$(25$ points$)$ A p$-$n$-$p BJT has emitter $($NE$),$ base $($NB$),$ and collector $($NC$)$ doping of $1020$ cm$3$

$,$

$1018$ cm$3$

$,$ and $1017$ cm$3$

$,$ respectively, and a base width WB of $0\mathrm{.}5$ micron. Given: T $=300$K$,$ ni

$=1\mathrm{.}5$ x $1010$ cm$-3$

$,$ $=12$ x $8\mathrm{.}85$ x $10-14$ F$/$cm$.$ Assume the emitter and collector regions are very

long.

a$.(5$ points$)$ Calculate the peak electric field at the CB junction for the normal active

mode of operation with a VCB $=50$ V$,$

b$.(5$ points$)$ and the CB depletion capacitance per unit area for the normal active

mode of operation with a VCB $=50$ V$.$

E$($n$+$

$)$ B$($p$)$ C$($n$-$

$)$

c$.(5$ points$)$ How much is the neutral base width narrowing at this voltage, ignoring the

EB depletion region?

d$.(5$ points$)$ What impact does neutral base width narrowing have on the output

characteristics of the BJT$?$

e$.(5$ points$)$ If the emitter$-$base forward bias is $0\mathrm{.}6$ V$,$ calculate the emitter current,

assuming negligible recombination in the base, and emitter injection efficiency of

$0\mathrm{.}9.$ The electron and hole mobilities are $500$ and $200$ cm$2$

$/$V$-$s$,$ respectively, and the

device cross section is $0\mathrm{.}1$ square micron. Ignore depletion width on emitter base

junction and VCB $=50$ V$.$