A MOSCAP is fabricated on a p$-$type silicon wafer with a doping concentration of $1015/$cm$3$

$.$

Aluminum is used as the gate material and the gate dielectric is silicon dioxide with a thickness of

$50$ nm$.$ Interface states and oxide charge can be neglected. $($Assume T $=300$K$,$ the work$-$function

of Aluminum is $3\mathrm{.}20$ V$,$ the electron affinity of Si is $3\mathrm{.}25$ V$,$ the band$-$gap of Si is $1\mathrm{.}12$ eV$,$ the