$1-$ An n$+-$polysilicon$-$gate n$-$channel Si$-$MOSFET with substrate doping

NA$=5$x$1015$ cm$-3.$ The insulator is SiO$2,$ and its thickness is $400$ A$.$ The

interface charge Qox $=5$x$1010$ qC$/$cm$2,$ the gate length is $1$ um$,$ and the

gate width is $40$ um

$($a$)$ Find Wm$,$ VFB$,$ and VT$.$

$($b$)$ For VG$=5$V$,$ obtain the current at VD$=1$V$.$

$($c$)$ For VG$=5$V$,($i$)$ find the saturation current, $($ii$)$ the current at

pinch$-$off, and $($iii$)$ the current at VD$=5$V$.$

$($d$)$ Are the currents in $($C$)$ equal to each other? Should they should

be equal, or this is just a coincident? Explain.

$($e$)$ Is this device enhancement or depletion mode device?