Metal interconnect lines in IC circuits form parasitic MOS capacitors as illustrated in Fig. 5-37. Generally, one wants to prevent the underlying Si substrate from becoming inverted. Otherwise, parasitic transistors may be formed and create undesirable current paths between the N+ diffusions. Al interconnect (qug = 4.1 eV) Insulating layer P-sub, N=1015 cr -3 cm FIGURE 5-37 (a) Find Vfb of this parasitic MOS capacitor. (b) If the interconnect voltage can be as high as 5 V, what is the maximum capacitance (F/cm²) of the insulating layer that can be tolerated without forming an inversion layer? (c) If the insulating layer thickness must be 1 μm for fabrication considerations, what should the dielectric constant K = E/ε0 of the insulating material be to make V₁ = 5 V? (d) Is the answer in (c) the minimum or maximum allowable K to prevent inversion? (e) At Vg = V₁ + 2 V (V₁ = 5 V), what is the area charge density (C/cm²) in the inversion layer? (f) At Vg = V₁ = 5 V, what is the high-frequency MOS capacitance (F/cm²)? t (g) At Vg = V₁ +2 V (V₁ = 5 V), what voltage is dropped across the insulating layer?