Wave-Mechanical Electron-Optical Modeling of Field-Emission Electron Sources

Electron source coherence has a very important influence on the imaging capabilities of modern electron microscopes. However, conventional electron source models that are based on geometrical electron optics implicitly assume that the emission from the source surface is fully incoherent, which can complicate the treatment of highly coherent field-emission sources. In an attempt to treat the wave-optical properties of electron sources, models inspired by light optics treatments of (partially) coherent sources, which assume a planar source and free wave propagation, have been developed. In this case the underlying assumptions are problematic, because the source surface of a field emitter can have a radius of curvature on the nanometer scale, and the emitted electrons are accelerated by a strong, inhomogeneous electrostatic field following emission. We introduce a model based on wave-mechanical electron optics that draws on a quantum mechanical description of electron emission and propagation to obtain a physically consistent treatment of the wave-mechanical properties of electron sources. We apply the model to investigate spatial resolution limits in low-energy electron holography and microscopy, where it is shown that aberrations and coherence properties of the electron source are crucial and interrelated. The wave-mechanical electron-optical model can, furthermore, be readily generalized to assess and improve electron source performance in other scenarios and techniques where spatial and temporal coherence, and electron-optical aberrations, are relevant.