$(20$ points$)$ An n$-$p$-$n BJT has emitter $($NE$),$ base $($NB$),$ and collector $($NC$)$ doping levels of $1019$

cm$3$

$,5$ x$1018$ cm$3$

$,$ and $1017$ cm$3$

$,$ respectively. It is biased in the normal active mode, with

an emitter$-$base voltage of $1$V$.$ If the neutral base width WB is $100$ nm$,$ the emitter is $200$ nm

wide, and we have negligible base recombination, calculate:

a$.(10$ points$)$ the emitter current,

b$.(5$ points$)$ emitter injection efficiency,

c$.(5$ points$)$ and base transport factor.