The energy distribution of an electron gun is one of the most important characteristics determining the performance of electron beam-based instruments, such as electron microscopes and electron energy loss spectroscopes. For accurate measurements of the energy distribution, this study presents a novel retarding field energy analyzer (RFEA) with the feature of an additional integrated pre-lens, which enables an adjustment of beam trajectory into the analyzer. The advantages of this analyzer are its compact size and simple electrode configuration. According to trajectory simulation theories, the optimum condition arises when the incident electron beam inside the RFEA is focused on the center of a retarding electrode. Comparing I–V curves depending on whether the pre-lens working or not, it is confirmed that the use of the pre-lens dramatically improves the energy resolution and efficiency of the signal acquisition process. The pre-lens RFEA was applied to characterize a Schottky electron gun under various temperatures and extraction voltages as operational conditions. When the tip temperature was increased by 50 K, we were able to measure an energy distribution broadening of 13.8 meV with the proposed pre-lens RFEA. The relative standard deviation of energy distribution was 0.7% for each working condition.

The problem of initial thermal velocity and the space charge effect of electron guns in numerical simulations have been investigated deeply. In general, the current software can meet the engineering requirements. However, the electron's initial thermal velocity and the space charge effect lack sufficient consideration. The above two factors significantly limit the performances of electron guns. Moreover, the parameters of electron guns are approximated based on a limited number of electron trajectories. Thus, the statistical distribution of the beam electron resulting from its initial thermal velocity is not considered adequately in present software. This paper introduces the equivalent meridional projected trajectory equation and the curvilinear axis evolution theory of the current density of toroidal electron sub-beam, and subsequently the current and charge density distributions in electron guns can be derived through iteration calculation. Based upon, the virtual crossover of an electron gun is determined by its current density distribution. As well as, a relevant numerical algorithm is developed and the related program is modified based on the popular commercial software SOURCE. Tungsten cathode guns, LaB6 cathode guns, field mission guns and Pierce guns are simulated respectively by examples. The calculations prove that the modified software is effective and practical.