## CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

### BibTeX

@MISC{Naidu_cip-datalibrary,

author = {Srinath Robin Naidu},

title = {CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN},

year = {}

}

### OpenURL

### Abstract

Towards predictable deep-submicron manufacturing

### Citations

398 |
A polynomial algorithm in linear programming
- Khachiyan
- 1979
(Show Context)
Citation Context ... finding a global minimum of a quadratic over a polytope is NP-complete. Ellipsoidal approximations of a polytope have been used in Khachiyan’s famous polynomial-time algorithm for linear programming =-=[50]-=-. Recent approaches to estimating the volume of convex bodies in high dimensions use an ellipsoid to approximate the volume of the convex body. Crucially for us, there are efficient ways of computing ... |

366 |
Measure Theory
- Halmos
- 1950
(Show Context)
Citation Context ...re only for completeness. The group of random orthogonal matrices can be shown to be a compact topological group [86]. Every compact topological group has a unique normalised left-invariant measure µ =-=[37]-=- such that µ(G) = 1, µ(HG) = µ(G), (A-26) where G denotes the group of all orthogonal matrices of order n. The measure µ is a group-theoretic analogue of the uniform probability density function over ... |

266 |
Comparison Methods for Queues and other Stochastic Model
- STOYAN
- 1983
(Show Context)
Citation Context ...pper and lower bounds for the distribution of the project completion time. We shall describe the salient aspects of the work of these researchers. First we shall need some definitions: Definition 2.2 =-=[87]-=-: (Stochastic ordering) A random variable X is said to be stochastically smaller than another random variable Y in the strong sense, if FX ≥ FY , where FX is the cumulative distribution function of X,... |

253 |
Approximate Calculation of Multiple Integrals
- Stroud
- 1971
(Show Context)
Citation Context ... cannot be used for integration because they are too inaccurate. A degree-7 formula appears to be more promising. The degree-7 formula we use for integrating over the entire unit sphere is drawn from =-=[88]-=- and is a derivative of a degree-7 rule used for integrating over the surface of a unit sphere. The degree-7 rule to integrate over the surface of the unit sphere makes use of the following points: (a... |

98 |
The efficient generation of random orthogonal matrices with an application to condition estimators
- Stewart
- 1980
(Show Context)
Citation Context ... Appendix. 7.5 Generating random orthogonal matrices Most of the methods for generating a random orthogonal matrix of the Haar distribution that is needed for the theorem above use Heiberger’s method =-=[86]-=-. The method consists of first generating an n × n matrix X with independent entries xij = Normal(0, 1). Then a QR factorisation of X is computed, X = QR. This provides a random matrix Q of the requir... |

83 | A general probabilistic framework for worst case timing analysis
- Orshansky, Keutzer
- 2002
(Show Context)
Citation Context ...struct the cumulative distribution function of the output delay distribution. Integration of a joint probability density function over a feasible region has been considered in [85], [96]. The work of =-=[75]-=- uses a linear model for the parameter variations, but computes bounds on the probability distribution of output delay using the theory of stochastic processes. This work assumes that the joint probab... |

74 |
Timing Analysis of Computer Hardware
- Hitchcock, Smith, et al.
- 1982
(Show Context)
Citation Context ... into account correlations due to path sharing. Unfortunately, with these general assumptions, only very weak bounds can be derived for the probability distribution of output delay. The work of [39], =-=[40]-=- must also be included in the list of path-based statistical timing approaches. The efficient generation of the top K critical paths in a circuit is central to path-based approaches; this topic is cov... |

65 |
On the complexity of computing the volume of a polyhedron
- DYER, FRIEZE
- 1988
(Show Context)
Citation Context ...n and Hickey is impressive for low dimensions, as the computational results at the end of this chapter show. The exponential complexity of Cohen and Hickey’s approach is not surprising - we know from =-=[19]-=- that estimating the volume of an arbitrary polytope (closed bounded polyhedron) is a #P-complete problem. Cohen and Hickey’s approach provides us a lower bound of the true volume to within a constant... |

