$8\mathrm{.}4($a$)$ The doping concentrations in a silicon pn junction are Nd $51015$ cm$3$ and Na $51016$ 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 specifi cations. $($ii$)$ Is the n$-$region or p$-$region concentration the factor that limits the forward$-$bias voltage? $($b$)$ Repeat part $($a$)$ if the doping con centrations are Nd $31016$ cm$3$ and Na $71015$ cm$3.$