A pn junction has Na $=1020$cm$3$ acceptor atoms and Nd $=1017$cm$3$ donor atoms. The intrinsic charge carrier concentration is ni $=1010$ cm$3,=11\mathrm{.}7,$ and kT$/$e $=0\mathrm{.}259$V$.$ Calculate: $($a$)$ the built$-$in potential, $($b$)$ the width of the depletion layer, $($c$)$ the width of the depletion layer in the n$-$type region of the junction, $($d$)$ the width of the depletion layer in the p$-$type side of the junction. $($e$)$ Comment on the widths calculated in part $($c$)$ and $($d$).[2][2][3][1][2]$