Abstract: Various embodiments of a method and apparatus for determining parametric timing yield and bottlenecks are disclosed which take into account correlation between electrical circuit paths through common timing arcs of an integrated circuit chip under design. Monte Carlo samples of timing arc delays are generated and used in computing timing yield and identify yield bottlenecks.

Abstract: A system receives a circuit description and measures of intrinsic delay, intrinsic delay variation, transition time and transition time variation for each stage and determines stage delay variation of each stage. The system receives a circuit description and derate factors and determines an intrinsic delay standard deviation and a correlation coefficient. The system determines a stage delay variation of each stage based on the determined factors. The system receives parameters describing an asymmetric distribution of delay values and generates a normal distribution of delay values. The system receives measures of nominal transition time at an output and input of a wire, and transition time variation at the input of the wire and determines a transition time variation at the output of the wire. The system receives measures of an Elmore delay and a nominal delay of the wire and determines a delay variation at the output of the wire.

Abstract: A system receives a circuit description and measures of intrinsic delay, intrinsic delay variation, transition time and transition time variation for each stage and determines stage delay variation of each stage. The system receives a circuit description and derate factors and determines an intrinsic delay standard deviation and a correlation coefficient. The system determines a stage delay variation of each stage based on the determined factors. The system receives parameters describing an asymmetric distribution of delay values and generates a normal distribution of delay values. The system receives measures of nominal transition time at an output and input of a wire, and transition time variation at the input of the wire and determines a transition time variation at the output of the wire. The system receives measures of an Elmore delay and a nominal delay of the wire and determines a delay variation at the output of the wire.

Abstract: A system receives a circuit description and measures of intrinsic delay, intrinsic delay variation, transition time and transition time variation for each stage and determines stage delay variation of each stage. The system receives a circuit description and derate factors and determines an intrinsic delay standard deviation and a correlation coefficient. The system determines a stage delay variation of each stage based on the determined factors. The system receives parameters describing an asymmetric distribution of delay values and generates a normal distribution of delay values. The system receives measures of nominal transition time at an output and input of a wire, and transition time variation at the input of the wire and determines a transition time variation at the output of the wire. The system receives measures of an Elmore delay and a nominal delay of the wire and determines a delay variation at the output of the wire.

Abstract: An arrival time propagation method and system for statistical circuit analysis that uses a conjugation operation and a negation operation to determine and adjust arrival times in a circuit model and to determine path ordering in a circuit.

Abstract: A system receives a circuit description and measures of intrinsic delay, intrinsic delay variation, transition time and transition time variation for each stage and determines stage delay variation of each stage. The system receives a circuit description and derate factors and determines an intrinsic delay standard deviation and a correlation coefficient. The system determines a stage delay variation of each stage based on the determined factors. The system receives parameters describing an asymmetric distribution of delay values and generates a normal distribution of delay values. The system receives measures of nominal transition time at an output and input of a wire, and transition time variation at the input of the wire and determines a transition time variation at the output of the wire. The system receives measures of an Elmore delay and a nominal delay of the wire and determines a delay variation at the output of the wire.

Abstract: A system receives a circuit description and measures of intrinsic delay, intrinsic delay variation, transition time and transition time variation for each stage and determines stage delay variation of each stage. The system receives a circuit description and derate factors and determines an intrinsic delay standard deviation and a correlation coefficient. The system determines a stage delay variation of each stage based on the determined factors. The system receives parameters describing an asymmetric distribution of delay values and generates a normal distribution of delay values. The system receives measures of nominal transition time at an output and input of a wire, and transition time variation at the input of the wire and determines a transition time variation at the output of the wire. The system receives measures of an Elmore delay and a nominal delay of the wire and determines a delay variation at the output of the wire.

Abstract: A system receives a circuit description and measures of intrinsic delay, intrinsic delay variation, transition time and transition time variation for each stage and determines stage delay variation of each stage. The system receives a circuit description and derate factors and determines an intrinsic delay standard deviation and a correlation coefficient. The system determines a stage delay variation of each stage based on the determined factors. The system receives parameters describing an asymmetric distribution of delay values and generates a normal distribution of delay values. The system receives measures of nominal transition time at an output and input of a wire, and transition time variation at the input of the wire and determines a transition time variation at the output of the wire. The system receives measures of an Elmore delay and a nominal delay of the wire and determines a delay variation at the output of the wire.

Abstract: A system and a method are disclosed for performing static timing analysis. Information describing a distorted input waveform is received by a static timing analyzer. A transition time of the distorted input waveform is determined. Based on the determined input transition time a nominal input waveform and a corresponding nominal output waveform are received. An input waveform distortion is computed based on the nominal input waveform and the distorted input waveform. An output waveform distortion is computed based on an augmented circuit and the input waveform distortion. A distorted output waveform is computed based on the nominal output waveform and the output waveform distortion. The waveforms are represented using the distortion values which are smaller than the actual waveform values, thereby allowing for compact representation. A time-shifted version of an uncoupled input waveform is used to perform conservative timing analysis of circuits that accounts for crosstalk in the circuit.

Abstract: A system and a method are disclosed for performing static timing analysis. Information describing a distorted input waveform is received by a static timing analyzer. A transition time of the distorted input waveform is determined. Based on the determined input transition time a nominal input waveform and a corresponding nominal output waveform are received. An input waveform distortion is computed based on the nominal input waveform and the distorted input waveform. An output waveform distortion is computed based on an augmented circuit and the input waveform distortion. A distorted output waveform is computed based on the nominal output waveform and the output waveform distortion. The waveforms are represented using the distortion values which are smaller than the actual waveform values, thereby allowing for compact representation. A time-shifted version of an uncoupled input waveform is used to perform conservative timing analysis of circuits that accounts for crosstalk in the circuit.

Abstract: The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV.

Abstract: A dual-box location-based on-chip variation (DBLOCV) can be used in STA to significantly reduce pessimism. The DBLOCV analysis includes forming a backward bounding box and a forward bounding box for a cell of the design. A first intermediate maximum distance from the cell to corners of the backward bounding box can be calculated using the coordinates. A second intermediate maximum distance from the cell to corners of the forward bounding box can be calculated using the coordinates. A derate value can be determined from the derate table using the maximum distance of the first and second intermediate maximum distances. STA can be performed using the derate value. At least one timing report can be generated based on the STA.

Abstract: The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV.

Abstract: The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV.

Abstract: The electrical circuit timing method provides accurate nominal delay together with the delay sensitivities with respect to different circuit elements (e.g., cells, interconnects, etc.) and variational parameters (e.g., process variations; environmental variations). All the sensitivity computations are based on closed-form formulas; as a consequence, the method provides rapidly and at low cost high accuracy and high numerical stability.

Abstract: The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV.

Abstract: The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV.

Abstract: The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV.

Abstract: The electrical circuit timing method provides accurate nominal delay together with the delay sensitivities with respect to different circuit elements (e.g., cells, interconnects, etc.) and variational parameters (e.g., process variations; environmental variations). All the sensitivity computations are based on closed-form formulas; as a consequence, the method provides rapidly and at low cost high accuracy and high numerical stability.

Abstract: The electrical circuit timing method provides accurate nominal delay together with the delay sensitivities with respect to different circuit elements {e.g., cells, interconnects, etc.) and variational parameters (e.g., process variations; environmental variations). All the sensitivity computations are based on closed-form formulas; as a consequence, the method provides rapidly and at low cost high accuracy and high numerical stability.