Modified growth theory for high supersaturation

Abstract

The classical BCF (Burton, Cabrera, Frank) growth theory assumes atomic step motion driven by the diffusion of adatoms toward the step acting as sinks. Stationary solutions of the diffusion equation have been obtained by BCF neglecting the movement of the coordinate system. By using a moving frame, as already done for a single-step flow model by Mullins and Hirth, we calculate the velocity of a periodic parallel sequence of steps, the distribution of adatoms, and the condensation coefficient as a function of the step distance for various supersaturations. This modification result in significant deviations from the original theory if a dimensionless normalized supersaturation parameterb which is proportional to the supersaturation exceeds one-half. Large values of this parameterb may occur for the high supersaturation found in Si-MBE (molecular beam epitaxy) for temperatures far below the melting point.