Numerical electronic device modeling for circuit simulators

Static and dynamic numerical device modeling based on dot product evaluation of multidimensional Bernstein polynomial interpolants to evaluate device operating characteristics is presented as an alternative to analytical modeling and table look-up modeling schemes that have been proposed. The model formulation satisfies the requirements imposed by the algebraic-differential equation solution algorithms of most simulators, namely continuity of the output variables and preservation of the monotonicity and concavity or convexity of the data. It is to be noted, however, that those are necessary but not sufficient conditions. Simulator convergence is improved by treating the intrinsic node charges as state variables and using their variations over iteration steps as an iteration criterion along with the node voltage variation checks. MOSFET is taken as a benchmark device. Experimental results to illustrate the effect of the basic premises of the numerical model on simulation performance are presented