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Accuracy and convergence properties of a one-dimensional numerical non-quasi-static MOSFETs model for circuit simulation

Accurate modeling of static currents, conductance and charge dynamics are essential for the design of digital and specially for analog circuits. In the analog domain, the shortcomings of many modeling approaches often originate from transistors biased between linear and saturation regimes where discontinuities limit the accuracy and the convergence properties. Moreover, the finite charging/discharging time of the channel may significantly degrade the performances of modern circuit architectures due to charge injection. However, most MOSFET models reveal poor prediction capabilities for high frequency operations for which quasi-static (QS) operation is often violated. In this paper we discuss the accuracy and numerical properties of a one-dimensional CAD-oriented model. It is shown that the proposed model is continuous over all operating regimes and suitable for the analysis of long and short channel MOSFETs. The most interesting feature of our model, an implicit non-quasi-static (NQS) treatment of the charge redistribution, is outlined. Finally, convergence properties are discussed with a special emphasis on the mobility model and on the related nonlinear resolution scheme.