Award Date


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering

First Committee Member

Yingtao Jiang

Second Committee Member

Biswajit Das

Third Committee Member

Mei Yang

Fourth Committee Member

Hui Zhao

Number of Pages



As CMOS technology continues to scale down, process variation introduces significant uncertainty in power and performance to VLSI circuits and significantly affects their reliability. If this uncertainty is not properly handled, it may become the bottleneck of CMOS technology improvement. As a result, deterministic analysis is no longer conservative and may result in either overestimation or underestimation of the circuit delay. As we know that Static-Timing Analysis (STA) is a deterministic way of computing the delay imposed by the circuits design and layout. It is based on a predetermined set of possible events of process variations, also called corners of the circuit. Although it is an excellent tool, current trends in process scaling have imposed significant difficulties to STA. Therefore, there is a need for another tool, which can resolve the aforementioned problems, and Statistical Static Timing Analysis (SSTA) has become the frontier research topic in recent years in combating such variation effects.

There are two types of SSTA methods, path-based SSTA and block-based SSTA. The goal of SSTA is to parameterize timing characteristics of the timing graph as a function of the underlying sources of process parameters that are modeled as random variables. By performing SSTA, designers can obtain the timing distribution (yield) and its sensitivity to various process parameters. Such information is of tremendous value for both timing sign-off and design optimization for robustness and high profit margins. The block-based SSTA is the most efficient SSTA method in recent years. In block-based SSTA, there are two major atomic operations max and add. The add operation is simple; however, the max operation is much more complex.

There are two main challenges in SSTA. The Topological Correlation that emerges from reconvergent paths, these are the ones that originate from a common node and then converge again at another node (reconvergent node). Such correlation complicates the maximum operation. The second challenge is the Spatial Correlation. It arises due to device proximity on the die and gives rise to the problems of modeling delay and arrival time.

This dissertation presents statistical Nonlinear and Nonnormals canonical form of timing delay model considering process variation. This dissertation is focusing on four aspects: (1) Statistical timing modeling and analysis; (2) High level circuit synthesis with system level statistical static timing analysis; (3) Architectural implementations of the atomic operations (max and add); and (4) Design methodology.

To perform statistical timing modeling and analysis, we first present an efficient and accurate statistical static timing analysis (SSTA) flow for non-linear cell delay model with non-Gaussian variation sources.

To achieve system level SSTA we apply statistical timing analysis to high-level synthesis flow, and develop yield driven synthesis framework so that the impact of process variations is taken into account during high-level synthesis.

To accomplish architectural implementation, we present the vector thread architecture for max operator to minimize delay and variation. Finally, we present comparison analysis with ISCAS benchmark circuits suites.

In the last part of this dissertation, a SSTA design methodology is presented.


Integrated circuits – Very large scale integration; Metal oxide semiconductors, Complementary; Process variations; SSTA; Statistical static timing analysis; VLSI


Electrical and Computer Engineering | Electronic Devices and Semiconductor Manufacturing | Signal Processing | VLSI and Circuits, Embedded and Hardware Systems