On the Microscopic Limit of the RD Model

The popular reaction–diffusion model for the negative bias temperature instability is discussed from the viewpoint of stochastic chemical kinetics. We present a microscopic formulation of the reaction–diffusion model based on the reaction–diffusion master equation and solve it using the stochastic simulation algorithm. The calculations are compared to the macroscopic version as well as established experimental data. The degradation predicted by the microscopic reaction–diffusion model strongly deviates from the macroscopic version and the experimentally observed behavior. Those deviations are explained as necessary consequences of the physical processes involved. The presented results show the impact of the unphysical assumptions in the reaction–diffusion model. Further, we generally question the suitability of the mathematical framework of reaction rate equations for a reactive-diffusive system at the given particle densities.