Problem $4(15\%)$

The capacitance$-$voltage characteristic at low and high frequency for a Si$\_(-)$SiO$\_(2)$MOS capacitor is

shown below. C$\_($max$)=4\mathrm{.}3\backslash$times $10^(-8)($F$)/($c$)$m$^(2),$C$\_($min$)=1\mathrm{.}45\backslash$times $10^(-8)($F$)/($c$)$m$^(2).$ Si dielectric constant is $11\mathrm{.}7,$

SiO$\_(2)$ dielectric constant is $3\mathrm{.}9.$

$($a$)$ Does this correspond to a p$-$type or n$-$type substrate? Which branch is high frequency?

$($b$)$ Draw MOS diagrams corresponding to point A$,$B$,$ and C $.$

$($c$)$ Calculate the oxide thickness in nanometers.