An $n$-type silicon bar is doped uniformly by phosphorous atoms to a concentration $4.5 \times 10^{13} / \mathrm{cc}$. The bar has cross-section of $1 \mathrm{~mm}^{2}$ and length of $10 \mathrm{~cm}$. It is illuminated uniformly for region $x<0$ as shown in the figure is. Assume optical generation rate $10^{21}$ Electron-Hole pairs per $cm^{3}$ per second, for this case. The hole lifetime and electron lifetime are equal, and equal to $1 \; \mu$ sec.
Evaluate the hole and electron diffusion currents at $x=34.6 \; \mu \mathrm{m}$.
Following expressions and data can be used in this evaluation
$$\mathrm{J}_{p}=q \mathrm{D}_{p} \frac{d p}{d x} ; \mathrm{Jn}=q \mathrm{D}_{n} \frac{d n}{d x}$$
where $\mathrm{D}_{p}=12 \mathrm{~cm}^{2} / \mathrm{sec}; d_{n} \; 30=\mathrm{cm}^{2} / \mathrm{sec}$.
$\qquad q=1.6 \times 10^{-19}$ coloumbs; $(k t / q)=26 \; \mathrm{mV}$.