Direct Sampling Methodology for Statistical Analysis of Scaled CMOS Technologies

The continued scaling of CMOS technologies introduces new difficulties to statistical circuit analysis and invalidates many of the methodologies developed earlier. The analysis of device parameter distributions reveals multiple sources of parameter correlations, some of which exhibit mutually opposing trends. We found that applying principal component analysis (PCA) to such heterogeneous statistical data may lead to confounding of data and result in underestimation of the total parameter variance. This imposes considerable constraints on the use of several methods of statistical circuit analysis based on PCA. Also, the highly nonlinear relationships between the device parameters become more pronounced and cannot be approximated as linear even in the differential range. As a result, the response surface models based on the linear expansion of the performance variable around the nominal point of the device model parameters may lead to significant prediction errors. To address these difficulties, we propose a conceptually simple and accurate approach of direct sampling that treats the extracted SPICE parameter sets and their physical locations as an inseparable set and thus bypasses the dangerous stage of statistical inferences. We illustrate the methodology by applying it to the statistical analysis of a production CMOS process.