An Investigation of the Charge Conservation Problem for MOSFET Circuit Simulation

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Abstract
MOSFET capacitor models implemented in circuit simulators currently do not guarantee charge conservation, which is extremely crucial for the simulation of dynamic RAM's, switched capacitor filters, and other MOS VLSI circuits. Several MOSFET capacitor models have been introduced in the literature; however, none of these models addresses the actual reasons of charge nonconservation in SPICE2. This charge conservation problem has been studied and the causes are found. Our investigations show that charge is the appropriate state variable, and that the nonconservation of charge in SPICE2 stems from a numerical integration problem quite independent of the device physics. A new charge model has been derived, implemented in SPICE2, and tested. The new model differs from the previous models in two respects. First, it uses both charge equations and capacitance equations. Second, the partitioning of the channel charge between the source and drain terminals is carried out by requiring the charge equations to satisfy self-consistent boundary conditions. A strong emphasis is placed on charge continuity, both in the conventional operating region and in the region of weak inversion and accumulation. Benchmark tests indicate that this new model conserves charge while reducing the simulation time by 18-85 percent compared to Meyer's model which was originally used in SPICE2.

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