56 | Timing Verification and the Timing Analysis Program
- Hitchcock
- 1982
(Show Context)
Citation Context ...he complexity of the statistical timing procedure. In this chapter, we shall lay the groundwork for the remaining chapters. We shall introduce the concept of a timing graph for static timing analysis =-=[39]-=- and show how it is closely related to the project completion diagram of the PERT problem. The PERT problem is a longstanding area of research in the field of operations research and we review the lit... |

54 | False-path-aware statistical timing analysis and efficient path selection for delay testing and timing validation
- Liou, Krstic, et al.
- 2002
(Show Context)
Citation Context ... of removing false paths from the analysis. False paths are those which are never sensitized by the logic of the circuit, and can affect the delay distribution if they are critical. [47], [48], [91], =-=[54]-=- have all looked at the false-path problem and come up with methods to remove them from consideration. It has been the focus of many researchers to accurately model correlations in the circuit, see fo... |

49 |
Timing yield estimation from static timing analysis
- Gattiker, Nassif, et al.
- 2001
(Show Context)
Citation Context ...reason not so far been widely used in industry. The impulsetrain approach of [66], [67], [55], the method of bounds [3] can all be seen as approaches that can handle path sharing alone, while that of =-=[30]-=- can be seen as one that handles correlation between gates alone. This chapter focuses attention on a timing model that was first suggested many years ago [96] and then abandoned because it appeared t... |

47 | Fast statistical timing analysis by probabilistic event propagation
- Liou, Cheng, et al.
- 2001
(Show Context)
Citation Context ...es include the bounds approach of [3] which tries to construct an upper and lower bound on the circuit delay distribution. Novel block-based approaches based on discrete computations are described in =-=[55]-=-, [66], [67]. The papers [55] and [67] take into account reconvergent path correlations but not correlations due to delay dependencies. There has been a fair amount of research dealing with the proble... |

38 |
Gate sizing using a statistical delay model
- Jacobs, Berkelaar
- 2000
(Show Context)
Citation Context ...f statistical techniques for yield optimisation is [21]. Gate-sizing using statistical models must also be considered within the domain of yield optimisation. An approach of this kind is described in =-=[43]-=-. [13] considers false-path analysis in conjunction with gate-sizing. An interesting approach of [89] considers the impact of design uncertainty on IC design. This is distinct from the statistical var... |

38 |
Within-chip variability analysis
- Nassif
- 1998
(Show Context)
Citation Context ...t it must be taken into account to ensure that the fab returns a profit. The topic of variability in the manufacture of digital integrated circuits has just started to receive a lot of attention [9] ,=-=[69]-=-, [70], [71], [72], [56]. It is recognized that variability must be handled all across the design process and not merely at the manufacturing stage. Variability causes “yield” loss where yield of a se... |

37 | Models of process variations in device and interconnect
- Boning, Nassif
- 2001
(Show Context)
Citation Context ...e that it must be taken into account to ensure that the fab returns a profit. The topic of variability in the manufacture of digital integrated circuits has just started to receive a lot of attention =-=[9]-=- ,[69], [70], [71], [72], [56]. It is recognized that variability must be handled all across the design process and not merely at the manufacturing stage. Variability causes “yield” loss where yield o... |

36 |
On the Complexity of Approximating the Maximal Inscribed Ellipsoid for a Polytope
- Khachiyan, Todd
- 1993
(Show Context)
Citation Context ...), where m is the number of constraints and n is the number of dimensions. The term n2 comes from having to solve linear systems containing an n × n linear system. The algorithm of Khachiyan and Todd =-=[51]-=- runs in time O(m3.5 ln( mR n ln R ) ln( )). It uses the same barrier method as the method of ɛ ɛ Nesterov and Nemirovskii but avoids using an n × n matrix variable. After further improvements, Anstre... |

