Statistical analysis of BTI in the presence of process-induced voltage and temperature variations

In nano-scale regime, there are various sources of uncertainty and unpredictability of VLSI designs such as transistor aging mainly due to Bias Temperature Instability (BTI) as well as Process-Voltage-Temperature (PVT) variations. BTI exponentially varies by temperature and the actual supply voltage seen by the transistors within the chip which are functions of leakage power. Leakage power is strongly impacted by PVT and BTI which in turn results in thermal-voltage variations. Hence, neglecting one or some of these aspects can lead to a considerable inaccuracy in the estimated BTI-induced delay degradation. However, a holistic approach to tackle all these issues and their interdependence is missing. In this paper, we develop an analytical model to predict the probability density function and covariance of temperatures and voltage droops of a die in the presence of the BTI and process variation. Based on this model, we propose a statistical method that characterizes the life-time of the circuit affected by BTI in the presence of process-induced temperature-voltage variations. We observe that for benchmark circuits, treating each aspect independently and ignoring their intrinsic interactions results in 16% over-design, translating to unnecessary yield and performance loss.