Simple solutions for modelling the non-uniform substrate doping

Present-day CMOS processes use ion implantation to adjust the threshold voltages and to avoid the punch through effect. The substrate doping in the transistor can thus no longer be considered as uniform, and accurate modelling of this effect is required for precise analog circuit simulation. Two new solutions taking this effect into account are proposed and compared with other existing approaches. The results of these new models are compared with 2-D device simulations and measurements of a 2 μm CMOS low voltage process