Electron optical properties of retarding field analyzers for high energy resolution spectroscopy

The results of trajectory simulation of charged particles through retarding mesh electrodes show why high energy resolution is reached with Retarding Field Analyzers (RFAs). The transmission function is obtained by adding all transmitted particles over the mesh aperture area for a specific kinetic energy of the particles. The transmitted trajectories are classified into different categories having single or multiple deflections. Each category contributes differently to building up the transmission function. The transmission function has a well-defined energy threshold followed by a steep increase giving a high energy resolution. The derivative of the transmission function gives the filtering function for a monoenergetic particle flux. Its shape is close to a right-angle triangular peak. The energy resolution measured as the full width at half maximum of the peak is derived from the strength of the electrostatic fields applied to the retarding mesh electrode. The transmission is calculated using relative units allowing scaling to a specific experimental configuration, and formulas are deducted to estimate the energy resolution. A RFA using a single mesh electrode able to reach an energy resolution of less than 1 eV at 8 keV beam energy illustrates these calculations.