$(20$ points$)$ Problem $8\mathrm{.}30$ Consider a GaAs pn junction diode with a cross$-$sectional area of A $=2$ x $104$ cm$2$ and doping concentrations of Na $=$ Nd $=7$ x $1016$ cm$3.$ The electron and hole mobility values are n $=5500$ cm$2/$V$-$s and p $=220$ cm$2/$V$-$s$,$ respectively, and the lifetime values are $0=$ n$0=$ p$0=2$ x $108$ s$.($a$)$ Calculate the ideal diode current at a $($i$)$ reverse$-$bias voltage of VR $=3$ V$,($ii$)$ forward$-$bias voltage of Va $=0\mathrm{.}6$ V$,($iii$)$ forward$-$bias voltage of Va $=0\mathrm{.}8$ V$,$ and $($iv$)$ forward$-$bias voltage of Va $=1\mathrm{.}0$ V$.($b$)($i$)$ Calculate the generation current at VR$=3$ V$.$ Assuming the recombination current extrapolated to Va $=0$ is Iro $=6$ x $1014$ A$,$ determine the generation current at $($ii$)$ Va $=0\mathrm{.}6$ V$,($iii$)$ Va $=0\mathrm{.}8$ V$,$ and $($iv$)$ Va $=1\mathrm{.}0$ V