## Graduation Year

2015

## Document Type

Dissertation

## Degree

Ph.D.

## Degree Name

Doctor of Philosophy (Ph.D.)

## Degree Granting Department

Computer Science and Engineering

## Major Professor

Srinivas Katkoori, Ph.D.

## Committee Member

Nagarajan Ranganathan, Ph.D.

## Committee Member

Hao Zheng, Ph.D.

## Committee Member

Bibiche Geuskens, Ph.D.

## Committee Member

Sanjukta Bhanja, Ph.D.

## Committee Member

Gregory McColm, Ph.D.

## Keywords

Low Power, IC Reliability, Self Similarity, Simulated Annealing, Interval Propagation

## Abstract

The rising power demands and cost motivates us to explore low power solutions in electronics. In nanometer Complementary Metal Oxide Semiconductor (CMOS) processes with low threshold voltages and thin gate oxides, subthreshold leakage power dominates total power of a circuit. As technology scales, Negative Bias Temperature Instability (NBTI) emerged as a major limiting reliability mechanism. It causes a threshold voltage shift which, over time, results in circuit performance degradation. Hence, leakage power and NBTI degradation are two key challenges in deep sub micron regime.

In this dissertation, interval arithmetic based interval propagation technique is introduced as an effective leakage optimization technique in high level circuits with little overhead. The concept of self similarity from fractal theory is adopted for the first time in VLSI research to handle large design space. Though there are some leakage and NBTI co-optimization techniques in literature, our vector cycling approach combined with a back tracking algorithm have achieved better results for ISCAS85 benchmarks. We did not find any previous research works on NBTI optimization of finite state machines (FSMs). The optimization techniques of NBTI optimization in FSMs is introduced in this dissertation as well and substantial NBTI optimization is reported.

Input vector control has been shown to be an effective technique to minimize subthreshold leakage. Applying appropriate minimum leakage vector (MLV) to each register transfer level (RTL) module instance results in a low leakage state with significant area overhead. For each module, via Monte Carlo simulation, we identify a set of MLV intervals such that maximum leakage is within (say) 10% of the lowest leakage points. As the module bit width increases, exhaustive simulation to find the low leakage vector is not feasible. Further, we need to search the entire input space uniformly to obtain as many low leakage intervals as possible. Based on empirical observations, we observed self similarity in the leakage distribution of adder/multiplier modules when input space is partitioned into smaller cells. This property enables uniform search of low leakage vectors in the entire input space. Also, the time taken for characterization increases linearly with the module size. Hence, this technique is scalable to higher bit width modules with acceptable characterization time. We can reduce area overhead (in some cases to 0) by choosing Primary Input (PI) MLVs such that resultant inputs to internal nodes are also MLVs. Otherwise, control points can be inserted. Based on interval arithmetic, given a DFG, we propose a heuristic with several variations for PI MLV identification with minimal control points. Experimental results for DSP filters simulated in 16nm technology demonstrated leakage savings of 93.8% with no area overhead, compared to existing work.

Input vector control can also be adopted to reduce NBTI degradation as well as leakage in CMOS circuits. In the prior work, it is shown that minimum leakage vector of a circuit is not necessarily NBTI friendly. In order to achieve NBTI and leakage co-optimization, we propose an input vector cycling technique which applies different sub-optimal low leakage vectors to primary inputs at regular intervals. A co-optimal input vector for a given circuit is obtained by using simulated annealing (SA) technique. For a given input vector, a set of critical path PMOS transistors are under stress. A second input vector is obtained using a back tracking algorithm such that most of the critical path PMOS transistors are put in recovery mode. When a co-optimized input vector is assigned to primary input, critical path nodes under stress with high delay contribution are set to recovery. Logic 1 is back propagated from the nodes to the primary inputs to obtain the second input vector. These two vectors are alternated at regular time intervals. The total stress is evenly distributed among transistor sets of two vectors, as the intersection of the two sets is minimized. Hence, the overall stress on critical path transistors is alleviated, thereby reducing the NBTI delay degradation. For ISCAS85 benchmarks, an average of 5.3% improvement is achieved in performance degradation at 3.3% leakage overhead with NBTI-leakage co-optimization with a back tracking algorithm compared to solely using co-optimization. A 10.5% average NBTI improvement is obtained when compared to circuit with minimum leakage input vector for 18% average leakage overhead. Also, an average NBTI improvement of 2.13% is obtained with 6.77% leakage improvement when compared to circuit with minimum NBTI vector. Vector cycling is shown to be more eﬀective in mitigating NBTI over input vector control.

Several works in the literature have proposed optimal state encoding techniques for delay, leakage, and dynamic power optimization. In this work, we propose, for the first time, NBTI optimization based on state code optimization. We propose a SA based state code assignment algorithm, resulting in minimization of NBTI degradation in the synthesized circuit. A PMOS transistor when switched ON for a long period of time, will lead to delay degradation due to NBTI. Therefore, in combinational circuits, an NBTI friendly input vector that stresses the least number of PMOS transistors on the critical path can be applied. For sequential circuits, the state code can significantly influence the ON/OFF mode of PMOS transistors in the controller implementation. Therefore, we propose to focus on state encoding. As the problem is computational intractable, we will focus on encoding states with high state probability. The following SA moves are employed: (a) code swap; and (b) code modification by flipping bits. Experiments with LGSYNTH93 benchmarks resulted in 18.6% improvement in NBTI degradation on average with area and power improvements of 5.5% and 4.6% respectively.

## Scholar Commons Citation

Pendyala, Shilpa, "Synthesis Techniques for Sub-threshold Leakage and NBTI Optimization in Digital VLSI Systems" (2015). *USF Tampa Graduate Theses and Dissertations.*

https://digitalcommons.usf.edu/etd/6012