$4\mathrm{.}12$ A material is doped such that electron concentration varies linearly across the sample, which is $0\mathrm{.}5m$ thick. Donor concentration varies from $0($at $x=0)$ to $\frac{{10}^{16}}{c}{m}^3($at $x=0\mathrm{.}5m).$ Write equations for total electron and hole concentrations as a function of distance $x.$ Determine electron and hole diffusion current densities if the diffusion coefficients are $D_n=30c\frac{m^2}{V}-$sec and $D_p=12c\frac{m^2}{V}-$sec$.$ Find the expression for Fer mi level $(E_F)$ as a function of $x.$