Free surfaces have been known to significantly influence the crystallization of tetrahedral liquids. However, a comprehensive understanding of the influence mechanism is still lacking at present. By employing molecular dynamics simulations, we find that the nucleation probability in nanoscale silicon films and droplets exhibits a ripple-like distribution spatially. This phenomenon is closely related to the structural order wave, which is induced by the density fluctuations arisen from the volume expansion in a confinement environment defined by free surfaces. By the aid of the intrinsic relation between the tetrahedral order and the density, the analytic results based on the density wave equation well account for the nucleation probability distributions in both films and droplets. Our findings reveal the underlying mechanism of the surface-assisted nucleation in tetrahedral liquids and provide an overall description of crystallization in liquid films and droplets.

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