Impact of O–Si–O bond angle fluctuations on the Si–O bond-breakage rate

Abstract

We extend the McPherson model for the silicon–oxygen bond-breakage in a manner to capture the impact of the O–Si–O angle fluctuations (typical for amorphous SiO 2) on the breakage rate. In the McPherson model the transition of the Si ion from the 4-fold coordinated position to the 3-fold coordination is considered as rupture of the Si–O bond. We have studied the potential barrier (separating these saddle points) transformation induced by the O–Si–O bond angle variations and found that the secondary minimum occurs at a critical angle of about 107.75°. Since the Si ion “finds” the way corresponding to the highest breakage probability we used the two-dimensional downhill simplex method in order to find the direction of this maximal rate. It was shown that if the O–Si–O angle deviates from its nominal value 109.48° (typical for α-quartz) corresponding to the regular SiO 4 tetrahedron the symmetry aggravates and the secondary minimum is rotated. Calculated dependencies of the breakage rate on the electric field demonstrate the linear slope in the log–lin scale thus reflecting the linear reduction of the activation energy for the bond-breakage vs. field. The family of distribution functions for breakage rate calculated with a fixed step of field shows that the curves do not change their form and are shifted in parallel with the field. This tendency supports the thermo-chemical model for the bond-breakage also in the case of strongly fluctuating O–Si–O angles. As a consequence, dependencies of the mean value of the rate, its standard deviation and the nominal rate (calculated for the angle of 109.48°) have the same slope on a log–lin scale. The wide spread of the breakage rate is reflected by the high value of its standard deviation.