The Research Of Performance Modeling And Parametric Yield Estimation Algorithms For Analog Integrated Circuits

Nowadays IC design moves steadily towards integration of complete systems ontoa single chip, but the analog design automation technologies still lag behind and becomethe bottleneck of the mixed analog/digital design．Circuit optimization is an importantmeans to realize analog IC design automation, meanwhile performance model basedcircuit optimization is now the focus of this technology. There are some problems withcurrent modeling techniques，some of them use device sizes as variables so that theinitial point has a huge impact on the circuit optimization; some of them cannot providephysical insights and are inconsistent with the designers’ habits, which hinder their wideapplication.Accurate estimation of IC parametric yield is the basis to successfully achieveparametric yield optimization, at the same time it is also a key point for making areasonable choice of suppliers or manufacturers. The central issue of parametric yieldestimation is to improve the accuracy of yield estimation by using least number ofsimulations. When faced with incomplete data samples with unqualified productsremoved, traditional yield estimation methods are no longer applicable, how to estimatethe yield quickly and easily under this case is also very worthy of study.This dissertation studies circuit performance modeling and parametric yieldestimation, which are the two key issues of analog IC design automation and yieldoptimization problems. Detailed research contents include the following:1. After analyzing the characteristics of analog circuit design and requirements forthe device model, this dissertation proposes the operating point driven (OPD)metamodels of MOS device parameters, or called OPD device metamodels. The modelstake the operating points and channel lengths of MOS transistors as input parameters,and the small signal parameters and the ratio of width to length as outputs parameters.During model construction, radial basis functions (RBF) are adopted to interpolate thescattered multivariate data obtained from a well tailored data sampling scheme designedfor MOS transistors. These device metamodels can be reused multiple times on a givensilicon technology and consistent with designers’ habits like common device models.OPD device metamodels can be used to automatically bias the circuit at a specific DCoperating point without doing simulation iterations. Since OPD device metamodels areaccurate at BSIM3v3level, the equation based circuit performance models are alsoaccurate aided by them. These device metamodels have been successfully applied to analog circuit design.2. The circuit performance models can be divided into principle-basedperformance equations and simulation-based metamodels, both kinds of performancemodels can be built by OPD device metamodels. Accuracy and generalization ability ofthese two kinds of models are compared through examples. Performance models basedon OPD device metamodels take the operating points and channel lengths of MOStransistors as input parameters, thus maximize design flexibility and can be used to findoptimum design scheme. But on the other hand, too many optimization variables alsoaffect the performance of the optimization algorithm.This dissertation proposes anesting-loop optimization formulation to tackle this problem. Operating points and thechannel length are used as optimization variables for outer loop and inner looprespectively. Thus both outer loop and inner loop can use relatively simple optimizationalgorithm to achieve optimum with fewer iterations, thereby improving the efficiency.3. The low accuracy of Monte Carlo method and Quasi Monte Carlo methods isdue to losing information of data. A novel integration-based yield estimation method isthen developed. This method tries to integrate the joint probability density function onthe acceptability region directly. To achieve this goal, the simulated performance data ofunknown distribution should be converted to follow a multivariate normal distributionby using Box-Cox transformation. In order to reduce the estimation variances of themodel parameters of the density function, OA-MLHS is used to generate samples in thedisturbance space during simulations. Since the information of data is fully utilized bythis method, accurate yield estimates can be obtained requiring only a small number ofsimulations without the need for modeling. This method can be used for yieldestimation with multidimensional non-normal performance data. The principle of thismethod is analyzed in detail. This method has been compared with other yieldestimation methods including Monte Carlo method under several combinations ofsample sizes and yield values to verify its superiority.4. Several yield estimation methods using truncated normal data are analyzed. Thepowers of several normality tests in identification of singly truncated normal samplesare compared. An empirical formula is presented to calculate the yield directly by thesample mean and standard deviation of singly truncated normal samples based on thetheoretical relation between process capability indices and the yield. The simple empirical formulas can achieve almost the same accuracy as MLE method but withmuch less amount of calculation. Besides, the empirical formula can also be used fordoubly truncated normal samples when some specific conditions are met.