## Projection-based performance modeling for inter/intra-die variations (2005)

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Venue: | in Proc. IEEE/ACM Int. Conf. Comput.-Aided Des., 2005 |

Citations: | 17 - 10 self |

### BibTeX

@INPROCEEDINGS{Li05projection-basedperformance,

author = {Xin Li and Jiayong Le and Lawrence T. Pileggi and Andrzej Strojwas},

title = {Projection-based performance modeling for inter/intra-die variations},

booktitle = {in Proc. IEEE/ACM Int. Conf. Comput.-Aided Des., 2005},

year = {2005},

pages = {721--727}

}

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### Abstract

Large-scale process fluctuations in nano-scale IC technologies suggest applying high-order (e.g., quadratic) response surface models to capture the circuit performance variations. Fitting such models requires significantly more simulation samples and solving much larger linear equations. In this paper, we propose a novel projection-based extraction approach, PROBE, to efficiently create quadratic response surface models and capture both interdie and intra-die variations with affordable computation cost. PROBE applies a novel projection scheme to reduce the response surface modeling cost (i.e., both the required number of samples and the linear equation size) and make the modeling problem tractable even for large problem sizes. In addition, a new implicit power iteration algorithm is developed to find the optimal projection space and solve for the unknown model coefficients. Several circuit examples from both digital and analog circuit modeling applications demonstrate that PROBE can generate accurate response surface models while achieving up to 12x speedup compared with the traditional methods. 1.

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Citation Context ...ing several circuit examples. For each example, two independent sampling sets, called training set and testing set respectively, are generated. The training set is created by Latin hypercube sampling =-=[12]-=-, which picks the most important samples based on statistical analysis; this is used for coefficient fitting. For testing and comparison, we collect 500 random samples as the testing set and use them ... |

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Citation Context ...etermined linear equation. 3.3 Comparison with Traditional Techniques There are several traditional techniques, such as principal component analysis [9], variable screening [10] or projection pursuit =-=[11]-=-, which aim to reduce the computation cost of response surface modeling. In this subsection, we compare PROBE with these traditional techniques and highlight their differences. Principal component ana... |

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Citation Context ...iations to ensure manufacturability and improve yield has been identified as a top priority for today’s IC design problems. In order to address this process variation problem, response surface models =-=[3]-=- are utilized to capture the circuit performance variations caused by manufacturing fluctuations. The objective of response surface modeling is to approximate the circuit performance (e.g., delay, gai... |

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Citation Context ...has a fitting cost of O(N 6 ) for solving the overdetermined linear equation. 3.3 Comparison with Traditional Techniques There are several traditional techniques, such as principal component analysis =-=[9]-=-, variable screening [10] or projection pursuit [11], which aim to reduce the computation cost of response surface modeling. In this subsection, we compare PROBE with these traditional techniques and ... |

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Citation Context ...ods. 1. Introduction As IC technologies scale to finer feature sizes, it becomes increasingly difficult to control the relative process variations, particularly due to sub-wavelength photolithography =-=[1]-=--[2]. The increasing fluctuations in manufacturing process have introduced unavoidable and significant uncertainty in circuit performance. Hence, modeling and analyzing these random process variations... |

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Citation Context ...on can reach ±35% in nano-scale technologies. This, in turn, implies the importance of applying high-order (e.g., quadratic) response surface models to guarantee high approximation accuracy [3], [6], =-=[7]-=-. Applying nonlinear response surface models is especially important for analog circuits, since many analog performances (e.g., offset voltage) can be strongly nonlinear in the presence of large-scale... |

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Citation Context ... 1. Introduction As IC technologies scale to finer feature sizes, it becomes increasingly difficult to control the relative process variations, particularly due to sub-wavelength photolithography [1]-=-=[2]-=-. The increasing fluctuations in manufacturing process have introduced unavoidable and significant uncertainty in circuit performance. Hence, modeling and analyzing these random process variations to ... |

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Citation Context ...of variational process parameters (e.g., VTH, TOX). These models are extensively applied in many applications such as statistical timing analysis [1], analog mismatch analysis [4], yield optimization =-=[5]-=--[6], etc. Most of the previous response surface models, e.g., [1], utilize linear approximations, which are efficient and accurate when process variations are sufficiently small. However, two recent ... |

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Citation Context ...ariational process parameters (e.g., VTH, TOX). These models are extensively applied in many applications such as statistical timing analysis [1], analog mismatch analysis [4], yield optimization [5]-=-=[6]-=-, etc. Most of the previous response surface models, e.g., [1], utilize linear approximations, which are efficient and accurate when process variations are sufficiently small. However, two recent chan... |

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Citation Context ...N 6 ) for solving the overdetermined linear equation. 3.3 Comparison with Traditional Techniques There are several traditional techniques, such as principal component analysis [9], variable screening =-=[10]-=- or projection pursuit [11], which aim to reduce the computation cost of response surface modeling. In this subsection, we compare PROBE with these traditional techniques and highlight their differenc... |