Consider a reverse biased $p^{+}-n$ junction diode. The diode has been biased with a biasing voltage $V_{AK}.$ The graph of $\frac{1}{C_j^2}$ versus $V_{AK}$ is shown in figure below, where $C_j$ is the junction capacitance. The diode has a junction area of ${10}^{-3}c{m}^2.$ Assume that $n_i=1\mathrm{.}5x{10}^{10}c{m}^{-3}$ and $(Si)=11\mathrm{.}8{}_0$

$($i$)$ Determine the value of built$-$in potential

$($ii$)$ Calculate the doping concentrations on both the sides of the junction.

$($iii$)$ Calculate the value of width W $($in $m)$ as shown in figure.

$($iv$)$ An inductor of $2\mathrm{.}2$ mH is placed in parallel with the diode. Calculate in resonant frequency $($in Hz $)$ of the circuit for reverse bias voltage of $-4$ V $.$