Using molecular dynamics analysis and a two-component diffusion model that accounts for the time-dependent crystal surface chemical reaction, we show by extensive numerical simulations that the recently observed prismatic facet growth suppression in single-crystal fibers is the combined action of self-shielding by crystal surface selectivity and self-channeling arising from a point effect due to fibers small diameters and large aspect ratios. We further show that the self-channeling leads to a pyramidal-face-aiming solute flow, resulting in accelerated single-crystal fiber growth. This mesoscopic stimulated matter growth acceleration theory can satisfactorily explain all experimental results reported to date. This new crystal fiber growth technology opens a realm of application possibilities for single-crystal fiber architectures in chip-size photonics.