Compensation for Lithography Induced Process Variations during Physical Design

This dissertation addresses the challenge of designing robust integrated circuits in the deep sub micron regime in the presence of lithography process variability. By extending and combining existing process and circuit analysis techniques, flexible software frameworks are developed to provide detailed studies of circuit performance in the presence of lithography variations such as focus and exposure. Applications of these software frameworks to select circuits demonstrate the electrical impact of these variations and provide insight into variability aware compact models that capture the process dependent circuit behavior. These variability aware timing models abstract lithography variability from the process level to the circuit level and are used to estimate path level circuit performance with high accuracy with very little overhead in runtime.The Interconnect Variability Characterization (IVC) framework maps lithography induced geometrical variations at the interconnect level to electrical delay variations. This framework is applied to one dimensional repeater circuits patterned with both 90nm single patterning and 32nm double patterning technologies, under the presence of focus, exposure, and overlay variability. Studies indicate that single and double patterning layouts generally exhibit small variations in delay (between 1-3%) due to self compensating RC effects associated with dense layouts and overlay errors for layouts without self-compensating RC effects. The delay response of each double patterned interconnect structure is fit with a second order polynomial model with focus, exposure, and misalignment parameters with 12 coefficients and residuals of less than 0.1ps. The IVC framework is also applied to a repeater circuit with cascaded interconnect structures to emulate more complex layout scenarios, and it is observed that the variations on each segment average out to reduce the overall delay variation.The Standard Cell Variability Characterization (SCVC) framework advances existing layout-level lithography aware circuit analysis by extending it to cell-level applications utilizing a physically accurate approach that integrates process simulation, compact transistor models, and circuit simulation to characterize electrical cell behavior. This framework is applied to combinational and sequential cells in the Nangate 45nm Open Cell Library, and the timing response of these cells to lithography focus and exposure variations demonstrate Bossung like behavior. This behavior permits the process parameter dependent response to be captured in a nine term variability aware compact model based on Bossung fitting equations. For a two input NAND gate, the variability aware compact model captures the simulated response to an accuracy of 0.3%. The SCVC framework is also applied to investigate advanced process effects including misalignment and layout proximity.The abstraction of process variability from the layout level to the cell level opens up an entire new realm of circuit analysis and optimization and provides a foundation for path level variability analysis without the computationally expensive costs associated with joint process and circuit simulation. The SCVC framework is used with slight modification to illustrate the speedup and accuracy tradeoffs of using compact models. With variability aware compact models, the process dependent performance of a three stage logic circuit can be estimated to an accuracy of 0.7% with a speedup of over 50,000. Path level variability analysis also provides an accurate estimate (within 1%) of ring oscillator period in well under a second.Another significant advantage of variability aware compact models is that they can be easily incorporated into existing design methodologies for design optimization. This is demonstrated by applying cell swapping on a logic circuit to reduce the overall delay variability along a circuit path. By including these variability aware compact models in cell characterization libraries, design metrics such as circuit timing, power, area, and delay variability can be quickly assessed to optimize for the correct balance of all design metrics, including delay variability.Deterministic lithography variations can be easily captured using the variability aware compact models described in this dissertation. However, another prominent source of variability is random dopant fluctuations, which affect transistor threshold voltage and in turn circuit performance. The SCVC framework is utilized to investigate the interactions between deterministic lithography variations and random dopant fluctuations. Monte Carlo studies show that the output delay distribution in the presence of random dopant fluctuations is dependent on lithography focus and exposure conditions, with a 3.6 ps change in standard deviation across the focus exposure process window. This indicates that the electrical impact of random variations is dependent on systematic lithography variations, and this dependency should be included for precise analysis.