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.

You can assume electron and hole mobility of $500$ and $100$ cm$2/$V$-$s$,$ respectively, in the

emitter, and $800$ and $250$ cm$2/$V$-$s in the base. The device gets heated up to $400$ K during

operation such that ni $=1012$ cm$3.$ Assume that the carrier lifetimes are $0\mathrm{.}1$ s everywhere.