$1.$ Consider a MOS capacitor with Al $($e$$M $=4\mathrm{.}15$ eV$)$ on a n$-$type Si wafer. The doping is ND $=$

$31017$ cm$-3$

$.$ The gate oxide $($SiO$2)$ thickness tox $=10$ nm$.$

$($a$)$ Calculate the surface potential at the onset of strong inversion.

$($b$)$ Calculate the work function difference $$MS$.$

$($c$)$ If the flat band voltage VFB is measured to be $-0\mathrm{.}5$ V$,$ calculate the total oxide charge

density.

$($d$)$ Calculate the threshold voltages VT$.$