$(35$ points$)$ A Si p$-$n$-$p transistor has the following properties at room temperature:

n $=$ p $=0\mathrm{.}1$ s

Dn $=$ Dp $=10$ cm$2$

$/$s

NE $=1019$ cm$3$

NB $=1016$ cm$3$

NC $=1016$ cm$3$

WE $=$ emitter width $=3$ m

WB$=$ metallurgical base width $=1\mathrm{.}5$ m

A $=$ cross$-$sectional area $=105$ cm$2$

T $=300$K$,$ ni $=1\mathrm{.}5$ x $1010$ cm$-3$

$,$ $=12$ x $8\mathrm{.}85$ x $10-14$ F$/$cm

a$.(5$ points$)$ Calculate the neutral base width WB for VCB $=0$ and VEB $=0\mathrm{.}6$ V$.$

b$.(10$ points$)$ Calculate the base transport factor and the emitter injection efficiency

for VEB $=0\mathrm{.}6$ V$,$ VCB $=0.$

c$.(4$x$5=20$ points$)$ Calculate $,$ $,$ IE$,$ IB and IC for VEB $=0\mathrm{.}6$ V$,$ VCB $=0.$