Transistor/gate level reliability modeling - Liu, Xu (2019)
The development of CMOS technology is a double-edged sword: for one thing, it provides faster,lowerpower-consuming,and smaller-size devices; for another,reliability issues such as Negative Bias Temperature Instability (NBTI) and Hot Carrier Injection (HCI) become severer, resulting in device/gate performance degradation. Compact and accurate modelling of these issues is equired in aid of IC design. Reliability modelling could be done at the transistor level: the device parameter shift ∆p(such as the threshold voltage ∆Vth) or performance (for example, the current Ion) shift are described as time-related (tstress) functions. At the gate level, the delay degradation is obtained with the insertion of the transistor-level parameter/performance shift equations. The timing analysis at the gate level is done with methods such as the static timing analysis (STA) rather than the time-consuming SPICE simulation, but the latter could be adopted for characterisation owing to its accuracy. The reliability models at the transistor level and the gate level interact with each other: the gate level model takes ∆p as an input, which must be derived from the transistor level model; the transistor level model determines ∆p with the value of tstress, which is a statistical parameter in the gate level model. The models achieve three goals: simplicity, time efﬁciency, and accuracy. The gate model called ”Aging-Gate” has been built up to take both NBTI ( ∆Vth) and HCI ( ∆Ion) into account; algorithms for tstress determination could be adopted for transistor level modelling. To simplify this model, HCI is also modelled with ∆Vth such that the gate model equations could be simpliﬁed. A surface-potential (øs)-based transistor model is also available, and tstress is to be incorporated in for ∆Vth determination. The so called ”recovery effect” in NBTI results in iterative methods that suffer from time-efﬁciency problems. The new model provides a compact algorithm that achieves equivalent accuracy, which signiﬁcantly improves the time efﬁciency. To ensure the efﬁciency, the original Aging-Gate model ignores the recovery effect by adopting a simple DC NBTI model, but this leads to overestimation of the delay degradation. The new model alleviates this since the "recovery effect" is considered, yet the time efﬁciency is maintained in that the new model is as fast as the DC model. Therefore, the accuracy is improved.