  Phonon-mediated particle detectors based on single crystals and operated at
millikelvin temperatures are used in rare-event experiments for neutrino
physics and dark-matter searches. In general, these devices are not sensitive
to the particle impact point, especially if the detection is mediated by
thermal phonons. In this Letter, we demonstrate that excellent discrimination
between interior and surface $\beta$ and $\alpha$ events can be achieved by
coating a crystal face with a thin metallic film, either continuous or in the
form of a grid. The coating affects the phonon energy down-conversion cascade
that follows the particle interaction, leading to a modified signal shape for
close-to-film events. An efficient identification of surface events was
demonstrated with detectors based on a rectangular $20 \times 20 \times 10$
mm$^3$ Li$_2$MoO$_4$ crystal coated with a Pd normal-metal film (10~nm thick)
and with Al-Pd superconductive bi-layers (100~nm-10~nm thick) on a $20 \times
20$ mm$^2$ face. Discrimination capabilities were tested with $^{238}$U sources
emitting both $\alpha$ and $\beta$ particles. Surface events are identified for
energy depositions down to millimeter-scale depths from the coated surface.
With this technology, a substantial improvement of the background figure can be
achieved in experiments searching for neutrinoless double-beta decay.
