A PN$*$ silicon diode has N$.=1016$ cm $3$ in P and N$,=1018$ cm$3$ in N$,$ T$,=$ E$,=1$ us and A $=1\mathrm{.}2$x$104$ cm$?.$ Determine: $($a$)$ the conductivities of the P and N regions; $($b$)$ the diode current when the applied voltage in the reverse direction is $0\mathrm{.}01$ V; $($c$)$ under V$.=0\mathrm{.}3$ V$,$ the excess minority carrier concentration at x$\text{'}=1$ um in N; $($d$)$ under V$.=0\mathrm{.}5$ V$,$ the electron current at x$\text{'}=1$ um in the N region. $(60$ pts$)$