Development of display-type ellipsoidal mesh analyzer: Computational evaluation and experimental validation

https://doi.org/10.1016/j.elspec.2014.05.001Get rights and content

Abstract

An advanced measurement system for two-dimensional photoelectron spectroscopy has been developed to overcome the difficulties faced in the display-type spherical-mirror analyzer (DIANA) having been used so far. One difficulty is to realize selected small area analysis and another is to obtain higher energy resolution. The developed system, which we call “display-type ellipsoidal mesh analyzer (DELMA)”, has an ellipsoidal mesh electrode as its key element, which allows a wide acceptance angle (>∼ ±45°) comparable to that of DIANA. In this paper we provide details of DELMA on its design and performance. For the imaging performance, we evaluated, using ray-tracing, some important factors that can affect the spatial resolution: off-axis aberration, the effect of shape and position errors, the disturbing effect of mesh holes, and chromatic aberration. In test experiments, a spatial resolution of around 20–30 μm was obtained. The ray-tracing results suggest that this resolution can be improved to be less than 10 μm by decreasing the size of mesh holes and the error of the mesh shape. We also provide computational results for the energy resolution obtained in various conditions. It depends not only on the size of the energy-selecting aperture but also on the size and shape of an irradiation spot. Experimental results for the energy resolution were in good agreement with computational results. An available resolution seems to be as good as in DIANA (∼0.5%). A much better resolution is possible in our system by the combination of DELMA and a high resolution concentric hemispherical analyzer. In test experiments using an angle-measurement device, a wide acceptance angle of around ±45° has been successfully confirmed. As a practical example of the angular analysis by DELMA, a photoelectron diffraction pattern measured for single crystalline graphite is shown.

Introduction

Photoelectron spectroscopy is a fundamental and widely used surface analysis technique that is still being developed [1]. A substantial progress has been made by the development of photoelectron emission microscope (PEEM) [2], [3], [4], which enabled photoelectron spectroscopy from a microscopic area that is selected by photoelectron imaging. Another progress is the development of two-dimensional (2D) photoelectron spectroscopy [5], which opened many new possibilities with the advances in light source technologies. A great deal of contribution to 2D photoelectron spectroscopy has been made by a display-type spherical-mirror analyzer (DIANA) [6], [7], [8]. This analyzer, which allows simultaneous angle-resolved measurement over a wide emission angle of 1π sr (±60°), has been successfully applied for, e.g., 3D Fermi Surface and band-structure analysis [9], [10], [5], photoelectron diffraction spectroscopy [11], photoelectron holography [12], and direct determination of 3D atomic arrangement by stereophotography [13], [14], [15].

Unfortunately, DIANA cannot perform selected-small-area analysis like in a PEEM system, because the magnification ratio of DIANA is 1:1 and the focus size is, at best, around 1 mm even if the irradiation-spot size is less than 0.3 mm. On the other hand, a PEEM system equipped with an energy filter can perform 2D photoelectron spectroscopy at low kinetic energies of around 30 eV. This is because a PEEM objective lens achieves a wide acceptance angle by a strong acceleration field between the sample and the lens entrance. However, the acceptance angle considerably decreases with increasing the photoelectron kinetic energy and it becomes less than around ±15° for kinetic energies greater than several hundred eV. Consequently, the PEEM cannot perform (or at least cannot perform efficiently) 2D photoelectron diffraction analysis and related measurements, which need kinetic energies greater than several hundred eV and acceptance angles of greater than around ±45°.

To overcome the above difficulties, a wide-acceptance-angle electrostatic lens (WAAEL) has been proposed [16], [17], [18], [19] and developed [20], [21], [22], [23]. This lens does not use a strong electric field around the sample, but it can achieve a wide acceptance angle comparable to that of DIANA. The key is the use of an ellipsoidal mesh in combination with other correction electrodes. Optimizing the mesh shape using ellipsoidal shape parameters and other parameters for fine deformation, it is possible to completely correct spherical aberration over a wide acceptance angle up to around ±60°. This enables photoelectron imaging and then selected-small-area analysis of 2D angular distribution.

