Next: 1.3 Characteristic Features of HCD Up: 1. Introduction Previous: 1.1 Historical Background
All models described above have been developed for the description of HCD observed in a particular class of devices. As such, they are empirical or phenomenological, at the best. However, a proper description of HCD may only be possible when the physical picture is accurately understood and captured by the model. There are five main physics-based concepts for hot-carrier degradation modeling elaborated so far:
The most important breakthrough in HCD modeling is due to Hess who introduced the interplay between a single- and a multiple-carrier mechanism for Si-H bond-breakage. Since these mechanisms are related to the fractions of "hot" and "colder" carriers, the idea that the matter is controlled by the carrier energy DF was first acknowledged [32]. Notwithstanding the fact that the model is able to explain such a key feature of HCD such as the hydrogen/deuterium isotope effect [33], the link between the device microscopic picture of the defect build-up and degradation of device characteristics is missing. An attempt to link these levels has been undertaken in the Penzin model [25]. In fact, this work (as the successor of the Hess work) presents a phenomenological treatment for HCD modeling. Another approach is the extension of the reaction-diffusion framework of the negative bias temperature instability (NBTI) in order to capture HCD [26,27]. This implies, however, that once stress is removed, full recovery should be observable within reasonable times. In reality, the recovery of HCD is very slow, thus suggesting that HCD is a reaction-limited process [34]. One more strategy for HCD modeling proposed by Rauch and LaRosa is called "energy-driven paradigm" [28,29]. For channel lengths less than 180nm, HCD was shown to be controlled by the single "knee" energy. This energy is related to the stress bias. Therefore, instead of operating with coordinate-dependent quantities (electric field, dynamic temperature, DF, etc) only a single bias-dependent parameter is considered. A combination of the Hess and Rauch approaches was proposed by Bravaix et al. [30,31]. In this concept the interaction between the single- and multiple-carrier mechanisms for Si-H bond-breakage has been considered. However, the crucial point is that the information about the carrier DF is substituted by some empirical factors. In spite of a certain success of all these approaches the main problem is that they capture only a fragment of the whole HCD mosaic. Therefore, the hierarchical ladder connecting the microscopic level of defect creation and the device simulation level is still not fully understood.
To summarize, over the last decades hot-carrier degradation modeling has evolved from simple empirical models to a more detailed understanding of the microscopic physics involving single particle (SP) and multiple particle (MP) processes. A detailed description of the physics requires knowledge of the carrier energy distribution function which can only be obtained from a solution of the Boltzmann transport equation (BTE). Most models in use today employ simplified solutions based on the average energy or, even more dramatic, the electric field, while in the ultimate simplification attempts are made to capture the physics using closed analytic expressions. Although computationally more efficient, these approaches are inevitably inaccurate, even though their limitations might not be that obvious when a limited range of bias conditions, temperatures, and channel-lengths is investigated. Therefore, after describing the main features of hot-carrier degradation, one proceeds to the detailed analysis of the existing physics-based HCD models finishing with the presentation and validation of a detailed model.