Physics-based modeling of hot-carrier degradation

Abstract

We present and verify a physics-based model of hot-carrier degradation (HCD). This model is based on a thorough solution of the Boltzmann transport equation. Such a solution can be achieved using either a stochastic solver based on the Monte Carlo approach or a deterministic counterpart that is based on representation of the carrier energy distribution function as a series of spherical harmonics. We discuss and check two implementations of our model based on these methods. The model is verified vs. the HCD experimental data measured in long-channel transistors as well as in ultra-scaled MOSFETs. Because both stochastic and deterministic methods have advantages and shortcomings, we study the limits of applicability of these methods. We aim to cover and link all main features of HCD, namely, the interplay between hot and colder carriers, which leads to two competing mechanisms of bond breakage and the strong localization of hot-carrier damage. Our model is linked and compared with other approaches to HCD simulations. Special attention is paid to the importance of the particular model ingredients, such as competing mechanisms of the Si-H bond dissociation, electron-electron scattering, variations in the bond-breakage energy, as well as its reduction due to the interaction between the dipole moment of the bond and the electric field. We also analyze the role of electron-electron scattering in HCD measured in devices with different gate lengths.