Maximum IR-drop in On-Chip Power Distribution Networks of Wire-Bonded Integrated Circuits

A compact IR-drop model for on-chip power distribution networks in wire-bonded ICs is presented. Chip dimensions, metal coverage and piecewise distribution of the IC consumption are taken into account to obtain closed form expressions for the maximum IR-drop as well as its place. Comparison with simulations shows an error as small as 2% in most the cases.Postprint (published version

CAD Techniques for Robust FPGA Design Under Variability

The imperfections in the semiconductor fabrication process and uncertainty in operating environment of VLSI circuits have emerged as critical challenges for the semiconductor industry. These are generally termed as process and environment variations, which lead to uncertainty in performance and unreliable operation of the circuits. These problems have been further aggravated in scaled nanometer technologies due to increased process variations and reduced operating voltage. Several techniques have been proposed recently for designing digital VLSI circuits under variability. However, most of them have targeted ASICs and custom designs. The flexibility of reconfiguration and unknown end application in FPGAs make design under variability different for FPGAs compared to ASICs and custom designs, and the techniques proposed for ASICs and custom designs cannot be directly applied to FPGAs. An important design consideration is to minimize the modifications in architecture and circuit to reduce the cost of changing the existing FPGA architecture and circuit. The focus of this work can be divided into three principal categories, which are, improving timing yield under process variations, improving power yield under process variations and improving the voltage profile in the FPGA power grid. The work on timing yield improvement proposes routing architecture enhancements along with CAD techniques to improve the timing yield of FPGA designs. The work on power yield improvement for FPGAs selects a low power dual-Vdd FPGA design as the baseline FPGA architecture for developing power yield enhancement techniques. It proposes CAD techniques to improve the power yield of FPGAs. A mathematical programming technique is proposed to determine the parameters of the buffers in the interconnect such as the sizes of the transistors and threshold voltage of the transistors, all within constraints, such that the leakage variability is minimized under delay constraints. Two CAD techniques are investigated and proposed to improve the supply voltage profile of the power grids in FPGAs. The first technique is a place and route technique and the second technique is a logic clustering technique to reduce IR-drops and spatial variation of supply voltage in the power grid

Parametric Yield of VLSI Systems under Variability: Analysis and Design Solutions

Variability has become one of the vital challenges that the designers of integrated circuits encounter. variability becomes increasingly important. Imperfect manufacturing process manifest itself as variations in the design parameters. These variations and those in the operating environment of VLSI circuits result in unexpected changes in the timing, power, and reliability of the circuits. With scaling transistor dimensions, process and environmental variations become significantly important in the modern VLSI design. A smaller feature size means that the physical characteristics of a device are more prone to these unaccounted-for changes. To achieve a robust design, the random and systematic fluctuations in the manufacturing process and the variations in the environmental parameters should be analyzed and the impact on the parametric yield should be addressed. This thesis studies the challenges and comprises solutions for designing robust VLSI systems in the presence of variations. Initially, to get some insight into the system design under variability, the parametric yield is examined for a small circuit. Understanding the impact of variations on the yield at the circuit level is vital to accurately estimate and optimize the yield at the system granularity. Motivated by the observations and results, found at the circuit level, statistical analyses are performed, and solutions are proposed, at the system level of abstraction, to reduce the impact of the variations and increase the parametric yield. At the circuit level, the impact of the supply and threshold voltage variations on the parametric yield is discussed. Here, a design centering methodology is proposed to maximize the parametric yield and optimize the power-performance trade-off under variations. In addition, the scaling trend in the yield loss is studied. Also, some considerations for design centering in the current and future CMOS technologies are explored. The investigation, at the circuit level, suggests that the operating temperature significantly affects the parametric yield. In addition, the yield is very sensitive to the magnitude of the variations in supply and threshold voltage. Therefore, the spatial variations in process and environmental variations make it necessary to analyze the yield at a higher granularity. Here, temperature and voltage variations are mapped across the chip to accurately estimate the yield loss at the system level. At the system level, initially the impact of process-induced temperature variations on the power grid design is analyzed. Also, an efficient verification method is provided that ensures the robustness of the power grid in the presence of variations. Then, a statistical analysis of the timing yield is conducted, by taking into account both the process and environmental variations. By considering the statistical profile of the temperature and supply voltage, the process variations are mapped to the delay variations across a die. This ensures an accurate estimation of the timing yield. In addition, a method is proposed to accurately estimate the power yield considering process-induced temperature and supply voltage variations. This helps check the robustness of the circuits early in the design process. Lastly, design solutions are presented to reduce the power consumption and increase the timing yield under the variations. In the first solution, a guideline for floorplaning optimization in the presence of temperature variations is offered. Non-uniformity in the thermal profiles of integrated circuits is an issue that impacts the parametric yield and threatens chip reliability. Therefore, the correlation between the total power consumption and the temperature variations across a chip is examined. As a result, floorplanning guidelines are proposed that uses the correlation to efficiently optimize the chip's total power and takes into account the thermal uniformity. The second design solution provides an optimization methodology for assigning the power supply pads across the chip for maximizing the timing yield. A mixed-integer nonlinear programming (MINLP) optimization problem, subject to voltage drop and current constraint, is efficiently solved to find the optimum number and location of the pads