Macroscopic theory of pulsed-laser annealing. III. Nonequilibrium segregation effects

During the past three years, phenomena associated with pulsed and cw laser annealing of semiconductors have generated intense interest among scientists in both fundamental and applied areas of solid-state physics and materials science. As a consequence, a coherent picture of the physical processes involved, at least on a macroscopic basis, is beginning to emerge. In the first two papers of this series, the results of heat and mass (dopant) transport calculations based on the melting model of pulsed-laser annealing were described in considerable detail. It was shown that dopant profiles observed after pulsed-laser annealing could not be fitted when values of the interface segregation coefficient $k_i^{}{}_{}{}^0$ appropriate for solidification under nearly thermodynamic equilibrium conditions were used in the dopant redistribution calculations. In this paper, a model is developed which relates the nonequilibrium interface segregation coefficient $k_i$ to $k_i^{}{}_{}{}^0$ and to the velocity of the liquid-solid interface during recrystallization of the molten region created by the laser radiation. The functional dependence of $k_i$ on the interface velocity cannot be calculated exactly, but simple approximate expressions for this dependence yield results which are in accord with the experimental data presently available. Moreover, with the use of the velocity dependence of $k_i$, it is shown that the model gives satisfactory agreement with the maximum nonequilibrium dopant concentrations which have been observed for an interface velocity of ∼4 m/sec. It is further shown that when the velocity-dependent $k_i$ is used in the theory of Mullins and Sekerka for cellular formation during solidification, agreement with the results of pulsed-laser annealing experiments is obtained, but if $k_i^{}{}_{}{}^0$ is used there is no agreement. The relationship of the model to the general concept of "solute trapping" introduced by Baker and Cahn is discussed and it is shown that the model satisfies the criterion for solute trapping.