The principle of aberration correction in WAAEL is based on that in a spherical mesh lens [24]. It is well known that positive spherical aberration is unavoidable for rotationally-symmetric electron lenses with no space charge [25]. A difficulty arises because the spherical aberration greatly increases with increasing the incidence angle. In WAAEL, the electric field around the mesh electrode is followed by a focusing field with positive spherical aberration. The field around the mesh electrode decreases the angular spread of electrons and simultaneously produces negative spherical aberration to cancel the positive spherical aberration produced by the focusing field. Fig. 1 explains the principle of our approach by an analogy with light optics. The analogy is based on the fact that the movement of electrons in an electrostatic field can be seen as successive refractions at equipotential surfaces. Here the square root of an electric potential plays the role of a refractive index. In Fig. 1(a), light rays start from a point source P0 and are refracted at a spherical interface S, obeying Snell's law, n 0 sin ϕ0 = n1 sin ϕ1, where n0 (n1) is the refractive index inside (outside) S and ϕ0 (ϕ1) is the angle of incidence (refraction) at S. The point source is located on axis at a distance of d = Rn1/n0 from the center of S, where R is the radius of S. In this case, a virtual image is produced at a distance of L = Rn0/n1 from the center of S with no spherical aberration, as shown by dotted lines. Negative spherical aberration can be produced by shifting the point source in the positive z direction, as shown in Fig. 1(b). Fig. 1(c) shows that negative spherical aberration can also be produced by deforming the spherical interface to an ellipsoidal shape. An important feature is that the negative spherical aberration can be greatly increased by increasing the ratio γ of the major to minor radii of the interface, which enables to cancel spherical aberration over a wide acceptance angle.

In WAAEL, there is no electric field between the sample and the lens entrance in contrast with PEEM systems, since the mesh (which is located at the entrance of the lens) and the sample are both grounded. Another significant feature is that WAAEL can be applied in a wide range of photon energies including the hard X-ray region (5–15 keV), because the voltage required for WAAEL is reasonably low (around −0.8 kV for a kinetic energy of 1 keV). The above features allow us to use WAAEL in various applications. For example, WAAEL has been successfully applied for the development of a hard X-ray photoelectron spectroscopy system [26]. Collection of photoelectrons by WAAEL can considerably increase the sensitivity of photoelectron spectrometers (around 25 times), and this is particularly important for hard X-ray photoelectron spectroscopy, because photoelectron intensities become very low in the hard X-ray region.

In this paper, we introduce an advanced measurement system for 2D photoelectron spectroscopy that has been developed by combining WAAEL with a lens system (for a brief report, see Ref. [27]). This measurement system enables us to measure 2D angular distribution from a small sample area selected by photoelectron imaging and insertion of a field-limiting aperture. We provide details of the developed system including computational evaluation and experimental validation of the performance of the system. The calculation was performed using the charge simulation method and ray tracing. For the imaging performance, we discuss some important factors that can affect the spatial resolution: off-axis aberration, the effect of shape and position errors, the disturbing effect of mesh holes, and chromatic aberration. We also discuss the energy resolution of the system taking into account the size and shape of an irradiation spot. We will show results of electron-gun and synchrotron-radiation experiments to compare with computational results.

Section snippets

Design

Fig. 2 shows the wide-acceptance-angle electrostatic lens (WAAEL) we have developed. The electron trajectories shown in the figure have initial angles from −45° to 45°. Fine focusing over this range is possible in the developed lens. The focus over a wider range up to around ±60° is also possible by modifying the lens design, while the space between WAAEL and the sample becomes considerably narrow for increasing the acceptance angle. The lens has an ellipsoidal mesh as its key element, which is

Design

Fig. 11 shows the two-dimensional analyzer we have developed combining the wide-acceptance-angle electrostatic lens (WAAEL) and a lens system. We call this analyzer “display-type ellipsoidal mesh analyzer (DELMA)”, as WAAEL plays the main role of the analyzer. As illustrated in the cross-sectional drawing of DELMA, a sample is irradiated by an X-ray or an electron beam, and then electrons emitted from the sample are focused by WAAEL for a wide range of emission angles. The present WAAEL can

Experimental results and discussion

The whole measurement system including the display-type ellipsoidal mesh analyzer (DELMA) is depicted in Fig. 20. Using an electron gun and synchrotron radiation, we tested the three basic functions of our system, i.e., spectroscopy, imaging, and angular-distribution measurement. Experiments using synchrotron radiation was performed at BL07LSU in SPring-8. We briefly show results of test experiments to demonstrate the three basic functions. Detailed experimental evaluation of the performance of

Conclusions

We have developed an advanced measurement system for two-dimensional photoelectron spectroscopy to perform selected-small-area analysis with high energy resolution, by combining a wide-acceptance-angle electrostatic lens (WAAEL) and a lens system composed of some electrostatic lenses. The developed system, which we call display-type ellipsoidal mesh analyzer (DELMA), has an ellipsoidal mesh electrode as its key element, which enables a wide acceptance angle comparable to that of DIANA

Acknowledgments

The synchrotron radiation experiments were performed at BL07LSU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2012A7431, 2012B7434). This research was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (S), 20224007, 2008.

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