A step$-$junction Si $p-n$ junction with a circular cross$-$sectional area of $2{10}^{-4}c{m}^2$ at $300$ K has the following properties:

$p-$region:

$N_a={10}^{17}c{m}^{-3}$

Minority carrier lifetime $({}_n)$:$1s$

Mobility $({}_p=200c\frac{m^2}{V}-$s$,{}_n=700c\frac{m^2}{V}-$s$)$

$n-$region:

$N_d={10}^{15}c{m}^{-3}$

Minority carrier lifetime $({}_p)$:$10s$

Mobility $-$s$,{}_p=400c\frac{m^2}{V}-$s