  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.
