Carrier quantization at flat bands in MOS devices

While the modeling of carrier quantization in strong inversion and accumulation has received extensive attention in the literature, it is commonly assumed that near flat bands a classical model is acceptable, due to the small surface electric field. We show that this picture is not correct. The presence of the abrupt potential discontinuity at the Si/SiO₂ interface causes a “dark space” of a few nanometers, where the carrier concentration is much smaller than in the bulk. This quantum effect causes a significant attenuation of the capacitance in the near-flat-band region for channel doping concentrations above 1.0¹⁷ cm^-3. The effect is also important at the polysilicon side, where a high doping concentration is used. The nonnegligible effects of the dark space on the C-V curve of MOS devices are shown