Date of Award


Publication Type


Degree Name



Electrical and Computer Engineering


Digital integrated circuits, Fast convergence, Linear time complexity, Signal reliability, Signal probability




J. Han



Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


As complementary metal–oxide–semiconductor (CMOS) devices shrink to nanoscale, digital integrated circuits (ICs) are more susceptible to various environmental parameters, such as temperature, supply voltage, wiring, noise, and fabrication process variations. This would reduce the circuit operation reliability (i.e., the probability that a circuit or component is performing its intended logic function). Signal probability (the probability that a digital signal is producing logic 1) is another factor that measures circuit’s dynamic behavior and power dissipation. Research shows that signal probability and reliability within ICs may interact with each other in a complicated way. Generally speaking, as signal probability changes due to input probability variations, so does the signal reliability, and vice versa. This motivates simultaneous evaluation of both for digital ICs towards their performance improvement. However, this evaluation could be a challenge especially for large-scale circuits, due to signal correlations caused by reconvergent fanouts within circuits. Out of two existing evaluation methods, i.e., numerical and analytical methods, the former can give high accuracy level at the cost of expensive computation, while the latter does exactly the opposite.

This thesis provides a hybrid solution by taking advantage of both numerical and analytical methods to achieve fast and accurate evaluation for signal probability and reliability for ICs (including both combinational and sequential circuits). First, we develop a categorization-based analytical model for combinational circuits to deal with a variety of signal correlations. For strongly correlated or independent cases, analytical solutions are applied for accurate results. For cases with moderate correlation strength, we use local bitstream simulations for fast estimation. Our simulation results show that the proposed method is hundreds of times faster than Monte-Carlo (MC) simulation, while keeping almost same level of accuracy.

We then extend the above method to sequential circuits (with finite-state-machine model) for probability and reliability evaluation. Since sequential circuits can be viewed as an unfolded network of combinational logic, our focus is on how both probability and reliability converge to a final stable state over a certain number of cycles/iterations. To improve the efficiency of this convergence process, we propose a two-step-convergence (TSC) model instead of using traditional step-size based convergence. Simulation results show that the proposed method speeds up the process by around 30% on average compared to traditional method while maintaining a high level of accuracy.

Finally, we study the impact of device aging on circuit reliability. After years of operation, CMOS (especially PMOS) devices would experience an increase in their threshold voltage, a phenomenon called Negative Bias Temperature Instability (NBTI). This aging effect leads to the increased gate delay with late arrival time of signals, making circuits temporally unreliable. Threshold voltage changes may also negatively affect the probability that transistors perform intended logical operations, causing them spatially more unreliable. Our investigation focuses on evaluation of the overall reliability at circuit-level by considering both spatial (solely considering the correctness of signal logic values) and temporal (considering the signal arrival time to catch up sampling action) aspects of it. This would help circuit designers predict the circuit lifetime. Simulations on benchmark circuits show that the reliability degradation rate due to aging effect ranges from 1.5% to 8.2% over one-year period, depending on specific circuits.