1.5 HCD Model Based on the Carrier Distribution Function

This work presents a more detailed approach for hot-carrier degradation modeling and tries to more accurately capture the physical picture behind this phenomenon. This model incorporates the crucial features of the previous approaches for hot-carrier degradation modeling. In contrast to previous HCD models the aim of this work is to cover and link all levels related to this effect, starting from the microscopic mechanisms of defect generation and ending at the device level.

**Figure 1.12:** The flowchart of the proposed model for hot-carrier degradation depicting three main modules: carrier transport module, module for microscopic mechanisms for defect creation, and module for simulations of the degraded devices.

The main approaches to hot-carrier degradation modeling described in the previous sections were carefully analyzed and a comprehensive framework of a physics-based HCD model was established. As was demonstrated within the model by Hess, the degradation is controlled by the interplay between Single- and Multiple-Particle mechanisms of Si-H bond dissociation. This interplay is controlled by the way the carriers are distributed over energy, that is by the carrier energy distribution function. These considerations suggest that carrier transport and microscopic mechanisms of defect creation are two essential sub-tasks of the general problem. The Penzin model attempts to link the microscopic mechanisms of defect creation and the device level. While the energy-driven paradigm elaborated by Rauch and LaRosa is focused on the substitution of the DF by some simple approximations, the Bravaix model combines this paradigm with defect generation concepts.

In contrast to previously proposed models, the full hierarchical ladder connecting the microscopic origin of the phenomenon and device simulation level is arranged. Therefore, there are three main modules in the physics-based HCD model: the carrier transport module, the section responsible for the defect build-up, followed by the device simulation module (Figure 1.12). The carrier transport module allows for a thorough evaluation of the carrier energy distribution function for a particular device architecture. The DF represents populations of "hot" and "colder" carriers and thus controls the interplay between the SP- and MP-mechanisms and is then employed by the post-processor calculating defect density profiles. These profiles with information about the trap density-of-states (DOS) are used as input data for device simulations considering the distortion of device electrostatics and additional scattering events induced by charged traps. Furthermore, the device characteristics (such as output and transfer characteristics, transconductance, threshold voltage shift, etc.) of the degraded transistor are calculated. The feedback to calibrate the model is given by comparison with the experimental device characteristics. The principal breakthrough associated with this concept is the self-consistent consideration of both the transport and degradation aspects. Different fragments of the main framework are based on physical models presuming some assumptions and simplifications and these fragments act as sources of possible errors. Therefore, a thorough verification of all output information (used as the input for other modules) is to be performed. It should be emphasized that the double-check of the approach is being made. First the simulated N_it profile is compared vs. that extracted from charge-pumping measurements. Finally the simulated (employing these N_it profiles) set of device characteristics and the experimental one are collated.