Q $3($a$)[12$ Marks$]$ Consider a p $+$n silicon diode with an intrinsic carrier concentration of $1\mathrm{.}5$ x $1010$ cm$-3.$ The doping is given by NA$=1018$ cm$-3$ and Nd$=1017$ cm$-3.($i$)$ Calculate the minority carrier concentration on each side of the junction. $($ii$)$ If the recombination time for electrons and holes is $1$ x $10-6$ s$,$ and Dn and Dp are $20$ cm$2/$s and $10$ cm$2/$s respectively, calculate the electron and hole diffusion lengths.