Generalized diffusion-reaction model for the low-field charge-buildup instability at the Si-SiO2interface

We present a unified phenomenological model of the low-field charge-buildup phenomenon at ultrathin ${\mathrm{SiO}}_2$-Si interfaces during negative-bias stresses at elevated temperatures and compare it with experiments. Based on the microscopic understanding of interfacial charges and neutral defects as trivalent silicon and its hydrogen compounds, the dissociation chemistry of hydrogen-passivated dangling silicon bonds is extensively studied by generalizing the diffusion-reaction concept to include charged as well as neutral diffusing species. The mathematical scheme consists of a detailed-balance equation for the first- or second-order chemical reaction and a diffusion equation for the charged or neutral reaction by-product whose interfacial concentration determines the reaction rate at the interface. This generalized diffusion-reaction concept is shown to provide a plausible explanation for the various dependencies of the phenomenon. The general solution of these coupled equations is characterized by its fractional-power time dependence, ∼${\mathit{t}}^{1/4}$ for example, and the corresponding exponential dependence on the activation energy over temperature, which comes from the temperature dependence of the diffusion coefficient. For the neutral diffusing species, this scheme provides no first-principles-based information on the oxide field (${\mathit{E}}_{\mathrm{ox}}$) dependence. Thus the experimentally observed field dependence, such as ∼${\mathit{E}}_{\mathrm{ox}}^{3/2}$, can be ascribed to the nature of the fundamental electrochemical reaction at the interface. On the other hand, for charged diffusing species, this scheme provides ${\mathit{E}}_{\mathrm{ox}}^1$ ${\mathit{t}}^{1/2}$ dependence. Comparison of these mathematical predictions with experimental data leads us to conclude that the low-field charge-buildup instability of the ultrathin ${\mathrm{SiO}}_2$-Si interface under negative-bias temperature stresses is successfully explained by our generalized diffusion-reaction model of neutral-diffusing (atomic or molecular) hydrogen with the boundary condition of an absorbing wall at the gate-electrode interface. DOI: http://dx.doi.org/10.1103/PhysRevB.51.4218 © 1995 The American Physical Society