Markus Jech Dipl.-Ing. Publications

Two of the main reliability issues in modern CMOS technologies are bias temperature instability (BTI) and hot-carrier degradation (HCD). Both degradation modes are reasonably well understood, both experimentally and from a theoretical point of view. BTI, particularly its recoverable component, is related to oxide defects and charge trapping in the gate stack. The four-state non-radiative multiphonon (NMP) model provides the physical framework to accurately describe this phenomenon and has been successfully applied across various technologies. HCD is more permanent, and it is widely accepted that hot-carrier induced damage is due to broken Si-H bonds at the Si-SiO₂ interface triggered by channel carriers. The most recent formulation of an HCD model links microscopic quantities, such as the non-equilibrium carrier energy distribution function (EDF), to the trap density at the interface. Two physically different but interacting processes, namely multi-vibrational excitation and an anti-bonding mechanism, are believed to cause hydrogen desorption.
Both models are able to capture the characteristics of each degradation mode individually. However, very little is known about the interplay between BTI and HCD. Only a handful of publications have been devoted to the possible interaction of these detrimental phenomena, and in particular the implications of an applied drain bias on the recoverable component of BTI. We present a first model approach to extend the existing NMP theory towards non-equilibrium processes by explicitly taking non-equilibrium EDFs for electrons and holes into account (see Fig. 1). Depending on the applied drain bias, possible non-equilibrium processes, such as impact ionization, may lead to the generation of secondary generated carriers, which can interact with the oxide trap. Thus, the characteristic defect behavior may change dramatically with increased V_D.
Fig. 2 shows the experimental characterization of a single trap for increased V_D versus simulation results obtained with the extended NMP model. Interestingly, the trap shows a rather unexpected and puzzling behavior with increased drain bias. However, the extended NMP model is able to accurately capture all measurement trends. While the characteristic capture time changes only slightly with increased drain bias, the emission time changes dramatically (upper panels). Thus, the defect's occupancy decreases since the defect would already have partially emitted its charge before the measurement setup switched to recovery conditions (middle/lower panels). A detailed analysis showed that this behavior is due to the pronounced interaction with secondary generated carriers for increased V_D.
Furthermore, we applied the extended framework to describe the reduction of the recoverable component of BTI with increased V_D in large-area MOSFETs. We compared two versions of the NMP model: The original NMP model developed for equilibrium conditions and our extended version. As can be seen in Fig. 3, the non-equilibrium NMP framework results in a much better agreement with experimental data and predicts the decrease of R rather well. As already mentioned above, oxide defects can interact with carriers generated by impact ionization. Thus, in the extended NMP model, not only is the drain side affected (by a lower electric field in the oxide), but so too are the channel and source side regions (secondary carriers are shifted towards the source side). Less defects therefore contribute to overall device degradation and recovery characteristics, which leads to a good agreement between the measurement trend and simulation results.

Fig. 1: A schematic that shows the possible interaction of a defect with the channel within the four-state NMP theory. In the full physical picture, the oxide defect can interact with the channel's valence and conduction band carriers.

Fig. 2: Experimental data set of a single defect for increasing drain bias conditions versus simulation results obtained with the NMP_neq. model. The two upper panels show capture and emission times for different V_G conditions. The middle and lower panels show the simulated occupancy for various stress times, as well as the resulting occupancy extracted at t_stress = 2 s, compared to experimental data.

Fig. 3: Recoverable component, R, for various stress regimes. As can be seen, the NMP_neq. model (solid lines) properly represents the experimental trend (open circles), while the NMP_eq. model (dashed lines) fails to predict R.