$8\mathrm{.}8$ A one sided p$+$n silicon diode has doping concentrations Na $=5$x$10^17$ and Nd $=8$x$10^15.$ The minority carrier lifetimes are tno $=10^-7$ and tpo $=8$x$10^-8.$ The cross sectional area A $=2$x$10^-4.$ Calculate a$)$ reverse biased saturation current, b$)$ forward bias current at i$)$ Va $=0\mathrm{.}45$V$,$ ii$)$ Va $=0\mathrm{.}55$V$,$ iii$)$ Va $=0\mathrm{.}65$