An effective method for solving the covariance equation for statistical modeling

Statistical circuit simulation requires model parameters that accurately represent the process deviations of semiconductor devices in every operating point. These variation parameters are derived from results of statistical measurements that are utilized primarily in order to control the manufacturing process. The backward propagation of variance (BPV) technique for statistical modeling has proven to be efficient for calculating statistical variations of model parameters including some correlations coefficients. In this paper the complete covariance equation is set up, normalized and solved by a least square method. The target parameter deviations are derived from the spec limits of the process control monitoring (PCM).