Statistics of Si-O Bond-Breakage Rate Variations Induced by O-Si-O Angle Fluctuations

The McPherson model for the Si-O bond-breakage has been extended in a manner to capture the effect of O-Si-O angle variations on the breakage rate. Using a distribution function of the O-Si-O bond angle, a series of breakage rate probability densities has been calculated as a function of the applied electric field. Using such a distribution function we have calculated the mean vale and the standard deviation of the breakage rate and compare them to the nominal rate corresponding to the fixed angle of 109.48deg observed in crystalline alpha-quartz. It is shown that the mean value of this rate is substantially higher than and the standard deviation is comparable with the nominal rate. Obtained dependencies demonstrate a linear trend in a log-fin space, thereby validating the thermo-chemical model for the time-dependent-dielectric breakdown also in the case of non-uniform O-Si-O angle distribution typical for amorphous silica.