The SiO2 TDDB Process 

Previous studies have shown that SiO2 Time-Dependent Dielectric Breakdown (TDDB) is a charge injection mechanism, the process of which may be divided into 2 stages - the build-up stage and the runaway stage.

During the build-up stage, charges invariably get trapped in various parts of the oxide as current flows in the oxide. The trapped charges increase in number with time, forming high electric fields (electric field = voltage/oxide thickness) and high current regions along the way.  This process of electric field build-up continues until the runaway stage is reached.

During the runaway stage, the sum of the electric field built up by charge injection and the electric fields applied to the device exceeds the dielectric breakdown threshold in some of the weakest points of the dielectric. These points start conducting large currents that further heat up the dielectric, which further increases the current flow.  This positive feedback loop eventually results in electrical and thermal runaway, destroying the oxide in the end.  The runaway stage happens in a very short period of time.

The presence of defects in the dielectric greatly reduces the time needed to transition from the build-up to the runaway stage.  These defects actually have the effect of 'thinning' down the oxide where they are located, since they are occupying space that should have been occupied by the dielectric. The effective electric field is higher in these thinned-out areas compared to defect-free areas for any given voltage. This is why it takes a lower voltage and shorter time to break down the dielectric at its defect points.

There are many lifetime equations used in the industry today to model the reliability of an oxide layer.  One of the simplest, however, can be seen in www.semicon.toshiba.co.jp. According to this site, TDDB may be modelled by: