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This dissertation reports on a new methodology to characterize and simulate a standard cell library to be used for statistical static timing analysis. A compact variation-aware timing model for a standard cell in a cell library has been developed. The model incorporates variations in the input waveform and loading, process parameters, and the environment into the cell timing model. Principal component analysis (PCA) has been used to form a compact model of a set of waveforms impacted by these sources of variation. Cell characterization involves determining equations describing how waveforms are transformed by a cell as a function of the input waveforms, process parameters, and the environment. Different versions of factorial designs and Latin hypercube sampling have been explored to model cells, and their complexity and accuracy have been compared. The models have been evaluated by calculating the delay of paths. The results demonstrate improved accuracy in comparison with table-based static timing analysis at comparable computational cost. Our methodology has been expanded to adapt to interconnect dominant circuits by including a resistive-capacitive load model. The results show the feasibility of using the new load model in our methodology. We have explored comprehensive accuracy improvement methods to tune the methodology for the best possible results. The following is a summary of the main contributions of this work to the statistical static timing analysis: (a) accurate waveform modeling for standard cells using statistical waveform models based on principal components; (b) compact performance modeling of standard cells using experimental design statistical techniques; and (c) variation-aware performance modeling of standard cells considering the effect of variation parameters on performance, where variation parameters include loading, waveform shape, process parameters (gate length and threshold voltage of NMOS and PMOS transistors), and environmental parameters (supply voltage and temperature); and (f) extending our methodology to support resistive-capacitive loads to be applicable to interconnect dominant circuits; and (e) classifying the sources of error for our variational waveform model and cell models and introducing of the related accuracy improvement methods; and (f) introducing our fast block-based variation-aware statistical dynamic timing analysis framework and showing that (i) using compiler-compiler techniques, we can generate our timing models, test benches, and data analysis for each circuit, which are compiled to machine-code to reduce the overhead of dynamic timing simulation, and (ii) using the simulation engine, we can perform statistical timing analysis to measure the performance distribution of a circuit using a high-level model for gate delay changes, which can be linked to their parameter variation.

Driven by the need for faster devices and higher transistor densities, technology trends have pushed transistor dimensions into the deep sub-micron regime. This continued scaling, however, has led to many challenges facing digital integrated circuits today. One important challenge is the increased variations in the underlying process and environmental parameters, and the significant impact of this variability on circuit timing and leakage power, making it increasingly difficult to design circuits that achieve a required specification. Given these challenges, there is a need for computer-aided design (CAD) techniques that can predict and analyze circuit performance (timing and leakage) accurately and efficiently in the presence of variability. This thesis presents new techniques for variation-aware timing and leakage analysis that address different aspects of the problem. First, on the timing front, a pre-placement statistical static timing analysis technique is presented. This technique can be applied at an early stage of design, when within-die correlations are still unknown. Next, a general parameterized static timing analysis framework is proposed, which supports a general class of nonlinear delay models and handles both random (process) parameters with arbitrary distributions and non-random (environmental) parameters. Following this, a parameterized static timing analysis technique is presented, which can capture circuit delay exactly at any point in the parameter space. This is enabled by identifying all potentially critical paths in the circuit through novel and efficient pruning algorithms that improve on the state of art both in theoretical complexity and runtime. Also on the timing front, a novel distance-based metric for robustness is proposed. This metric can be used to quantify the susceptibility of parameterized timing quantities to failure, thus enabling designers to fix the nodes with smallest robustness values in order to improve the overall design robustness. Finally, on the leakage front, a statistical technique for early-mode and late-mode leakage estimation is presented. The novelty lies in the random gate concept, which allows for efficient and accurate full-chip leakage estimation. In its simplest form, the leakage estimation reduces to finding the area under a scaled version of the within-die channel length auto-correlation function, which can be done in constant time.

Driven by the need for faster devices and higher transistor densities, technology trends have pushed transistor dimensions into the deep sub-micron regime. This continued scaling, however, has led to many challenges facing digital integrated circuits today. One important challenge is the increased variations in the underlying process and environmental parameters, and the significant impact of this variability on circuit timing and leakage power, making it increasingly difficult to design circuits that achieve a required specification. Given these challenges, there is a need for computer-aided design (CAD) techniques that can predict and analyze circuit performance (timing and leakage) accurately and efficiently in the presence of variability. This thesis presents new techniques for variation-aware timing and leakage analysis that address different aspects of the problem. First, on the timing front, a pre-placement statistical static timing analysis technique is presented. This technique can be applied at an early stage of design, when within-die correlations are still unknown. Next, a general parameterized static timing analysis framework is proposed, which supports a general class of nonlinear delay models and handles both random (process) parameters with arbitrary distributions and non-random (environmental) parameters. Following this, a parameterized static timing analysis technique is presented, which can capture circuit delay exactly at any point in the parameter space. This is enabled by identifying all potentially critical paths in the circuit through novel and efficient pruning algorithms that improve on the state of art both in theoretical complexity and runtime. Also on the timing front, a novel distance-based metric for robustness is proposed. This metric can be used to quantify the susceptibility of parameterized timing quantities to failure, thus enabling designers to fix the nodes with smallest robustness values in order to improve the overall design robustness. Finally, on the leakage front, a statistical technique for early-mode and late-mode leakage estimation is presented. The novelty lies in the random gate concept, which allows for efficient and accurate full-chip leakage estimation. In its simplest form, the leakage estimation reduces to finding the area under a scaled version of the within-die channel length auto-correlation function, which can be done in constant time.

With the importance of data security at its peak today, many reconfigurable systems are used to provide security. This protection is often provided by FPGA-based encrypt/decrypt cores secured with secret keys. Physical unclonable functions (PUFs) use random manufacturing variations to generate outputs that can be used in keys. These outputs are specific to a chip and can be used to create device-tied secret keys. Due to reliability issues with PUFs, key generation with PUFs typically requires error correction techniques. This can result in substantial hardware costs. Thus, the total cost of a $n$-bit key far exceeds just the cost of producing $n$ bits of PUF output. To tackle this problem, we propose the use of variation aware intra-FPGA PUF placement to reduce the area cost of PUF-based keys on FPGAs. We show that placing PUF instances according to the random variations of each chip instance reduces the bit error rate of the PUFs and the overall resources required to generate the key. Our approach has been demonstrated on a Xilinx Zynq-7000 programmable SoC using FPGA specific PUFs with code-offset error correction based on BCH codes. The approach is applicable to any PUF-based system implemented in reconfigurable logic. To evaluate our approach, we first analyze the key metrics of a PUF - reliability and uniqueness. Reliability is related to bit error rate, an important parameter with respect to error correction. In order to generate reliable results from the PUFs, a total of four ZedBoards containing FPGAs are used in our approach. We quantify the effectiveness of our approach by implementing the same key generation scheme using variation-aware and default placement, and show the resources saved by our approach.

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