Problem #$3$: An p$-$channel MOSFET has an n$+$ polysilicon gate on a n$-$type substrate doped ND $=8$x$1016$cm$-3.$

Assume the oxide is $10$nm thick, Qi $=$ q x $5$x$1011$ C$/$cm$2.$

A$)$ Calculate the flat band voltage, maximum depletion width, and the threshold voltage.

B$)$ Design a threshold adjust implant to shift the threshold voltage to $0\mathrm{.}5$V $($i$.$e$.$ find the dopant dose and type$).$

C$)$ What amount of additional interface charge Qi$\_$add$/$q can be tolerated before the threshold of part B$)$ shifts by

$10\%.$