Copper drift in current interconnect structures is a reliability issue leading to premature low-k dielectric breakdown. Copper ions drift through insulating low-k dielectrics leading to an increase in the local electric field that, if high enough, could lead to device failure. We have solved the coupled continuity and Poisson's equation using the boundary condition that the flux of copper ions equals zero (J(t,L)=0) at the cathode or dielectric-semiconductor interface. We show that the choice of J (t,L)=0 (no flux) boundary condition in the model of copper ion drift causes an internal field enhancement at the cathode due to the accumulation of copper ions. The ultimate breakdown of the dielectric occurs due to a combination of the field increase exceeding the intrinsic breakdown strength as well as the intrinsic bond breakage due to thermal and field effects. In this paper we also show that the field dependence of the intrinsic bond breakage shows an E2 dependence in the presence of copper ions enabling an excellent fit to the time-to-failure data on Cu/th-SiO2/Si devices for all fields and all temperatures.