Statistical analysis of defect-caused laser damage in thin films.

An analysis of the statistics of laser-induced damage to thin films is carried out for the commonly assumed single-defect model, in which damage is caused by irradiation of identical, randomly distributed defects in the film. The probability for damage due to a single irradiation with a beam of Gaussian spatial profile is calculated, and it is shown that observed variations with beam size of the intensity required to maintain a constant high probability for damage are accounted for by this expression. The multiple-shot damage probability is then calculated, assuming that irradiation is started at a low value of energy and increased stepwise, for two cases, an N-on-1 experiment where the beam irradiates the same site each time and a 1-on-1 experiment where the beam is moved to a new site with each shot. The damage thresholds, defined to be the median values of the distribution functions for these two cases, are compared to one another and to the thresholdfor a single-shot experiment. Moreover, the dependence of the threshold on the size of the pulse-to-pulse energy increment is determined. Finally, the effect of a second damage mechanism involving damage to the host material is determined by calculating the mean and variance of the probability density function. These results are shown to be in good agreement with prior measurements of the beam-size dependence of threshold.