$(20$ pts$)$ You are given a MOSOM $($metal$-$oxide$-$semiconductor$-$oxide$-$metal$)$ device as shown $($silicon and oxide layers are each $0\mathrm{.}1m$ as labeled$).$ Silicon is undoped and asi $3$cow.

s$)(4$ pts$)$ Determine VFB

$($b$)(4$ pts$)$ A voltage of $2$ volts is applied to the left metal while the right metal is grounded. Determine the voltage drop in the undoped silicon.

$($c$)(4$ pts$)$ Draw the band diagram with the device biased as in part $($b$)$ of this problem. Make sure to include $($quasi$)$ Fermi level in silicon.

$($d$)(4$ pts$)$ Draw the CV characteristics of this device in low and high AC measurement frequency.

$($e$)(4$ pts$)$ What is the maximum capacitance value?