Analysis and Applications of a Heralded Electron Source

We analytically describe the noise properties of a heralded electron source made from a standard electron gun, a weak photonic coupler, a single photon counter, and an electron energy filter. We argue the traditional heralding figure of merit, the Klyshko efficiency, is an insufficient statistic for characterizing performance in dose-control and dose-limited applications. Instead, we describe the sub-Poissonian statistics of the source using the fractional reduction in variance and the fractional increase in Fisher Information. Using these figures of merit, we discuss the engineering requirements for efficient heralding and evaluate potential applications using simple models of electron lithography, bright-field scanning transmission electron microscopy (BFSTEM), and scanning electron microscopy (SEM). We find that the advantage in each of these applications is situational, but potentially significant: dynamic control of the trade-off between write speed and shot noise in electron lithography; an order of magnitude dose reduction in BFSTEM for thin samples (e.g. 2D materials); and a doubling of dose efficiency for wall-steepness estimation in SEM.