34 |
PREDICT—Probabilistic estimation of digital circuit testability
- SETH, PAN, et al.
- 1985
(Show Context)
Citation Context ...ny given gate are logically independent. A number of techniques have been proposed in the literature to deal with logical correlations. One such technique is the supergate technique first proposed by =-=[81]-=-. The technique consists of first decomposing the original circuit into sub-circuits such that the inputs to each sub-circuit are logically independent. The specific circuit decomposition scheme we us... |

33 |
Statistical Circuit Modeling and Optimization
- Duvall
- 2000
(Show Context)
Citation Context ... semiconductor manufacturing has been going on for many years. There has been significant research effort but very little in terms of industrial implementation. The main reasons for this according to =-=[27]-=- are the complexity of most statistical design techniques, the orthogonality of statistical design techniques to the worst-case methods used in industry making their adoption in an industrial environm... |

33 |
Computational complexity of PERT problems
- Hagstrom
- 1988
(Show Context)
Citation Context ...6 Theoretical complexity of the PERT Problem It is useful to study the complexity of the PERT problem in a deep computational sense because it gives us a direct insight into our own problem. Hagstrom =-=[36]-=- has shown that the problem of determining even a single point on the completion-time distribution of a PERT network, in general, is #Pcomplete even if we assume that each task has a two-point distrib... |

32 | Impact of Interconnect Variations on the Clock Skew of a Gigahertz Microprocessor
- Liu, Nassif, et al.
- 2000
(Show Context)
Citation Context ...account to ensure that the fab returns a profit. The topic of variability in the manufacture of digital integrated circuits has just started to receive a lot of attention [9] ,[69], [70], [71], [72], =-=[56]-=-. It is recognized that variability must be handled all across the design process and not merely at the manufacturing stage. Variability causes “yield” loss where yield of a semiconductor process can ... |

32 | Modeling and forecasting of manufacturing variations
- Nassif
- 2000
(Show Context)
Citation Context ...ust be taken into account to ensure that the fab returns a profit. The topic of variability in the manufacture of digital integrated circuits has just started to receive a lot of attention [9] ,[69], =-=[70]-=-, [71], [72], [56]. It is recognized that variability must be handled all across the design process and not merely at the manufacturing stage. Variability causes “yield” loss where yield of a semicond... |

31 |
Bounding the project completion time distribution in PERT networks
- DODIN
- 1985
(Show Context)
Citation Context ...oblem for digital integrated circuits. Given the complexity of the PERT problem even in the case of simple discrete distributions (which we shall postpone to the next section), many researchers [65], =-=[26]-=-, [52], [49], [82] have turned their attention to providing good upper and lower bounds for the distribution of the project completion time. We shall describe the salient aspects of the work of these ... |

27 | On Numerical Solution of the Maximum Volume Ellipsoid Problem
- Zhang, Gao
- 2003
(Show Context)
Citation Context ...epresent the shape of the polytope reasonably well. The reader may note that this happens in more general situations as well. Ellipsoids have geometric properties that are very desirable. For example =-=[100]-=- states that one can find the global minimum of any quadratic over an ellipsoid in polynomial time, while the general problem of finding a global minimum of a quadratic over a polytope is NP-complete.... |

24 |
and S.Ghanta,, "Efficient Algorithms for Extracting the k Most Critical Paths in Timing Analysis
- Yen
- 1989
(Show Context)
Citation Context ... included in the list of path-based statistical timing approaches. The efficient generation of the top K critical paths in a circuit is central to path-based approaches; this topic is covered by [97],=-=[98]-=-. Two flavours of the critical path generation problem are presented: the first collects all paths with delays greater than a given threshold and the second collects the top K paths in decreasing orde... |

23 | Fully symmetric interpolatory rules for multiple integrals over infinite regions
- Genz, Keister
- 1996
(Show Context)
Citation Context ...e in the number of points needed for integration as the number of dimensions in the integral increases. Specifically, we discuss the low variance Monte-Carlo spherical integration method of Alan Genz =-=[31]-=-,[32]. The method’s various redeeming features are discussed. We show that it is polynomial in the number of dimensions, a highly desirable property considering that we may have to deal with a lot of ... |

