Process variations can reduce the accuracy in estimation of interconnect performance. This work presents a process variation based stochastic model and proposes an effective analytical method to estimate interconnect ...Process variations can reduce the accuracy in estimation of interconnect performance. This work presents a process variation based stochastic model and proposes an effective analytical method to estimate interconnect delay. The technique decouples the stochastic interconnect segments by an improved decoupling method. Combined with a polynomial chaos expression （PCE）, this paper applies the stochastic Galerkin method （SGM） to analyze the system response. A finite representation of interconnect delay is then obtained with the complex approximation method and the bisection method. Results from the analysis match well with those from SPICE. Moreover, the method shows good computational efficiency, as the running time is much less than the SPICE simulation＇s.展开更多
The hourly values of the ionospheric F2 layer critical frequency, foF2, recorded at Wakkanai ionosonde station （45.4°N, 141.7°E） have been collected to construct a middle-latitude single-station model for ...The hourly values of the ionospheric F2 layer critical frequency, foF2, recorded at Wakkanai ionosonde station （45.4°N, 141.7°E） have been collected to construct a middle-latitude single-station model for forecasting foF2 under geomagnetic quiet and disturbed conditions. The module for the geomagnetic quiet conditions incorporates local time, seasonal, and solar vari- ability of climatological foF2 and its upper and lower quartiles. It is the first attempt to predict the upper and lower quartiles of foF2 to account for the notable day-to-day variability in ionospheric foF2. The validation statistically verifies that the model captures the climatological variations of foF2 with higher accuracy than IRI does. The storm-time module is built to capture the geomagnetic storm induced relative deviations of foF2 from the quiet time references. In the geomagnetically disturbed module, the storm-induced deviations are described by diumal and semidiumal waves, which are modulated by a modified magnetic activity index, the Kf index, reflecting the delayed responses of foF2 to geomagnetic activity forcing. The coeffi- cients of the model in each month are determined by fitting the model formula to the observation in a least-squares way. We provide two options for the geomagnetic disturbed module, including or not including Kalman filter algorithm. The Kalman filter algorithm is introduced to optimize these coefficients in real time. Our results demonstrate that the introduction of the Kalman filter algorithm in the storm time module is promising for improving the accuracy of predication. In addition, comparisons indicate that the IRI model prediction of the F2 layer can be improved to provide better performances over this region.展开更多
Due to continuous process scaling, process, voltage, and temperature （PVT） parameter variations have become one of the most problematic issues in circuit design. The resulting correlations among performance metrics ...Due to continuous process scaling, process, voltage, and temperature （PVT） parameter variations have become one of the most problematic issues in circuit design. The resulting correlations among performance metrics lead to a significant parametric yield loss. Previous algorithms on parametric yield prediction are limited to predicting a single-parametric yield or performing balanced optimization for several single-parametric yields. Consequently, these methods fail to predict the multiparametric yield that optimizes multiple performance metrics simultaneously, which may result in significant accuracy loss. In this paper we suggest an efficient multi-parametric yield prediction framework, in which multiple performance metrics are considered as simultaneous constraint conditions for parametric yield prediction, to maintain the correlations among metrics. First, the framework models the performance metrics in terms of PVT parameter variations by using the adaptive elastic net （AEN） method. Then the parametric yield for a single performance metric can be predicted through the computation of the cumulative distribution function （CDF） based on the multiplication theorem and the Markov chain Monte Carlo （MCMC） method. Finally, a copula-based parametric yield prediction procedure has been developed to solve the multi-parametric yield prediction problem, and to generate an accurate yield estimate. Experimental results demonstrate that the proposed multi-parametric yield prediction framework is able to provide the designer with either an accurate value for parametric yield under specific performance limits, or a multi-parametric yield surface under all ranges of performance limits.展开更多
文摘Process variations can reduce the accuracy in estimation of interconnect performance. This work presents a process variation based stochastic model and proposes an effective analytical method to estimate interconnect delay. The technique decouples the stochastic interconnect segments by an improved decoupling method. Combined with a polynomial chaos expression （PCE）, this paper applies the stochastic Galerkin method （SGM） to analyze the system response. A finite representation of interconnect delay is then obtained with the complex approximation method and the bisection method. Results from the analysis match well with those from SPICE. Moreover, the method shows good computational efficiency, as the running time is much less than the SPICE simulation＇s.
基金supported by the CMA (Grant No. GYHY201106011)the National Basic Research Program of China ("973" Project) (Grant No. 2012CB- 825604)+1 种基金the National Natural Science Foundation of China (Grant Nos. 41074112, 41174137, 41174138)the Specialized Research Fund for State Key Laboratories
文摘The hourly values of the ionospheric F2 layer critical frequency, foF2, recorded at Wakkanai ionosonde station （45.4°N, 141.7°E） have been collected to construct a middle-latitude single-station model for forecasting foF2 under geomagnetic quiet and disturbed conditions. The module for the geomagnetic quiet conditions incorporates local time, seasonal, and solar vari- ability of climatological foF2 and its upper and lower quartiles. It is the first attempt to predict the upper and lower quartiles of foF2 to account for the notable day-to-day variability in ionospheric foF2. The validation statistically verifies that the model captures the climatological variations of foF2 with higher accuracy than IRI does. The storm-time module is built to capture the geomagnetic storm induced relative deviations of foF2 from the quiet time references. In the geomagnetically disturbed module, the storm-induced deviations are described by diumal and semidiumal waves, which are modulated by a modified magnetic activity index, the Kf index, reflecting the delayed responses of foF2 to geomagnetic activity forcing. The coeffi- cients of the model in each month are determined by fitting the model formula to the observation in a least-squares way. We provide two options for the geomagnetic disturbed module, including or not including Kalman filter algorithm. The Kalman filter algorithm is introduced to optimize these coefficients in real time. Our results demonstrate that the introduction of the Kalman filter algorithm in the storm time module is promising for improving the accuracy of predication. In addition, comparisons indicate that the IRI model prediction of the F2 layer can be improved to provide better performances over this region.
基金Project supposed by the Natural Science Foundation of Jiangsu Province （Nos. BK20161072, BK20150785, and BK20130877） and the National Natural Science Foundation of China （Nos. 61502234 and 71301081）
文摘Due to continuous process scaling, process, voltage, and temperature （PVT） parameter variations have become one of the most problematic issues in circuit design. The resulting correlations among performance metrics lead to a significant parametric yield loss. Previous algorithms on parametric yield prediction are limited to predicting a single-parametric yield or performing balanced optimization for several single-parametric yields. Consequently, these methods fail to predict the multiparametric yield that optimizes multiple performance metrics simultaneously, which may result in significant accuracy loss. In this paper we suggest an efficient multi-parametric yield prediction framework, in which multiple performance metrics are considered as simultaneous constraint conditions for parametric yield prediction, to maintain the correlations among metrics. First, the framework models the performance metrics in terms of PVT parameter variations by using the adaptive elastic net （AEN） method. Then the parametric yield for a single performance metric can be predicted through the computation of the cumulative distribution function （CDF） based on the multiplication theorem and the Markov chain Monte Carlo （MCMC） method. Finally, a copula-based parametric yield prediction procedure has been developed to solve the multi-parametric yield prediction problem, and to generate an accurate yield estimate. Experimental results demonstrate that the proposed multi-parametric yield prediction framework is able to provide the designer with either an accurate value for parametric yield under specific performance limits, or a multi-parametric yield surface under all ranges of performance limits.
