Session 6B: Statistical Modeling and Yield Prediction

6B-1 (Time: 15:50 - 16:15)

Title Determination of Optimal Polynomial Regression Function to Decompose On-Die Systematic and Random Variations
Author *Takashi Sato, Hiroyuki Ueyama, Noriaki Nakayama, Kazuya Masu (Tokyo Inst. of Tech., Japan)
Abstract A procedure that decomposes measured parametric device variation into systematic and random components is studied by considering the decomposition process as selecting the most suitable model for describing on-die spatial variation trend. In order to maximize model predictability, the log-likelihood estimate called corrected Akaike information criterion is adopted. Depending on on-die contours of underlying systematic variation, necessary and sufficient complexity of the systematic regression model is objectively and adaptively determined. The proposed procedure is applied to 90-nm threshold voltage data and found the low order polynomials describe systematic variation very well. Designing cost-effective variation monitoring circuits as well as appropriate model determination of on-die variation are hence facilitated.}
No Slides

6B-2 (Time: 16:15 - 16:40)

Title Within-Die Process Variations: How Accurately Can They Be Statistically Modeled?
Author Brendan Hargreaves, Henrik Hult, *Sherief Reda (Brown Univ., USA)
Abstract Within-die process variations arise during integrated circuit (IC) fabrication in the sub-100nm regime. These variations are of paramount concern as they deviate the performance of ICs from their designers’ original intent. These deviations reduce the parametric yield and revenues from integrated circuit fabrication. In this paper we provide a complete treatment to the subject of within-die variations. We propose a scan-chain based system, vMeter, to extract within-die variations in an automated fashion. We implement our system in a sample of 90nm chips, and collect the within-die variations data. Then we propose a number of novel statistical analysis techniques that accurately model the within-die variation trends and capture the spatial correlations. We propose the use of maximum-likelihood techniques to find the required parameters to fit the model to the data. The accuracy of our models is statistically verified through residual analysis and variograms. Using our successful modeling technique, we propose a procedure to generate synthetic within-die variation patterns that mimic, or imitate, real silicon data.
No Slides

6B-3 (Time: 16:40 - 17:05)

Title Chebyshev Affine Arithmetic Based Parametric Yield Prediction Under Limited Descriptions of Uncertainty
Author Jin Sun, Yue Huang (The Univ. of Arizona, USA), Jun Li (Anova Solutions, USA), *Janet M. Wang (The Univ. of Arizona, USA)
Abstract In modern circuit design, it is difficult to provide reliable parametric yield prediction since the real distribution of process data is hard to measure. Most existing approaches are not able to handle the uncertain distribution property coming from the process data. Other approaches are inadequate considering correlations among the parameters. This paper suggests a new approach that not only takes care of the correlations among distributions but also provides a low cost and efficient computation scheme. The proposed method approximates the parameter variations with Chebyshev Affine Arithmetics (CAA) to capture both the uncertainty and the nonlinearity in Cumulative Distribution Functions (CDF). The CAA based probabilistic presentation describes both fully and partially specified process and environmental parameters. Thus we are capable of predicting probability bounds for leakage consumption under unknown dependency assumption among variations. The end result is the chip level parametric yield estimation based on leakage prediction. The experimental results demonstrate that the new approach provides reliable bound estimation while leads to 20% yield improvement comparing with interval analysis.

6B-4 (Time: 17:05 - 17:30)

Title Distribution Arithmetic for Stochastical Analysis
Author *Markus Olbrich, Erich Barke (Leibniz Univ. of Hannover, Germany)
Abstract This paper presents a novel arithmetic which allows calculations with fluctuating values. Given the distributions of initial random variables, the moments (such as expected value, variance and higher moments) of any calculated variable can be determined. Our approach is not limited to normal distributions and works with linear and nonlinear functions. Correlations between variables are taken into account automatically by the arithmetic. Examples show the accuracy and runtimes compared to Monte Carlo simulation.

6B-5 (Time: 17:30 - 17:55)

Title Handling Partial Correlations in Yield Prediction
Author Sridhar Varadan (Texas A&M Univ., USA), *Janet Wang (Univ. of Arizona, USA), Jiang Hu (Texas A&M Univ., USA)
Abstract In nanometer regime, IC designs have to consider the impact of process variations, which is often indicated by manufacturing/parametric yield. This paper investigates a yield model - the probability that the values of multiple manufacturing/circuit parameters meet certain target. This model can be applied to predict CMP (Chemical-Mechanical Planarization) yield. We focus on the difficult cases which have large number of partially correlated variations. In order to predict the yield for these difficult cases efficiently, we propose two techniques: (1) application of Orthogonal Principle Component Analysis (OPCA); (2) hierarchical adaptive quadrisection (HAQ). Systematic variations are also included in our model. Compared to previous work, the OPCA based method can reduce the error on yield estimation from 17.1%-21.1% to 1.3%-2.8% with 4.6X speedup. The HAQ technique can reduce the error to 4.1%-5.6% with 6X-9.4X speedup.
Last Updated on: January 31, 2008