MOSFET Channel Charge Profile: A 2D Gradual-Channel Model

This is the 2D companion to the 3D CMOS inverter scene, and it reaches the same device behaviour by resolving physics the 3D model never touches. Rather than animating carriers along a fixed path once a single lumped current has been solved, this simulator integrates the gradual-channel approximation to obtain the inversion-charge density and channel potential at every position between source and drain for both the NMOS and PMOS device, so the channel visibly tapers to a pinch-off point exactly where the physics predicts it. On top of that it models the drain-body pn junction as a one-sided step junction whose depletion width grows with the square root of reverse bias and shrinks with body doping — a genuine electrostatic effect with no counterpart in the 3D scene's carrier animation — so the depletion boundary around each drain visibly breathes as the inverter switches and as you adjust doping.