$9\mathrm{.}2($a$)$ A Schottky barrier diode formed on n$-$type silicon has a doping concentration of Nd $51015$ cm$3$ and a barrier height of B$00\mathrm{.}65$ V$.$ Determine the built in potential barrier Vbi. $($b$)$ If the doping concentration changes to Nd $1016$ cm$3,$ determine the values of B$0$ and Vbi. Do these values increase, decrease, or remain the same? $($c$)$ Repeat part $($b$)$ if the doping concentration is Nd $1015$ cm$3.$