$6\mathrm{.}10$ Consider an abrupt asymmetric $P^{+}N$ junction diode. All the action in this device is dominated by the lowly doped n$-$type region. At a certain bias point, the excess minority concentration in the quasi$-$neutral n$-$type region has a distribution as sketched below:

Chapter $6$ PN Junction Diode

$x_n$ is the edge of the SCR$.w_n$ is the surface. In this region, $D_h=5c\frac{m^2}{s}.$ Assume low$-$level injection.

Answer the following questions for the bias point that corresponds to the diagram:

$($a$)$ Calculate the diode current density.

$($b$)$ Calculate the total amount of excess minority carrier charge.

$($c$)$ Calculate the diffusion capacitance.

$($d$)$ Calculate the dominant time constant.