A CMOS capacitor with n$+$ Poly Si as metal gate has $100$ nm thick oxide $($SiO$2)$ layer, $1\mathrm{.}5*1016/$cm$3$ substrate carrier density, $8*10-8$ C$/$cm$2$ oxide layer charge density, and $-6*108$ C$/$cm$2$ depletion layer charge density. Find $($a$)$ the oxide capacitance, $($b$)$ the maximum depletion width, $($c$)$ the modified work function. $[$Given: Pr $($SiO$2)=3\mathrm{.}9,$ P$0=8\mathrm{.}854*10-14$ F$/$cm$]$