Macroscopic theory of pulsed-laser annealing. I. Thermal transport and melting

Pulses of radiation from ruby and Nd:YAG $Q$-switched lasers have been used recently to anneal the lattice damage caused by ion implantation of semiconductors. Other similar applications include the laser-induced diffusion of thin dopant films deposited on the surface of samples, recrystallization of doped amorphous films deposited on single-crystal substrates, and the removal of precipitates present after conventional high-temperature dopant diffusion. All of these processes can be understood in terms of models and calculations based on macroscopic diffusion equations for heat and mass transport, cast in a finite-difference form to allow for the temperature and spatial dependences of the thermal conductivity, absorption coefficient, reflectivity, and other quantities. Results of calculations on silicon with the models show that the near-surface region of a sample can melt and stay molten for times of the order of 100 nsec during which dopant diffusion in the liquid state and nonequilibrium segregation during ultrarapid recrystallization are sufficient to explain the major features of the experimental results. In this paper, a description of the model used in our heat-transport calculations is given. Results of the modeling are illustrated by a variety of calculations which should be of particular interest to experimentalists working with pulsed-laser annealing. These results include, e.g., the effects of pulse duration, shape, and energy density, the effects of assumptions made about the latent heat of amorphous silicon, the effects of substrate heating, the role played by the absorption coefficient in determining melt-front penetration, and the duration of surface melting.