A p$-$type silicon sample has a hole concentration of $1017$ cm$3.$ The diffusion coefficient for holes

is Dp $=12$ cm$2/$s$.$

a$)$ If the hole concentration varies linearly from $1017$ cm$3$ to $51016$ cm$3$ over a distance of

$50$ m$,$ calculate the diffusion current density.

b$)$ Compare this to the drift current density if an electric field of $103$ V$/$cm is applied and the

mobility for p$-$type silicon is $450$ cm$^2/$V$$s$.$