A silicon sample is doped with $1015$ donors$/$cm$3$ and has a hole$-$lifetime of $0\mathrm{.}5$ s$.$

Assuming all the donors to be ionized, determine:

$($a$)$ the photo generation rate, which will produce $4$x$1014$ excess EHP in steady state.

$($b$)$ the sample resistivity before and after illumination and the percentage of conductivity due to

minority carriers. Assume n$=3$p $=1200$ cm$2/$Vs$,$ T $=300$ K$.$

$($c$)$ how far are the electron and hole populations from their equilibrium values while under

illumination?