Characterizing Intra-Die Spatial Correlation Using Spectral Density Fitting Method

In this paper, a spectral domain method named the SDF (Spectral Density Fitting) method for intra-die spatial correlation function extraction is presented. Based on theoretical analysis of random field, the spectral density, as the spectral domain counterpart of correlation function, is employed to estimate the parameters of the correlation function effectively in the spectral domain. Compared with the existing extraction algorithm in the original spatial domain, the SDF method can obtain the same quality of results in the spectral domain. In actual measurement process, the unavoidable measurement error with arbitrary frequency components would greatly confound the extraction results. A filtering technique is further developed to diminish the high frequency components of the measurement error and recover the data from noise contamination for parameter estimation. Experimental results have shown that the SDF method is practical and stable.

[1]  A. V. Skorohod,et al.  The theory of stochastic processes , 1974 .

[2]  Xuan Zeng,et al.  Characterizing Intra-Die Spatial Correlation Using Spectral Density Method , 2008, ISQED 2008.

[3]  Farid N. Najm,et al.  Modeling and Estimation of Full-Chip Leakage Current Considering Within-Die Correlation , 2007, 2007 44th ACM/IEEE Design Automation Conference.

[4]  Vijay Pitchumani.  Embedded tutorial I: design for manufacturability , 2005, ASP-DAC '05.

[5]  Sachin S. Sapatnekar,et al.  Statistical timing analysis under spatial correlations , 2005, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[6]  Dae-Wook Kim,et al.  A Unified Statistical Model for Inter-Die and Intra-Die Process Variation , 2005, 2005 International Conference On Simulation of Semiconductor Processes and Devices.

[7]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[8]  Yu Cao,et al.  Modeling of intra-die process variations for accurate analysis and optimization of nano-scale circuits , 2006, 2006 43rd ACM/IEEE Design Automation Conference.

[9]  Sherief Reda,et al.  Within-die process variations: How accurately can they be statistically modeled? , 2008, 2008 Asia and South Pacific Design Automation Conference.

[10]  Yu Hen Hu,et al.  Statistical timing analysis with path reconvergence and spatial correlations , 2006, Proceedings of the Design Automation & Test in Europe Conference.

[11]  Sani R. Nassif.  Design for Variability in DSM Technologies , 2000 .

[12]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[13]  Costas J. Spanos,et al.  Modeling within-die spatial correlation effects for process-design co-optimization , 2005, Sixth international symposium on quality electronic design (isqed'05).

[14]  Kurt Keutzer,et al.  Impact of spatial intrachip gate length variability on theperformance of high-speed digital circuits , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[15]  Jinjun Xiong,et al.  Robust Extraction of Spatial Correlation , 2007, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[16]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[17]  Gabriele Steidl,et al.  Fast Fourier Transforms for Nonequispaced Data: A Tutorial , 2001 .