The total current in a semiconductor is constant and is composed of electron drift current and hole diffusion current. The electron concentration is constant and is equal to ${10}^{16}c{m}^{-3}.$ The hole concentration is given by

$p(x)={10}^{15}{e}^{(-xL)}c{m}^{-3}$

where $L=12m$ and $x0.$ The hole diffusion coefficient is $D_p=12c\frac{m^2}{s}$ and the electron mobility is ${}_n=1000c\frac{m^2}{V}-$s$.$ The total current density is $J=4\mathrm{.}8\frac{A}{c}{m}^2.$ Calculate:

$($i$)$ the hole diffusion current density versus $x,$

$($ii$)$ the electron drift current density versus $x,$

$($iii$)$ plot the electron drift current density and hole diffusion current density on a single $($J versus $x)$ graph.

$($iv$)$ the applied electric field versus $x$ and its value at $x=0$

$($v$)$ plot the graph of electric field versus $x.$