## Statistical Performance Modeling and Optimization

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Citations: | 8 - 5 self |

### BibTeX

@MISC{Li_statisticalperformance,

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

title = {Statistical Performance Modeling and Optimization},

year = {}

}

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### Abstract

As IC technologies scale to finer feature sizes, it becomes increasingly difficult to control the relative process variations. The increasing fluctuations in manufacturing processes have introduced unavoidable and significant uncertainty in circuit performance; hence ensuring manufacturability has been identified as one of the top priorities of today’s IC design problems. In this paper, we review various statistical methodologies that have been recently developed to model, analyze, and optimize performance variations at both transistor level and system level. The following topics will be discussed in detail: sources of process variations, variation characterization and modeling, Monte Carlo analysis, response surface modeling, statistical timing and leakage analysis, probability distribution extraction, parametric yield estimation and robust IC optimization. These techniques provide the necessary CAD infrastructure that facilitates the bold move from deterministic, corner-based IC design toward statistical and probabilistic design. 1

### Citations

49 |
Robust Extraction of Spatial Correlation
- Xiong, Zolotov, et al.
(Show Context)
Citation Context ...istance. Discontinuity will appear at the boundary of every individual region. Most recently, several techniques have been proposed to address the aforementioned discontinuity problem. The authors in =-=[119]-=- proposed an efficient numerical algorithm to extract the spatial correlation function based on measurement data. The correlation extraction is formulated as a nonlinear optimization problem that can ... |

28 | Correlation-preserved non-Gaussian statistical timing analysis with quadratic timing model
- Zhang, Chen, et al.
(Show Context)
Citation Context ... various parametric yield estimation problems. 3.3.2 Convolution-Based Probability Extraction In addition to APEX, an alternative approach for probability extraction is based on numerical convolution =-=[125]-=-. In this sub-section, we first show the mathematic formulation of the convolution-based technique, and then compare these two methods (i.e., APEX vs. convolution) in Section 3.3.2.2. 3.3.2.1 Mathemat... |

14 | Criticality Computation in Parameterized Statistical Timing. ACM/IEEE international workshop on timing issues in the specification and synthesis of digital systems (TAU
- Xiong, Zolotov, et al.
- 2006
(Show Context)
Citation Context ... an arc sits on the critical path. The path sensitivity and the arc sensitivity discussed in this sub-section are theoretically equivalent to the path criticality and the edge criticality proposed in =-=[115, 120]-=-. More details on path criticality and edge criticality can be found in Section 4.3.s4.2 Statistical Timing Sensitivity Analysis 443 4.2.1 Statistics of Slack and Critical Path We first give a compreh... |

12 |
An efficient yield optimization method using a two step linear approximation of circuit performance
- Wang, Director
- 1994
(Show Context)
Citation Context ...wn in Figure 3.19.s414 Transistor-Level Statistical Methodologies Most statistical transistor-level optimization techniques can be classified into four broad categories: (1) direct yield optimization =-=[29, 30, 97, 116]-=-, (2) worst-case optimization [24, 28, 51, 58], (3) design centering [1, 6, 99, 117], and (4) infinite programming [67, 122]. The direct yield optimization methods [29, 30, 97, 116] search the design ... |

11 |
Ellipsoidal method for design centering and yield estimation
- Wojciechowski, Vlach
- 1993
(Show Context)
Citation Context ...b)) and then integrate the multi-dimensional probability density function over the approximated ellipsoid. Such an ellipsoid approximation has been widely used in both analog and digital applications =-=[1, 6, 45, 99, 117]-=-. Next, we will discuss the ellipsoid approximation technique in detail.s404 Transistor-Level Statistical Methodologies x 1 x 2 (a) (b) Fig. 3.17 Approximate the feasible space by an ellipsoid for par... |

8 |
Optimization with ellipsoidal uncertainty for robust analog IC design
- Xu, Hsiung, et al.
(Show Context)
Citation Context ...lassified into four broad categories: (1) direct yield optimization [29, 30, 97, 116], (2) worst-case optimization [24, 28, 51, 58], (3) design centering [1, 6, 99, 117], and (4) infinite programming =-=[67, 122]-=-. The direct yield optimization methods [29, 30, 97, 116] search the design space and estimate the parametric yield for each design point by either numerical integration or Monte Carlo analysis. The d... |

4 |
The mask error factor in optical lithography
- Wong, Ferguson, et al.
- 2000
(Show Context)
Citation Context ...ng) can cause focus variations. Illumination performance is mainly related to the polarization control of the laser. As shown in Figure 2.1, mask errors can be puncture, burr, blotch, mask bias, etc. =-=[118]-=- Since mask errors affect all the dies within the same mask, the variations caused by mask errors are systematic. Furthermore, regions within a design with relatively low aerial-image contrast will be... |

4 | ORACLE: Optimization with recourse of analog circuits including layout extraction
- Xu, Pileggi, et al.
(Show Context)
Citation Context ...systematic and random variations may further increase. To reduce systematic variations, IC designers start to utilize restricted layout patterns for both digital circuits [48, 86] and analog circuits =-=[121, 123]-=-. Random mismatches, however, can hardly be controlled by circuit layout. As feature sizes become smaller and each transistor contains fewer atoms in its gate channel, random mismatches are expected t... |

4 |
Correlation aware statistical timing analysis with nonGaussian delay distributions
- Zhan, Strojwas, et al.
(Show Context)
Citation Context ...rator. However, it is possible to approximate the auxiliary constraint faux as a quadratic function of X. Such a MAX(•) approximation problem was widely studied for statistical static timing analysis =-=[18, 19, 23, 113, 115, 124]-=-, and it has recently been tuned for analog/RF applications in [55]. Various algorithms for MAX(•) approximation are available and they will be discussed in detail in Chapter 4. Once the auxiliary con... |

2 | Metal-mask configurable RF frontend circuits - Xu, Boone, et al. - 2004 |