Consider an ideal MOS structure that consists of a n+-poly-Si gate, a 9-nm SiO2 insulator, on a p-Si substrate with a doping level NA=3×1017 cm−3. Treat the n+− poly Si gate as a metal in which the Fermi level sits at the conduction band edge irrespective of bias (i.e., work function equals to the electron affinity of Si,4.04eV ). The Si bandgap is 1.12eV. The effective density of states of the valence band is NV= 3.1×1019 cm−3. The dielectric constant of SiO2 and Si is 3.9 and 12 , respectively. The intrinsic carrier concentration ni is 1010 cm−3. At room temperature and for VG=−3 V,0 V,0.3 V, and 3 V, calculate the values for (a) the threshold voltage; (b) the operation regions (i.e., accumulation, depletion, inversion) at four VG; (c) the surface potential at four VG; (d) the total charge per unit area in the semiconductor, and the breakdown into each type (e.g., free electron, free hole, depletion charge), at four VG; (e) the electric field in the oxide at four VG; (f) the extension of the depletion region in the semiconductor at four VG; (g) the low-frequency capacitance per unit area at four VG; (h) the high-frequency capacitance per unit area at four VG.