8  Conclusions

Scaling devices down to the nano-meter regime increases the probability of functional failure due to single point defects or parametric fluctuations, such as fluctuations in the doping. The effect of single point defects and parametric fluctuations on the figures of merit, such as the threshold voltage, of MOSFETs are intertwined. In the first part of this thesis it has been shown that, in scaled devices, the characteristic discrete threshold voltage shifts caused by charged single defects (step-heights) is highly dependent on the exact positions of the dopants and defects in the device. Thus the effect of potential fluctuations caused by the random discrete doping (RDD) has been assessed first, since in sub-100nm node devices the discreteness of the doping cannot be ignored anymore. Afterwards, the electrostatic interaction of charged single point defects and random discrete dopants has been investigated, neglecting the charge reaction kinetics of the single point defects. In these studies it has been shown that an electrostatic and drift-diffusion-based picture to determine the characteristic step-heights caused by single defects is insufficient. Subsequently it has been shown that effects other than pure electrostatic influences, such as fluctuations in the charge carrier mobility, need to be taken into account. In this respect a drift-diffusion-based transport model, even with quantum mechanical corrections, is insufficient to reproduce the step-heights caused by single charged defects. When taking the trapping kinetics into account, two main modes of defect creation have been discussed, namely the bias temperature instability (BTI) and hot-carrier degradation (HCD). For BTI, the modelling of the tremendously electric field and temperature dependent defect creation as well as the charge trapping kinetics have been discussed. The most accurate model for the recoverable component of BTI today is the four-state non-radiative multiphonon model, where it was shown that this model can not only reproduce classic BTI degradation experiments, but also can explain trap assisted tunneling after bias temperature stress to high accuracy. Additionally, it has been shown that the electric field dependence of BTI, which is modelled using a non-radiative multiphonon theory, can lead to problems of trap self-interaction in self-consistent simulations. This self-interaction is independent of the employed transport model and has been shown to artificially broaden the distribution of the trapping time constants. However, it is possible to assess the amount of self-interacting traps by comparing first-order trapping kinetics to the trapping kinetics predicted by a self-consistent simulation. Since trap self-interaction is closely related to the field dependence of the characteristic trapping time constants, trap self-interaction is not an issue when investigating HCD. In the latest models, developed in the course of this thesis, standard SRH charge trapping kinetics are assumed for hot-carrier induced traps which show a weak dependence of the trapping time constants on the electric field. Contrary to the trapping kinetics of hot-carrier induced defects, the creation of the same defects is highly dependent on the electric field. However, it has been shown that defect creation caused by hot carriers is highly sensitive to the kinetic energy of the charge carriers and cannot be modelled by taking the electric field into account alone. Thus, to investigate HCD one needs exact information on the energy distribution of charge carriers. This in turn requires an efficient method to solve the Boltzmann Transport equation (BTE) for at least 2D devices. As laid out in this thesis, the usual Monte Carlo approach is insufficient for HCD, due to the inherent numerical noise in the solution. In this respect the deterministic approach to expand the BTE in spherical harmonics (SHE) has proven to be the method of choice for investigations into hot-carrier degradation. Finally, employing the SHE-based simulator ViennaSHE it was exhaustively shown that the developed hot-carrier model can predict HCD in devices of different channel lengths for various stress conditions.