$10$pts $(2$pts for each$)$

An N$-$MOSFET and a P$-$MOSFET are fabricated with substrate doping concentration of $6{10}^{17}c{m}^{-3}.$ The gate oxide thickness is $5$ nm $.$

$($a$)$ Find threshold voltage of the $N-$ MOSFET when $N^{+}-$poly$-$Si is used to fabricate the gate electrode.

$($b$)$ Find threshold voltage of the P$-$MOSFET when $N^{+}-$poly$-$Si is used to fabricate the gate electrode.

$($c$)$ Find threshold voltage of the $P-$ MOSFET when $P^{+}-$poly$-$Si is used to fabricate the gate electrode.

$($d$)$ Assume that the only two voltages available on the chip are the supply voltage $Vdd=2\mathrm{.}5V$ and $Vdd=0V.$ What voltages should be applied to each of the terminals $($body$,$ source, drain and gate$)$ to maximize the source$-$to$-$drain current of the N MOSFET?