$7\mathrm{.}2$ For the MOS capacitor at $300$K has an Al gate and a p$-$Si substrate with p$=$ Na$=3*10^16$ cm$^-3.$ The oxide thickness is $55$ nm$.$ There is no charge at the interface

$($a$)$ Calculate the threshold voltage for N$\_($f$)=0.$

$($b$)$ Calculate the threshold voltage for N$\_($f$)=3\backslash$times $10^(10)$cm$^(-2).$

$($c$)$ Describe how the threshold voltage would be expected to vary with p$,$N$\_($f$),$ and t$\_($ox$).$