Timing uncertainty in 3-D clock trees due to process variations and power supply noise

Clock distribution networks are affected by different sources of variations. The resulting clock uncertainty significantly affects the frequency of a circuit. To support this analysis, a statistical model of skitter, which consists of clock skew and jitter, for 3-D clock trees is introduced. The effect of skitter on both the setup and hold time slacks is modeled. The variation of skitter is shown to be underestimated up to 36% if process variations and dynamic power supply noise are considered separately, which highlights the importance of this unified treatment. Potential scenarios of supply noise in 3-D integrated circuits (ICs) are investigated. 3-D circuits generated from industrial benchmarks are simulated to show the skitter under these scenarios. The mean and standard deviation of skitter can vary up to 60% and 51%, respectively, due to the different amplitudes and phases of supply noise. The tradeoff between skitter and the power consumed by clock trees is also shown. A set of guidelines are presented to decrease skitter in 3-D ICs. By applying these guidelines to industrial benchmarks, simulations show a decrease in the mean skitter up to 31%

Exploiting robustness in asynchronous circuits to design fine-tunable systems

PhD ThesisRobustness property in a circuit defines its tolerance to the effects of process, voltage and temperature variations. The mode signaling and event communication between computing units in a asynchronous circuits makes them inherently robust. The level of robustness depends on the type of delay assumptions used in the design and specification process. In this thesis, two approaches to exploiting robustness in asynchronous circuits to design self-adapting and fine-tunable systems are investigated. In the first investigation, a Digitally Controllable Oscillator (DCO) and a computing unit are integrated such that the operating conditions of the computing unit modulated the operation of the DCO. In this investigation, the computing unit which is a self-timed counter interacts with the DCO in a four-phase handshake protocol. This mode of interaction ensures a DCO and computing unit system that can fine-tune its operation to adapt to the effects of variations. In this investigation, it is shown that such a system will operate correctly in wide range of voltage supply. In the second investigation, a Digital Pulse-Width Modulator (DPWM) with coarse and fine-tune controls is designed using two Kessels counters. The coarse control of the DPWM tuned the pulse ratio and pulse frequency while the fine-tune control exploited the robustness property of asynchronous circuits in an addition-based delay system to add or subtract delay(s) to the pulse width while maintaining a constant pulse frequency. The DPWM realized gave constant duty ratio regardless of the operating voltage. This type of DPWM has practical application in a DC-DC converter circuit to tune the output voltage of the converter in high resolution. The Kessels counter is a loadable self-timed modulo−n counter, which is realized by decomposition using Horner’s method, specified and verified using formal asynchronous design techniques. The decomposition method used introduced parallelism in the system by dividing the counter into a systolic array of cells, with each cell further decomposed into two parts that have distinct defined operations. Specification of the decomposed counter cell parts operation was in three stages. The first stage employed high-level specification using Labelled Petri nets (LPN). In this form, functional correctness of the decomposed counter is modelled and verified. In the second stage, a cell part is specified by combing all possible operations for that cell part in high-level form. With this approach, a combination of inputs from a defined control block activated the correct operation for a cell part. In the final stage, the LPNs were converted to Signal Transition Graphs, from which the logic circuits of the cells were synthesized using the WorkCraft Tool. In this thesis, the Kessels counter was implemented and fabricated in 350 nm CMOS Technology.Niger Delta Development Commission (NDD

Circuit Design, Architecture and CAD for RRAM-based FPGAs

Field Programmable Gate Arrays (FPGAs) have been indispensable components of embedded systems and datacenter infrastructures. However, energy efficiency of FPGAs has become a hard barrier preventing their expansion to more application contexts, due to two physical limitations: (1) The massive usage of routing multiplexers causes delay and power overheads as compared to ASICs. To reduce their power consumption, FPGAs have to operate at low supply voltage but sacrifice performance because the transistors drive degrade when working voltage decreases. (2) Using volatile memory technology forces FPGAs to lose configurations when powered off and to be reconfigured at each power on. Resistive Random Access Memories (RRAMs) have strong potentials in overcoming the physical limitations of conventional FPGAs. First of all, RRAMs grant FPGAs non-volatility, enabling FPGAs to be "Normally powered off, Instantly powered on". Second, by combining functionality of memory and pass-gate logic in one unique device, RRAMs can greatly reduce area and delay of routing elements. Third, when RRAMs are embedded into datpaths, the performance of circuits can be independent from their working voltage, beyond the limitations of CMOS circuits. However, researches and development of RRAM-based FPGAs are in their infancy. Most of area and performance predictions were achieved without solid circuit-level simulations and sophisticated Computer Aided Design (CAD) tools, causing the predicted improvements to be less convincing. In this thesis,we present high-performance and low-power RRAM-based FPGAs fromtransistorlevel circuit designs to architecture-level optimizations and CAD tools, using theoretical analysis, industrial electrical simulators and novel CAD tools. We believe that this is the first systematic study in the field, covering: From a circuit design perspective, we propose efficient RRAM-based programming circuits and routing multiplexers through both theoretical analysis and electrical simulations. The proposed 4T(ransitor)1R(RAM) programming structure demonstrates significant improvements in programming current, when compared to most popular 2T1R programming structure. 4T1R-based routingmultiplexer designs are proposed by considering various physical design parasitics, such as intrinsic capacitance of RRAMs and wells doping organization. The proposed 4T1R-based multiplexers outperformbest CMOS implementations significantly in area, delay and power at both nominal and near-Vt regime. From a CAD perspective, we develop a generic FPGA architecture exploration tool, FPGASPICE, modeling a full FPGA fabric with SPICE and Verilog netlists. FPGA-SPICE provides different levels of testbenches and techniques to split large SPICE netlists, in order to obtain better trade-off between simulation time and accuracy. FPGA-SPICE can capture area and power characteristics of SRAM-based and RRAM-based FPGAs more accurately than the currently best analyticalmodels. From an architecture perspective, we propose architecture-level optimizations for RRAMbased FPGAs and quantify their minimumrequirements for RRAM devices. Compared to the best SRAM-based FPGAs, an optimized RRAM-based FPGA architecture brings significant reduction in area, delay and power respectively. In particular, RRAM-based FPGAs operating in the near-Vt regime demonstrate a 5x power improvement without delay overhead as compared to optimized SRAM-based FPGA operating at nominal working voltage