Closed-form theory of nuclei separation on highly anisotropic surfaces

During deposition on surfaces of highly anisotropic diffusion, nucleation behaves as it would on a one-dimensional substrate, or effectively deposition in two-dimensions (2D). This Article reports a close-form theory for nuclei separation during physical vapor deposition in 2D. In comparison and contrast, this closed-form theory agrees with existing theories in scaling, but gives the coefficient that was previously unknown. Further, this theory shows that the nuclei separation in 2D is an order-of-magnitude larger than in three dimensions. The insights from such comparison and contrast are critical in analyzing nucleation on surfaces of various anisotropy.