Abstract:
Accurate standard cell modeling is significant for circuit timing analysis and yield estimation. With voltage decreasing to near-threshold, cell delay distribution become...Show MoreMetadata
Abstract:
Accurate standard cell modeling is significant for circuit timing analysis and yield estimation. With voltage decreasing to near-threshold, cell delay distribution becomes asymmetrical and has a longer tail due to various process variation effects. In this brief, we propose a novel statistical model to fit the shape of the cell delay by using log-extended-skew-normal (LESN) distribution. It estimates the values of mean, standard deviation, and 3\sigma delay precisely by matching the kurtosis of the cell delay distribution. By changing the parameters of the LESN model, it can be used for up to the normal voltage region (1.1V) and down to the sub-threshold voltage region (0.4V). Considering the effect of load capacitances, the parameters of LESN distribution are further modeled so that the model can be used for different fanout constraints. Tested by INV, NAND2, and NOR2 with 28 nm technology, the average error of estimating the skewness is less than 6%, while the error for the kurtosis is less than 4%. Meanwhile, the average errors of -3\sigma and +3\sigma delay estimation are about 1.27% and 1.82% from 0.4V to 1.1V, respectively.
Published in: IEEE Transactions on Circuits and Systems II: Express Briefs ( Volume: 69, Issue: 6, June 2022)
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- IEEE Keywords
- Index Terms
- Statistical Models ,
- Skewness ,
- Distribution Of Parameters ,
- Inductive Load ,
- Delay Estimation ,
- Delay Values ,
- Delay Distribution ,
- Kurtosis Of Distribution ,
- Voltage Region ,
- Normal Distribution ,
- Random Variables ,
- Monte Carlo Simulation ,
- Distribution Characteristics ,
- Log-likelihood ,
- Probability Density Function ,
- Low Voltage ,
- Shape Of Distribution ,
- Long Tail ,
- Lookup Table ,
- Tail Of Distribution ,
- Multivariate Adaptive Regression Splines ,
- Simple Scenario ,
- Supply Voltage ,
- SPICE Simulations ,
- Global Variables ,
- Skew-normal Distribution ,
- Drain Current ,
- Standard Deviation Of Distribution ,
- Technology Node ,
- Gaussian Random Variables
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Statistical Models ,
- Skewness ,
- Distribution Of Parameters ,
- Inductive Load ,
- Delay Estimation ,
- Delay Values ,
- Delay Distribution ,
- Kurtosis Of Distribution ,
- Voltage Region ,
- Normal Distribution ,
- Random Variables ,
- Monte Carlo Simulation ,
- Distribution Characteristics ,
- Log-likelihood ,
- Probability Density Function ,
- Low Voltage ,
- Shape Of Distribution ,
- Long Tail ,
- Lookup Table ,
- Tail Of Distribution ,
- Multivariate Adaptive Regression Splines ,
- Simple Scenario ,
- Supply Voltage ,
- SPICE Simulations ,
- Global Variables ,
- Skew-normal Distribution ,
- Drain Current ,
- Standard Deviation Of Distribution ,
- Technology Node ,
- Gaussian Random Variables
- Author Keywords