nanosecond excimer laser beam is absorbed by the semiconductor by electron-hole excitations and other absorption mechanisms resulting in thermal equilibrium of the carriers in less than 10^-13 sec. The laser energy is transferred to the lattice by photon emission processes (heat) in times of the order of 10^-12 sec, and thus for nanosecond irradiation regimes, the plasma effects of excited carriers are negligible [3]. The laser energy manifests itself in the form of heat, and the thermal effects of nanosecond laser irradiation can be determined by the solution of one-dimensional heat flow equation with appropriate boundary conditions, while taking into account the phase changes occurring in the material. A three-dimensional solution is not required because of the very short processing times (~200 ns) and the large transverse dimensions of the laser beam, which result in thermal gradients many orders of magnitude greater in the perpendicular direction to the surface than compared to the transverse directions [3,4]. The one-dimensional heat-flow equation is given by

where, x refers to the direction perpendicular to the plane of the sample and t is the time, and the subscripts i = 1,2 refer to the solid and liquid phase, respectively. The terms ρ, C, K, R, and α correspond to the temperature dependent mass density, specific heat capacity, thermal conductivity, reflectivity and absorption coefficient of the incident laser beam, respectively. I_o corresponds to the time dependent laser intensity striking the surface. The boundary conditions at the front and back surface assume that there are no thermal losses which approximately hold for nanosecond processing times. The solid-liquid interface is assumed to be at the melt temperature, and the position of the interface S is determined by the heat balance equation at the interface given by

where K_s and K₁ are the solid and liquid thermal conductivities at the interface, and L is the latent heat per unit volume of the material. The presence of a moving solid-liquid interface, and the temperature dependent thermophysical and optical properties make the analytical solution of the heat flow equation intractable, and thus approximate numerical techniques have to be applied. To solve Equation (1), we have adopted a higher order implicit finite difference method in which the thermal gradients at the interface are accurately determined for calculating the interfacial velocity[4]. The temperature dependent optical and thermal properties and the time dependent laser intensity have been taken into account in this solution.

The laser irradiation of ion-implanted samples leads to the removal of the implantation damage up to the distance of the maximum melt depth. The underlying defect-free substrate acts as a seed for subsequent crystal growths, resulting in removal of ion-implantation damage and electrical activation of the dopant atoms. To verify the working of the heat flow program the simulated values of the maximum melt depths were compared with the experimental values obtained by excimer laser irradiation of ion-implanted samples at various energy densities. Figure 1A shows TEM micrographs of boron-implanted samples which were irradiated with XeCl laser having a trapezoidal pulse shape and full width at half maximum (FWHM) of 25 and 70 × 10^-9 sec, and energy density varying from 1.0 to 2.5 J/cm². A complete removal of the dislocation loops in the annealed region together with a sharp transition between the annealed and unannealed regions is observed. The V-shaped dislocations are created because the melt front intersects the dislocation loops, and the two segments of the dislocation grow back to the surface because the dislocation cannot end inside the perfect lattice.