Find the gate$-$semiconductor work function difference in a MOSFET with a n$-$type silicon substrate and a p polysilicon gate. Assume $N_d={10}^{14}c{m}^{-3}$ in the substrate.

$($a$)0\mathrm{.}32$ V

$($b$)0\mathrm{.}796$ V

$($c$)-0\mathrm{.}82$ V

$($d$)-0\mathrm{.}16$ V

$($e$)-0\mathrm{.}32$ V