High frequency capacitance versus voltage plots for a

metal$-$insulator$-$semiconductor $($MIS$)$ structure are

shown at the right $($NdF$3$ and SiO$2$ comprise the

insulator$).$ Four voltage sweeps are indicated where the

bias is applied to the aluminum metal. The first sweep

starts at $+5$ volts and ends at $-5$ volts, the second sweep

is in the opposite direction, and the third and fourth

voltage sweeps repeat this cycle

Note that the $2$nd and $4$th C$-$V curves exhibit a flatband voltage of about $+1\mathrm{.}8$ volts. Assuming the

NdF$3/$SiO$2$ insulator has a bandgap of about $8$ eV draw an accurately$-$scaled band diagram at

equilibrium for this MIS structure after the $2$nd or $4$th voltage sweep. $($Hint: First draw the band

diagram with $+1\mathrm{.}8$ volts applied to the metal.$)$Al$/$NdF$3/$SiO$2/$Si