Simulation models for robust design using location depth methods

For the cost-effective production of integrated circuits, one important aspect is the accurate simulation of electronic circuits with regard to process variation. Process variation is described as the range of simulation (SPICE) parameters, but to reduce the costs of simulation they are replaced by easily available e-test parameters. An approximate algorithm for the location depth (multivariate ranking) selects all data points with location depth less than or equal to one as boundary points for the multidimensional data set of e-test parameters. The corresponding SPICE parameter values are simply obtained by linear mapping. To increase the robustness of the simulation the region covered by the set of boundary points is extended by determining the point with the deepest location (multivariate median) and adding to each boundary vector a fixed portion of the vector from the median to the boundary vector. This natural extension also covers moderate process shifts without changing the covariance structure of the data. These methods are integrated into an automated generation flow to be applicable in a production and circuit design environment. The statistical methods are validated by simulation experiments of typical analog/mixed-signal circuit designs.