$($a$)$ Consider an n polysilicon$$silicon dioxide$$n$-$type silicon MOS structure. Let

Nd $41015$ cm $3.$ Calculate the ideal fl at$-$band voltage for tox $20$ nm $200.$

$($b$)$ Considering the results of part $($a$),$ determine the shift in fl at$-$band voltage for

$($i$)$ Q ss $41010$ cm $2$ and $($ii$)$ Q ss $1011$ cm $2.($c$)$ Repeat parts $($a$)$ and $($b$)$ for an

oxide thickness of tox $12$ nm $120.$