The time-dependent dielectric breakdown of metal-oxide-semiconductor capacitors with 6 nm and 8 nm Ta2O5 gate dielectric layers is investigated. During constant voltage stress of the capacitors, a small increase in the time-dependent gate current is observed, followed by the occurrence of erratic fluctuations. After the occurrence of such a small jump, the current-voltage characteristics reveal increased gate current in the low gate voltage region, as compared to the current-voltage characteristics of fresh (unstressed) devices. In addition the gate current is shown to behave like a power law of the applied gate voltage. All above features are characteristics of the so-called soft breakdown event which has been previously reported for ultra-thin SiO2 layers.