Problem $16\mathrm{.}28-$modified $(2\mathrm{.}5$ pt $)$

Consider a CMOS inverter fabricated in a $28-$nm CMOS process for which $V_{DD}=0\mathrm{.}9V,V_{En}=-V_{tp}=0\mathrm{.}3V,$ and ${}_n{C}_{ax}=750\frac{A}{V^2},{}_p{C}_{ax}=680\frac{A}{V^2}.$ In addition, $Q_y$ and $Q,$ have $L=28nm$ and $(\frac{W}{L}{)}_{}=1\mathrm{.}0.$

$($a$)$ Find $W_B$ that results in $V_M=\frac{V_{DD}}{2}.$ What is the silicon area utilized by the inverter in this case?

$($b$)$ For the matched case in $($a$),$ find the values of $V_{ON},V_{OL},V_{IH},V_{IL},N{M}_L,$ and $N{M}_N.$

$($c$)$ For the matched case in $($a$),$ find the output resistance of the inverter in each of its two states.