Quantum Mechanical Treatment of Si-O Bond Breakage in Silica Under Time Dependent Dielectric Breakdown Testing

Using a generalized Mie-Gruneisen bonding potential, a quantum mechanical treatment (WKB method) for Si-O bond breakage in silica is presented under the conditions of high electric field, hole injection and hydrogen release. The full spectrum of bound-state energy eigenvalues is used to calculate the transmission probability whereby bond breakage occurs when the Si-ion goes from 4-fold to 3-fold coordination. When this full spectrum of bound-state energy eigenvalues is considered, it is shown that, due to the mass of the Si-ion and the width of the potential energy barrier separating the 4-fold and 3-fold coordinated bonding positions, the tunneling probability is relatively small and thus the transmission probability is described well by thermionic emission. It is further shown that stretched bonds, hole capture and hydrogen release can all have a significant impact on the barrier height and thus greatly impact the transmission probability.