The kinetics of the melt front is crucial in understanding the nature of laser-solid interactions. Figure 2A shows the position of the solid-liquid interface of XeCl laser irradiated samples as a function of time for different pulse energy densities and durations. The slope of the curves corresponds to the velocity of the melt front at any instant. The figure shows that above a certain energy density and after a certain time interval, the surface starts to melt, and the melt front penetrates several thousands angstroms before heading back to the surface. The solidification velocity is approximately a few meters per second, which is about five orders of magnitude greater than the normal crystal growth velocity. The maximum solidification velocity dS/dt can be estimated as

where D corresponds to the thermal diffusivity, T_m the melt temperature, and C is constant factor between 1.5 to 2.0, the exact value depending on the shape of the laser pulse.

The maximum melt depths for excimer XeCl laser irradiation of silicon at different energy densities and pulse durations is shown in Figure 1B. For both 25 and 50 ns laser pulses, the maximum melt depth is found to be proportional to the energy density. The x intercept corresponds to the minimum energy required for propagation of the melt front into the substrate (E_th). The melting threshold can be estimated from energy balance considerations [4], and is approximately equal to

where R₁ is the liquid reflectivity and τ correspond to the pulse duration. If we perform an energy balance, the maximum melt depth Δx_t as a function of energy density is given by

where C₁ = (1-R₁)/(ρC_pT_m + L) is constant for a particular material and corresponds to the slope of the graph in Figure 1B. The value of C₁ for silicon is 3800Å J^-1 cm², which is quite close to the value obtained from detailed heat flow calculations (3870Å J^-1 cm²).

Another important aspect in the understanding of the laser-solid interactions are the temperature profiles generated during intense nanosecond laser irradiation. Figure 2B shows the surface temperature of silicon as a function of time for a 25 ns excimer laser pulse having different energy densities. It is seen from this figure that the surface temperature rises rapidly until it reaches the melting point of the material, where it pauses momentarily until the change in reflectivity upon melting of silicon is compensated, and then rises again until its maximum value. On cooling, the surface temperature quickly drops to the melt temperature and remains there until the interface recedes to the surface. From energy balance considerations, we can estimate the temperature rise as a function of energy density. The temperature rise above the melting temperature ΔT is equal to

This expression shows the parabolic nature of the surface temperature rise above the melt temperature with increasing pulse energy density. For silicon, the value of the constant in Equation (6) is equal to 242 K/(J cm^-2)² for a 25 ns pulse, which corresponds closely to the value of 242 K/(J cm^-2)² obtained from detailed heat flow calculations.

FRONT MATTER (R1-R8)

1 SESSION 1 - WATER TREATMENT: ADVANCED PHOTOOXIDATION PROCESSES (1-34)

2 SESSION 2 - WASTE TREATMENT (35-58)

3 SESSION 3 - MATERIALS PROCESSING AND SYNTHESIS (59-96)

4 SESSION 4 - SOLAR PUMPING OF LASERS (97-108)

5 SESSION 5 - PHOTOCHEMICAL SYNTHESIS (109-116)

6 SESSION 6 - FUEL PROCESSING ADN THERMOCHEMICAL/PHOTOCHEMICAL CYCLES (117-136)

7 SESSION 7 - ADVANCED RESEARCH (137-140)

8 PLENARY SESSION (141-144)

APPENDIX A: WORKSHOP AGENDA (145-152)

APPENDIX B: LIST OF PARTICIPANTS (153-155)