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Despite extensive experimental and theoretical studies, the atomistic mechanisms responsible for dielectric breakdown (BD) in amorphous (a)-SiO2 are still poorly understood. A number of qualitative physical models and mathematical formulations have been proposed over the years to explain experimentally observable statistical trends. However, these models do not provide clear insight into the physical origins of the BD process. Here, we investigate the physical mechanisms responsible for dielectric breakdown in a-SiO2 using a multi-scale approach where the energetic parameters derived from a microscopic mechanism are used to predict the macroscopic degradation parameters of BD, i.e., time-dependent dielectric breakdown (TDDB) statistics, and its voltage dependence. Using this modeling framework, we demonstrate that trapping of two electrons at intrinsic structural precursors in a-SiO2 is responsible for a significant reduction of the activation energy for Si-O bond breaking. This results in a lower barrier for the formation of O vacancies and allows us to explain quantitatively the TDDB data reported in the literature for relatively thin (3-9 nm) a-SiO2 oxide films. [ABSTRACT FROM AUTHOR]