# NBTI and Power Reduction Using an Input Vector Control and Supply Voltage Assignment Method
## 1 Introduction
[PERSON] et al., proposed two kinds of gate replacement methods, and combined them with an IVC approach to reduce the leakage power and NBTI effect simultaneously [7]. [PERSON] et al., proposed a combination method of internal node control (INC) and IVC, and also proposed a linear-time heuristic that can quickly determine the near-optimal placements for INC selection [14]. [PERSON] et al. proposed a transmission gate (TG) insertion method, and applied an integer linear programming (ILP) formulation to select the location for TG insertion [15]. Experimental results have demonstrated that compared with IVC only, the above methods can improve the controllability of the state of the internal gates significantly, leading to better NBTI mitigation and leakage reduction. However, these methods will change the structure of the device and bring in extra power and area penalties. Recently, some kinds of adaptive method have been proposed to mitigate the aging effect of CMOS devices. These methods will adjust the working parameters of the devices, such as frequency, body bias voltage, and supply voltage, according to the aging rate. [PERSON] et al., proposed the use of adaptive body bias (ABB) and adaptive supply voltage (ASV) to guarantee the performance of a CMOS circuit. They also proposed a hybrid approach with ABB and synthesis to mitigate the aging effect [16]. [PERSON] et al., proposed a method to find a set of supply and body biasing voltage values, and apply them to circuit clusters in a standard cell-based design, which can minimize the total power consumption while satisfying the circuit performance requirement [17]. [PERSON] et al. proposed a scheduled voltage scaling technique, which increases the supply voltage gradually to compensate for NBTI-induced degradation [18]. In [19], the authors proposed an adaptive method to tune the parameters of a digital system, such as supply voltage and clock frequency, over its lifetime in the presence of circuit aging. They also proposed three kinds of control policies to tune the operating parameters of the system. [PERSON] et al., proposed a supply voltage assignment method to co-optimize power consumption and NBTI effect for the CMOS devices [10]. Among these methods, supply voltage assignment (SVA) is commonly used because of its easy implementation, and we also use SVA to compensate for NBTI-induced delay degradation in this paper. However, to our knowledge, no references have analyzed the impact of an input vector on the implementation process of the SVA method, and combined the SVA and IVC methods together to reduce the NBTI effect and power dissipation. As discussed before, SVA can effectively compensate for performance degradation by increasing the supply voltage (\(V_{dd}\)) of the circuit. However, a high \(V_{dd}\) will also result in an increase of power consumption, as well as an accelerated aging process. Because both the NBTI effect and leakage power are dependent on the input vector in standby mode, the circuit designer should find the optimal input vector that can reduce NBTI and leakage simultaneously. However, the impacts of the input vector on delay degradation and leakage power are not in a same direction; the optimal input vector for minimizing the postaging delay may not be the best one to minimize the leakage power and vice versa. In order to solve this problem, a novel NBTI and leakage co-optimization algorithm based on an ILP formulation is proposed in this paper. This method can consider these two issues simultaneously and find the optimal input vector that can provide a balanced tradeoff between performance and power. Then, the globally best input vector is used when the circuit is in standby mode, and SVA is applied as a subsequent method to further mitigate NBTI effect while reducing the power dissipation at the same time. The remainder of this paper is organized as follows. In Section 2, basic NBTI-induced delay degradation and power computation models are introduced.