Projection-Based Piecewise-Linear Response Surface Modeling for Strongly Nonlinear VLSI Performance Variations

Large-scale process fluctuations (particularly random device mismatches) at nanoscale technologies bring about highdimensional strongly nonlinear performance variations that cannot be accurately captured by linear or quadratic response surface models. In this paper, we propose a novel projection-based piecewise linear modeling technique, P2M, to address such a modeling challenge with affordable computational cost. P2M borrows the projection pursuit idea from mathematics to convert a high-dimensional modeling problem to a low-dimensional one. In addition, a new piecewise-linear model template is proposed and tuned for strongly nonlinear performance variations. By exploiting the unique piecewise-linear nature of the model template, a robust numerical algorithm is further developed to determine all model coefficients by solving a sequence of over-determined linear equations. Several circuit examples designed in a commercial 65nm CMOS process demonstrate that compared with the traditional quadratic modeling, P2M achieves 2x error reduction with negligible computational overhead