Consider an ideal MOS capacitor maintained at T $=300$K with the following parameters: $$ Gate material is p$+$ polycrystalline$-$silicon $($work function $$M $=5\mathrm{.}2$ eV$)$ Substrate is n$-$type Si$,$ with doping concentration $1018$ cm$-3($assume that this is nondegenerate$)$ Oxide thickness xo $=2$ nm$.$ Dielectric constant $=3\mathrm{.}9.$ Si bandgap $=1\mathrm{.}12$ eV$.$ ni$=1$e$10$ cm$-3.$ Electron affinity$=4\mathrm{.}05$ eV$.$ Dielectric constant $=11\mathrm{.}3.$ Assume no oxide charges. a$)$ What is the flat$-$band voltage, VFB$,$ of this capacitor?