Sketch the four band diagrams across all mos structures in

Question

MOS Band Diagrams. Consider four simple cases of the MOS capacitor, all combinations of low gate metal work function (e.g. Al qΦ_M ≈ 4.05 eV), high gate metal work function (e.g. Pt qΦ_M ≈ 5.15 eV), n+type silicon and p+type silicon substrate. Assume the substrate is highly doped, such that E_F coincides with E_C (n+) and E_V (p+) respectively. The SiO₂ thickness is 2 nm. Please assume silicon electron affinity is qX_S = 4.05 eV and band gap is E_G = 1.1 eV.

(a) Sketch the four band diagrams across all MOS structures in equilibrium (V_G = 0 V).

(b) Sketch the four band diagrams exactly at threshold (V_G = V_T), as the surface is inverted. Is the threshold voltage V_T >0 or <0 in each case?