Boundary condition and initial value effects in the reaction-diffusion model of interface trap generation/recovery

A simple standard reaction-diffusion (RD) model assumes an infinite oxide thickness and a zero initial interface trap density, which is not the case in real MOS devices. In this paper, we numerically solve the RD model by taking into account the finite oxide thickness and an initial trap density. The results show that trap generation/passivation as a function of stress/recovery time is strongly affected by the condition of the gate-oxide/poly-Si boundary. When an absorbent boundary is considered, the RD model is more consistent with the measured interface-trap data from CMOS devices under bias temperature stress. The results also show that non-negligible initial traps should affect the power index n when a power law of the trap generation with the stress time, tn, is observed in the diffusion limited region of the RD model.