Abstract
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.
Highlights
In modern high-resolution electron microscopy the spatial and temporal coherence properties of the electron source play a crucial role in determining the instrument resolution [1,2,3]
From our simulations we can conclude that the composite hologram must be constructed such that phase shifts caused by electron-optical aberrations are accounted for, which is interesting because Low-energy electron holography (LEEH) is typically considered to be an “aberration-free” technique [9,11]
We introduce a wave-mechanical electron-optical model that can consistently simulate the wave and particle-optical properties of electron sources and provide physical insight into the relation between coherence, aberrations, and the geometry of the emitter
Summary
In modern high-resolution electron microscopy the spatial and temporal coherence properties of the electron source play a crucial role in determining the instrument resolution [1,2,3]. A key concept in the conventional theory of electron sources is the brightness, which is typically assessed by simulating the classical trajectories of electrons emitted by the cathode [4,5,6]. For extremely small sources that produce highly coherent electron beams, it was shown that the concept of brightness, which is based on geometrical optics principles, can become meaningless and a wave-optical treatment of the source becomes necessary [7]. Even for sources that are not extremely small, the spatial coherence of the electron wave plays an important role that is not captured by conventional electron source theory.
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