A Statistical Analysis of Absorptive Laser Damage in Dielectric Thin Films Available to Purchase

The Weibull distribution arises as an example of the theory of extreme events. It is commonly used to fit statistical data arising in the failure analysis of electrical components and in DC breakdown of materials.

This distribution is employed to analyze time-to-damage and intensity-to-damage statistics obtained when irradiating thin film coated samples of SiO₂, ZrO₂, and Al₂O₃, with tightly focused laser beams. The data used is furnished by Milam. The fit to the data is excellent; we often obtain least squared correlation coefficients greater than 0.9.

It is found almost universally that statistical models of breakdown, such as the lucky electron theory, oversimplify the damage process by neglecting nonlinear interactions and anisotropies induced by impurities. Thus, the fundamental intensity I relation on pulse length t_p often deviates from the classical t_p^-½ dependence resulting from 2-photon absorption without diffusion, or from linear absorption with diffusion, to dependencies as high as t_p^-0.22 for the former to t_p^0.44 for the latter. This fact, coupled with the experimental nonobservability of higher than 2-photon absorption seems to imply that the avalanche mechanism is the most likely initiator of the plasma requisite for lattice meltdown.

Statistical confidence bands for material survivability as a function of laser intensity and pulse length can be constructed; this lends high practical utility to the Weibull distribution as an engineering diagnostic tool.