Physics-based mathematical conditioning of the MOSFET surface potential equation

The traditional form of the implicit equation for the surface potential (φ_s) in metal-oxide-semiconductor field-effect transistors (MOSFETs) works well except near the flatband point φ_s=0 where it is both unphysical and ill-conditioned mathematically. This represents a significant difficulty for recent surface potential-based models, which require φ_s evaluation from the accumulation to the strong inversion region. Detailed physical analysis combined with two-dimensional numerical simulations is used to develop a physics-based well-conditioned version of the surface potential equation.