$p-n$ Junction*
Explain the origin of the depletion layer in an abrupt $p-n$ junction and discuss how the junction causes rectifcation to occur. Stating your assumptions, show that the total width $w$ of the depletion layer of a $p-n$ junction is:
$$
w=w_{n}+w_{p}
$$
where
$$
w_{n}=\left(\frac{2 \epsilon_{r} \epsilon_{0} N_{A} \phi_{0}}{e N_{D}\left(N_{A}+N_{D}\right)}\right)^{1 / 2}
$$
and a similar expression for $w_{p}$ Here $\epsilon_{r}$ is the relative permittivity and $N_{A}$ and $N_{D}$ are the acceptor and donor densities per unit volume, while $\phi_{0}$ is the difference in potential across the $p-n$ junction with no applied voltage. You will have to use Poisson's equation to calculate the form of $\phi$ given the presence of the ion charges in the depletion region. D Calculate the total depletion charge and infer how this changes when an additional voltage $V$ is applied.
$D$ What is the differential capacitance of the diode and why might it be useful to use a diode as a capacitor in an electronic circuit?