Despite its obvious inability to predict experimental recovery data, the Reaction-Diffusion (RD) model is still used to explain and interpret negative bias temperature stress data from (mostly p-channel) Metal-Oxide-Semiconductor (MOS) transistors. It has recently been proposed that the inability of the RD model to properly predict the observed recovery transients is due to the incomplete description of atomic motion in the one-dimensional macroscopic formulation of the theory. It has been argued that proper consideration of the three-dimensional atomic motion would lead to a delayed repassivation of dangling bonds in long-term recovery, since hydrogen atoms have to hover along the interface in order to find unoccupied dangling bonds.
In order to investigate this claim, we have developed a microscopic formulation of the modified RD model and simulated it using the kinetic Monte Carlo algorithm. A comparison of the results of the macroscopic and the atomistic formulation shows that while the recovery behavior predicted by the RD theory is not affected by the change of the formulation, dramatic changes arise in the degradation behavior of the microscopic RD model, making it also incompatible with experimental degradation data. It was found that the strong deviation of the microscopic model from the well-known behavior of its macroscopic counterpart comes from the large distance between the dangling bonds, which lead to an initial behavior in which bi- molecular reactions do not occur (see picture). This physically reasonable regime is not obtained from the macroscopic RD model.
As the microscopic formulation is the physically more accurate description, but is incompatible with both experimental degradation and recovery, the validity of the RD process itself has to be questioned. Furthermore, a review of the stochastic theory of the chemical kinetics of RD systems reveals that the implicit assumption of homogeneity along the silicon-silicon dioxide interface in the RD model for Negative Bias Temperature Instability (NBTI) is not justifiable at the low defect densities found in MOS devices.