Problem $8\mathrm{.}4(10$ points$)$

$($a$)$ The doping concentrations in a silicon pn junction are Nd $=5$ x $1015$ cm$3$ and

Na $=5$ x $1016$ cm$3.$ The minority carrier concentration at either space charge edge

is to be no larger than $10$ percent of the respective majority carrier concentration.

$($i$)$ Determine the maximum forward$-$bias voltage that can be applied to the junction

and still meet the required specifications. $($ii$)$ Is the n$-$region or p$-$region

concentration the factor that limits the forward$-$bias voltage?

$($b$)$ Repeat part $($a$)$ if the doping concentrations are Nd $=3$ x $1016$ cm$3$ and

Na $=7$ x $1015$ cm$3.$