An outline of new and previously published results of solid-phase epitaxy of implanted Si layers induced below room temperature by electron irradiation in the transmission electron microscope is given. The basic features of the process (i.e., the dependence of epitaxial growth rate on temperature of the target, electron energy, dose rate of irradiation) are discussed and compared with the trends reported in the literature for ion-beam-induced epitaxy obtained in a higher-temperature range (typically 200 less-than-or-equal-to T less-than-or-equal-to 400-degrees-C). The aim is to demonstrate that the fundamental characteristics of electron-beam-induced epitaxy are consistent with the extrapolation to low temperature and low mass of irradiating particles of the features of ion-beam-induced epitaxy, if appropriate assumptions on the kinetics of the defects responsible for the transformation are made. To better clarify this point it is shown that both a purely interface- and a purely diffusion-limited model of particle-induced epitaxy can in principle reproduce the very essential features of the process: the key point being the assumptions made on the dominant mechanism of defect reaction. In fact, while a linear-recombination scheme seems appropriate to explain the results of electron-induced epitaxy below room temperature, a dominant bimolecular-reaction mechanism seems necessary to reproduce the essential features of ion-induced epitaxy. Possible influences on electron-beam-induced epitaxy of electronic excitation or elastic collisions under the threshold for production of Frenkel pairs are also qualitatively discussed.