$10\mathrm{.}6$ Consider a MOS capacitor with an n$-$type silicon substrate. A metal$$semiconductor

work function difference of ms $0\mathrm{.}30$ V is required. Determine the silicon doping

concentration required to meet this specifi cation when the gate is $($a$)$ n polysilicon,

$($b$)$ p polysilicon, and $($c$)$ aluminum. If a particular gate cannot meet this

specifi cation, explain why.