in which three bands, corresponding to the X, A, and B states of the cation, are identified. The expanded view of the A band is shown in Fig. 3.7(b). The spectral feature agrees well with the literature.³ The anisotropy parameters of Ar, Kr are analyzed using equation (1-4) and compared with the literature values in Table 3.1 and 3.2, respectively.

The anisotropy parameters are in agreement with the literatures.

3.2 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

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.

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

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

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

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

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