Electron-energy Analyzer CHA

In electron spectroscopic techniques - among which XPS is the most important -analysis of the energies of electrons ejected from a surface is central. Nowadays universally employed is the concentric hemispherical analyzer (CHA). 

Energy analyzers cannot be discussed without discussion of energy resolution, which is defined in two ways. Absolute resolution is defined as AE, the full width at half-maximum (FWHM) of a chosen peak. Relative resolution is defined as the ratio R of AE to the kinetic energy E of the peak energy position (usually its centroid), that is, R = AE/E. Thus absolute resolution is independent of peak position, but relative resolution can be specified only by reference to a particular kinetic energy. 

In XPS, closely spaced peaks at any point in the energy range must be resolved, which requires the same absolute resolution at all energies. 

The CHA is shown in schematic cross-section in Fig. 2.5 [2.5]. Two hemispheres of radii ri (inner) and T2 (outer) are positioned concentrically. Potentials -Vi and -V2 are applied to the inner and outer hemispheres, respectively, with V2 greater than Vi. The source S and the focus E are in the same plane as the center of curvature, and Tq is the radius of the equipotential surface between the hemispheres. If electrons of energy E = eVo are injected at S along the equipotential surface, they will be focused at Eif  

If electrons are injected not exactly along the equipotential surface, but with an angular spread Aa about the correct direction, then the energy resolution is given by  

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