21 |
A survey of optimization techniques for integrated-circuits design
- Brayton, Sangiovanni-Vincentelli
- 1981
(Show Context)
Citation Context ...he acceptability region boundaries are moved away as far as possible from the design centre in order to increase yield. Design centring based approaches have been described in the works of [5], [35], =-=[12]-=- and [95]. In fact the ellipsoidal method of design centring presented by [95] bears some similarity with our own approach. Implicit methods of yield optimisation do not attempt to construct an approx... |

21 |
Timing Analysis of Combinational Circuits Including Capacitive Coupling and
- Choi, Walker
- 2000
(Show Context)
Citation Context ...rcuit simulation. In each circuit simulation, each signal propagation delay is sampled from its distribution, and then a static timing analysis is performed to get the output delay. For example [10], =-=[15]-=- follow this approach. The procedure is repeated over thousands of trials, and the output delay distribution is deduced from the collection of output delays. The main advantage of Monte-Carlo analysis... |

21 | Worst-case analysis and optimization of VLSI circuit performances
- Dharchoudhury, Kang
- 1995
(Show Context)
Citation Context ...to have the same worst-case process parameters, so that the cost of finding the worst-case parameters can be amortized across several circuits. Worst-case approaches may be found in the works of [1], =-=[20]-=-. The work of [68] examines the impact of worst-case circuit modelling on predicting circuit performance.s6 Chapter 1. Introduction 1.3 Statistical circuit modelling Statistical Circuit models do not ... |

21 |
The Impact of Variability on
- Nassif
(Show Context)
Citation Context ... taken into account to ensure that the fab returns a profit. The topic of variability in the manufacture of digital integrated circuits has just started to receive a lot of attention [9] ,[69], [70], =-=[71]-=-, [72], [56]. It is recognized that variability must be handled all across the design process and not merely at the manufacturing stage. Variability causes “yield” loss where yield of a semiconductor ... |

17 | Statistical Timing Analysis using Bounds
- Agarwal, Blaauw, et al.
- 2003
(Show Context)
Citation Context ...sts of a symbolic simulation of the circuit with delays sampled from the respective distributions, together with a pruning technique. More recent block-based approaches include the bounds approach of =-=[3]-=- which tries to construct an upper and lower bound on the circuit delay distribution. Novel block-based approaches based on discrete computations are described in [55], [66], [67]. The papers [55] and... |

17 |
Bounding distributions for a stochastic acyclic network
- Kleindorfer
- 1971
(Show Context)
Citation Context ...for digital integrated circuits. Given the complexity of the PERT problem even in the case of simple discrete distributions (which we shall postpone to the next section), many researchers [65], [26], =-=[52]-=-, [49], [82] have turned their attention to providing good upper and lower bounds for the distribution of the project completion time. We shall describe the salient aspects of the work of these resear... |

17 | A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks
- Ludwig, Mohring, et al.
- 2001
(Show Context)
Citation Context ...d the distribution of project completion time assuming project delay distributions to be Gaussian, beta, exponential or gamma distributions. Discrete distributions have also been the subject of study =-=[58]-=-. 2.5 Solving the PERT problem Solving the PERT problem in the deterministic case is easy - indeed, one can adopt the same approach as used in static timing analysis. First one levelizes the network. ... |

16 |
VLSI Yield Prediction and Estimation: A Unified Framework
- Maly, Strojwas, et al.
- 1986
(Show Context)
Citation Context ...wires, which could lead to bridging faults and opens which could lead to stuck-at faults. Researchers have come up with critical area models that determine the sensitivity of a layout to spot defects =-=[61]-=-. All in all, this is a relatively well-studied problem. (2) Parametric variations: These are random variations in operating conditions such as temperature and supply voltage, or in material propertie... |

15 | A statistical static timing analysis considering correlations between delays
- Tsukiyama, Tanaka, et al.
(Show Context)
Citation Context ...looked at the false-path problem and come up with methods to remove them from consideration. It has been the focus of many researchers to accurately model correlations in the circuit, see for example =-=[92]-=-, [55], [66], [67], [53]. Most researchers in PERT assume that the activity durations are independent. On the other hand, this assumption is not so common among researchers in statistical static timin... |

