A theory for columnar microstructure is presented. Column orientation is predicted, and the tangent rule is shown to be an approximate special case of a more general relationship. Results also predict that columns occur only at low substrate temperature. All of these results agree with experimental data. In addition, a relationship is found between column width and mean square diffusion length. The theory substantiates the empirical suggestion that adatom mobility is an important parameter governing column development.

• Received 10 June 1985

DOI:https://doi.org/10.1103/PhysRevLett.56.1396