An extensive review  of focused electron beam induced deposition (FEBID) appeared on the arXiv recently. FEBID has met with considerable commercial success for photomask repair. An additive technique, it is used to fill in “mouse bites” or to extend features that turned out to be too small to reliably print.
FEBID has many more applications, including nano-structured deposition of metals, alloys, intermetallic compounds, etc. As with laser-driven 3D printing, FEBID can directly write three-dimensional structures, albeit on the nanometric scale. [Note: Two photon lithography can yield 3D structures at least down to the few hundred nanometer scale. See ref. 2.]
There are, of course, limitations. With most materials, it is exceedingly difficult to get rid of contaminants, typically carbon and oxygen. Further, suitable precursors typically have to be custom made. They are usually injected in a gaseous state. Finally, determining suitable electron beam energies, dwell times and so forth is typically a trial and error process.
The chemical reactions which liberate metal from precursor are predominantly initiated by secondary electrons. The reactions occur near the beam/solid impact point, but as we know from e-beam lithography, back-scattered electrons can emit secondary electrons at quite some distance from the beam entry point, including the beam exit in the case of free-standing 3D structures.