14 |
Statistical integrated circuit design
- Director, Feldmann, et al.
- 1993
(Show Context)
Citation Context ...ave also been considered. These techniques are not afflicted by the curse of dimensionality and use sampling techniques. Examples of statistical methods for yield optimisation are the papers of [17], =-=[23]-=-, [77], [57]. A good place to find a summary of statistical techniques for yield optimisation is [21]. Gate-sizing using statistical models must also be considered within the domain of yield optimisat... |

14 |
Integrated circuit quality optimization using surface integrals
- Feldmann, Director
- 1993
(Show Context)
Citation Context ...n reality, very little is known of the JPDF except perhaps that it is unimodal. An example of a direct approach to yield optimisation is the boundary integrals8.2. Background 135 formulation of [28], =-=[29]-=-. Here the yield integral is formulated as a surface integral using Stoke’s theorem and expressions are derived for the yield gradients which are then used in optimisation. The computational and model... |

12 |
The approximation of multiple integrals by using interpolatory cubature formulae,” in Qualitative approximation
- Mysovskikh
- 1980
(Show Context)
Citation Context ...tion and V is the surface area of the unit sphere in n dimensions. Another degree-3 formulas126 Chapter 7. Randomised quadrature that is slightly more expensive than the previous one is the following =-=[63]-=-, [64]: I(f) ≈ � V � 2(n + 1) i=n+1 � � f(ui) + f(−ui) � . (7.8) i=1 The n + 1 points ui are the vertices of a regular n-simplex with the vertices located on the surface of the unit sphere. This rule ... |

12 |
Probabilistic PERT
- Nadas
- 1979
(Show Context)
Citation Context ...sis problem for digital integrated circuits. Given the complexity of the PERT problem even in the case of simple discrete distributions (which we shall postpone to the next section), many researchers =-=[65]-=-, [26], [52], [49], [82] have turned their attention to providing good upper and lower bounds for the distribution of the project completion time. We shall describe the salient aspects of the work of ... |

12 |
Bounding distributions for a stochastic PERT network
- Shogan
- 1983
(Show Context)
Citation Context ...integrated circuits. Given the complexity of the PERT problem even in the case of simple discrete distributions (which we shall postpone to the next section), many researchers [65], [26], [52], [49], =-=[82]-=- have turned their attention to providing good upper and lower bounds for the distribution of the project completion time. We shall describe the salient aspects of the work of these researchers. First... |

12 |
An integrated and efficient approach for MOS VLSI statistical circuit design
- Yang, Hocevar, et al.
- 1986
(Show Context)
Citation Context ...handle path sharing alone, while that of [30] can be seen as one that handles correlation between gates alone. This chapter focuses attention on a timing model that was first suggested many years ago =-=[96]-=- and then abandoned because it appeared to be intractable. We reexamine the model in this thesis and propose some new solution techniques to deal with the intractability. The rest of this thesis consi... |

11 |
Two algorithms for determining volumes of convex poly- hedra
- COHEN, HICKEY
- 1979
(Show Context)
Citation Context ...over a polytope In this chapter we present methods to calculate the integral that gives us the yield for a particular performance. We examine first a “brute-force” method proposed by Cohen and Hickey =-=[16]-=- of complexity exponential in the number of dimensions but linear in the number of paths of the system. This method is therefore applicable when we can reduce the number of dimensions to a small numbe... |

11 |
A new statistical approach to timing analysis of vlsi circuits,” VLSI Design
- Lin, Wu
- 1998
(Show Context)
Citation Context ... problem and come up with methods to remove them from consideration. It has been the focus of many researchers to accurately model correlations in the circuit, see for example [92], [55], [66], [67], =-=[53]-=-. Most researchers in PERT assume that the activity durations are independent. On the other hand, this assumption is not so common among researchers in statistical static timing analysis. This means t... |

