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The current $I$ in a forward biased $P^{+} N$ junction shown in figure (a) is entirely due to diffusion of holes from $x=0$ to $x=L$. The injected hole concentration distribution in the m-region is linear as shown in figure (b), with

$p(0)=\frac{10^{12}}{\mathrm{~cm}^3}$ and $L=10^{-3} \mathrm{~cm}$. Determine:

(a) The current density in the diode assuming that the diffusion coefficient holes is $12 \mathrm{~cm}^2 / \mathrm{sec}$.

(b) The velocity of holes in the $n$-region at $x=0$.