Architectural level delay and leakage power modelling of manufacturing process variation

PhD ThesisThe effect of manufacturing process variations has become a major issue regarding the estimation of circuit delay and power dissipation, and will gain more importance in the future as device scaling continues in order to satisfy market place demands for circuits with greater performance and functionality per unit area. Statistical modelling and analysis approaches have been widely used to reflect the effects of a variety of variational process parameters on system performance factor which will be described as probability density functions (PDFs). At present most of the investigations into statistical models has been limited to small circuits such as a logic gate. However, the massive size of present day electronic systems precludes the use of design techniques which consider a system to comprise these basic gates, as this level of design is very inefficient and error prone. This thesis proposes a methodology to bring the effects of process variation from transistor level up to architectural level in terms of circuit delay and leakage power dissipation. Using a first order canonical model and statistical analysis approach, a statistical cell library has been built which comprises not only the basic gate cell models, but also more complex functional blocks such as registers, FIFOs, counters, ALUs etc. Furthermore, other sensitive factors to the overall system performance, such as input signal slope, output load capacitance, different signal switching cases and transition types are also taken into account for each cell in the library, which makes it adaptive to an incremental circuit design. The proposed methodology enables an efficient analysis of process variation effects on system performance with significantly reduced computation time compared to the Monte Carlo simulation approach. As a demonstration vehicle for this technique, the delay and leakage power distributions of a 2-stage asynchronous micropipeline circuit has been simulated using this cell library. The experimental results show that the proposed method can predict the delay and leakage power distribution with less than 5% error and at least 50,000 times faster computation time compare to 5000-sample SPICE based Monte Carlo simulation. The methodology presented here for modelling process variability plays a significant role in Design for Manufacturability (DFM) by quantifying the direct impact of process variations on system performance. The advantages of being able to undertake this analysis at a high level of abstraction and thus early in the design cycle are two fold. First, if the predicted effects of process variation render the circuit performance to be outwith specification, design modifications can be readily incorporated to rectify the situation. Second, knowing what the acceptable limits of process variation are to maintain design performance within its specification, informed choices can be made regarding the implementation technology and manufacturer selected to fabricate the design

Fault modeling, delay evaluation and path selection for delay test under process variation in nano-scale VLSI circuits

Delay test in nano-scale VLSI circuits becomes more difficult with shrinking technology feature sizes and rising clock frequencies. In this dissertation, we study three challenging issues in delay test: fault modeling, variational delay evaluation and path selection under process variation. Previous research of fault modeling on resistive spot defects, such as resistive opens and bridges in the interconnect, and resistive shorts in devices, lacked an accurate fault model. As a result it was difficult to perform fault simulation and select the best vectors. Conventional methods to compute variational delay under process variation are either slow or inaccurate. On the problem of path selection under process variation, previous approaches either choose too many paths, or missed the path that is necessary to be tested. We present new solutions in this dissertation. A new fault model that clearly and comprehensively expresses the relationship between electrical behaviors and resistive spots is proposed. Then the effect of process variations on path delays is modeled with a linear function and a fast method to compute coefficients of the linear function is also derived. Finally, we present the new path pruning algorithms that efficiently prune unimportant paths for test, and as a result we select as few as possible paths for test while the fault coverage is satisfied. The experimental results show that the new solutions are efficient and accurate

Fault simulation and test generation for small delay faults

Delay faults are an increasingly important test challenge. Traditional delay fault models are incomplete in that they model only a subset of delay defect behaviors. To solve this problem, a more realistic delay fault model has been developed which models delay faults caused by the combination of spot defects and parametric process variation. According to the new model, a realistic delay fault coverage metric has been developed. Traditional path delay fault coverage metrics result in unrealistically low fault coverage, and the real test quality is not reflected. The new metric uses a statistical approach and the simulation based fault coverage is consistent with silicon data. Fast simulation algorithms are also included in this dissertation. The new metric suggests that testing the K longest paths per gate (KLPG) has high detection probability for small delay faults under process variation. In this dissertation, a novel automatic test pattern generation (ATPG) methodology to find the K longest testable paths through each gate for both combinational and sequential circuits is presented. Many techniques are used to reduce search space and CPU time significantly. Experimental results show that this methodology is efficient and able to handle circuits with an exponential number of paths, such as ISCAS85 benchmark circuit c6288. The ATPG methodology has been implemented on industrial designs. Speed binning has been done on many devices and silicon data has shown significant benefit of the KLPG test, compared to several traditional delay test approaches

Max Operation in Statistical Static Timing Analysis on the Non-Gaussian Variation Sources for VLSI Circuits

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