11 |
Relating statistical MOSFET model parameter variabilities to IC manufacturing process fluctuations enabling realistic worst case design
- Power, Donnellan, et al.
- 1994
(Show Context)
Citation Context ...nts on production wafers must proceed in parallel with manufacturing chips. It is here that simulation and so-called short-loop experiments come into play. Direct parameter extraction is described in =-=[79]-=-. Statistical models are derived from process specifications in [83]. In this work, principal component analysis is used to reduce the complexity of statistical models. The basics10 Chapter 1. Introdu... |

11 |
Ellipsoidal method for design centering and yield estimation
- Wojciechowski, Vlach
- 1993
(Show Context)
Citation Context ...ability region boundaries are moved away as far as possible from the design centre in order to increase yield. Design centring based approaches have been described in the works of [5], [35], [12] and =-=[95]-=-. In fact the ellipsoidal method of design centring presented by [95] bears some similarity with our own approach. Implicit methods of yield optimisation do not attempt to construct an approximation o... |

10 | Assessment of true worst case circuit performance under interconnect parameter variations
- Acar, Nassif, et al.
(Show Context)
Citation Context ...tend to have the same worst-case process parameters, so that the cost of finding the worst-case parameters can be amortized across several circuits. Worst-case approaches may be found in the works of =-=[1]-=-, [20]. The work of [68] examines the impact of worst-case circuit modelling on predicting circuit performance.s6 Chapter 1. Introduction 1.3 Statistical circuit modelling Statistical Circuit models d... |

10 | Improved complexity for maximum volume inscribed ellipsoids
- Anstreicher
(Show Context)
Citation Context ...in time O(m3.5 ln( mR n ln R ) ln( )). It uses the same barrier method as the method of ɛ ɛ Nesterov and Nemirovskii but avoids using an n × n matrix variable. After further improvements, Anstreicher =-=[4]-=- obtained an O(m3.5 ln( mR)) algorithm ɛ for the problem.s6.3. MAXDET problem 89 z2 Polytope Maximum Volume Ellipsoid Figure 6.1: Maximum volume ellipsoid approximation to feasible polytope. We shall ... |

10 | A survey on solution methods for task graph models
- BACCELLI, JEAN-MARIE, et al.
- 1993
(Show Context)
Citation Context ...th each task. The problem for the operations researcher is then to determine if the project network so defined has an acceptable completion time. A task graph relevant to PERT is shown in Figure 2.3. =-=[6]-=- is a recent survey on the techniques used to solve the PERT problem. 2.4 The PERT problem and Combinational logic networks As has already been mentioned in the introduction to this chapter, there is ... |

10 |
Parametric yield optimization for MOS circuit blocks
- Hocevar, Cox, et al.
- 1988
(Show Context)
Citation Context ...hat if the feasible region can be assumed to be convex, and the JPDF is unimodal, then design centring is equivalent to inscribing the largest JPDF-norm body into the feasible region. In contrast, in =-=[41]-=-, the acceptability region boundaries are moved away as far as possible from the design centre in order to increase yield. Design centring based approaches have been described in the works of [5], [35... |

10 |
A Study of Variance Reduction Techniques for Estimating Circuit Yields
- Hocevar, Lightner, et al.
- 1983
(Show Context)
Citation Context ...ather loose lower bound - the gain in variance is larger than k. At this point, it is pertinent to situate this method of variance reduction in the context of other schemes proposed in the literature =-=[42]-=-. [42] discusses importance sampling, the method of control variates and stratified sampling as possible means to reduce variance. The general observation made in this paper is that in order to obtain... |

9 |
Design centering by yield prediction
- Antreich, Koblitz
- 1982
(Show Context)
Citation Context ... in [41], the acceptability region boundaries are moved away as far as possible from the design centre in order to increase yield. Design centring based approaches have been described in the works of =-=[5]-=-, [35], [12] and [95]. In fact the ellipsoidal method of design centring presented by [95] bears some similarity with our own approach. Implicit methods of yield optimisation do not attempt to constru... |