Q$4)$ Consider ni $=1\mathrm{.}51010$ cm$-3$

$,$ Na $=61015$ cm$-3$

$,$ determine the metal$-$semiconductor work

function difference in a MOS structure with p$-$type silicon for the case when the gate is:

$($a$)$ Aluminum

$($b$)$ n$+$ polysilicon

$($c$)$ p$+$ polysilicon